摘要:

GENERAL DISCUSSION Dr. K. A. Dill (Stanford University) said: It is clear that an interphase between two crystalline regions cannot have a density higher than that of the crystal itself. Any model of chain folding must obey this requirement. However, Sir Charles presents the view that this criterion is sufficient to reject random re-entry models, and thus to favour regular folding models. I will show, on the contrary, that this density constraint only eliminates pathological models, and it is not sufficient to argue against a liquid-like amorphous interphase. The changeover in disorder across a boundary from the crystal phase to the amorphous phase need not require any change in density. This notion was first presented by Flory,' and has arisen again more recently in a different context.*t3 The idea is that rather than chain density, it is broadly the chain flux which is associated with the degree of disordering.Chain flux is taken to be the number of chains passing through a planar unit area, whereas the density is the number of chain monomers per unit volume. One way to change the chain flux is to fold the chains back into the crystal from which they emanate. Fig. 1 shows an example of this. In layers A and above, there is complete align- ment of chains, and thus perfect order. Between layers B and C (the amorphous region), there are several possible alternative conformations available to these inter- iAINS FIG. 1.-Schematic diagram of ordered and amorphous regions within the polymer showing the variation in chain flux.GENERAL DISCUSSION 105 phase chains, and this conformational freedom can be thought of as an entropic dis- order.The dissipation of chain flux caused by the folding back of some of the chains directly results in conformational freedom for the other, surrounding chains. In this way, the disordering across the AB interface can be achieved with no change in density. Though the degree of this disordering is specified by the chain flux, the topological details are almost completely arbitrary. Thus there is no particular significance to the number of tight folds shown in the figure. Foldbacks are only one mechanism by which chain flux can be altered. The occur- rence of chain ends (terminations), a change in the average chain direction (angled packing, for example), or indeed a change in monomer density can also affect chain flux, and thereby affect the degree of disordering.The conclusion is that random re-entry models such as those shown in fig. 1 need not be inconsistent with .the density requirement. One pathological model, which indeed would be eliminated because of an unacceptably high interphase density, is one in which all chains emanating from the crystal interface are of a length greater than the width of the interphase. Indeed such a model, no matter whether the folding is regular or of the c-c switchboard ” type, is a physically impossible one. Nevertheless, subject only to the limitation that the interphase density cannot exceed that of the crystal, many reasonable models are possible (including those which allow for either solid- or liquid-like ordering).Therefore, adjacent or non-adjacent chain re-entry can neither be rejected nor supported on the basis of the density requirements in the interphase. P. J. Flory, J. Amer. Chem. SOC. 1962, 84, 2857. P. G. de Gennes, Phys. Letters, 1974, 47A, 123. K. A. Dill and P. J. Flory, unpublished. Prof. F. C. Frank (Uniuersity of Bristol) (communicated): Dr Dill would appear to have produced a counter-example to my conclusion about the proportion of chains making prompt re-entry, since in fig. 1 only 6 out of 16 stems do this, less than a half of my minimum, which is z 2 / 3 . However, his is a two-dimensional model, in which no chain crossings occur. I see no very satisfactory way by which my mode of argu- ment can be applied to his example.Two-dimensionally, the factor D is n12, instead of 2, but its relevance to a model with no crossings is not clear. With no crossings, the factor A must drop out: but inspection of Dill’s figure shows that a factor B > 1 is present. The sample is small, with “ end-effect ” constraints on randomness evident from the fact that no chains cross its right or left boundaries. It is doubtless mere coincidence that 16(1 - 2/n) = 5.8. One may like to look on fig. 1 as a projection on to two dimensions from three. Then the absence of crossings is unaccounted for: but, also, the density in the dis- ordered region is now greater. It must always be borne in mind (and often is not) that if chain deviations in the third dimension occur then when the density in the dis- ordered region looks the same as that in the crystal (projected perpendicular to its chains), it is actually greater.Thus, nothing that Dr. Dill has said gives me reason to doubt my own conclusion. Personally, I consider it unwise to use the term “ flux ” where nothing flows, and nothing analogous to flow is present, i.e., there is no arrow attachable to a chain to represent the positive direction along it, except by arbitrary convention. “ Number of chains passing through a planar area ”, in conjunction with a specification of the orientation of that plane is unambiguous : calling it “ flux ” can be misleading.106 GENERAL DISCUSSION Dr. A. K. Dill (Stanford University) (communicated) : Although fig. I is 2-dimen- sional, these notions can be applied as readily in 3 dimensions.Consider for example, fig. 1 to be in the x-y plane, and to be one lattice unit thick in the z direction. A 3-dimensional structure can most simply be construted by stacking slabs such as this one normal to the z-axis. From this state, alternative configurations could be generated by the artifice of breaking some of these x-y plane bonds and exchanging them with bonds in the same or other planes, subject only to the obvious rules that the number of bonds and chain ends must be conserved in the process. Indeed this simple construct shows how 3-dimensional examples can be produced, and thereby adequately demonstrates the generality of the above arguments. Dr. D. M. Sadler (University of Bristol) said : Deductions from neutron scattering, with a substantial proportion of folds which are not adjacently re-entrant, are in ap- parent conflict with space filling requirements.Clearly, for further progress it is essential to show (in principle at least) how the two can be reconciled. I wish to do this by invoking a transition layer of finite thickness between the crystal core and any surface amorphous layer (see also the paper by Prof. Mandelkern). The severe res- trictions recalled by Sir Charles Frank apply to an abrupt transition. I present in fig. 2 a schematic description of a particular model for the transition layer, illustrating several important features in a qualitative form. Most impor- tantly, the folds are at different depths below the outer surface of the crystal. The -I I n i 1 I I "amorphous" layer ---- disordered layer 20-30A _ _ _ - - uystal "core" FIG.2.-Schematic two-dimensional diagram of a transition layer structure. Essential features are (1) distribution of fold heights, the outer folds having room to " leapfrog " over the inner ones; (2) some persistence of the straight stem conformation into the transition layer (this feature is exaggerated in this simplified diagram). two-dimensional representation suffices to show how this enables folds further out to " leapfrog " over the tighter folds. Also, to some degree the all-trans stem confor- mation penetrates further into the transition layer than it would into a truly " amor- phous " layer. The existence of a transition layer alleviates the severity of the space filling requirements but does not remove them.It seemed to me as a reasonable guess that a mixture of fold types, adjacent and those involving stem separations two and three times as large, would probably be allowed. This corresponds to most stem separations being < z 12 A. The neutron scattering data1 were analysed to seeGENERAL DISCUSSION 107 if a distribution of stem separations in this range was compatible with the observed intensities. The (positive) outcome of this exercise is described in a later contribu- tion, after the paper by Dr. Stamm. I now wish to indicate how this model for the transition layer follows naturally from earlier work (ca. 1970) on single crystals, and is not simply an ad hoc escape from an apparent impasse. In chronological order we have (a) theoretical predictions, (b) a special system with an unusually large number of constraints on the models possible and (c) a very extensive body of work based on degradation technique.(a) No theory predicts a uniform fold depth: if fluctuations are allowed kinetic theory predicts a distribution in depths of the order of 10 A.2 (b) Crystals of low molecular weight (number average <3000 where one stem cor- responds to a molecular weight of 1000) show dislocation networks in the twist bound- ary formed between overlying layer^,^ showing unequivocally that there is in this case crystallographic continuity between different layers in spite of the (usual) crystallinity deficit of ~ 2 0 % . The only structure possible involves an interpenetration of crystal layers (which is promoted by numerous chain ends), see fig.13 of ref. [3(b)]. This requires a surface roughness, together with a significant number of surface chains in the all-trans conformation. This was confirmed by the degradation technique (see below). (c) Nitric acid and ozone degradation combined with gel permeation chromato- graphy also led to a model with variations in fold depth^^^,^,^ and could provide de- tailed information not only on the distributions of depths but also on the length of chain associated with a fold. In essence the method exploits the identification of molecular fragments corresponding to single and multiple stem traverses,6 for example a degradation product of purely single stems means that enough crystal has been removed for all the folds to be cut.The crucial observation is that the stem length decreases systematically as the population of single traverses increases relative to all the other fragments. This even enables an experimental measure of the distribution of fold depths5 and a unique fold depth can be excluded. The ratio of molecular weight of double to single traverses is close to two, thus limiting the degree of non- adjacency, since the double traverse includes a chain sequence corresponding to a fold. At intermediate stages of degradation (corresponding to a " cut " through the outer layers of folds) the ratio is slightly greater than two, and decreases with further degradation, showing that the chain sequence in the fold is shorter for folds deeper in the crystal. The existence of non-adjacent folding even in single crystals (see the paper by Yoon and my comment to it) would require " leapfrogging " here too, and hence in retrospect we see that the outer folds ought to be longer.Implicit in everything so far is the hypothesis that the transition layer as so en- visaged is compatible with the usual indications of disorder. In that crystals with rough surfaces and no true amorphous layers show the usual crystallinity deficit [see under (b)] this we accept as an experimental fact. In summary, a transition layer which has previously been invoked to relationalize a large body of evidence on the nature of the surface layers now enables us to explain how a significant degree of non- adjacency, as indicated by neutron scattering, can be reconciled with space filling re- quirements.D. M. Sadler and A. Keller, Macromolecules, 1977, 10, 1128. J. D. Hoffman, J. I. Lauritzen, E. Passaglia, G. S. Ross, L. J. Frohlen and J. J. Weeks, Kolloid-Z., 1969, 231, 564. D. M. Sadler, A. Keller, Kolloid-Z,, (a) 1970, 239, 641; (b) 1970, 242, 1080. A. Keller, E. Martuscelli, D. J. Priest and Y . Udagawa, J. Polymer Sci. A-2, 1971, 9, 1807. G. N. Pate1 and A. Keller, J. Polymer Sci. A-2, 1975, 13, 2259. D. J. Blundell, A. Keller, I. M. Ward and I. J. Grant, J. Polymer Sci. B, 1966, 4, 781.108 GENERAL DISCUSSION Dr. E. A. DiMarzio, Dr. C. M. Guttman and Dr. J. D. Hoffman (National Bureau of Standards, Washington, D.C.) said: We can show that there exists a unique rela- tionship between the amount of chain folding and the properties of the amorphous component in polymer crystals of lamellar morphology.Consider a crystalline poly- mer of lamellar morphology of degree of crystallinity xc. Accepting a two-phase model with the tight adjacent re-entry folds (if any) considered as part of the crystalline phase we can write P C L ~ c l c + Pala x c = where Zc and la are the lamellar thickness of the crystalline and amorphous regions and pc and pa are the crystalline and amorphous densities in CH, units per unit volume or more generally monomer units per unit volume. We can also write where fc is the average number of CH2 units in a run of crystalline segments and fa the average number of CH2 units in a run of amorphous segments. If we recognize that there is a strict alternation of crystalline and amorphous runs in each chain and if we assume infinite molecular weights then eqn (2) is obvious. Eqn (1) and (2) can be combined to obtain (3) 1.27FC pc 1.27Fa The left-hand side is the average number of stems in a run of crystalline CH2 units and Fa/la is the ratio of the average number of CH, units in a run of amorphous segments to the lamellar thickness of the amorphous layers.The point of eqn (3) is that there exists a unique connection between the number of folds in a crystalline lamella and the properties of the intervening amorphous regions. Yoon and Flory' have estimated on the basis of a computer simulation that a quenched polyethylene crystal with xc = 0.65, la = 90 A and Zc = 160 A has an average run length in the amorphous phase of 1305 20 CH2 units.This result has been checked and verified by Guttman et aL2 Using these values and the value pa/pc = 0.85 we obtain from eqn (3) a value of 2.15 stems per cluster (stems per run). It is to be emphasized that this number is a lower bound because as soon as the ran- dom walk touches a surface, it is forced by the rules of Yoon and Flory to become a stem. However, in reality, we must allow the random walk to sometimes reflect off the surface. If it always reflects off, the value of fa would become infinite. If it never reflects off, we would have the lower bound of 2.15 stems per cluster. This corresponds to minimum probability of adjacent re-entry of 0.53. Thus, simple space filling arguments applied to the Yoon and Flory model show a substantial amount of tight adjacent re-entry chain folding exists provided we assume a two-phase model.A more complete consideration of the interface region (the region where the chains fold back) will not obviate the packing difficulties that we have focused on in the above two-phase model, but will lead to a more complete understanding of the kind of tight folding which occurs at the interface. We imagine that tight folds can exist which skip or leap-frog thus forming an interface. The packing constraints among these folds will limit the amount of non-adjacent re-entry which can occur just as the pack- ing difficulties considered above limited the numbers and size of loose loops. How- ever, tight folds that skip several stems are allowed. Indeed, Sadler has suggested in r, =&-).GENERAL DISCUSSION 109 these proceedings that an interface of equal amounts of adjacent, next to adjacent, and next to next to adjacent folding explains his single crystal neutron scattering best. His depiction does not seem to show density difficulties.Obviously, one must focus on the interface layer both experimentally and theoretically to determine the con- straints on non-adjacent re-entry. We wish to suggest that a system studied by Lotz et aL3 of an amphiphilic diblock copolymer of poly(ethy1ene oxide) copolymerized with polystyrene provides a system in which the kind of folding might be assessed experimentally. These systems were prepared with the following properties. 20 < la/A < 54; 62 < lc/l$ < 100; 670 < r;/A < 1322 208 < rAlA < 582 (4) where r;, r; are the contour lengths of the amorphous and crystalline portions.Note that these systems satisfy eqn (3) because there is one amorphous and one crystalline portion per molecule. They show 11-13 stems per cluster (rb/Zc = 11-13). One could by low-angle X-ray and neutron scattering and by wide-angle X-ray scat- tering determine the amount of poly(ethy1ene oxide) that is taken up by the folds (by determination of width and density of the interface), and thereby make an estimate of the average number of segments per fold. D. Y . Yoon and P. J. Flory, Polymer, 1976, 18, 509. C. M. Guttman, E. A. DiMarzio and J. D. Hoffman, Faraday Disc. Chem. SOC., 1979, 68,297. B. Lotz and A. J. Kovacs, Kolloid-Z., 1966, 209, 97; B. Lotz, A. J.Kovacs, G. A. Basset and A. Keller, Kolloid-Z., 1966, 209, 11 5 . Prof. P. J. Flory and Dr. D. Y. Yoon (Z.B.M., San Jose) said: Eqn (3) of DiMarzio et al. can be rewritten as follows: ti, = pala/l .2’7pc = 0.67 la where fia is the average number of amorphous CH, units per crystalline stem and 1, is expressed in A. For 1, = 90 A, n, = 60 CH2 groups. Their eqn (1) and (2) are not required for the derivation of this trivial mass balance equation. Their estimate of the “ amount of chain folding ” from our calculations (extraneous for this purpose) rests on the assumption that successive stems are connected by regular folds inter- spersed with long random coiled sequences (= 130 bonds in length). This scheme corresponds to our “ y ” model, a model we used for exploratory calculations only.It was rejected for more realistic calculations in which the constraint of regular folding was not imposed. In employing the y model, DiMarzio et al. inevitably obtain results that bespeak regularly folded sequences (albeit short ones) because this is a require- ment deliberately introduced in the model itself. Space filling arguments alone do not show a substantial amount of regular folding, as DiMarzio et al. claim. It has been shown1 on other grounds, however, that dissipation of the flux of chains emanating from the surface of a lamella (of infinite area) requires a substantial fraction of the chains to return eventually to and re-enter the lamellar crystal, or to terminate at a chain end. Re-entry need not be, and generally will not be, in adjacency to the previous stem.If loops between crystalline stems are comprehended by the term “ folds ”, then it is important to draw a distinction between “ regular folding ” with adjacent re-entry and irregular folds connecting non-adjacent stems. Loops or folds in the latter category involve entanglements with other chains and with loops from the adjoining crystal lamella. These entanglements impose severe restrictions110 GENERAL DISCUSSION on plastic flow and should affect other properties also, as we have pointed out.2 Thus, the distinction between folding and regular folding with adjacent re-entry is by no means a trivial one. f P. J. Flory, J . Amer. Chem. Soc., 1962, 84,2857. P. J. Flory and D. Y . Yoon, Nature, 1978,272, 226. Dr. F. Dowell (Oak Ridge National Laboratory, Tennessee) (communicated) : It is worthwhile to note the following " odd-even " effects, which may be pertinent to the subject of short-range order in n-alkanes.In pure n-alkanes, there is a " saw- tooth '' variation in the plot of the normal melting temperature against carbon number as the carbon number varies from odd to even.' In a homologous series of pure liquid crystals with alkyl tail chains, there are odd-even alternations of the nematic- isotropic transition temperature, entropy change, nematic order parameter, and frac- tional volume change as the tail carbon number alternates from odd to even.*p3 Also observed in mixtures of n-a1 kane solutes in various liquid-crystal solvents with alkyl tail chains is the odd-even alternation of the mixture nematic-isotropic transition temperature as a function of the number of carbon atoms in the solute alkane;^ these effects are observed at very small concentrations of the solute, suggesting that while the particular molecular interaction responsible for the effect may only operate over a small volume, the eEect itself is thermodynamically significant.American Petroleum Institute Research Project 44, Selected Values of Properties of Hydro- carbons and Related Compounds (Texas A & M University, College Station, Texas, 1968). W. H. de Jeu and W. A. P. Claassen, J. Chem. Phys., 1978, 68, 102, G. A. Oweimreen and D. E. Martire, J . Chem. Phys., 1980,72, 2500. ' S. Martelja, J. Chem. Phys., 1974, 60, 3599. Prof. R. S. Stein (University of Massachusetts) said: An additional method to assess order in amorphous polymers similar to those discussed by Prof.Flory and Fis- cher involves observation of the stress-optical coefficient in the rubbery state. The theories of Kuhn and Grun, and Treloar, extended by Flory and coworkers, relate the stress-optical coefficient to molecular anisotropy . Measurements have been made by Flory's group, Gent, Saunders and ourselves on the effect of swelling rubbers on the value of this anisotropy. Swelling separates molecules from each other and decreases any contribution from intermolecular ordering. The value of measured anisotropy is affected by swelling. From anisotropic solvents the result is usually to increase the measured anisotropy over that of the dry polymer, probably due to orient- ation of the solvent molecules by the oriented polymer.However, for isotropic sol- vents such as CC14, the swollen polymer usually exhibits a lower anisotropy than the dry polymer, presumably because of the disruption of molecular ordering by the sol- vent. However, the decrease is usually only by about a factor of two, suggesting that there is not a great deal of ordering in the dry polymer. This amount of ordering appears to be similar to that which Prof. Flory observed by light-scattering depolari- zation and can presumably be explained in a similar way. Also, it is of interest to note that the valxe of the stress-optical coefficient obtained for the swollen polymer is similar to that obtained for a solution of the polymer by streaming birefringence mea- surements.Since the theories of these two techniques are quite different, though both are based upon random-coil models of the polymer chain, it is difficult to see how this result could be explained on the basis of an amorphous-state model involving appreci- able order.GENERAL DISCUSSION 111 Prof. E. T. Samulski (University of Connecticut) said : The search for molecular orientational correlations and local order in n-alkanes with the aim of inferring the presence or absence of local order in polymer chains is a very reasonable approach to this subject. Prof. Fischer has described results obtained from isotropic systems, namely, the neat fluid alkanes and their dilute solutions (utilizing “ inert ” solvents). It may be of peripheral interest to note that alkanes may be studied in anisotropic systems, as solutes in nematic liquid-crystal solvents.However, the large aniso- tropies inherent to the nematogenic solvent preclude the use of most of the ex- perimental techniques described today (perhaps with the exception of the diffraction techniques). On the other hand, the presence of a macroscopically oriented fluid enables one to utilize special features of n.m.r. that relate directly to the orientational correlations and local structural order of the solute. Specifically, if perdeuterated alkanes solubilized in nematogens are investigated, the quadrupolar splitting in the deuterium n.m.r. spectra of‘the alkane can be utilized to determine the degree of ordering of the alkane and its configurationally averaged molecular geometry.The latter gives quantitative information about the perturba- tions imposed on the alkane’s configurational freedom by the anisotropic environment (the “ mean field” of the nematogen). Such information may serve as a useful benchmark for studies designed to characterize “ order ’’ in amorphous polymers in those extreme cases where such “ order ” is anticipated, e.g., in highly strained elasto- mers. Dr. A. H. Windle (Cambridge University) said: In their paper Fischer et al. comment that WAXS is insensitive to orientation correlations between molecules and cannot therefore be used in a straightforward manner to distinguish between bundle, meander and random-coil models. The introduction in our paper of the random packing of spheres device for representing the packing of polyethylene molecules in the melt has additionally enabled us to explore the effect of segmental orientational correlations by direct calculation.The results of this approach, which has been pursued by G. Mitchell in our laboratory, are shown in fig. 3, The first moments of the interference function have been calculated for units of polyethylene chains con- sisting of 4 carbon atoms in the all-trans conformation arranged symmetrically along a line centred in each randomly packed sphere. The use of the polyethylene unit, which has an aspect ratio of about one, is a convenient basis for the calculation; how- ever the results are seen as being applicable to polymers in general. As the orienta- tional correlation is increased in the absence of any rotational correlation or change in packing, there is at first very little change in the interference function and it is not until the orientation, expressed as Herman’s function C0.5 (3 ( cos2p } - l)], exceeds 0.5 that changes in the interference function become apparent. These calculations also throw light on the observation of Colebrook and Windlel that extension of PMMA and PS glasses to give the maximum obtainable orientation ( z 0.3) produced no detectable change in the circumferentially averaged interference function, although the two-dimensional diffraction pattern showed a marked fibre texture.They thus indicate that it is not necessary to postulate molecular orientation correlation to account for the insensitivity of the pair distribution function to orienta- tion, and thus support the general argument of Fischer and Dettenmaier.2 We would also like to point out that, even though the WAXS is not affected by modest levels of orientation, careful analysis of such scattering can give really quite detailed information as to the local molecular conformation and in particular indi- cates the mean distance over which the molecule is straight.We consider straightness over a distance of at least two to three times the mean molecular diameter to be a112 GENERAL DISCUSSION 1 , I I 0 1 2 3 4 5 6 7 s / A FIG. 3.-Effect of changing orientation function [f = 0.5 (3 < c0s3p > - l)] on the calculated scattering for segments of a polyethylene molecule disposed in accordance with the random packing of spheres.The values offare as marked on the curves. necessary precondition for parallelism. Knowledge of the polymer density can also provide a cross check on the realism of any particular type of molecular packing through comparison of the positions of the calculated and observed intermolecular peaks. A. Colebrooke and A. H. Windle, J, Macromol. Sci., 1976, B12, 373. E. W. Fischer and M. Dettenmaier, J. Non-Cryst. Solids, 1978, 31, 181. Prof. D. H. Everett (University of Bristol) said : Prof. Fischer provides evidence for the incipient ordering of n-alkane chains in the pure liquid state, the degree of order- ing, as measured by Ad2 at T = 80 "C, being related to T - T, (where 7'' is the melting point) by a form of equation suggested by Frenkel's heterophase fluctuation theory.Such ordering is enhanced in the close vicinity of a graphite surface, as evidenced by mea- surements of the enthalpies of immersion (A,H) of unit area of graphitized carbon black in pure alkane liquids.14 It is interesting that the excess enthalpy (A,H -GENERAL DISCUSSION 113 AwHo) of immersion (where AwHo relates to an unstructured liquid hydrocarbon such as hexane) follows an equation closely similar to that employed by Fischer (fig. 4): ln(AwH - AwHo) = C - D(T - Tm). (2) It has been suggested that this enhanced ordering is related to the close fit which characterizes an extended alkane chain on the basal plane of graphite:5 the ordering s Q 0 FIG. 4.-Enthalpy of wetting of Graphon graphitized carbon black (a, = 87 m2 g-') at 25°C: (a) AwH/mJ m-z against (T - Tm)/K, left-hand scale; (b) log (AwH - 120)/mJ m-' against (2' - Tm)/K, right-hand scale.0, 0 Everett and Findenegg; (3 Clint et al.; 8 Robert. [Reproduced from ref. (3), by permission]. may be regarded either as incipient epitaxy or surface-liquid crystal formation under the influence of surface forces. It would be interesting to know whether similar ordering occurs near the surface of a polyethylene crystal, and whether such effects play any part in the crystallization process. J. H. Clint, J. S. Clunie, J. F. Goodman and J. R. Tate, Nature, 1969, 223, 51. D. H. Everett and G. H. Findenegg, Natwe, 1969, 223, 52. D. H. Everett and G. H. Findenegg, J. Chem. Thermodynamics, 1969, 1, 573. C. E. Brown, D. H. Everett, A. V. Powell and P.E. Thorne, Farachy Disc. Chem. Soc., 1975, 59,97. A. J. Groszek, Proc. Roy. Soc. A , 1970, 314, 473. Mr. D. Rigby and Dr. R. F. T. Stepto (UMIST) (communicated): Fischer et al. state that the experimental variation with temperature of the effective optical aniso- ropy (d2) for n-alkane liquids is in the opposite sense to that predicted by the Monte Carlo calculations of Lemaire and Bothorel ' who postulate two thermodynamically- stable, coexisting states for n-C17H36. The calculations, based on a model of seven molecules in a box, were carried out using a Metropolis method. In such a method, existing molecular configurations are perturbed to define new configurations of the whole system with, in the limit of infinite size of sample, configurations occurring with frequencies in proportion to their statistical weights.A Metropolis method has been used, for example, in calculations involving an isolated chain interacting with an infinite surface, when an equilibrium description was achieved only after x2 x lo6114 GENERAL DISCUSSION molecular configurations had been generated.2 For systems at high densities of chain segments, such as liquids, many generated configurations have to be rejected because they are of high energy. Accordingly, convergence to a sample representative of equilibrium will probably only be achieved after several million perturbations. Thus, the samples of 60 000 at a given density used by Lemaire and Bothorel will probably detect only local minima in configurational space, corresponding to transient struc- tures in the liquid. Longer Monte Carlo runs, and runs with various initial configura- tions and systems of various numbers of molecules are needed to ascertain the signifi- cance of the structures found.Such calculations would probably indicate a population of transient structures, of which the two states found by Lemaire and Bothorel may or may not be typical. B. Lemaire and P. Bothorel, J. Polymer Sci., Polymer Letters Ed., 1978, 16, 321. M. La1 and R. F. T. Stepto, J. Polymer Sci., Polymer Symp., 1977, 61,401. Dr. A. H. Windle (Cambridge University) said: We should like to comment on the relevance of Prof. Pechhold’s bundle model to the PE melt. We have applied the method of comparing the calculated interference function for a model structure with the experimentally determined scattering, as outlined in our paper, to a molecule in a conformation appropriate to the meander model.Kinks with sequences gtg and gtg have been inserted at random in an otherwise all-trans polyethylene chain and the interference function calculated for a mean molecular length of 25 A. The propor- tion of kinks has been adjusted to give 40% gauche bands. When one bears in mind that the mean run length in the all-trans configuration for such a molecule is only 3-4 backbone bands, the angularity of the calculated scattering apparent in fig. 5(b) is striking. It bears as much resemblance to the scattering from an all-trans run of 30 A, which would be appropriate to the bundle model, as it does to that from a random chain and indeed the experimental scattering.We suggest that the reason why the calculated scattering from the bundle model has such an angular appearance, is that kinks which preserve the molecular orientation also preserve the periodicity of the backbone carbon atoms as projected onto the molecular axis. For example, the kink gtg shortens an otherwise all-trans molecule by exactly 42. It is apparent that a meander model containing sufficient 2gl kinks to reduce the trans population to 60%, built in run lengths of the order of 25 A to take into account the presence of incorporated folds, does not predict WAXS in accord with observa- tion. Fig. 5 demonstrates that a polyethylene molecule built according to “ random ” statistics gives significantly better agreement with experiment.Prof. W. Pechhold (University of UZm) said: The short range order we discussed for molten PE [cf. fig. l(b) in my paper] is not fully represented by a random distribu- tion of kinks on a trans-chain. More likely it is a mixture of short pieces of tgtg, gtgt, gtgt, gtgt helices and z 30% trans pieces, each of which is arranged within small lateral clusters. Could Dr. Windle try to carry out his reduced intensity calcula- tions on this short-range order model, a set of representative atomic coordinates of which we could supply? Prof. E. W. Fischer (Uniuersity of Mainz) said: I wish to point out that the numbers of intra-segmental correlation (4-5 bonds) found by Windle et al. are in excellent agreement with the results of Sight-scattering measurements reported in our paper.The very weak inter-segmental orientational correlation as revealed by depolarized light scattering cannot be detected by WAXS, since the pair correlation functionGENERAL DISCUSSION 115 \ L .- u) I I I I I I I 1 0 2 4 6 8 10 12 S A FIG. 5 . 4 ~ ) “ Bundle ”: all-trans 30 A long. (b) ‘‘ Meander ”; 40% gauche (gtg and gtg kinks), 25 A long. (c) “ Random coil ”: ~ 4 0 % gauche, modified 3-state chain. (d) Experimental (140°C). gcc(r) of the carbon atoms is rather insensitive with regard to orientation correlations.’ So the statement of Windle et al. that “ there is effectively zero correlation of segmen- tal orientation ” is again in agreement with d.p.s. results. In the case of atactic polystyrene WAXS investigations gave no clear answer to the problem of inter-segmental correlation.It may be mentioned that d.p.s. measure- ments prove definitely that there exists only inter-segmental correlations,2 see table 1. TABLE 1 .-EFFECTIVE OPTICAL ANISOTROPY a2 PER MONOMER UNIT (OR PER MOLECULE RESPECTIVELY) CALCULATED FROM THE DEPOLARIZED INTENSITY H,. OF MONOMER UNIT IS 28 x 10-48cm-6. styrene 130 ethylbenzene 46.5 1,3 -dip henyl bu tane 51 oligostyrene (M, = 400) 54 polystyrene in solution, Ehrenburg et al. 54 polystyrene in bulk 55 polystyrene calculated for the rotational isomeric state model, Flory et al. 48 E. W. Fischer and M. Dettenmaier, J. Non-Cryst. Sol., 1978, 31, 181. * M. Dettenmaier and E. W. Fischer, Makrumol. Chem., 1976, 175, 1185. Dr. R. Lovell, Mr. G. R. Mitchell and Dr. A. H. Windle (Cambridge Uniuersity) (communicated): We should like to reply to Dr.Yoon’s informal observations on our paper, particularly with reference to the determination of the local conformation in116 GENERAL DISCUSSION syndiotactic PMMA. Our experimentally based conformation corresponds to the lowest on the energy map calculated by Sundararajan and Floryl and it additionally suggests that predictions made by other authors on the basis of their own maps are ~ r o n g . ~ , ~ The WAXS analysis approach also gives a measurement of the mean run- length of the molecule in the preferred conformation. In the case of s-PMMA this value is equivalent to between 12 and 16 backbone carbon atoms for the (loo, lo", -lo", -10") conformation. It is in accord with the results of chain statistical cal- culations of Yoon and Flory which were based on low-angle scattering measurements in solution and the bulk (neutron ~cattering)~q~ and the prediction of the near-trans minimum in the energy map.l P.R. Sundararajan and P. J. Flory, J. Amer. Chem. Soc., 1974, 96, 5025. A. Tanaka and Y . Ishida, J. Polymer Sci., Polymer Phys., 1974, 12, 335. F. P. Grigoreva, T. M. Birshtein and Yu.Ya. Gotlib, Polymer Sci., U.S.S.R., 1967, 9, 650. D. Y . Yoon and P. J. Flory, Polymer, 1975,16, 645. R. G. Kirste, J . Makromol. Chem., 1967, 101, 91. R. G. Kirste, W. A. Kruse and J. Shelton, J. Makromol. Chem., 1972, 162, 299. Dr. E. D. T. Atkins (University of Bristol) said: I wish to draw attention to a highly extended conformation for isotactic polystyrene recently discovered in polystyrene gels.X-ray diffraction patterns obtained from oriented gels of isotactic polystyrene have showed that 12 styrene monomers are contained in a repeat distance of 3.06 nm.l Thus the average axial advance per styrene monomer is 0.255 nm. This value is only marginally less than the theoretical value of 0.26 nm (the value depends on the precise value of the bond angle chosen in the linked carbon backbone) expected for an all- trans conformation. Such a conformation is shown in fig. 6 and the details presented in a recent publication.2 Recent conformational analyses for isotactic polystyrene using the virtual bond method have provided additional and independent support for such an extended m0de1.~ < 3.06nm + /a/ /b/ ~- FIG. 6.-Computer drawn projections of the highly extended near all-trans conformation of isotactic polytyrene.(a) Projection perpendicular to helix axis, (b) projection parallel to helix axis. Previous conformational calculations 4-6 have highlighted essentially two chain conformations for isotactic polystyrene : a three-fold helix with an axial advance per monomer of 0.22 nm, which matched well the experimental results of Natta et al.' for crystalline isotactic polystyrene, and a slowly curving conformation with almost zero (or zero) axial advance.6 E. D. T. Atkins, D. H. Isaac, A. Keller and K. Miyaska, .I. Polymer Sci., Polymer Phys. Ed., 1977, 15, 21 1 . ' E. D. T. Atkins, D. H. Isaac and A. Keller, J. Polymer Sci., Polymer Phys. Ed., 1980, 18, 71.GENERAL DISCUSSION 117 P.R. Sundararajan, Macromolecules, 1979, 12, 575. A. M. Liguori and P. de Santis, J. Polymer Sci., C, 1969, 16, 4583. D. Y. Yoon, P. R. Sundararajan and P. Flory, Macromolecules, 1975, 8, 776. L. Beck and D. C. Hagele, Colloid Polymer Sci., 1976, 18, 228. 'I G. Natta, P. Corradini and I. W. Bassi, NUDUO Cimento, Suppl. I , 1960, 15, 68. Dr. A. H. Windle (Cambridge University) said: In replying to Dr. Atkins comments on the structure of polystyrene with particular reference to his discovery of the unusual structure of oriented i-PS gels, I would like to make two points. First: We concur that any conformational model proposed to account for the observed X-ray scattering must be sterically viable and have a reasonably low cal- culated energy. We are aware of the confusion which has arisen, because some authors chose to define the backbone bond rotation angles of an isotactic molecule in alternating senses down the chain.All the rotation angles in our paper are defined in the same sense. Secondly: We wish to point out that the model which Dr. Atkins has proposed for the i-PS gel structure, while no doubt corresponding to a low energy conformation and indeed successfully explaining the more subtle aspects of the diffraction pattern, fails to account for what is the dominant feature of the pattern; that is the strong meridional maximum corresponding to a repeat, projected onto the molecular axis, of 5.1 A. The projected repeat for his molecule is 2.55 A. Prof. L. Mandelkern (Florida State University) said: Since Dr. Atkins has brought up the question of gels, and in particular the structure of isotactic polystyrene, it would appear appropriate to clarify this phenomenon and place it in proper perspective and also to rectify some of the misconceptions that have developed in the last few years with respect to gelation.Gelation, resulting from the crystallization of copolymers from dilute and moderately dilute solutions, as contrasted with the formation of the usual lamellar type of crystallite, has been well established and well known for a num- ber of years.' Isotactic polystyrene can be considered a copolymer, from the point of view of its crystallization behaviour, because of the FZ 1 mol % of stereo-irregular units and F Z ~ mol % of head-to-head placemenk2 Hence, in view of the above its gelation, as well as that of other stereo-irregular polymers, should not be sur- prising.' What has been different are the reporfs3p4 that at high crystallization temperatures the conventional lamellar crystallites are observed, while at lower crystallization tem- peratures gels are formed.The morphological structure of the crystalline regions in the latter case has been associated with the fringed micelle model. This behaviour is not limited to i-polystyrene but has also been reported for ethylene-butene copoly- mem2 For this copolymer, compositional fractionation has been demonstrated to occur and is the reason for the two types of crystallization that are observed. A similar type of molecular fractionation takes place with polystyrene. It is noteworthy that the gel portion will never form lamellae; the lamellae will not form gels when separated and crystallized at the lower temperatures. Thus some type of constitu- tional fractionation must have taken place. With this understanding of the phenomenon then, the crystallization of the gel portion takes place at a much lower temperature than is usual.Thus the oppor- tunity exists for the formation of a polymorphic form of reduced thermodynamic stability. This is what happens in the case of polystyrene. The new crystalline form has a reduced melting temperature and a chain conformation that is being elucidated by Dr. Atkins and his colleague^.^ However, this new form is a consequence of the gelation, i.e., the lowered crystallization temperature, and not its cause.Gelation118 GENERAL DISCUSSION occurs in many cases without any change in crystal structure'y2 and is a phenomenon worthy of study on its own. A further point of recent confusion has been the development of crystallinity in a partichlar sample of poly(viny1 chloride) by virtue of solvent treatment and Poly(viny1 chloride) qualifies as a copolymer by virtue of stereo-irregular units and long-chain branching. The gelation of this polymer is well known,' and the use of appropriately chosen solvents to induce or accelerate crystallization in potentially crystallizeable polymers was demonstrated many years ago for olefin-catalysed poly- styrene7 and isotactic poly(methy1 metha~rylate).~.~ Hence the observations with this polymer should not be surprising in view of the principles enunciated above and the previous results on similarly constituted polymers.L. Mandelkern, CrystufZizutioiz of Polymers (McGraw-Hill, N.Y., 1964), pp. 113 and 308. R. Benson, J. Maxfield, D. E. Axelson and L. Mandelkern, J. Polymer Sci., Polymer Phys. Ed., 1978,16, 1583. P. J. Lemstra and G. Challa, J. Polymer Sci., Polymer Phys. Ed., 1975, 13, 1809. M. Girolamo, A. Keller, K. Miyasaka and V. Overbergh, J. Polymer Sci., Polymer Phys. Ed., 1976, 14, 39. E. D. T. Atkins, D. H. Isaac, A. Keller and K. Miyasaka, J. Polymer Sci., Polymer Phys. Ed., 1977, 15, 211. P. J. Lemstra, A. Keller and M. Cudby, J. Polymer Sci., Polymer Phys. Ed., 1978, 16, 1507. ' J. L. R. Williams, J. Van Den Berghe, W. J. Duhmage and K. R. Dunham, J. Amer. Chem. Soc., 1956, 78, 1260; 1957,79, 1716.T . G. Fox, B. S. Garrett, W. E. Goode, S. Gratch, J. F. Kincaid, A. Spell and J. D. Stroupe, J. Amer. Chem. SOC., 1958, 80, 1768. A. A. Korotkov, S. P. Mitsengendlev, U. N. Krasuhne and L. A. Volkova, High Molecular Weight Compounds, 1959, 1, 1319. Prof. A. Keller (University of Bristol) said: In the light of Prof. Fischer's comments I would like to transmit some of our own experiences with polystyrene. In the course of elongational flow experiments on solutions of both atactic and isotactic polystyrene birefringence effects were observed which were unaccountable on the basis of the elongation of isolated molecu1es.l We decided that they are caused by the alignment of anisotropic particles of the size of 1000 A or larger.' All the evidence indicated that the particles were themselves constituted of polystyrene and as such must have been present in the initially glassy structure prior to dissolution.We cannot tell what fraction of the material was in the form of these particles, possibly only a very small fraction. I do not wish to draw general conclusions about the nature of the glassy state on this basis, merely to draw attention to the fact that molecular aggregates can exist in what otherwise would normally be considered as a glass. I do not question that it may be possible to remove or avoid such aggregates and assert the truly struc- tureless nature of the glass if this were the objective of the investigation. What the above findings indicate is that observation of structures in the glass need not neces- sarily represent foreign inclusions nor experimental artefacts.Whatever their rele- vance to the glassy state as such, when present, they are part of the solid and can be potentially of consequence for its characterization and application. The existence of aggregates in polystyrene has been asserted previously in various types of solution studies [e.g. ref. (2)]. They have been usually referred to as entanglements or micro- gels, The principal addition of the observations just mentioned is that the aggregates in question are intrinsically anisotropic particles. I feel that they are of potential interest for the understanding of polystyrenes as available, irrespective of how they may affect arguments concerning the glassy state. My next comment is an addition to the comment by Prof.Mandelkern on thermo- reversible polystyrene gels. As Prof. Mandelkern himself acknowledges in his recentGENERAL DISCUSSION 119 paper’ it was ourselves who invoked the necessity of the copolymeric nature of the chains for producing thermoreversible gels through cry~tallization.~ I am therefore particularly pleased that his own work provides support for this contention. Never- theless, I would like to place it on record that not everybody concurs, in view of the fact that some of the isotactic polystyrene samples which have been used are considered for all practical purposes fully isotactic by n.m.r. tests [see ref. (2)]. I am no judge of these n.m.r. tests myself. All I wish to point out is that with the present amount of information available the possibility of a purely isotactic chain producing gel by crystallization at very high supercoolings, and this with a chain conformation different from that in the usual isotactic (see Dr.Atkins’ comment) remains a realistic possibility. I admit that in this case we do not understand the reasons for the unusual chain conformation nor the reason why a stable gel forms at all, i.e., why the crystallizing system does not precipitate out of solution. I could say more to this point ; however, this belongs to the subject of crystallization. D. P. Pope and A. Keller, Colloid Polymer Sci., 1977, 255, 633 and unpublished. W. Philippoff, Trans. SOL. Rheol., 1963, 7, 45. R. Benson, J. Maxfield, D. E. Axelson and L. Mandelkern, J . Polymer Sci., PoZymer PhyJ.Ed., 1977, 15, 21 1. M. Girolamo, A. Keller, K. Miyasaka and N. Overbergh, J. Polymer Sci., Polymer Phys. Ed., 1976, 14, 39. E. D. T. Atkins, D. H. Isaac, A. Keller and K. Miyasaka, J. Polymer Sci., Polymer Phys. Ed,, 1976, 15, 211. E. D. T. Atkins, D. H. Isaac and A. Keller, J . Polymer Sci., Polymer Phys. Ed., 1980 18, 71. Prof. I. M. Ward (University of Leeds) said : Prof. McBrierty has provided a very good survey of the application of pulsed n.m.r. techniques to studies of heterogeneity in polymers. Very useful information can also be gained from less sophisticated broad-line studies, and some of our recent work is relevant to papers presented at this meeting. I refer particularly to the use of broad-line n.m.r. to determine molecular orientation, an area in which Prof.McBrierty and T undertook very successful colla- borative w0rk.l More recently, at Leeds University we have used n.m.r. in studies of orientation in poly(methy1 methacrylate) (which links with Dr. Windle’s recent re- searches), and in poly(viny1 ~hloride).~ In ultra-high modulus oriented polyethylene, a three-component signal can be obser~ed.~ We have attributed the intermediate component to oriented molecules joining the crystalline regions, and the small narrow component to low molecular weight material or the mobile ends of molecular chains. Prof. Mandelkern has discussed the value of such measurements for isotropic poly- ethylenes.6 It is particularly interesting to note that in slow-cooled isotropic poly- ethylene (i.e., material crystallized at low degrees of supercooling) a mobile fraction can also be observed.We believe that this supports our contention that segregation of low molecular-weight material occurs, as discussed by Prof. Wunderlich.’ This material can act as a plasticizer in the drawing process, to considerable advantage. V. J. McBrierty and I. M. Ward, Brit. J. AppE. Phys. ( J . Phys. D), 1968, 1, 1529. M. Kashiwagi, M. J. Folkes and I. M. Ward, Polymer, 1971, 12, 697. R. Lovell, G. R. Mitchell and A. H. Windle, Faraday Disc. Chem. SOC., 1979, 68, 46. M. Kashiwagi and I. M. Ward, Polymer, 1972, 13, 145. J. B. Smith, A. J. Manuel and I. M. Ward, Polymer, 1975, 16, 57. L. Mandelkern, Faraday Disc. Chem. SOC., 1979, 68, 310. ’ B. Wunderlich, Faraday Disc. Chem. SOC., 1979, 68, 239.Prof. E. W. Fischer (University of Maim) said: With regard to 4 of the 5 polymers investigated by Dr. Uhlmann, the results agree completely with those of our SAXS measurements;1 however, PVC was not studied by us. We disagree, however, with120 GENERAL DISCUSSION respect to the temperature dependence of the density fluctuations of amorphous poly- mers. The results of SAXS measurements show2 that eqn (1) of Uhlmann's paper is wrong. There is a strong temperature dependence of the density fluctuations below Tg, as has also been observed by Ruland et aL3 Recent neutron scattering experi- ments with PMMA showed4 in addition that this temperature dependence of the density fluctuation is not caused by phonons but it is due to free volume fluctuations which depend on temperature.There is also no reason to believe that " the configurational fluctuations at Tg should be retained in the glassy material ". In the case of polymers it is well known that there are conformational changes on a small scale below Tg as revealed by various kinds of relaxation studies. These changes couple to density fluctuations as the scat- tering experiments show. J. H. Wendofland E. W. Fischer, Kolloid-Z., 1973, 251, 884. E. W. Fischer, J. H. WendorfT et al., A.C.S. Polymer Prepr., 1974, 15 (2), J. Macromol. Sci., 1976, B12,41. J. Rathje and W. Ruland, Colloid Polymer Sci., 1976, 254, 358. M. Hoffmann and E. W. Fischer, unpublished results. Dr. A. H. Windle (Cambridge University) said: I should like to comment on Prof. Uhlmann's SAXS work on polymer glasses.He concludes that the features which are responsible for the increase in SAXS at very small angles are not representative of the bulk structure of thermoplastic polymers. Recently Richard Waring has carried out an experiment in our laboratory in which he measured SAXS from highly purified methyl methacrylate monomer (MMA) and observed the effect of polymerization in situ. The results (fig. 7) show that there was no detectable rise in the scattering at 7 - 6- + 5 5- 4- n 0 1 i s2 103 FIG. 7.-(a) Pure monomer, (6) 20, (c) 70, ( d ) 100% polymerized. very low angles for the pure monomer, but on polymerization in the X-ray cell a marked upturn developed, which from the slope of the Gunier plot gave a characteris- tic size in the region of 200 A. It is difficult to see how extraneous matter could have been added to the sealed monomer during polymerization.The scattering might be due to voids; however, the fact that it persists even after the polymer is annealed at T' = 30 "C for several hours seems to suggest that this is not the cause.GENERAL DISCUSSION 121 Fig. 8 is a plot of the intensity above the phonon background expressed as 2n I(s)sds as a function of the weight fraction polymer for samples polymerized in situ and for those made as equilibrium mixtures from polymer and monomer. /om 0 MMA PMMA FIG. 8.-Plot of intensity above the phonon background as a function of weight fraction polymer. The trend shows qualitatively similarities to light-scattering data 'p2 and reinforces the view that the scattering is from hetereogeneities which although small are repre- sentative of the bulk structure of the pure polymer.R. L. Addleman, Ph.D. Thesis (Imperial College, London, 1974). J. V. Champion, Furuday Disc. Chem. SOC., 1979, 68, 122. Prof. D. R. Uhlmann (Massachusetts Instirute of Technology) said: X-ray diffrac- tion studies of amorphous materials with elements of low atomic number, such as the polyolefins, are characterized by a significant component of Compton (incoherent) scattering. The intensity of such scattering, which contains no structural information, can at large values of sinO/A far exceed the coherent scattering, which contains the desired structural information. It would be helpful if Dr. Windle would indicate how he and his co-workers handled the problem of Compton scattering in their studies.Secondly, diffraction data at large values of k (4n sin O/A) are important for ob- taining detailed information about structure at small distances. Such data have been used to great advantage in studies of the classic oxide glasses, SiO, and B203; and the occurrence of relatively sharp interatomic distances in these glasses gave rise to modulations in intensity measured out to k values >20 A-l. In contrast, for a T120-Si02 glass as well as for a number of alkali silicates, variations in interatomic distances are apparently sufficiently large that significant modulations in intensity are not observed beyond k z 10-12 A-'. I note that the data reported by Dr. Windle122 GENERAL DISCUSSION and his co-workers do not extend beyond k z 12 A-1, and I wonder if this reflects the absence of significant modulations in intensity beyond this range, or the fact that data were not obtained out to larger values of k.Because of the importance of high-k data to resolving questions of frequently-occurring interatomic distances in amorphous structures, the comments of Dr. Windle would be most useful. Dr. J. V. Champion (City of London Polytechnic) said: I would like to report a recent light-scattering study of the thermal polymerization of a glassy polymer. n-Butyl methacrylate was thermally polymerized at 70 "C, and both the Brillouin spectrum and the angular dependent total scattering intensity envelope were con- tinuously measured throughout from 0 to 100% conversion. This material was selected as the polymerization could be performed at a temperature well in excess of the glass transition temperature of the final polymer (Tg z 12.5 "C) reducing the effects of the formation of local strain fields in the polymerizing material, and to ensure all impurities, including dust, were removed from the original material.An excess scattered intensity over and above that due to the normal thermal den- sity fluctuations was found to appear during the polymerization process, initially oc- curring at ~ 7 0 % conversion, and rising until 100% conversion was reached. This excess scattering manifests itself in the magnitude of the Landau-Placzek (L.P.) ratio and the dissymmetry of the total (integrated) scattered intensity (2). The rise in the L.P. ratio at 70% conversion shows that the excess scattering is not due to impurities or dust and occurs at the point of auto-acceleration in the polymerization process with the possibility of inhomogeneous reaction mechanisms occurring.The increase in 2 to a value of 1.20 at 100% conversion over a value of 2 = 1 .OO between 0 and 70;< con- version shows the formation of regions of heterogeneity. If we assume that these regions are spherical then they are of a diameter of at least 20 nni. If they are sur- rounded by regions of monomer, this leads to a heterogeneity concentration of the order of 1 %, whilst if they are surrounded by matrix of density only slightly different from the inhomogeneity (Ap/p z 1%) then the concentration would be in the order It has also been shown that the concentration of these regions of heterogeneity only increases with any further change of thermal history of the sample, and in parti- cular, increasing significantly when the material is cooled to Tg.of %lo%. Mr. R. Waring and Dr. A. H. Windle (Cambridge University) (communicated): Prof. Fischer has suggested informally to us that one possible explanation of the increase in our SAXS from PMMA at particularly low angles is the presence of mono- mer in equilibrium with the polymer. In reply we can only refer back to fig. 8 of our comment on Uhlmann's paper. The addition of monomer to PMMA leads to a re- duction in the SAXS at low angles. If its presence were due to monomer then an increase in monomer content should further increase the SAXS scattering.Prof. E. L. Thomas (University of Massachusetts) said: I agree with Prof. Uhl- mann's conclusions regarding the absence of order (the so-called " nodules ") in cer- tain glassy amorphous polymers. However, in his presentation today, and his earlier publications, there are several misconceptions of the image formation process in elec- tron microscopy, and consequently, his interpretations of the origin of the " pepper and salt " structures observed in bright field and the speckle observed in dark field are in error. The interpretation of high resolution electron micrographs of disordered materials is complex. Since it was essentially the early (naive) interpretation of the bright field and dark field images from glassy amorphous polymers which raised theGENERAL DISCUSSION 123 question of the degree of order in amorphous polymers’ it is important correctly to describe what one sees in the images and why.Prof. Uhlmann’s main contention is that the observed structures are artefacts arising from (a) improper focus and (b) use of microscopes of insufficient resolution. In fig. 4 of his paper he shows a bright field through-focus series, in which “ no per- ceivable ” structure is observed in the in-focus micrograph and he further implies that the corresponding situation holds true for dark field. We have recently systematic- ally studied atactic polystyrene thin films under a variety of electron optical condi- tiow2 Our results demonstrate that polymer thin films can be considered as weak phase objects and their images well understood by means of the transfer theory of image f~rmation.~ The “ domains ” visible in defocus bright field images are due to the spatial frequency filtering by the microscope system.The bright field image is controlled by the microscope transfer function sinx(K), where x is the phase shift of the scattered electrons due to the microscope optics, and is, for an objective lens de- focus Az and spherical aberration coefficient C,, given by : x(K) = nA(Az)K2 + $,A3K4. Fig. 9 shows plots of sinx(K) as a function of objective lens defocus. Sinx is a sensi- tive function of objective lens defocus and will cause contrast reversal and alter- natively highlight or suppress particular object frequencies in the image. Pioneering work by Thon4 has shown how we can evaluate the transfer function of the microscope and has well demonstrated how the microscope transfer function accounts for the observed bright field “ pepper and salt ” structures of thin amorphous carbon films. The experimental microscope transfer function can be obtained from an optical trans- form of the image, which yields an intensity distribution proportional to the square of the transfer function.Fig. 10 shows a defocused bright field micrograph of atactic polystyrene with an apparent domain size of z 5 0 A. The inset shows good agree- ment between the calculated value of sinx and the experimentally observed transfer function. Near focus (Az N 0), sinx is very small for the low object frequencies and oscillates strongly at high frequencies (see fig.9) so the strong transfer intervals become very narrow and the visible structure is now of very fine scale. The behaviour and appearance of the bright field micrographs of thin a-PS films are therefore entirely consistent with microscope transfer function modulated images of an amorphous sample acting as a weak phase object. The dark field image intensity is given by the superposition of the scattered components which fall into the objective aperture, modulated by exp[ix(K)]. Intensity peaks occur due to in-phase combina- tions at particular locations in that image plane. These peaks can in general result from (1) ordered regions; “ real ” image, (2) fortuitous superposition; “ statistical ” image. By changing the objective lens focus it is possible to distinguish between the two types of images.The effect of defocus is to alter the phases of the scattered waves. If the image is due to statistical peaking, a change in focus will just cause new for- tuitous combinations to give rise to intensity peaks and hence bright spots will appear but there will be no change in the average spot size and no single best image focus set- ting. For images resulting from the presence of real object order, defocusing will cause the spots to blur if the defocus is larger than the depth of field ( x 1000 A for an objective aperture of lom3 rad) but the spots will remain fixed and of constant inten- sity. Uhlmann’s suggestion that the dark field speckle arises from the same mechan- ism as does the bright field “ pepper and salt ” structure with the implication that this speckle would disappear at exact focus in dark field is completely wrong.The situation for dark field is more complicated.124 GENERAL DISCUSSION sin X 2 .o 1 .o FIG. 9.-Plots of sin ~ ( k ) as a function of objective lens defocus. Fig. 11 illustrates the effect of variations of the objective lens defocus on the dark- field image. Micrographs 1 l(a)-(c) correspond to successive changes of 1700 8, underfocus from the initial Az z 0 setting (determined viewing the bright field image). Fig. 1 l(d) was recorded with the focus varied during the exposure over a 10 200 8, range. As fig. ll(a)-(d) show, the size of the dots is not affected by objective lens defocus; behaviour typical of statistical images. The effect of defocus on the inten- sity and location of the dots is as follows: at relatively small defocus (Az E 1700 8,) a good correspondence between successive images is found but the intensity of some of the dots is modified.Comparing images with 3400 8, change in focus, the proportion of stable dots decreases to ~ 5 0 % . A few dots appear remarkably stable (circled). A large variation of defocus leads to an almost completely new image in fig. 1 l(d). The behaviour of the vast majority of the dots with respect to changes of objective lens defocus is entirely consistent with a statistical image rather than a real ordered domain image interpretation. Our results for this particular polymer glass strongly indicate that ordered structures on the scale of 10-100 8, or more do not exist, thusFIG. 10.-Defocused bright field micrograph of atactic polystyrene.[To face page 124FIG. 11 .-Effect of varying the objective lens defocus on the dark-field image. FIG. 12.-Electron micrograph of a replica from a glass slide after washing with ethanol. [To face page 125GENERAL DISCUSSION 125 reconciling the electron microscopy studies with the many scattering studies which failed to find evidence for such structures. ’ G. S. Y. Yeh and P. H. Geil, J. Macromol. Sci. (Phys.), 1967, B1, 235. E. L. Thomas and E. J. Roche, Polymer, 1979,20, 1413. K. Hanszen, Advances in Optical and Electron Microscopy, ed. R. Barer and V. E. Cosslett (Academic Press, London, 1973), vol. 4. F. Thon and B. M. Siege], Ber. Bunsenges. phys. Chem., 1970, 74, 1 16. Dr.D. Vesely (Brunel University) said: The first comment I would like to make is related to the nodular structure in the range 5-20 A. An extensive study of radiation damage to amorphous polymers1 showed clearly that they have a very similar beam sensitivity to that of crystalline polymers. It was also shown that for this reason the high resolution electron microscopy of undamaged amorphous polymers is not possible and the structure observed at high magnification (as in Uhlmann’s paper or in the work of Yeh and others) is that of amorphous carbon. The contrast features of amorphous materials at high resolutions were studied extensively in the last 15 years and are now well explained theoretically as artefacts due to the imaging properties of the electron microscope [e.g.ref. (2)]. My second comment is related to the 500-1000 A nodular structure observed by etching and replication. After careful studies of the etching of amorphous polymers it was concluded that the nodular structure is not related to the etching but to the washing-off residue (or absorbed solvent). Etching usually forms etch-pits and is not selective; however, the residue forms small droplets on the surface which can be replicated. To prove this point a clean glass slide was washed with different solvents and replicated. A whole range of nodular structures was revealed [fig. 12 or ref. (3)] identical to those observed on polymers. In conclusion, it seems to me that there is no valid electron microscopy evidence to support the existence of nodular structures in amorphous polymers.D. Vesely, A. Law and M. Bevis, EMAG 75 (Academic Press, N.Y., 1975), p. 333. F. Thom, Electron Microscopy in Materials Science (Academic Press, N.Y., 1971), p. 570. D. Vesely, EMAG 79 (Inst. Phys. Conf. Ser. No. 52, 1980), p. 299. Dr. D. T . Grubb (Cornell University) said: Prof. Uhlmann disagrees with the elec- tron microscopy of Yeh et al. who saw nodules; Prof. Thomas disagrees with Prof. Uhlmann’s analysis. I am not going to disagree with either of them, I will instead try to show that their work is irrelevant to the point at issue. The point is whether or not amorphous polymers are truly random in structure. The recent high resolu- tion transmission electron miscroscopy that has just been described shows that the specimens are random, indistinguishable from evaporated carbon films.However, the high radiation doses which must have been used in these experiments is known to destroy all order in crystalline polymers. Thus even a single crystal of polyethylene is indistinguishable from evaporated carbon after sufficient irradiation, and we should not expect any partially ordered material to retain its partial order after a similar dose. The question then is whether it is possible to observe “ microcrystals ” (40 A or less) in polymers by transmission electron microscopy, using the limited radiation dose which will not destroy order. When the dose is limited, the resolution is also limited as the detail must stand out from electron shot noise. The standard equation is: d = S/C(Jf)’ where d = size resolved ; C = contrast ; J = electron flux per unit area; f = fraction of electrons used in image.126 GENERAL DISCUSSION With the simple assumptions that for dark field and for bright field c = 1, f = fDF = (nt/<)2 where t = crystal thickness; c = extinction distance; and if the crystal to be re- solved is isometric, t = d, giving For 100 kV electrons and hydrocarbon materials of density 1, 5 21 1000 A and d can be obtained for chosen values of J.Jle A-2 dBF/ A dDF/ A f D F M D F 1 80 40 0.016 3 700 6 60 26 7 x 6 000 60 40 14 2 x 10-3 10 500 We see that in the range of interest (2) dDF < contrast visibility limit of 0.05. So dark field must be used, and with le The figures of 6e A-2 and 60e A-2 represent the doses required to destroy all order in polyethylene and isotactic polystyrene respectively.It would appear that the required resolution is easily obtainable, but note that from eqn ( 1 ) with C = 1 for dark field Jfd2 = 25, that is, the crystal image contains 25 electrons only. Yes with single emulsion X-ray films requiring xO.le pm-2 for a correct exposure, 25 electrons will darken a 15 pm spot, and the film resolution is x 10 pm. This given film speed requires a given magnification for the image, M D F in the table above. Standard electron image film may need 50-100 electrons to darken a resolvable spot. (b) Can this image be seen and recognized? No; the image will be a dust-like speck, impossible to identify positively as a crystal. A crystal image containing 4 x 4 resolvable spots, requiring 400 electrons might be recognizable.For J = 60e A-2 this gives a minimum crystal size of 28 A, dDF 7 A, M~~ 20 000 x . Using isotactic polystyrene the true visibility limit can be obtained by trial, using quenched samples annealed for short times to produce small crystals. Experiment shows that the above calculation is optimistic, particularly in its neglect of the scatter from the amorphous material which is collected in dark field. For thin films, ~ 7 . 5 x A-1 of the beam may appear as background, reducing contrast and increasing the smallest visible crystal size to 35 A in a 35 A thick film. Fig. 13 is dark-field micro- graph of an isotactic polystyrene film quenched and annealed for 1 h at 125 "C. The diffraction pattern of this material shows it to be largely crystalline.Fig. 14 is a similar micrograph of a film annealed for 5 min at 125 "C, which has no crystalline order visible in the diffraction pattern. There is a preferential crystallization of lamel- lae at the edge of the film, with the lamellae normals parallel to the edge. Light regions are easily seen in fig. 13. One marked by an arrow in fig. 14 is extremely difficult to see. The specimen film was much 40 I$ can be resolved. (a) Can this image be recorded? It is approximately 60 x 200 8, in size.FIG. 13.-Dark-field electron micrograph of crystalline isotactic polystyrene. Scale bar is 500 A. FIG. 14.-Dark-field electron micrograph of largely amorphous isotactic polystyrene. Arrow indicates a crystal. Scale bar is 500 A. [To face page 126FIG. 15.-Electron micrographs of amorphous polycarbonate, ion-etched 10 min by oxygen ions (ion current 0.24 mAcm-2): (a) untreated; (6) annealed 72 h at 110°C.; (c) treated like (b), then annealed 20 min at 160°C; quenched.[To face page 127GENERAL DISCUSSION 127 too thick at this point ( z 300 A) so the calculated minimum visible crystal size for the image was 55 A. If the crystal is not visible in the reproduction this merely proves the point that it is near the noise limit. They will be visible or not, depending on the true value of 5. More radiation resistant poly- mers could be studied successfully, but they tend to be rigid rods [polyimides, poly- (para-xylylene)] and it is not clear that the observation of ordered regions in these materials would be of such interest. Dr.W. F. X. Frank (University of Ulm) said : In fig. 15 three pictures of ion-etched polycarbonate are shown.’ The only difference between the three is the annealing history. Ion etching, coating with carbon-platinum and the production of the elec- tron micrographs were carried out simultaneously under exactly the same conditions. An eventual influence of over- or under-focusing must be the same in all three sec- tions of the photograph. Consequently it would appear that a real material property, whatever it may be, is presented here. The procedure has been repeated several times with the same result. Thus in polystyrene crystals of 40 A cube are at the edge of the possible. W. F. X. Frank, H. Goddar and M. A. Stuart, J. Polymer Letters, 1976, 5, 711.Dr. D. J. Blundell (ICI, Welwyn) (communicated): I wish to draw attention to our recent SAXS studies on PVC’ in order partly to substantiate Prof. Geil’s comment that PVC, because of its low crystallinity, is a special case and partly to emphasize a discrepancy with the data submitted by Prof. Uhlmann. I also wish to make a further comment on the important issue as to whether SAXS is a suitable method for testing for the presence of nodules in fully amorphous polymers. We have examined various conventional mouldings of commercial PVC some of which had been water-quenched and some of which had been annealed. By WAXS we estimated the crystallinities of all these samples to be of the order 5-10%, which in our experience is typical of conventionally moulded samples.We also examined an X-ray amorphous sample that had been prepared by Dr. Wenig at Huls by the excep- tional procedure of shock heating to 900°C for 15 s. The slit smeared SAXS of all samples was recorded in the region > 10 min. The amorphous sample showed a con- stant background scatter consistent with density fluctuations, while the conventional samples gave an excess above the fluctuation level in the low angle region. This excess scatter showed a break in slope at about 17 min which suggested that it could be divided into two components. The scatter 1 1 7 min was attributed to large hetero- geneities such as voids. The component 7 17 min was found to have a continuous profile for the water quenched samples but possessed a distinct shoulder for annealed samples, which on desmearing became resolved as a peak.The invariant integral [SI(s)ds] was calculated for these second components. It is well known that for scatter from a two-phase system, this integral can be equated to ~ ( 1 - 9) (AP)~, where Ap is the density difference between phases and p is the volume fraction of one phase. By assuming a value of Ap equivalent to the difference between the crystalline and amorphous densities of PVC, it was found that the invariant integral for all cases pre- dicted a value for q of the same order as that suggested by WAXS. Together with the systematic variation in the profile on annealing, this is strong evidence that the excess scatter > 17 min is associated with the two phase structure of crystallites embedded in an amorphous matrix.These findings are in sharp contrast to Prof. Uhlmann’s de- duction that any crystallites can only be of the order of 0.1 %. I can offer no explana- tion as to why Prof. Uhlmann did not detect this scatter. Our own conclusions cer- tainly agree with the other evidence cited by Prof. Geil when he asserted that PVC should not be classed as amorphous.128 GENERAL DISCUSSION Even though conventional PVC samples are not amorphous, I believe the above results are still very relevant to the question as to whether SAXS can be used to dis- prove the existence of nodules in true " amorphous " polymers. We have analysed both the continuous curves and those with shoulders and have concluded that both are entirely consistent with the PVC crystals having a nodular morphology similar to that seen in some electron micrographs.They lead to the picture of fringed-micellar crystalline nodules z 30-40 A in diameter with z 100 A between the nodule centres. I propose that this picture of the PVC morphology is close to the vision of nodules in amorphous polymers, the main difference being the lack of 3D order within the nodules. Assuming this to be so, the first point to note is that the volume fraction of nodules is only ~ 5 % and not the 50% usually presumed (cf. text of Uhlmann). On this account alone, the expected scattered intensity from the nodules will be 10 times less than usually presumed. The second point to note is that A p will be lower than for the above crystalline PVC. Our experience with highly drawn PET leads us to suspect that highly oriented, amorphous PET has a density no higher than 0.035 above that found in isotropic amorphous samples, i.e., less than a quarter of that between crystal and amorphous phases.Taking this figure as a guide for the A p between semi-ordered domains and disordered matrix and noting that the scatter is proportional to the square of A p then one would expect any scatter from the proposed nodules to be at least ten times less than the excess scatter > 17 min shown by our own conventional PVC samples. Com- parison with our data suggests that this degree of scatter will be barely detectable above the normal constant density-fluctuation background. Hence in my opinion, if nodules were present in amorphous polymers, I doubt whether their presence could be easily detected by SAXS and that SAXS cannot therefore be used to disprove their existence.D. J. Blundell, Polymer, 1979, 20, 934. Prof. A. Keller (University of Bristol) said: First I wish to make a general point which I feel is relevant to all the arguments claiming or refuting visible structures in the glass. We have to distinguish between differences in objectives lying behind such studies. There are studies which are directed towards the elucidation of the " glassy state " as such while there are others which are concerned with the examination of a particular material or sample because this is of interest for some reason or other. In the latter case the sample may not be in the ideal glassy state, whatever the latter may be, either because it contains some fortuitous or extraneous ingredients or because it is not ideally glass forming.Confusion can and does arise when the latter case is not recognized for what it is, and is being used in argumentation about the nature of the glassy state. A particularly important instance when the glass forming ability of the material may be questioned arises with materials which are intrinsically capable of crystallizing like poly(ethy1ene terephthalate) or polycarbonates. Here one may easily observe genuine structures with the electron microscope which, however, need not relate to the glassy state but could represent incipient or residual crystallinity. I note that several works in the debate in fact refer to observations made on such intrinsically crystallizable materials.For studies of the glassy state ideally of course one should select material which is intrinsically uncrystallizable. However, this may not be as simple a matter as it sounds, as no chain is totally irregular ; even a nominally totally atactic chain (if such exists) will have extended runs of a particular isomer which in principle might produce embryonic crystals at high undercoolings or stereo associations as is known to existGENERAL DISCUSSION 129 with PMMA. Whatever the case the usual commercial PVC is certainly not an intrinsically uncrystallizable material, an issue to which I shall address myself in the second part of my comment. PVC being such an important technological polymer is subject of much scrutiny for its own sake, in particular whether it is crystalline or not and to what extent.Prof. Geil has already made his point, here I am adding my own. Fig. 16 and 17 are X-ray diffraction patterns of commercial PVC prepared by gelling solutions. The diffrac- tion patterns which Prof. Geil has shown are unoriented versions, the ones I am show- ing here are from gels which have been stretched.l It is on such stretched samples that these unexpectedly well developed diffraction patterns (unexpected for commer- cial PVC) have been first recognized.’ For particulars I have to refer to the actual publications.’-2 The degree of crystallinity is substantial, although not readily asses- sable numerically on oriented samples. But what was more important from our point of view was the extent of order as revealed by the comparative sharpness of the reflections.We see, therefore, that the notion that commercial PVC is uncrystalliz- able is not tenable, with important consequences as regards properties and the iso- meric constitution of the chains.l This raises serious doubts as regards the suitability of PVC as a test material for demonstrating the intrinsically structureless nature of the glassy state, particularly when its ability to form crystals is not recognized and hence no deliberate precautions are taken to avoid crystallization. It is to be noted that Prof. Uhlmann’s samples were solution processed. These are broadly the conditions which gave rise to the diffraction patterns which myself and Prof. Geil have just shown. Regardless of whether they contain structures which are detectable by electron microscopy or by low-angle X-ray scattering there is the strong likelihood that such samples are not amorphous by more straightforward testing.P. J. Lemstra, A. Keller and M. Cudby, J . Polymer Sci., Pot’ymer Phys. Ed., 1978, 16, 1507. S. J. Guerrero, A. Keller, P. L. Soni and P. H. Geil, J. Polymer Sci., Polymer Phys. Ed., in press. Dr. M. Stamm (K.F.A., Jiilich) said: I would like to present other experiments, which also indicate the absence of bundle-like structures. As Prof. Fischer has already pointed out at this Discussion, measurement of the magnetic birefringence is a very sensitive probe of orientation correlations in polymers. We not only did experiments on n-alkane and polyethylene melts and solutions, which are reported in our paper, but also on solutions and melts of various other polymers such as for example polystyrene, polycarbonate, poly(viny1 carbazole) and aromatic polyamides. An example is given in fig.18. The Cotton-Mouton constant C, of polystyrene has been measured over a wide temperature range including the glassy and molten state. These experiments give no indication of the presence of ordered regions, but may on the contrary be understood in terms of Flory’s model of the glass transition. In the melt (T > Tg) C, can be cal- culated on the basis of the rotational isomeric state theory, and polystyrene can be described as a very flexible molecule with no intermolecular correlations. As the temperature approaches Tg there is no indication for an increasing intra- or inter- molecular correlation, but the segmental motion freezes in at Tg and only a restricted side chain motion of the polymer chains is possible for T < Tg.Prof. D. R. Uhlmann and Prof. J. B. Vander Sande (Massachusetts Institute of Technology) (communicated) : Prof. Thomas has misunderstood the presentation here and has misread, misinterpreted or misunderstood our earlier publications in the area of electron miscroscopy of polymers. What is clearly indicated in our earlier pub-130 GENERAL DISCUSSION 0 40 80 120 160 T I O C FIG. 18.-Temperature dependence of the Cotton-Mouton constant C, of polystyrene in the glassy state and in the melt. lications, despite Prof. Thomas’s statements to the contrary, is that (a) objective aper- ture size, (b) objective lens defocus, and (c) instrument resolution (which depends on wavelength, 3, ; spherical aberration coefficient, C, ; chromatic aberration coefficient, C,, etc.) can markedly affect the structure observed at high resolution.In particular, the “ pepper and salt ” structure observed in thin samples of crystalline or amorphous materials can exhibit a size which depends on the parameters mentioned above. The thrust of Prof. Thomas’ “ comments ” is simply to restate conclusions which we have already published or are otherwise well-known in the electron microscopy community. However, there is one rather disturbing comment made by Prof. Thomas which suggests that he has grossly misread our earlier publications. Prof. Thomas states, on two occasions, that “ Uhlmann’s suggestion (our italics) that the dark field speckle arises from the same mechanism as does the bright field “ pepper and salt ” structure with the implication that this speckle would disappear at exact focus in dark field .. .”. On no occasion has such a statement been suggested, or in any other way proposed, by either of us, whether orally or in writing. Such offhand remarks by Prof. Thomas have misconstrued our views, and do not contribute to enlightenment of the issues. In fact, the substance of Prof. Thomas’ comments could have been considerably abbreviated to say “ I have confirmed the finding of the MIT group that ‘ ordered structures on the scale of 10-100 A or more do not exist ’ in poly- styrene ”. Prof. Geil’s informal comments raise some interesting, even if obfuscating, points. He first focuses attention on PVC, and suggests that this polymer “ contains a small degree, on the order of loo/,, of crystallinity ”.He goes on to say that his films cast from DCE, which he indicates have 12% crystallinity, are similar to commercial rigid PVC, and further indicates that casting from DMP yields films which are even more highly crystalline (22%). In assessing these statements, it should first be noted thatFIG. 16.-X-ray diffraction pattern of commercial PVC. The sample was prepared by gelling from solution, the gel was stretched and heat treated subsequent1y.l Stretch direction vertical. FIG. 17.-As fig. 16, another preparation without heat treatment (although in the light of latest work ’ the need for heat treatment to produce the distinction between fig.16 and 17 is inconclusive). In ref. (1) the sharp meridional reflection was attributed to a new chain conformation. Latest work’ however, has shown that it is due to crystals orienting with their a axis along the stretch direction. Accordingly there are two crystal populations in the sample underlying fig. 17: one produces c the other a axis orientation on stretching. We associate the former with micellar (network forming) the latter with lamellar, possibly chain folded crystals connected to or enmeshed in the network orienting with lamellar planes in the stretch direction. [To face page 1300.054pm FIG. 19.-Scanning transmission electron micrograph (bright field/annular dark field) of microtomed thin section of EPON 812 epoxy stained with uranyl acetate. Resin cured with TETA for 2 h at 120°C.[To face page 131GENERAL DISCUSSION 131 few workers in the field of amorphous materials, whether polymeric or non- polymeric, would refer to crystallinities in the range 10-12% as a " small degree of crystallinity ',; and if Prof. Geil is serious about his belief that rigid PVC is 10-12% crystalline (and can be treated to 22% crystallinity), he should refer to PVC as a semicrystalline polymer. Such a designation would clarify the point at issue. An abundance of work on commercial, free-radical produced PVC has indicated that it is largely atactic. Bovey et al.' indicate, e.g., that for PVC polymerized at 50 "C (the range of most commercial processes), the fraction of syndiotactic dyads is z 55%; and the concentration of syndiotactic tetrads is almost exactly what is predicted from the fraction of dyads. This suggests that much longer syndiotactic sequences than indicated by the n.m.r.data do not occur in sizable amounts. On this basis, the probability of a syndiotactic sequence only 23 8, long is x 1.5%; and the probability of a sequence as long as 54 A is only ~0.0004. Other n.m.r. work2 indicates an even smaller fraction of syndiotactic dyads for PVC polymerized at 60 "C, i.e., ~ 5 1 % . On this basis, the probability of a syndiotactic sequence 23 8, long is M 0.009; and the probability of a syndiotactic sequence 54 A long is w 0.000 16. On the basis of either of these n.m.r. results, the development of 10-22% crystallinity on a scale of 200 A in such a material would require substantial revision of our under- standing of polymer crystallization.Natta and Corradini3 shed further light on the " crystallinity " of PVC by carrying out X-ray diffraction studies on oriented fibres. Their work indicated the existence of laterally ordered domains ( w 50 A wide) with " rather poor order along the length of the chains." As noted by these authors, " The lack of order along the c axis can be attributed to imperfections in the syndiotactic arrangement of the C1 atoms." Such considerations would lead naturally to the notion of liquid crystal domains in PVC, for which some reasonable arguments could be made. The notion of 200 8, thick lamellar crystals present in significant volume fractions seems, however, almost ludi- crous.In this light, the technique(s) used by Prof. Geil to infer his suggested percentage crystallinity would seem to merit close scrutiny. Density measurements on films cast from solution are far from convincing in this regard (e.g., what was the basis for choos- ing pa; how is the value selected affected by stabilization processes; what are the effects of retained solvent, etc. ?). Prof. Geil next cites the work of Blundell as indicating discrete maxima in SAXS curves without applying a Lorentz factor to the data. Without commenting at length on the highly questionable use of such a factor in the present application (which can well produce maxima from curves that are simple monotonic functions), it should be noted that the raw data, from which Dr.Blundell's maxima are supposedly obtained, show no maxima in the range of scattering angle where maxima are indicated in the data with the Lorentz factor. See, e.g., the range x20-13 mrad for the data given by solid circles in fig. 1 of ref. (4). In light of the scatter seen in the data at higher scattering angles, anything but a smooth curve drawn through the region of 13 mrad is unreasonable, and even after desmearing the smooth curve would not yield a diffrac- tion maximum. The data of Wenig cited by Prof. Geil do show SAXS maxima for two of the three PVC samples examined, an observation which remains curious. The sizes inferred from these SAXS maxima are much larger than the " crystallite " sizes inferred from corresponding WAXS maxima (23-64 A). Prof.Geil next attempts further obfuscation by questioning our use of a Bonse- Hart system and making an erroneous statement about the use of this instrument for carrying out SAXS studies for angles corresponding to Bragg spacings < x 100 A. He conveniently neglects the close agreement found between Bonse-Hart data and132 GENERAL DISCUSSION data obtained using a Kratky camera (the type employed, e.g., by Dr. Blundell, whose data Prof. Geil seems to appreciate). If Prof. Geil had bothered to note fig. 2 in our paper on PVC,’ which he is discussing, he would have seen such agreement indicated. He would also have seen such agreement if he had read our paper on PC, fig. 2 of which compares the results of Lin and Kramer,6 a reference cited by Prof.Geil in his com- ments, with our own Bonse-Hart data.7 Further, if Prof. Geil had taken the care to read other papers in the field [e.g., ref. (8) on SiOe from our laboratory], he would have seen similar close agreement. Next, if Prof. Geil prefers to designate the heterogeneities which he reported in PVC as “ irregular ~ 2 0 0 8, thick lamellar structures ” rather than nodules, we would be happy to stand corrected. This designation makes clearer the Geil thesis, which apparently suggests lamellar crystallites, reminiscent of other, semi-crystalline poly- mers. It is interesting to note that we are not alone in referring to Prof, Geil’s hetero- geneities in PVC as nodules [see, e.g., ref. (4) and Dr. Blundell’s comments at this Discussion]. After waxing eloquent about PVC, Prof.Geil gives short shrift to other amorphous polymers, such as PS, PMMA, PC and PET. This is perhaps associated with the accumulating weight of evidence, from studies using a variety of techniques [ref. (9)-( 1 I), e.g.1, against heterogeneities as essential structural features of such materials. In this regard, Prof. Geil’s statement that “ there is no question . . . that an E 100 A surface structure exists in these polymers, a structure which is affected by process history ” leads us to question whether he now agrees that his nodules are not repre- sentative of the bulk polymer structure, and that they rather represent surface struc- tures. We are pleased that Prof. Geil agrees that “ normal molecular weight distribution do not yield discrete SAXD ”, but are disturbed by his misreading of the results of the WAXS results presented at this Discussion.While Prof. Geil takes the results as suggesting “ that a regular conformation is maintained ’’ for sequences of 16-20 back- bone bonds in PMMA and 12 bonds in PS, the authors of the paper in question indi- cate that “As with the study of a-PMMA we have not yet managed to model the packing of a-PS. Although the intrasegmental scattering dominates above s = 2.0 A-l, it may be influenced by the intersegmental component so that some appreciation of the packing is needed before we can confidently propose a conformation.” Fur- ther, even if regular packing over 15-25 8, did occur, it is by no means apparent how such packing would be “ compatible (our italics) with some locally o r d e d domains of even twice this size ”, as suggested by Prof.Geil. Prof. Geil’s discussion of our microscopy is simply erroneous. In some cases, we used a supporting C film, 150 A thick on one side of a 600 A -thick specimen and a covering C film w50 8, thick on the other side; in other cases, the supporting film was not used, and a somewhat smaller sample thickness (~400-500 8,) was examined. Carbon films of the indicated thicknesses are highly transparent to electrons, and can- not confuse the observation of structural features on a scale such as the 100 A noted by Prof. Geil; and his analogy to viewing latex particles is simply incorrect. An appropriate analogy for observing 100 A nodules (if they existed) would be viewing through glass plates an assemblage of latex particles, packed at 50% volume fraction, through a thickness of perhaps 5 particle diameters. Clearly this presents no problem, even for smaller nodules (if they existed), as any reasonable microscopist is well aware.As microscopists are also well aware, the “ pepper and salt ” features which we reported would not be readily observable in a sample 1000 8, thick. Further, Prof. Geil’s statement that “ Films no more than 2-3 nodules thick would be required for any attempt to resolve the nodules by direct transmission microscopy with imageGENERAL DISCUSSION 133 formation due to density effects ’’ is likewise incorrect, as any reference to standard texts on electron microscopy1’’ l3 would indicate. It corresponds to the condition of no image overlap, which is far too restrictive.Prof. Geil next objects to our use of the second diffraction ring to produce our dark field images, and suggests that the innermost ring would have been more suitable. We did, in fact, make dark field observations using the innermost diffraction ring, and found speckle of about the same size as when the second diffraction ring was used. Once again, this size was sufficiently small that no sensible interpretation of structure could be made. The issue of beam damage in the electron microscope is raised by both Prof. Geil and Dr. Grubb. We agree that beam damage does occur when polymers are viewed in the electron miscroscope; and we have observed, using the scanning transmission electron microscope, the destruction of a crystalline diffraction pattern from poly- ethylene in a few seconds of beam exposure.In light of such damage, it is all the more remarkable that Profs. Geil and Yeh could have observed heterogeneities in both bright field and dark field microscopy of glassy polymers, and associated these heterogenei- ties with regions of local order. It should be noted here that in our previous work14 precautions, such as minimal beam current, minimal time of exposure, and lowest possible magnification consistent with required resolution were maintained in an effort to reduce as far as possible the effects of beam damage. As noted in the verbal presentation of our paper, concern about effects such as beam damage and desire to achieve enhanced contrast led us to carry out scanning transmission electron miscroscopy of amorphous polymers stained by uranyl acetate.The polymers investigated to date are glassy themoplastics (such as PS, PC and PET) as well as thermosetting polymers (such as epoxies and polyimides). The stain provides improved contrast for viewing heterogeneities and also imparts greater per- manence to the contrast since diffusion of the stain is required for elimination of the contrast (as opposed to unstained polymers, where even short-range structural re- arrangements can wipe out ordered regions). In this regard, we are pleased to report that the glassy thermoplastics, the subject of the present discussion, still show no struc- tures like Prof. Geil’s nodules. These observations of essentially featureless micro- structures in the thermoplastics were carried out under conditions where heterogeneities are clearly seen in the thermosets.Fig. 19 provides clear evidence of heterogeneities in an epoxy resin-and gives assurance that beam damage in the electron microscope would not have prevented observation of heterogeneities in the stained samples, if they had been present. Prof. Geil’s comments concerning beam damage are also incorrect or misleading. First, the beam current and image magnification are not intimately related, as pro- posed by him. The transmission electron microscope (TEM) is a “ flooding probe ” instrument, meaning that the beam size is large relative to the resolution of the instru- ment. The minimum beam diameter in most TEMs is M 1 pm. Such a small beam size can be maintained independent of the magnification in the image produced by the microscope, although this is usually not done, especially at the lowest magnifications. It is safe to say that whether one is operating at a screen magnification of 50 000 x or 500 000 x , the beam current would be identical.Jt is the gun geometry, gun operating characteristics, and first and second condenser lens settings that govern illumination. Statements relating beam current to magnification are nonsensical at the resolutions being discussed here. Using the fallacious connection between magnification and beam current, Prof. Geil suggests that electron microscopy by Geil and Yeh was carried out at low magni-134 GENERAL DISCUSSION fications (and hence, according to his scenario, low beam damage), while ours employed high magnifications.Yeh’s worki5 employed magnifications of 60 000-100 000 x ; and the lack of a significant difference in beam current between such magnifications and those employed by us has been discussed above. Prof. Geil also indicates that “ the only dark and bright field micrographs published from our laboratory, using polyethylene terephthalate, were taken at 25 5000 magnifica- tion, with beam conditions known to retain crystallinity in polyethylene, and photo- graphically enlarged.” In making this statement, Prof. Geil has apparently over- looked his paper with Klement,16 where as stated in their summary, ‘‘ The morphology of thin films of polycarbonate (PC), isotactic polymethyl methacrylate (1-PMMA), and isotactic polystyrene (I-PS) were studied by bright field diffraction, and dark field transmission, electron microscopy.” They go on to state “ High resolution dark field micrographs confirm this morphology .. .” Surely high resolution micrographs must represent magnifications higher than 5000 x ! Aside from a specific concern about the dramatic effects of electron beams on PMMA, a polymer well-known for its radiation sensitivity, there is a general problem with photographic enlargement of electron micrographs taken at 5000 x . At such low magnifications, it is generally not possible to focus the instrument well enough to permit reliable optical enlargement by more than about 5 x . Even if a through-focus series was taken for each micrograph published, a fact not cited in any of the publica- tions, an effective upper limit to optical enlargement is about 10 x (at higher enlarge- ments, one sees the grain in the plates).Considering that the resolution of the human eye is 250.2 mm, an optical enlargement of 5 x on a 5000 x micrograph would provide a resolution of ~ 8 0 A. This would be a poor way to investigate structural features on the scale of the nodules reported in several of the materials. The comments of Dr. Blundell concerning SAXS from PVC are also subject to considerable reservation. First, his annealed samples (one compounded with heat stabilizer, one not) were heat treated in air at 125 “C for 1 h after initial treatment at 180 “C for 2 min. This can hardly be regarded as a conventional moulding cycle. Even with such treatment the raw SAXS data show only a shoulder at about 28 = 10 mrad.After desmearing and applying a Lorentz factor, a peak is seen-but centred NN 13 mrad, with no hint of a peak in the region of 10 mrad. A comment is made that desmeared data without the Lorentz factor also show peaks, but these peaks were not shown. The Lorentz factored peaks yielded Bragg spacings of 92 A for the sample without stabilizer and 1 16 A for the stabilized samples. These values are, respectively, much smaller than the 200 A lamellae of Prof. Geil and much larger than the 30-40 A radii of gyration of heterogeneities inferred from Guinier plots of the SAXS data. When these variations are stirred vigorously and mixed with a touch of spice, one may arrive at a model of “ fringed-micellar crystalline nodules about 30-40 A in dia- meter with about 100 A between the nodule centres”.The relation between such structures and Prof, Geil’s 200 A lamellar crystals is far from clear, as is the origin of discrete diffraction maxima from poorly organized irregular structures. In this re- gard, it would be most helpful if believers in crystallite models for PVC would agree on the content and form of the crystal for whose existence they believe they have found evidence. Of greater note for the question of nodular or lamellar structures in rigid PVC are the data obtained by Dr. Blundell on samples which had not been subject to such severe annealing. These indicate scattering which decreases monotonically with increasing scattering angle (the form of the scattering observed by us).Desmearing procedures would not produce diffraction maxima from such data. The principal difference between Dr. Blundell’s data and our own on rigid PVC lies in the total percent crystal-GENERAL DISCUSSION 135 linity, which Blundell estimates as 3-4% for his samples A and B. In contrast, if all the heterogeneities in our sample were crystallites, they would be present only to a total of ~ 0 . 5 % (not the 0.1% mentioned by Dr. Blundell in his comments at this Discussi on) . Dr. Blundell goes on to generalize from his fringed micelle crystallite model of PVC to the structure of other amorphous polymers, and questions the very use of SAXS to disprove the existence of nodules in amorphous polymers. To arrive at this conclusion, however, he is forced to introduce a new model of nodular structures, viz., the nodules are no longer the structures seen by Prof. Geil and his associates in their electron miscroscopes, which generally occupy high volume fractions (in the range of 50%).Since the presence of nodules in such volume fractions having the crystal excess density are inconsistent with the SAXS data, one must appeal to nodules present in much smaller volume fractions, whose size bears no inherent relation to the heterogeneities seen in the electron microscope. Once again, the nodule hypothesis seems like a concoction of chameleons, whose guise changes with each new piece of data. Further, even so drastic a change in volume fraction of nodules as suggested by Dr. Blundell in his modified nodule model, i.e., from 50% seen in the electron micro- scope to 5%, would not decrease the SAXS intensity by the factor of 10 which he sug- gests.The SAXS intensity is proportional to C(1-C); and hence the suggested change in C from 0.5 to 0.05 would change the expected intensity by a factor of ~ 5 . Dr. Blundell’s final appeal, to the density of oriented amorphous PET as represent- ing a limit on the density of nodules in this polymer, seems likewise fanciful. Is he thereby suggesting that the nodules do not represent regions of local order (as sug- gested by other proponents of the nodular hypothesis), but rather represent regions of local orientation ? If so, one must wonder about the origin of such randomly oriented regions of high orientation. The thrust of Dr.Blundell’s argument is then not directed to the utility of SAXS for proving or disproving the existence of nodular structures as originally proposed and often believed, but to whether it is possible to redefine the nodules as regions of local orientation or crystalline regions occupying a small volume fraction, which bear no intrinsic relation to the electron miscroscope observations, so they can be made con- sistent with the SAXS data. We agree with Prof. Keller’s comments that one must distinguish between poly- mers such as PC and PET which are inherently capable of crystallizing and atactic polymers such as PS, PMMA and PVC. Indeed, we have made this distinction on several occasions [e.g., ref. (7)] in questioning how nodular structures of the size re- ported could possibly represent regions of local order in atactic polymers. From the fact that a material such as PC or PET is inherently capable of crystallizing, however, it should not be concluded that it will contain a detectable degree of crystallinity when subject to a given thermal history.Recall, for example, the familiar soda-lime- silicate glasses of commerce, which are certainly capable of crystallizing, but which are free of detectable crystallinity as ordinarily prepared. We would take issue with Prof. Keller’s comments concerning PVC, in part for reasons discussed above. With specific reference to Prof. Keller’s remarks, it should be noted that our SAXS work was not carried out on solution-cast films, but on rigid sheet supplied by American Hoechst Co.[see ref. (5)]. An upper limit to the degree of crystallinity in this material, obtained by assuming all the heterogeneities are crystal- lites, is ~ 0 . 5 % . The X-ray diffraction patterns of Prof. Keller on stretched PVC gels clearly indicate orientation. The crystallinity is more difficult to assess. As indicated in ref. (1) fromI36 GENERAL DISCUSSION Prof. Keller's comments, the estimated coherent diffraction lengths along the chain direction, estimated assuming a crystallite model, range from 36 to 153 A, depending on the " reflection " chosen for effecting the estimate. This highly interesting but puzzling paper indicates that " Even if there were sufficient regularly arranged syndio- tactic units to produce the observed structure B [corresponding to the '' best developed crystallinity "I, which would be unexpected in itself, this does not seive to account for structwreA and, in particular, for the 5.28L reflection in the meridian." N.m.r.data on the polymer investigated indicate that the probability of sequence lengths required for structure B is " negligibly small "; and this discrepancy with the model of sizable crystallites was of concern to Prof. Keller and his co-workers. We share his concern, and suggest that the interpretation of the diffraction patterns be revised. Since PVC has attracted so many comments at this Discussion, it seems appro- priate to restate the facts and our conclusions therefrom. First, there is no doubt about the " anomalous " rheological properties of PVC compared with other amor- phous polymer^.^^*^^ To account for these properties, appeal has been made to the existence of a three-dimensional array of crystallites which serve as crosslinks between the chains.Our SAXS data on PVC indicate a maximum possible concentration of crystallites of only z 0.5% (assuming all the heterogeneities responsible for the SAXS are crystallites). Also inconsistent with the observations of lamellar crystals are our electron microscope results, carried out using the same sample preparation techniques as Prof. Geil, which indicate the absence of observable crystallinity in rigid PVC. Different samples of PVC, such as those polymerized at different temperatures, may well have different probabilities of developing crystallinity on various scales. Avail- able n.m.r.data on PVC, free-radical polymerized at typical temperatures, indicate a very small probability of developing lamellar crystals 200 A in thickness. One is left with the possibility of small volume fractions of physically thin crystals, or larger volume fractions of liquid crystal domains which may differ in density from the matrix by much less than crystallites. Elucidation of such possibilities should be a fruitful area for future investigations. The comments of Prof. Fischer and Dr. Windle concerning SAXS raise interesting points. Prof. Fischer correctly notes that both he and Dr. Ruland have observed a temperature dependence of the density fluctuations below Tg. It is noteworthy, how- ever, that SAXS work in our laboratory on Si02 has confirmed the results of Porai- Koshits in Leningrad,19 and indicate no temperature dependence of the density fluctua- tions below Tg.In this case, the data cover a range of more than 900 "C, from about 0.2 Tg to Tg, compared with a much smaller range for the polymers, from about 0.7 7'' to Tg. The origin of this difference is not clear, as is the physical basis for expecting the density fluctuations to change below Tg. Even if the density fluctuations in polymers do change below Tg, this would have no effect on the conclusions of our papers concerning nodules. Further, the fine quality of the agreement between the SAXS results of Prof. Fischer and ourselves, obtained on four glassy polymers of different origin and using different diffraction equipment, provides increased confidence in the generality of the results for the poly- mers considered.The change in SAXS intensity at very small angles on polymerization does not convince one that the heterogeneities responsible for the scattering are intrinsic to the polymer. From the form of the data, it appears that the heterogeneities decrease in size between 20% polymerized and 70% polymerized, and then increase in size between 70% polymerized and 100% polymerized. Surely this is curious for intrinsic features of the material. More likely sources of the heterogeneity scattering are adventitious impurities or voids. Persistence of such scattering (at the same level?) after annealingGENERAL DISCUSSION 137 at Tg + 30 “C for several hours does not seem conclusively to eliminate void scatter- ing; but impurities would perhaps seem more likely (e.g., small concentrations of gels, dirt, etc.).In this regard, Prof. Fischer has reported SAXS data on purified PS which indi- cated the absence of heterogeneity scattering at very small angles; and our own SAXS data on a waveguide-quality acrylic copolymer also indicate the absence of hetero- geneity scattering at very small angles. While our data in this case did not extend to as small angles as our initial study of PMMA, it did cover a range where heterogeneity scattering was seen in the initial work. The combined results of these studies provide support for our previous suggestion that the heterogeneities responsible for scattering at very small angles are extrinsic to the polymers. Even if this were not the case, however, it would not affect our conclu- sions about nodular structures (since the scattering at very small angles can be associ- ated with small concentrations of large heterogeneities). The “ structures ” observed in Dr Frank’s series of micrographs are almost surely not associated with the internal structure of the sample.First, the “remarkable changes taking place during annealing were not observed with unetched samples ” (cited by Dr. Frank). This suggests that the observations are an artifact of ion beam interaction with the sample surface, which does not properly portray the true structure of the sample. It is well known that ion-beam etching produces topo- graphical features on samples which are not related to the structure of the sample.Work carried out in our laboratory on metals (e.g., stainless steels or metal alloy glasses) and ceramics (e.g., MgO and SO2) has indicated that structures which are non-representative of the bulk materials can readily be produced. These often take the form of mourrds (“ nodules ”) in ceramics and lath-like structures (“ lamellae ”) in metals. Secondly, replication is not an accurate method for revealing surface structures on the scale presented in Dr. Frank’s work unless reproducibility has been established. It is well known that consecutive replicas shot of the same sample can indicate notably different structures, and apparent (not real) structures can easily be produced for single crystal sapphire or fused silica. Without establishing such reproducibility, the apparent trends observed in Dr.Frank’s work must be considered fortuitous. It should also be noted that the apparent structural changes reported by Dr. Frank were observed at temperatures near or well below the glass transition. It is difficult to imagine how regions of local order would increase in size at temperatures well below Tg, and then decrease in size upon treatment near Te (a temperature well below the melting point of PC). Dr. Grubb has organized his comments on the viability of “ nodule ” observations in electron microscopy with two assumptions that are not stated. First, he assumes that diffraction contrast is the governing contrast mechanism; secondly, he assumes that all observations are being made in a conventional TEM. Each of these assump- tions requires additional review.Besides diffraction contrast, samples can also provide contrast by mass-thickness variations. The intensity I exiting a sample of thickness t with scattering cross-section Q is: I = Ioe-Qf (1) where Zo is the incident intensity. cross-section Q, in an amorphous film of thickness t, it can be shown that12 For a “ nodule ” of thickness At and scattering QnAt x 0.05138 GENERAL DISCUSSION if 5% contrast is needed for observation. Using Qn = 10 x lo4 cm’l, then At = 50 A, certainly within the regime of the nodular structures of interest. First, this contrast is observed in bright-field, would be enhanced in an out-of-focus condition and would not be as readily destroyed by radiation effects as diffraction contrast. Secondly, the model from which eqn (1) and (2) are drawn is a single scattering model and requires that objects be sufficiently thin that only single scattering applies. Our second issue with Dr.Grubb is that he has not considered the advantages of the scanning transmission electron miscroscope (STEM) for analysis of polymer microstructures. Dramatic improvements in contrast can be obtained in a properly equipped STEM through contrast enhancement techniques. Proper combined use of the bright-field detector and annular dark-field detector can enhance contrast to strengthen the arguments presented above for more careful consideration of mass- thickness contrast as a viable contrast mechanism. Third, Dr. Grubb has constructed a table relating electron flux to resolvable “ nodule ” size in bright-field or dark-field, based upon a shot noise limit.He rules out bright-field observations of nodules by defining crystallite resolutions 240 A as being of no utility. This, of course, is not the case for PC and PET where nodules 100-200 A in size have been reported. In fact, nodules of this size would negate Dr. Grubb’s assumption that C =fDF. Once bright-field becomes a viable viewing tech- nique, the remainder of his comments on film sensitivities, associated resolutions and useful magnifications lose their relevance. Finally, we are pleased by the comments of Dr. Stamm, who has provided further convincing evidence against the presence of ordered regions in glassy polystyrene. More work of this type should provide important insight into the structure of amor- phous polymers.In conclusion, we would reiterate our suggestion from our paper presented at the Discussion that the controversy concerning nodular structures in amorphous thermo- plastics be laid to rest, “ and that attention be directed to more fruitful areas such as the structural changes involved in crystallization and the structural differences between surfaces and bulk material ”. Two points should be made in this regard. F. A. Bovey, F. P. Hood, E. W. Anderson and R. L. Kornegay, J. Phys. Chem., 1967,71,312. Talamini, Mukromol. Chem., 1967, 100,48. G. Natta and P. Corradini, J. Polymer Sci., 1956, XX, 251. D. J. Blundell, Polymer, 1979, 20, 934. R. J. Straff and D. R. Uhlmann, J. Polymer Sci., 1976, 14, 353. W. Lin and E. J. Kramer, J.Appl. Phys., 1973,44,4288. A. L. Renninger and D. R. Uhlmann, J. Non-Cryst. Solids, 1974, 16, 325. G. D. Wignall and G. W. Longman, J. Mater. Sci., 1973, 8, 1439. ’ A. L. Renninger, G. G. Wicks and D. R. Uhlmann, J. Polymer Sci., 1975, 13, 1247. lo G. D. Patterson, Polymer Preprints, 1974, 15, 14. l1 A. E. Tonelli, J. Chem. Phys., 1970, 53, 4339. l2 R. D. Heidenreich, Fundamentals of Transmission Electron Microscopy (Wiley, New York, l3 P. Hirsch, Electron Microscopy of Thin Crystals (Krieger, New York, 1977). l4 M. Meyer, J. Vander Sande and D. R. Uhlmann, J. Polymer Sci., 1978, 16,2005. l5 G. S. Y . Yeh, J. Macromol. Sci.-Phys., 1972, B6, 451. 1964). J. J, Klement and P. H. Geil, J. Macsomol. Sci. Phys., 1972, B6, 31. T. Alfrey, Jr, N. Wiederhorn, R. Stein and A.Tobolsky, J . Colloid Sci., 1949, 4, 211. l8 T. Alfrey, Jr, N. Wiederhorn, R. Stein and A. Tobolsky, Ind. Eng. Chem., 1949, 41, 701. l9 E. A. Porai-Koshits, J . Non-Cryst. Solids, 1977, 25, 86. Dr. G. C . Stevens (C.E.R.L. Leatherhead) said: Prof. Uhlman, whilst discounting the presence of significant bulk heterogeneity in linear thermoplastics, based on hisGENERAL DISCUSSION 139 own small-angle X-ray scattering and microscopy studies indicates that such a con- clusion may not pertain to crosslinked epoxy resin systems. Recent results obtained on anhydride cured diglycidyl ether of bisphenol-A (DGEBA) epoxy systems sup- port this latter view but also highlight the need to consider the possible influence of inhomogeneous reaction mechanisms and subsequent domain competition during the formation of amorphous polymers both linear and crosslinked. This was amply demonstrated by the contribution of Dr Champion on the polymerization of butyl methacrylate. In this respect we should examine the significance of the low level of SAXS assessed heterogeneity and its relationship to the connectiveness of the matrix rather than discount it as impurities or inclusions. Microscopically observed surface heterogeneity in epoxy systems is generally larger than that reported for linear amorphous polymers. In the case of multi- oligomer DGEBA-anhydride systems heterogeneity in the range 50-250 nm is ob- served. This negates arguments of microscope resolution limits and satisfies Prof. Fischer’s requirement that the heterogeneity, to be defined, should be larger than the extent of thermal density fluctuations (a point overlooked in the Discussion). Observation of the light-scattering envelope and Brillouin spectra with tempera- ture and the dissolution behaviour of the light scattering of two unreacted DGEBA OH CHr /o. CH --CH2-0 ~ ~ @ 0 - C H 2 - C H I - C H r O a!@;-ct$-c~- A\ CH, C”3 CH3 systems exhibiting different molecular weight distributions and different epoxide and hydroxyl group contents indicate the presence of molecular aggregates with sizes up to 35 nm, whose number and size decrease with increasing temperature. Evidence suggests that the aggregates form principally from intermolecular epoxide-hydroxyl- group hydrogen bonding. This produces regions of high hydroxyl group content capable of inducing inhomogeneous reaction. Infrared absorption spectroscopy and light-scattering observations during reaction provide a number of interesting optical parameter-chemical group behavioural rela- tions and correlations as tabulated below in order of the most rapid extent of change behaviour. These and other detailed observations indicate the existence of a matrix TABLE 2.-oPTICAL PARAMETER - CHEMICAL GROUP CORRELATION chemical change optical parameter change rapid immediate anhydride consumption on addition accompanied by associated carboxylic group formation anhydride consumption : 1 st-order kinetics aromatic ester formation : 1 st-order kinetics branched ether formation: Q-order kinetics immediate increase ir, disymmetry decrease : kinetics system disymmetry 1 st-order refractive index increase: 1 st-order kinetics phonon velocity increase and phonon attentuation decrease: +-order kinetics slow140 GENERAL DISCUSSION controlled inhomogeneous reaction mechanism in which the initial molecular aggre- gates act as reaction nucleation sites where initiating reactions involve free hydroxyl group ring-opening of anhydride groups. Two correlations of particular interest are the total aromatic ester-refractive index and the branched ether-phonon shift correla- tions. In terms of the inhomogeneous reaction model proposed for these systems,1 matrix density is controlled by inter-nuclei reactions and growth which exhibit a rela- tively higher aromatic ester group content, whereas longitudinal phonon velocity and hence longitudinal modulus is controlled by nuclei interconnections which are rela- tively ether rich. Thus, in contrast to amorphous linear polymeric systems, both physical and chem- ical contributions to matrix connectiveness and properties are expected. Indeed, the fact that nodular features appear in fracture surfaces may result from spatial variations in mechanical properties rather than density. The act of fracture may sub- sequently introduce surface density heterogeneity. Inhomogeneous reaction mech- anisms may be unavoidable in most amorphous polymer systems and the concept of competing domains, diffuse domain boundaries and matrix connectiveness are perti- nent. Modification of this situation in solution reactions and phase stability and molecular mobility considerations are important aspects in favour of homogeneous matrix arguments. To lay this controversy to rest and direct efforts to more obvious topics as sug- gested by Prof. Uhlman would undermine further understanding of the amorphous polymer solid-state and structure-property relationships. G. C. Stevens, J. V. Champion, P. Liddell and A. Dandridge, 26th Int. Symp. Macromolecules, Mainz 1979, Paper CI-8 and Chem. Phys. Letters, in press.

ISSN:0301-7249    

DOI:10.1039/DC9796800104

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

ADDITIONAL REMARK Prof. P . H . Geil (University of Illinois) said: This contribution was presented and discussed at the meeting, but by an oversight was not submitted to the Editor. Prof. Uhlmann well summarizes the observations of nodule structures in amor- phous polymers in his Introduction; in particular we emphasize three of these ob- servations. (1) A 50-100 A diameter structure is seen by replication and direct transmission electron microscopy. It is noted that, for most polymers, the observa- tions have been made using shadowed (“ replicated ”) samples and there is no question, we believe, that there is a surface texture of the observed size (e.g., fig. 20). (2) Dark- field observations of similar size structure. We note, however, that both dark-field and direct transmission (bright-field) observations have been considerably more limited than those using shadowed samples.(3) Changes in the nodule structure have been observed with process history, e.g., annealing below the glass transition temperature (Tg) (fig. 21) and drawing. However, I suggest he then only tends to confuse the legitimate problem as to their physical origin and presence in bulk polymers, rather than contributing to its solution. PVC is a special case since it is commonly accepted, despite Uhlmann’s claim to the contrary [ref. (1) and this paper], that PVC contains a small degree, on the order of lo%, of crystallinity. In fact it is only under extreme processing conditions (rapid heating to a high tempera- ture followed by quenching4 that amorphous PVC can be prepared and its physical properties are considerably different from the normal, partially crystalline material.I show here as an example, a suspension polymerized PVC cast from two different solvents, dichloroethane (DCE) and dimethyl phthalate (DMP) (fig. 22). The crystallinity of these samples, as determined from their density (assuming pc = 1.49 and pa = 1.385) are 12 and 22%, respectively.6 The pattern from the sample cast from DCE is similar to that obtained from normal, commercially prepared rigid PVC. I believe it is obvious, just by inspection, that these PVC samples are partially crystalline. In general, discrete small-angle X-ray diffraction (SAXD), i.e., maxima, have been obtained only from plasticized PVC. and in Hendus’s original work [described in ref. (lo)], it was specifically pointed out that no discrete diffraction was observed from the rigid PVC samples used.On the other hand, Wenig5 and Blundel1,ll using certain rigid PVC samples, have been able more recently to obtain discrete SAXD. Of significance here is the fact that in all of these contrary to the implications of Prof. Uhlmann,l maxima in the SAXD curves were observed even before the application of Lorentz-geometric corrections (multiplication of the data by O2 to correct for Lorentz effects and the increase in diameter of a diffraction ring with increasing radius). Thus the question here with respect to X-ray diffraction from PVC is why do Prof. Uhlmann and his co-workers find no evidence for crystallinity >0.5% or dis- crete SAXD? Is it his sample [which is only defined as obtained from American Hoechst Co., with no indication as to polymerization type (Wenig finds discrete SAXD from bulk and suspension resin but not from emulsion resin), stabilizer con- tent, etc.], or is it his equipment and technique (a Bonse-Hart small-angle scattering Consider first his results on poly(viny1 chloride) (PVC).In our142 ADDITIONAL REMARK system, as used by Uhlmann,' is excellent for measurements at very small angles, but much less suitable for detection of weak scattering, as obtained from PVC, at angles corresponding to Bragg spacings smaller than z 100 8, due to its effective, non-variable, very fine slit width). With respect to the electron microscopy of PVC, and the presence of nodules therein, Prof.Uhlmann has also implied results to us that are contrary to our papers. In particular, in ion-etched rigid PVC,7 in contrast to Prof. Uhlmann's claimg that we report a 200 A nodule structure, we describe an irregular ~ 2 0 0 A thick lamellar structure, similar to that originally observed by Geymeyer." In a later papers [his ref. (12) in ref. (12)], again in contrast to his claim that we see no such structure in freeze-fractured rigid PVC, we do report the presence of particles 250-500 A in size in samples which were annealed at 125 "C for 15 h before fracturing, but state their relationship to the nodule structure in plasticized PVC is not clear. In fact, in that paper we clearly state that we do not have an adequate description of the morphology of rigid PVC.It is only in plasticized PVC that my co-workers and I have claimed the clear presence of a nodule structure, on freeze-fractured surfaces, with corresponding SAXD patterns, an observation that has been confirmed by a number of electron microscope techniques re~ent1y.l~ It would thus seem appropriate that it is only with such samples that Prof. Uhlmann and his co-workers should attempt to prove their absence. With respect to SAXD from amorphous polymers, I agree with Prof. Uhlmann that normal molecular weight distribution polymers do not, to my knowledge, yield discrete SAXD. However, there is considerable evidence in the literature, still sub- ject to conformation, that fractionated, oriented or annealed amorphous polymers contain heterogeneities in density on the same order of size as the nodules that have been reported as being observed by electron microscopy [e.g., ref. (14)-(17)].It would, perhaps, be appropriate for Prof. Uhlmann to examine samples prepared in a similar manner before concluding that SAXD is inconsistent with the presence of heterogeneities on the order of 100 8, and smaller in amorphous polymers, particu- larly since wide angle X-ray diffraction results (Windle's paper in this Discussion) suggest that a regular conformation is maintained for sequences of 16-20 backbone bonds in atactic poly(methy1 methacrylate) and the order of 12 bonds in atactic poly- styrene. These values correspond to average lengths of 15-25 A, certainly compatible with some locally ordered domains of even twice this size.With respect to Prof. Uhlmann's electron microscope studies of amorphous polymers as reported in this and, more fully, in a previous paper,12 I can most simply state that I would not expect to see anything related to the polymer sample using the techniques described by Prof. Uhlmann and thus am not surprised that he observes nothing except a pepper and salt " noise ". In his Introduction he correctly states that nodule sizes of 50-100 A (from our laboratory >75 A only) have been reported, but then he claims " the fine scale (20 A apparent structure seen in some previous investigations may simply reflect the use of microscopes of insufficient resolution or may result from the lack of proper focus in taking the micrographs" (Uhlmann's paper, this Discussion).We have never claimed physical reality or even the observa- tion, of structures averaging <20 A in size in amorphous polymers and I doubt that any knowledgeable electron microscopist would, without great attention to problems of focus, phase contrast, etc., but, on the other hand, there is no question, despite his conclusion, that a E 100 A surface structure exists in these polymers, a structure which is affected by process history. Why do Prof. Uhlmann and his co-workers not see this nodule structure? There are at least three reasons. (1) In non-shadowed samples consisting of films more thanFIG. 20.-Linear polyethylene quenched to the glass and replicated at liquid nitrogen temperatures’. FIG. 21 ,-Amorphous linear polyethylene, as in fig. 20, annealed for 4 h at 170 K, .. .20 K below Tg.3 [To face page 142DC E DMP FIG. 22.-X-ray diffraction patterns from dried films of PVC cast from (a) dichloroethane and (b) dimethyl phthalate. The outer ring is from calcium fluoride used for calibration6 [To face page 143ADDITIONAL REMARK 143 600 A thick (the technique he describes may result in two films, totalling >lo00 A in thickness), as used by Prof. Uhlmann for his direct transmission studies,IZ the superposition of the images of 50-100 A diameter nodules, if randomly packed through the thickness of the film, would prevent their observation. Even with the maximum difference in electron density of nodule and surroundings, it would be like trying to see the individual particles in a film of randomly packed latex particles when the total density of the particles is projected onto a single plane.This effect alone would prevent their observation even if a stain could be found that would distinguish between regions of varying degrees of order. Films no more than 2-3 nodules thick would be required for any attempt to resolve the nodules by direct transmission microscopy with image formation due to density effects. (2) For dark-field microscopy he reports in this paper and ref. (12), that he used the second (an intramolecular) diffraction ring to produce his images. It would seem to be more suitable, for intensity and interpretation purposes, to use the innermost diffrac- tion ring, a ring generally attributed to intermolecular spacings. (3) As discussed also by Prof.Thomas in this meeting, with the beam currents required to take micro- graphs at 500000 magnification, as done by Prof. Uhlmann,12 beam damage would nearly instantaneously destroy any order originally there. Thus any contrast effects due to such order, in either bright- or dark-field, could not be observed. (The only dark- and bright-field micrographs published from our laboratory,ls using polyethylene terephthalate, were taken at z 5000 magnification, with beam conditions known to retain crystallinity in polyethylene, and photographically enlarged. Yeh’s work on atactic polystyrene,17 claiming a z 3 0 L$ average size in dark field, was done using “ low beam intensities, 500 A thick films and magnification of 60 000 to 100 000 ”. While the film thickness effect, as in (1) is not of as much concern in diffraction contrast microscopy, individual properly oriented domains “ lighting up ”, the beam damage problem would be.) On the basis of the above, it is then not surprising that Prof.Uhlmann reports seeing only a fine scale pepper-and-salt structure in his samples; however, these results, I maintain, are of no value as a contribution to the question of local order in amorphous polymers and, furthermore, explain none of the observations he itemizes at the beginning of his paper. In conclusion, we are still left with the question for amorphous polymers as to whether the nodules are only a surface and thin film effect, or a bulk property (in crystallizable polymers such as polyethylene terephthalate and polycarbonate they could, e.g., be crystalline nuclei whose formation is enhanced by the surface; it is in this type of amorphous polymer that their presence can be least questioned). For poly(viny1 chloride), on the other hand, the question clearly is not their existence but rather their origin and effect on properties.Thus, while we disagree with Prof. Uhlmann in many of his statements, inferences and results, including his final con- clusion that the controversy on local order in amorphous polymers can be laid to rest, we do agree that attention should be directed to effects of crystallization from these glasses and differences between surfaces and bulk material. R. S. Straff and D. R. Uhlmann, J . Polymer Sci., 1976, 14, 353. R. Lam and P. H. Geil, paper presented at the American Physical Society meeting, Chicago, IL, March 1979, to be published.R. Smith, paper presented at the 2nd Int. Conf. on PVC, Lyon, France, 1976, method described in ref. (5). W. Wenig, J . Polymer Sci., 1978, 16, 1635. P. L. Soni, Ph.D. Thesis (Case Western Reserve University, Cleveland, Ohio, 1979). ’ See for example, J. Breedon Jones, S. Barenberg and P. H. Geil, PoZyrner, 1976, 20, 903.144 ADDITIONAL REMARK D. M. Gezovich and P. H. Geil, Int. J. Polymer. Mater., 1971, 1, 3. C. Singleton, J. Isner, D. M. Gezovich, P. K. C. TSOU, P. H. Geil and E. A. Collins, Polymer Eng. Sci., 1974, 14, 371. C. Singleton, T. Stephenson, J. Tsner, P. H. Geil and E. A. Collins, J. Macromol. Sci. (Phys.) 1977, B14, 29. lo R. Bonart, Kolloid-Z., 1956, 213, 1. l1 D. J. Blundell, Polymer, 1979, 20, 934. l2 M. Meyer, J. Vandersande and D. R. Uhlmann, J. Polymer Sci., 1978, 16, 2005. l3 IUPAC working party on Structure and Properties of Commercial Polymers, subgroup on subprimary particles in PVC-identification and elucidation of their role during flow. Report in preparation. l4 P. J. Hargett and S. M. Aharoni, J. Macromol. Sci. (Phys.), 1976, B12, 290. l5 A. V. Sidorovich and Yu. S. Nadezhin, J. Macromol. Sci. (Phys.), 1976, B16, 35. l6 P. J. Hargett and A. Siegmann, J. Appl. Phys., 1972,43,4357. l7 W. Lin and E. S. Kramer, J. Appl. Phys., 1973, 44,4288. l8 G. S. Y. Yeh and P. H. Geil, J. Macromol. Sci. (Phys.), 1967, B1, 235. l9 G. S. Y . Yeh, J. Macromol. Sci. (Phys.), 1972, B6, 451.

ISSN:0301-7249    

DOI:10.1039/DC9796800141

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

Crystalline Polymers; an Introduction BY A. KELLER H. H. Wills Physics Laboratory, University of Bristol, Royal Fort, Tyndall Avenue, Bristol BS8 1TL Received 1st November, 1979 In contrast to Sir Charles Frank, I do not regard it as my task to discriminate between right and wrong even if I were able to do so, but rather to ensure that all the ingredients of the arguments are in front of you and to point out how they relate to the individual papers and vice versa. I shall try to show that this is neither as widely spread nor as grave as generally believed. To do this I shall first circumscribe its area and then attempt to penetrate the smoke which is enveloping it so as to reach the fire from which it emanates and to identify its source. We all know there is conflict in the subject of polymer crystallization.THE THREE AREAS OF POLYMER CRYSTALLIZATION In service of the above purpose I shall first outline the whole subject of polymer crystallization and then close in on those aspects which feature in the papers pre- sented and will foreseeably be brought up in the discussions. It serves my purpose to proceed in the historic sequence. The crystallization of polymers can be classed under the following three headings. (I) Crystallization concurrent with chain growth, i.e., polymerization. (11) Crystal- lization of long chains induced by orientation. (111) Crystallization of long chains under quiescent conditions. For the sake of completeness I shall just mention (I), dwell briefly on (11) and then proceed to (111) which is our main subject in this discus- sion.(I) CRYSTALLIZATION CONCURRENT WITH POLYMERIZATION Crystallinity attained in this " nascent " state is one of the commonest, yet least explored, aspects of our subject. One facet of it has acquired special significance recently. This is the formation of macroscopic polymer crystals. Such crystals are obtainable in specially favourable instances when the monomers forming a macro- scopic crystal can be joined up into chains by solid-state polymerization so that the crystal itself is preserved. Such crystals have unique properties. In the case of poly(su1phur nitride) (fig. l), to quote one example, the crystals conduct electricity like metals along the crystal axis corresponding to the chain direction, and in fact can become superconducting at sufficiently low temperatures.This whole field, while confined to speciality polymers, is of great potential future interest. It will be intro- duced in detail by Prof. Wegner, therefore I shall say no more of it here. I merely remark that while a subject of great fascination it is not a source of major conflicts.146 CRYSTALLINE POLYMERS (11) CRYSTALLIZATION INDUCED B Y ORIENTATION The principles are familiar [e.g., ref. (2)-(5)] and are schematized by fig. 2. Long chains when stretched out are prone to form fibrous crystals; in fact only under these ... I II Ill iv FIG. 2.-Schematic representation of orientation-induced crystallization. (a) Formation of smooth extended-chain fibres: (i) random coils; (ii) the chains have become oriented by external influences; (iii) the preoriented chains have crystallized.(6) Formation of fibre-platelet composites (" shish- kebabs "). Here not all the chains have been aligned and at stage (iii) only the oriented chains crystallize, the unoriented chains are left in their random conformation. The latter use the crystalline fibres already formed as nuclei for subsequent crystallization in the form of chain folded platelets (iv). The molecular detail as drawn is not meant to prejudge the nature of the chain-folded structure. conditions do they give rise to fibres, with chains predominantly in an extended form (fig. 3). However, such apparently structureless, smooth fibres are obtained only under exceptional circumstances ; normally they are overgrown by platelets giving rise to the familiar composite fibre-platelet morphology, the so-called shish-kebabs (fig.4). As is well documented, the platelets result through folded crystallization of chains which have remained unextended. These chains then avail themselves of the fibres created by the orientation induced crystallization and use them as nuclei for subsequent epitaxial crystallization in the way schematized in fig. 2. The unaligned chains which fold can either be dangling hairs attached at one end to the central fibre, or totally separate chains within the solution giving rise to fine-scale undetachable and larger-scale removable (by solvent treatments) platelet overgrowth, respectively. As a comment aside, with relevance to arguments relating to chain folding (see later) shish-kebabs provide a convincing demonstration of the fact that chain folding is not influ- enced by a pre-existing crystal face, and in particular that the chains will fold even when presented with an extended chain substrate.Thus the trend for the initially unaligned chains to fold is so strong that they will do so in spite of the inducement to crystallize in a state of higher thermodynamic stability offered by the pre-existing substrate, a salient fact of observa- tion which is one of the cornerstones of the kinetic theories. The subject of orientation-induced crystallization can be subdivided into the fol- lowing separate headings : Method of chain alignment, mechanism of crystallization, the structure of the resulting crystal entities and the physical properties thereof.His- torically the first method of chain alignment was the stretching of networks, such as occurs in rubbers, while the more modern studies of shish-kebabs, initiated by Pen- nings, utilized the chain-stretching effect of flowing solutions and in some instancesFIG. 1 .-Example of a macroscopic single crystal. Poly(su1phur nitride) obtained by simultaneous polymerization and crystallization. 1 division = 0.5 mm (Stejny et aZ.l). [To face page 146FIG. 3 .--Smooth fibre of polyethylene obtained by orientation induced crystallization from solution via the surface-growth technique of Pennings .z Transmission electron micrograph [Hill, quoted in ref. (3)]. FIG. 4.-An example of a polyethylene shish-kebab. Transmission electron micrograph. The dark dots are due to the gold decoration applied in this particular study (Hill et aL6).[To face page 147A . KELLER 147 that of r n e l t ~ . ~ ’ ~ There is only one paper on this whole extensive subject in our Dis- cussion, that by Posthuma de Boer and Pennings, which now makes the stretching of networks again the central issue combining it with the study of shish-kebab formation. The area of orientation-induced crystallization is not the subject of the central con- troversies anticipated in this Discussion. This is not to say that there are no acute problems as regards the origin of fibre formation, the structure of the fibres and that of the overgrowth. In fact there are some quite recent developments which indicate that the stretching of network structures, in the form of thermoreversible gels, has a more fundamental part to play in shish-kebab formation than envisaged even under conditions where the presence of such networks has not been suspected.6 We may possibly hear more about this in the course of the Discussion.The drawing of material already crystalline, while not explicitly the topic of the present meeting, is nevertheless of some relevance to the subject in question. Even if the principal processes involve deformation of crystals, crystallization induced by orientation is likely to be also operative. Further, the structure and properties of the resulting fibrous entities have some affinity to what is attained by explicitly orientation- induced crystallization. In the present discussion the paper by Capaccio et aE.deals amongst others with structure problems in such fibres, while the paper by Ballard et al. contains the first recorded application of the neutron scattering technique to what happens when a solid crystalline polymer is cold drawn. CLASSIFICATIONS I N THE AREA OF CRYSTALLIZATION OF QUIESCENT SYSTEMS I shall commence my introduction to quiescent systems by drawing attention to two salient classifications. SOLUTIONS A N D MELTS The subject divides itself into studies on solutions and those on melts. The dis- tinction involved is both a matter of principle and of practicalities. The former of course relates to the distinction between the behaviour of dilute and condensed systems and is therefore fundamental, while the latter relates to the facility and hence effective- ness by which the systems can be studied.In case of solutions, in contrast to melts, the resulting crystal entities are usually isolated and can be separated from the sur- rounding medium, hence become more readily amenable to structural studies, or alternatively if there is connectivity, this becomes directly apparent (see below). LAMELLAE A N D MICELLES There are at least two basic types of morphology which 1 denote as lamellae and micelles (fig. 5). I realize that the molecular details of fig. 5 may well provoke some disapproval, in particular the regular sharp folds within the lamellae and the mode of chain termination in the micelles, both of which are the subject of the central contro- versy on which I am zeroing in gradually. In fig. 5, however, my emphasis is not on the molecular detail in itself, (it is not my intention to prejudge it at this stage, the participants may well replace these sketches with versions of their own preference) but on the fact that lamellae epitomize the particulate nature of the crystallization pro- duct, while the micelles an intrinsic connectedness.In solution crystallization the two are quite distinct: lamellae give rise to suspensions while the micelles lead to gels. In fact it is the spectacular “ setting ” of solutions in the course of crystallization which148 CRYSTALLINE POLYMERS has led to the postulate of the fringed micellar structure recently, a process found to be thermoreversible [e.g., ref. (7) and ( S ) ] . FIG. 5.-Schematic representation of the two basic morphologies arising in the course of crystallization in a quiescent system.(a) Lamellae, which in dilute systems are separate entities. The molecular arrangement is chain folded. (The regular and adjacently re-entrant representation in this drawing is not meant to prejudge the existing debates on this issue.) (b) Micelles creating an overall con- nectedness which leads to a network where the crystals are the junctions. In solutions this gives rise to a gel which is thermoreversible. As in (a) the molecular detail is not to be taken literally. Of course the fringed micellar model itself is not new, in fact historically it has much preceded the lamellae. What is comparatively new in its recent come-back is the explicit way it has become identifiable through the gelation effect it produces.While the molecular details remain as yet to be established, that much appears certain that the crystallization occurs by confluence of several chains along limited lengths so as to produce the connectivity by which it is manifest. While by its very nature the above method of discrimination is confined to solutions, there are increasing indica- tions that the same underlying distinction is also valid for crystallization from the melt.g I included it here for two reasons. First, to have this potentially important classification on the map and second because it may be relevant to some of the material to be discussed. The latter point arises from the fact that gelation crystallization is promoted by very high supercoolings.In fact in suitable cases a competition between lamellae and micelles (as inferred from gelation), increasingly in favour of the latter, could be followed as the supercooling was being increased.’ Gelation crystallization does not feature in the present papers. Qualitatively this is consistent with the small critical nucleus size at high undercoolings which would facilitate a kind of nucleative collapse of suitably oriented nearby chain portions. Further, the small size of the stable nucleus involved would minimize the chain crowding problem at the crystal interface, an issue of which we have heard from Sir Charles Frank and of which we shall hear more later. In addition, molecular heterogeneity also promotes gelation crystallization. Whether departure from strict chain uniformity is a necessary criterion or not is a matter under current consideration,’** Now, crystallization at very high supercoolings does feature in the discussion : explicitly so in the paper by Cutler et al.displaying the strange melt memory effectsA . KELLER 149 described there, and implicitly in melt crystallized polyethylene samples used through- out the neutron scattering work by the necessity of avoiding segregation of the iso- topically tagged molecules. I do not know whether in either of these cases the micel- lar morphology has taken over fully or partially from the lamellae, although I guess that the likelihood of this being the case is particularly high in the first-mentioned work. Whatever the case I consider it important to be aware of the existence of the mor- phological distinction in question, as it would be futile to draw conclusions about lamellae and chain folding (and this in the negative sense) when lamellae may not be present (or at least not entirely so), apriori.LAMELLAE A N D CHAIN FOLDING The rest of my Introduction will be confined to the lamella, which is the subject of the papers and the centre of the controversies. First I shall make the point that the existence of lamellae is now undisputed; this is apparent from all the papers. What is not quite as apparent is that the same applies to chain folding as such in as far as chain folding means the predominant re-entry of the chains into one and the same lamellar entity, my principal thesis being that chain folding is a necessary attribute of the lamellar morphology. When the lamellae are isolated single entities, as in solution crystallization (fig.6), then given that the chains are perpendicular, or at a large angle to the basal plane, folding is a straightforward necessity as the chains have nowhere else to go. This was the original basis of the chain-folding postulate in 1957 and remains as true now as it was then [see e.g. ref. (10) for a review]. It applies equally to multilayer crystals where the layers splay apart. When the layers are contiguous as in melt-crystallized material (fig. 7) some additional arguments, which are nevertheless still quite straight- forward, need invoking. First, there is the self-evident issue of what should terminate crystal growth at the lamellar interface, particularly in such a regular manner as is observed.Clearly the folding back of the chains provides a natural mode of such a termination. Second, if regardless of the previous issue we do envisage lamellae separated by amorphous interlayers due to the chains emanating from the lamellae and traversing from one lamella to the next, then we reach a situation of impossible overcrowding within these interlayers which can only be relieved by a substantial amount of backfolding. This is the subject which has been dealt with by Sir Charles Frank in his General Introduction and will be brought up again by the paper of Gutt- man et al. in a critique of the Yoon-Flory model. It is not as if the controversy just indicated affected the main issue itself. Namely, even according to the Yoon-Flory interpretation of neutron scattering data on rapidly crystallized p~lyethylene,'~ 70 % of the chains must fold back into the same lamellae from which they have emerged, even without taking the overcrowding problem into consideration (the subject of the above-mentioned criticisms).We can conclude, therefore, that there is overall agree- ment as regards the necessity of invoking at least a predominant, if not exclusive, chain folding in lamellar structures. So much about eye-catching headlines such as " The folded chain's last stand "I4 which has created much puzzlement, if not confusion, in the general public and unnecessary polarization of attitudes amongst the specialists, Controversies, such as referred to above, are not related to the existence or non-exist- ence of chain folding but to its nature.It is with the latter with which I shall be con- cerned in some of the sections to follow. However, before ending the present section I wish to make two comments. The first refers to nomenclature. Thus the term " folding '' is being used with different meanings by different authors. Above I used it without prejudice as regards the I feel that a few words are needed to underline this.150 CRYSTALLINE POLYMERS structure of the fold and manner of re-entry, while with some authors it relates to sharpness of the folded portion and/or adjacency of re-entry, a narrowing down of the use of the term, which if not explicitly specified can lead to alteration of the message on further transmission. Statements like " at this stage the loop can be regarded as a fold " featuring also in the present papers are clearly not helpful.I plead therefore for explicitness in nomenclature. Neither the lamellar habit nor chain folding, whatever its nature, have been a priori predictions from chain statistics. They were the results of experimental discoveries, to which chain statistics has been applied sub- sequently (with differing results by different authors as is also apparent from the present papers) in an attempt to account for the observations. I mention this not so much as to stake a claim for priorities on behalf of the experimentalists concerned, but rather to point out that the various models, having been arrived at aposteriori, have not yet proven their predictive power.Consequently neither of them has any claim for uniqueness. My second comment is historical. ORIGIN OF CHAIN FOLDING The enquiry as regards the origin of chain folding leads to the subject of theories of chain-folded crystal growth, on which I only have a very few comments to make at this place. First, the main experimental observations will be recalled which need accounting for. These are (a) the phenomenon of chain folding itself (b) the unifor- mity of the fold length 2, at least to the level as manifest by the uniformity of the lamel- lar thickness, and ( c ) the experimentally observed dependence of 2 on supercooling (AT). Theories which achieved notable success in this respect are all kinetically based and rely on specific model considerations [e.g. ref.(15)-(17)]. A common feature of all the models is the adjacency of fold re-entry, which, as I shall come to shortly, is the actual disputed issue. Does this mean that the validity of all these theories may be correspondingly in dispute? First, I have it from authorities such as the late Lauritzen that there is nothing contained in the theories for which strict adjacency is intrinsic. Apart from the fact that the authors of the theories had some confidence in this feature of the model, adjacent re-entry provided the simplest pathway to describe mathematically. The description of any other path of chain deposition would have been incomparably more complicated, and the fact remains that such has never been attempted by those who object to adjacent re-entry.It is to this last point I shall be attaching my second mitigating comment. Namely, if, on the grounds that adjacent re-entry is unacceptable, even as an approxi- mation, the theories are rejected, we are left without any theoretical structure, or even a qualitative explanation for what we observe. The view often voiced and first ex- pressed by myself1* that the crystal thickness, irrespective of the nature of folding, is determined by the critical nucleus size, while true, is simply not enough. In any phase transition the new phase has to pass through the size of the critical nucleus; but this is outgrown and not locked in as a permanent feature of the resulting texture, a characteristic unique to chain-folded crystallization of polymers. Or more specific- ally, the two-dimensional secondary surface nucleus, usually invoked in the present case, would not be able to grow laterally with a finite rate while preserving its critical dimension along the chain direction.In order to explain both, namely that a dimen- sion related to the critical nucleus along the chain direction is locked in, while the nucleated strip spreads in a perpendicular direction, the kinetic model theories are required. This is not to say that the success of a theory in itself could justify a wrong To the above question I wish to make some mitigating remarks.FIG. 6.-Example of an isolated crystal layer. Transmission electron micrograph of a solution- grown polyethylene crystal. The crystal was prepared for electron microscopy in a manner so as to retain the three-dimensional configuration which it had while in suspension.This, amongst others, reveals a four-sector structure (Bassett et nl."). FIG. 7.-Example of a contiguous lamellar structure in a melt-crystallized sample of polyethylene. The material was a sharp fraction crystallized at a low undercooling (128 "C). Transmission electron micrograph of a stained section. An area showing a cross-section view of the lamellae was selected [To face page 150 (Grubb and Keller). l2FIG. 8.-Interior of a spherulitic polyethylene crystallized from the melt at a low undercooling (128.8 "C). Scanning electron micrograph. The three-dimensional detail is revealed thanks to solvent extraction of low molecular-weight material such as had not crystallized at 128.8 "C, only on subsequent cooling. In addition to providing a method for exploring the interior morphology, it demonstrates that molecular-weight segregation has occurred, showing that long-range movement of chains can take place on crystallization.For lettering see original paper (Winram et aZ.).21 [To face page 151A . KELLER 151 model, but merely that in the state of present uncertainties the above considerations represent a not unimportant factor on the balance sheet. Those who on the above grounds are inclined to dismiss the kinetic theories of chain folding altogether, of course will not be concerned with the in-house problems of these theories themselves. Such problems nevertheless exist for those who con- sider these theories seriously. The weightiest one is the situation under high super- coolings.It will be recalled that in all early findings with polyethylene and other highly crystallizable polymers I was about inversely related to AT. The theories were set up amongst others to account for these observations. These theories, however, have led to unrealistic consequences at high supercoolings (the “ blow up ” of Z). When later such high supercoolings became experimentally accessible through choice of appropriate polymer (e.g., isotactic polystyrene, nylons) a constant minimum Z value was observed. In the light of it the original theories were modified so as to account for this new fact.19 I do not wish to enter into the feasibility of the physical assumptions and mathematical procedures which went into these modifications.I merely come to the point that the present Discussion contains a paper, that by Point, which can account for the observed I against AT behaviour over the full range of AT by building the kinetic theories on an initially broader base than done hitherto. THE MOBILITY ISSUE Ever since organizations visible on all levels of microscopy have become apparent, some of them surprisingly distinct, in fact even separable from their surroundings, the question has arisen that contrary to previous apriori expectations the chains may move with greater facility within the melt in the course of crystallization than previously suspected, at least at sufficiently low supercoolings. With the recognition of chain folding the question has become more explicit: namely how far does the expected mobility allow the chains to fold on the time scale in question and, vice versa, how far are the folded structures which are observed or inferred compatible with existing ideas of mobility? In view of the disputes relating to stem adjacency these same ques- tions are now being referred to adjacently re-entrant folding in particular, an issue featuring repeatedly throughout the present papers.There is nothing I can or wish to add to what Sir Charles Frank already said pertaining to this particular point in his General Introduction. I merely restate for completeness that we are facing the view expressed by Yoon and Flory that the mobility of the chains is a priori inadequate for adjacently re-entrant folding while two papers, the one by Klein and the other by Di Marzio et al., both taking count of the possibilities allowed for by de Gennes’ repta- tion, coupled with crystallization force, conclude that such folding is at least permis- sible on mobility grounds.The paper by Guenet et aZ., even if not explicitly on mobility as such, contains a passage which spans the two opposing views under the appropriate circumstances even without allowance for reptation. The last work relates to isotactic polystyrene where conditions of crystallization can be varied within wider limits than with polyethylene, the subject of the other papers, a point to which I shall return later. The most striking manifestation of large-scale molecular motion in the course of crystallization, at least under low supercoolings, is molecular fractionation when crvstallizing a polydisperse system.This phenomenon has been extensively studied by Wunderlich from whom we have a contribution to this topic. To this I wish to add by referring to the morphological implications of such fractionation. Following up Wunderlich’s earlier work we have observed some years ago 2o that isothermally crystallized polyethylene contained at least two lamellar populations : a thicker one152 CRYSTALLINE POLYMERS formed isothermally at the intended crystallization temperature, and a thinner one which consisted of initially uncrystallized material which had solidified subsequently on cooling, and we succeeded in identifying both electron-microscopically as two dis- tinct lamellar stacks. The fact that the stacks of thinner lamellae consisted of low molecular-weight material which had fractionated during crystallization could be directly verified by extracting the latter from the solid by selective solvents (Wunder- lich’s method) and determining the molecular weights of both extract and residue, by g.p.c. Reverting to electron microscopy, the missing thinner lamellae, hence those containing lower molecular-weight material, could be identified in the form of appro- priate cavities.The scanning electron-microscope picture of fig. 8 should illustrate the effect. This picture is added here for the further reason that it also displays the clearly defined, in places separate, lamellae as formed from the melt which is relevant also to what I said in the preceding sections. Molecular-weight segregation and its electron miscroscopic diagnosis also features in the works by Bassett and collabora- tors : some of it is contained in the contribution by Bassett and Hodge to the present Discussion.Molecular segregation effects during crystallization can occur under a variety of circumstances due to a variety of inhomogeneities in the material. Some of these are being listed also in the paper by Hoffman et al. One of these, which is of particular significance for the present, is segregation of isotopically different species. As known, the neutron scattering work, which plays such an important part in the present developments, relies on cocrystallization of deuterated guest chains with protonated hosts or vice versa. At least in the case of polyethylene, the principal test material so far, the situation is greatly complicated by segregation of the two kinds of isotope which, as known, requires the employment of high supercoolings to ensure rapid crystallization in order to minimize the segregation effect.There is no reason, there- fore, to rejoice or despair, whatever the case may be, on finding that chains which had been deliberately immobilized in fact have not moved. THE NATURE OF CHAIN FOLDING With the nature of chain folding we have reached the broader area of the current conflicts. In discussing it, it is important to distinguish between the two aspects covered by the above heading: the structure of the fold itself and the manner of stem re-entry. The two issues are distinct both conceptually and as regards experimental approach.It is regrettable that much of the polemical literature fails to discriminate between the two and equates adjacency and non-adjacency of stems with regularity and irregularity of the folds, respectively. I think I need not belabour the point that the structural features thus equated need not be synonymous. THE STRUCTURE OF THE FOLD The two alternatives so often debated are crystallographically regular and random fold configurations. Of the regular configurations sharp folds, such as would occur with adjacent stem re-entry, are receiving special attention. A question often raised is whether a regular sharp fold is possible at all by apriuri energetic considerations. With paraffinoid chains the existence of such a configuration has been inferred as early as 1933 when Muller observed that cyclic paraffins crystallize with the chains as closely packed as in crystals of linear paraffins,22 which means that the rings must be collapsed implying The answer to this is simply “ yes ”.A .KELLER 153 the equivalents of sharp folds at both ends. This subject was taken up again in 1960 by Burbank and myself23 mapping out the sharp folds in a preliminary crystal struc- ture analysis on a cyclic paraffin. The structure was eventually fully solved and the sharp bend precisely described in 1968 by Kay and N e ~ m a n . ~ ~ Having shown that sharp folds can and do exist it is now a further matter whether a long chain, as opposed to a ring, will itself choose this configuration when crystalliz- ing.The difficulty with a simple chain, like polyethylene, is that it is totally feature- less to provide clear handles for the purpose, short of a detailed structure analysis, which in the lack of macroscopic crystals is not possible. In view of this, efforts were directed towards the determination of the average ‘‘ quality ” of the fold surface, that is, whether it consists of a crystallographically regular or of an irregular random structure as second best to a structure determination with atomic resolution. For this purpose first the lamellae had to be subdivided into a crystal core and a fold surface portion, done amongst others by low-angle X-ray scattering and selective etching tech- niques, to which more recently the low-frequency Raman technique has been added.The paper by Capaccio et al. in the present Discussion now adds a further chapter to the application of the Raman technique, in this instance combined with selective degradation, in the service of this problem. During extensive past works on the fold structure problem a kind of consensus has been reached, never fully concurred with by myself, that the fold surface is essentially equivalent to an amorphous layer, the transition between the crystalline amorphous two-phase structure, thus consti- tuted by the lamella, being sharp within a few Angstrom ~ n i t s . ~ ~ , ~ ~ The present paper by Mandelkern now revives this issue. Amongst many others it makes a case for a substantial transition layer of intermediate order when going from crystal core out- wards towards the surface.It will be interesting to see from the discussion how this squares with all the earlier evidence quoted in favour of a sharply delineated two- phase structure. Chains which are chemically more complex containing either bulky members of specific shapes, and/or specifically interacting groups (e.g., hydrogen 01 ionic bonds) offer certain handles by which the nature of the fold can be more directly approached through a combination of model building, crystal-structure analysis and auxiliary techniques. A salient example is the morphologically well explored system of an aromatic silicon p01ymer.~’ Biopolymers offer similar opportunities which in some cases have in fact been e x p l ~ i t e d . ~ ~ * ~ ~ In all these cases regular, sharp folds were made at least plausible to different degrees. I hope we shall hear of some of it in the discussion contributions.MODE OF STEM RE-ENTRY The nature of stem re-entry is the true focal point of the controversy in the field of polymer crystallization. At this point I have homed in on the fire which is the source of the smoke obscuring our vision far beyond the area actually covered by the debate, This is the issue to which most of the disputed experimental results and their interpretation is pertinent. There is only one experimental method which is directly specific to stem-stem interactions and thus should be potentially decisive. This is the infrared method introduced by Krimm in 1968 and pursued by him and associates ever since. To Krimm’s great credit this is the first instance that isotopic substitution was applied to explore the chain trajectory of a chain-folded polymer.His technique utilizes deuterium-tagged polyethylene introduced as a guest component into the protonated host. In this way the environment of the isotopically labelled guest stems can be probed by examining splitting effects arising in appropriate infrared bands such as154 CRYSTALLINE POLYMERS rely on interactions between isotopewise (but not symmetrywise) identical segments in the crystal core of the lamellae. In earlier works this method of analysis has led to the assertion of adjacent re-entry, in the first place in solution-grown single crystals and secondly, through more subtle effects, in melt-crystallized material. Krimm’s latest paper in the present Discussion is confined to solution-grown crystals where, through refinement of experimentation and through more rigorous evaluation, it reconfirms the adjacent nature of the stem re-entry, together with some additional specifications of th.e folded system.Clearly, as will also be apparent fur- ther below, this paper has a singular position amongst the rest and requires special attention accordingly. I personally would also like to know about the present status of this work as regards melt crystallization. Perhaps we shall hear about it in the Dis- cussion. The other method pertinent to the issue of stem adjacency is that of neutron scat- tering. However, as this is the most extensive single item on the agenda I shall devote a separate section to it in what follows.NEUTRON SCATTERING STUDIES As will be familiar it is the advent of neutron scattering, as applied to polymers, which has sparked off the recent upsurge of activities in the field of the polymeric solid state, the crystalline state in particular, with all the controversies which have ensued, I am of course aware of the fact that there is an expectancy of a spectacular confronta- tion in this respect in the course of the meeting. Those who look forward to this may be disappointed, as in what I have to say I may spoil some of the show. I hope it will become apparent at the end that the alignment of the opposing forces is not as hard and fast, and that there is no such unambiguous distinction between friend and foe as some of the reverberations of the controversy may suggest.As is well known, the technique relies on the elastic scattering of isotopically distinct guest molecules em- bedded in a medium of their, isotopic differences apart, chemically identical species. The scattering then should give information on the size, shape and trajectory of a polymer molecule within its own, in the present instance crystalline, environment. When evaluating claims and generalizations made on the basis of the findings, it is useful to bear the following four points in mind. (1) The angular range of scattering inuolued. Scattering at the lowest angles pro- vides information about the global conformation of the chains, radius of gyration (A,) in particular. Scattering at increasing angles yields progressively more informa- tion about the smaller scale features of the molecules.An illustration of a schematic scattering curve relating to polyethylene is contained by fig. 9 indicating the different angular ranges involved. It is regrettable that, in the course of the controversies, par- ticularly in its second-hand reporting, sweeping generalizations are often made on the basis of information gained within only a narrowly defined angular range. Even in the case of otherwise scholarly works, like is not always compared with like as regards scattering angles when results or conclusions by different authors are compared, interpreted or re-evaluated. Adding to the confusion terms like “ small ”, “ inter- mediate ” and “high ” angles do not always refer to identical angular ranges (see e.g., fig.9) in the different works. I can do no more here than to plead for scrupulous explicitness in the Discussion as regards scattering angles. Far the largest portion of the neutron scattering works relating to crystallinity refer to polyethylene, and hence the often controversial generalizations arising therefrom originate from studies on this polymer alone. Polyethylene, however, is not the only polymer to serve as a model substance (2) Polyethylene vis-A-vis other polymers.A . KELLER 155 for the study of the crystalline texture in general, and in fact presents some problems of its own as will be apparent below. (3) Within the confines of polyethylene itself there is the distinction between solu- tion and melt crystallization where the two lead to different results.There can be no complete generalization as regards crystallization on the basis of one of these aspects alone. SANS lal (G u I n i er 1 q=411 sin R / A ! FIG. 9.-Illustration of the different angular ranges involved in the neutron scattering studies. The illustration is drawn as for polyethylene up to the (200) Bragg reflection. SANS = small-angle scattering, WANS = wide-angle scattering. Amongst others the diagram shows the different conventions used to define the SANS and " intermediate " ranges. 8 = scattering angle, R = wave- length. (4) The problems can and have been approached in two distinct ways: (i) deduc- tively, by taking a particular sample and analysing its scattering in a particular scat- tering range to maximum achieveable depth ; (ii) inductively, correlating scattering effects obtained by varying materials, samples crystallization conditions etc.The convincing power of these two approaches may be different according to the problem in question and in any event can illuminate the same issue from different angles as will be apparent below. POLYETHYLENE CRYSTALLIZED FROM SOLUTION First I shall consider polyethylene as crystallized from solution. I apologize for being, perhaps understandably, parochial in this subject by presenting it from the standpoint of our own laboratory. In the first instance my emphasis will be on the rather remarkable agreement which has been reached between the different laboratories engaged in this subject, a point which may not be apparent from the reading of the individual papers such as feature in the present Discussion, and shall proceed to the disagreements thereafter.As first announced in 1976,31 and extensively documented in a later paper,32 we deduced from the functional dependence of the scattering intensity on the scattering angle in the intermediate angular range (see fig. 9) that the scattering entity is in the156 CRYSTALLINE POLYMERS form of a sheet consistent with the picture of chains laying down along the prism faces (which in this instance are (110)) of a growing crystal (fig. 10). This picture is fully consistent with the sectorized nature of the crystals themselves established long ago [see e.g., review (10) and the example shown by fig. 61. There is now full agreement as regards the overall sheet-like nature of a given molecule in single crystals as the present papers by Yoon and Flory, Stamm et al. will show, to which a previous work by Summerfield et aZ.33 needs adding.From a more detailed consideration of the intensities we could also reach some conclusions as regards the thickness of the sheets. In some instances this corresponded closely to that of a single molecular layer along FIG. 10.-The sheet (dashed lines) defined by the molecule along a growth face in solution-grown crystals as identified by neutron scattering in the range q = 0.2 - 0.5 A-l (see fig. 9). In reality the sheet is much thinner relative to its other dimensions. Molecular details within the sheet are left unspecified. (1 10) but in several others, particularly for higher molecular-weight labelled species this thickness was greater.Eventually this last point has found a satisfactory explana- tion in the model of superfolding, a structure concept featuring abundantly in the present papers, which, however, was arrived at along a different route.34 As I con- sider it both important and instructive, this I shall proceed to describe in brief. The relevant scattering experiments involved the lowest angles (the Guinier range, fig. 9), hence the determination of R, as a function of molecular weight (M,). As a preliminary, it is known that in the molten state and during crystallization from the melt (see later) R, cc M i , a fact represented by the appropriate points in fig. 11. In contrast, we have that in the case of single crystals R, was only inappreciably affected by M, (fig.ll), a most unexpected finding as R, should vary linearly with M, in case the length of the ribbon increased proportionally with the length of the depositing chain. This near invariance of R, with M,, however, would follow if the chain-folded ribbon itself doubled up beyond a certain length, and so forth on further increase of chain length (fig. 12), as now the thickening of the ribbon would add only inappreciably to R, as long as the ribbon thickness remains small compared to its length. Now we see from the present papers that there is again general agreement as regards superfolding (Yoon and Flory and Stamm et aZ.3. In fact the same is invoked by Krimm and Cheam to account for band-splitting effects in their infrared analysis.Satisfactory as this overall agreement is, the difference in approach merits a comment as it illustrates the difference between, and the complementary nature of, the deductive and inductive approaches I mentioned under paragraph (4) above. The purely analytical approach requires the hypothesis of a model which needs then to be tested, while the inductive approach, such as used above relying on R,, suggests the model itself which nevertheless then needs analytical confirmation. The point I am trying to make is that the purely analytical approach, while necessary, is not al- ways adequate in itself. The agreement as regards superfolding goes beyond structure studies. The con- cept nicely dovetails with observations on growth kinetics from melts and with theA .KELLER 5 - Q? 50- I57 ensuing theoretical explanation, as it accords with expectations from Regime I1 crystal- lization at high (but not excessive) undercoolings as referred to in the paper by Hoff- man et al. While solution crystallization has not been analysed with respect to the Regime I and I1 distinction, it is to be expected that the appreciable supercooling at 70 "C in the experiments underlying fig. 11 is in the I1 growth regime. 150. A A X 0 0 0 0 0 0 0 200 M '12 W 4 00 FIG. 11 .-Radius of gyration (R,) values for polyethylene as determined from neutron scattering in the Guinier range (see fig. 9) as a function of molecular weight (M,). The triangles and the cross refer to molten material (taken from two different experimental sources) displaying the R, cc M%' relation.It is this insensi- tivity of R , to M, which has led to the superfolding concept (Sadler and Keller).34 In contrast, with single crystals (circles) R , is much less affected by M,. Having emphasized the points of agreement, I am coming at last to the source of disagreements in the area of solution-grown crystals, As apparent from the paper by Yoon and Flory and referred to by Sir Charles Frank this relates to the issue of stem adjacency within the chain-folded, and with suitably high molecular weights, super- folded ribbons. According to the analysis by Yoon and Flory of the data by Sadler and Keller 32 and those of Summerfield et ~ 2 1 . ~ ~ it is based on a discrepancy of a factor of two in the absolute scattering intensity as compared with expectations from strictly adjacent fold re-entry.Yoon and Flory therefore require a " stem dilution " by a factor of 2-3 and make this a principal issue of contention. The first reaction to this may well be, as mentioned in passing by Sir Charles Frank, how far is a factor of two significant in an experimental and interpretative issue of this complexity to make its consequences the centre of a major controversy. As I tried to point out we have gone a long way to have reached a level of consensus where the actual differences are re- duced to a disagreement of about a factor of two. This should not be lost from sight. But who disagrees with whom? At this stage I am anxious to have the record clear. We ourselves have been aware of stem dilution from the very beginning. The corresponding result was stated in our paper even if not exploited in specifying a molecular model.The explicit expression of this was the value of nA, the deuterium occupancy per unit area of the molecular strip, which is lower, on average by a factor158 CRYSTALLINE POLYMERS . . . . . . . . . . . . . . . . a . . . . . . . . . . . . . . . - .*. a:. . . . . . . :a: m:. . . . . . . . . . , . . . . . . . . . . . . . . * . a . . . . . . . * . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ' e a e . * . ' . * . * m * a : . . .:.:.;m::'...:. ....... a:.: ...:.:.:.:. . . . .-.**em:. : .;err:. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a . . . . . . . I . . . I . . . . . . . . . . . . a:.:. . . . . . . . . . 'a'. . . . I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . * . . . * e . . . . . . . . . I . . . . . . * . . . * . . . . . . . . . * . . . . . . . . . . . * . . . . " .. . . . . . . . . . . . . . . FIG. 12.-Diagrammatic representation of superfolding (based on Sadler and Keller.34) The poly- ethylene lattice is being viewed along c (the chain direction). The heavy dots represent the stems of a given molecule folding along (110). A given row of heavy dots represents a chain folded ribbon which doubles up on itself beyond a certain length [to be consistent with sheet thickness data not necessarily in a strictly consecutive manner, see ref. (34)]. (a) The stems along a given row are adja- cent. (b) Partial non-adjacency (stem dilution) as required by closer matching of the experimental data in ref. (32). This representation, implicit in ref. (32) and (34), now accords with Yoon and Flory in the present Discussion. of 2, than what was expected for complete stem adjacency.At that stage, however, we were mainly concerned with the establishment of a sheet-like nature of the chain in solution-grown crystals (as opposed to melt crystallization, see below), with the thickness of the layer and with the ensuing recognition of super-folding. Under the given circumstances the departure of n A values from that of exact adjacency seemed comparatively minor for making a special issue of it, particularly as we could not be sure how consistently it will recur. In brief, the exact fit in the nA values was not our priority at the time. We now know better3* and concur with Yoon and Flory as regards the stem dilution, fig. 12(b) being drawn accordingly. However, we differ from Yoon and Flory in as far as we regard this stem dilution as a departure fromA .KELLER 159 strict adjacency rather than evidence for a switchboard. Irrespective of this latter difference we are both at variance with the conclusions of Krimm and Cheam as regards complete adjacency on the basis of their infrared data. I need to add here that our own infrared work using Krimm’s method but admittedly in a more empirical man- ner is, however, consistent with a stem dilution by a factor of about 2,30 hence with the neutron scattering results. Accordingly, the situation arises where Krimm’s infrared work favours complete adjacency while all the rest of the experiments require a certain amount of stem dilution, this stem dilution itself being placed in a different perspective (departure from adjacency vis-h-vis switchboard), in relation to the subject of polymer crystallization as a whole by different authors. When referring to the factor of two in question, I recognize that the issue of com- plete or incomplete adjacency (to a factor of two) has important implications. The crowding problem at the fold surface immediately arises with a diluted stem re-entry and requires attention for this special case.If agreement as regards stem dilution by a factor of two became universal the further issue arises as to why exactly by this factor? Is there a special reason for it, or is it only the property of one kind of pre- paration in a broader behaviour spectrum? After all, by necessity, the crystals in question were all grown at 70 “C, a restriction imposed by the isotope segregation prob- lem, which corresponds to high supercooling! Whatever the final situation and its implication, to my mind this is no longer a global conflict but rather a well focused and reasoned argument such as arises frequently in the course of scientific research. POLYETHYLENE CRYSTALLIZED FROM THE MELT The study of melt crystallization of polyethylene by neutron scattering preceded the corresponding studies on solution-crystallized material and has led to substantially different results at all angles of scattering.It has turned out that in the fast cooled specimen, the use of which was necessitated by the segregation problem referred to earlier, R, remained unaffected by crystallization : both its absolute value and its molecular-weight depend- ence corresponded to that pertaining to the melt. It appears, therefore, that at least the global configuration of the chain remains unaltered, the chain merely “ freezing in ” on crystallization.This particular conclusion has been the most publicized aspect of the neutron scattering studies and correspondingly impressed itself more than anything else on the public image with its implication that very little is happening to a chain on crystallization. Extension of the neutron scattering studies on melt- crystallized samples to higher angles occurred in several ~ t a g e s . ~ ’ . ~ ~ Even in the first (q up to 0.2 A-1, fig. 9) it has become apparent that adjacent re-entry cannot be representative of the chain trajectory, and in fact it was this work which has led to the original Yoon-Flory modelI3 of the melt crystallized material often referred to in the papers of the present Discussion.Even so, folding had to be invoked by the authors of the model, to keep R, within the bounds of the experiment, leading to the 70% re- entry probability of a given chain into the same lamella (irrespective of method of re-entry) referred to earlier in this Introduction. This model is computed for a single chain threading in and out of the lamellae forming interlamellar amorphous zones in the course of it, and takes no cognizance of the space requirement by neighbouring chains emanating from the same crystal. This leads to the overcrowding problem referred to by Sir Charles Frank in his General Introduction and pointed out in a quantitative form by Guttman et al.in their critique of the model. As the range of scattering angles was progressively further extended [up to q = (a) Guinier range. (b) Higher scattering angles.I60 CRYSTALLINE POLYMERS 0.5 A-1 fig. 91 it became possible to recognize the asymptotic scattering behaviour of individual rods corresponding to the straight chain traverses through the This behaviour contrasted sharply with the sheets deduced in solution grown crys- t a l ~ , ~ ~ ~ ~ ~ a distinction directly apparent from the different functional dependence of the intensity with angle in the two cases within the equivalent range of scattering angles. Further examinations reveal, in the first place, that it is the straight stems which make the principal contribution to the scattering pattern.Consequently, the details of the extra-crystalline loops in the various molecular models are not so much relevant in themselves for the scattering problems, only as far as they determine the actual placement of the stems. Secondly; it has become apparent that the stem placements themselves are not totally unrelated, and it is on this point that papers in the present discussion mainly differ. Stamm et al. envisage a stem assembly due to the same chain which, if I understand well, is close to what would correspond to the freezing-in of the chain with allowance for local equilibration to a most probable stem placement. Guttman et al. first purport to show that the Yoon-Flory model, as treated by the authors, in itself implies a considerable clustering of stems, and then proceed to interpret the scattering data of ref.(35) in their own way, claiming an even higher degree of clustering such as contains up to 60-80% of adjacent re-entry. 1 have know- ledge that Sadler and Harris have ideas of their own about the degree of clustering implicit in the data of ref. (32); we may hear of this in the Discussion. Thus it seems to emerge that the issue under debate will be the quantitative definition of the grouping of chain traverses belonging to a given molecule within a lamella with the associated implications for the degree of adjacency. We see that again the issue becomesrather sharply focused on"a concrete quantitative point. It is then a further stage whether a given case is to be considered as a departure from a random switchboard or a dilution of complete adjacency.Instead of anticipating the possible outcome of these arguments, at this stage I rather raise some qualifications as regards the significance of the particular issue for the understanding of polymer crystallization. First there is the sample type. As repeatedly mentioned before, samples crystai- lized by rapid cooling, while possibly significant for certain applications, are hardly the most suitable ones on which to establish the general rules for crystallization. Apart from the obvious fact that the chains will not have a chance to arrange them- selves in their most preferred fashion, the possibility of passing into different mor- phological regimes at high undercoolings also presents itself, as I said at the beginning. If on the other hand one maintains that the relevant supercoolings are not really higher than is usual for polymeric materials, or if by some improvement of technique truly low supercoolings became achievable, another type of difficulty would be en- countered.Namely, it has been known for some time that lamellar crystals, during melt crystallization of polyethylene in particular, can thicken during storage at the cystallization temperature, in fact lamellae already formed can thicken before the crystallization itself has run to completion. (The isothermal thickening process first postulated by Hoffman and week^.)^^,^' This isothermal thickening is becoming increasingly evident currently. It is being referred to by Hoffman et al. in their pre- sent contribution, it features explicitly in the paper by Kovacs and Straupe in con- nection with their admittedly special materials, and it is turning up with increasing frequency and prominence in our own recent investigations at Bristol.Fig. 13 is an electron-micrograph of a highly monodisperse sample crystallized isothermally. The stacks of layers, resembling rather rows of beads, in a pocket formed by the surrounding more extended thinner First a recent pictorial example.FIG. 13.-Singular features in a bulk-crystallized polyethylene indicative of isothermal thickening of lamellae during crystallization. The sample and method of examination are identical to those in fig. 7. Lamellae as in fig. 7 are seen in top and bottom portions. The rows and thick beads on the right are the thickened regions, and presumably so are some more isolated oblongs in middle left.In the less featured central region the lamellae are not in cross-sectional view within the overall isotropic sample. Several details displayed by the electron micrograph are still not understood presently. [To face page 160A . KELLER 161 lamellae, are most likely the results of incipient lamellar thickening. More repre- sentatively, fig. 14 is an earlier example from our published work which, however, has not been given all the attention even by ourselves that it may deserve. As will be apparent from the caption the full difference in thickness values between the lower and upper curves is the result of thickening during crystallization. It follows therefore that samples of that kind as in fig.14, after complete crystallization (upper curve), 700 - 600 - *a 5 rn 500- - c c CI c - .- : 400- 5 b oc 200 9 peak2 ? - d $ 120 122 124 126 128 cryst a I I isa t ion temperature / "C FIG. 14.-Prominent illustration of lamellar thickening in the course of isothermal crystallization of polyethylene. The curves represent the lamellar thickness, as assessed by low-frequency Raman technique as a function of crystallization temperature. The solid circles (upper curve) correspond to long crystallization times during which the primary crystallization has reached completion at the corresponding temperatures. The open circles (lower curve) correspond to a crystallization time of 1 h during which, particularly at the higher crystallization temperatures, the primary crystallization would not yet be complete.The difference in the lengths represented by the two curves corresponds to the isothermal lamellar thickenings (for other symbols see original source) (Dlugosz et ~ 1 . ' ~ ) . consist entirely of lamellae which have reorganized during the crystallization process itself. Thus issues such as stem adjacency and the like, whatever the answers may be, will no longer relate to the primary crystallization process but to the subsequent process of thickening. This calls for the understanding of the thickening process, not only because thickening and the underlying chain refolding is important in itself, but because only in this way can knowledge gained on samples of this kind be referred back to the primary crystallization process.The study of chain refolding by neutron scat- tering therefore appears imperative. There is a short mention of such a study in the paper by Ballard et al. In Bristol such work is being pursued currently in a systematic162 CRYSTALLINE POLYMERS manner by Sadler, who is investigating the effect of deliberately induced thickening in the comparatively well explored system of solution-grown polyethylene single crystals. We may hopefully hear of some preliminary results in the Discussion. However, isothermal thickening has implications which go beyond the neutron scattering problems. A glance at fig. 14 will show that isothermal chain refolding can not only affect the lamellar thickness, but can alter the whole shape of the I against T, (crystallization temperature) curve. The 2 against T, curves, as we know them, form the basis of all the theories and hence are at the root of our present understanding.If they can be different from what we believe them to be, this would have serious reper- cussions. In fact there exists one new approach, that by R a ~ l t , ~ * who starts from the premise that the primary crystallization yields one fixed lamellar thickness only, for all values of T, (such as so far observed only at very high supercoolings, see my earlier remark relating to Point’s paper), and all variations of 2 with T, (when observed) are due to subsequent thickening. We shall probably hear more of this in the Discussion. OTHER POLYMERS As raised under paragraph (2) above, polyethylene is not the only polymer to be studied in the search of the true nature of polymer crystallization.By embracing polypropylene and isotactic polystyrene, Ballard et al. and Guenet, Picot and Benoit respectively have significantly widened the scope of the application of neutron scattering in service of the central enquiry. These two polymers have the significant advantage over polyethylene that they do not exhibit the isotope segregation effect, thus permit- ting the examination of samples crystallized at low supercoolings. On the debit side, however, polypropylene is little understood morphologically, while polystyrene has intrinsically low crystallinity. Even so, the advances achieved with these polymers appear to be notable indeed. While the above two studies are not strictly comparable, a feature common to both is that wide variations in behaviour in one and the same polymer could be attained by appropriate variations in materials and crystallization conditions, such as can serve to reconcile the differences arising with polyethylene.For example, in the case of polystyrene the existence of sheets of folded chains could be deduced even in melt-crystallized samples. Further, the radius of gyration could be observed to change (in melt-crystallized samples!) and the conditions for the in- variance, or alternatively variations, of R, could to some extent be circumscribed and controlled. It is refreshing to note that the strait-jacket of an invariant R, has at last been cast off and with it the restrictive and oversimplified view that nothing hap- pens on crystallization.After all it would be a poor show for neutron scattering if it could not even detect that a polymer has crystallized! SOME GENERAL REMARKS We may reflect at this point whether and when the right questions have been asked. I maintain that some of the questions in the recent past have been fallacious and largely contributed to the polarization of views. The fallacy, I feel, has been to believe that one single set of neutron scattering data on one rather arbitrarily chosen piece of polyethylene can decide the whole issue of how a polymer crystallizes and the nature of its structure. The history of science has taught many lessons about the fallacious beliefs in a single decisive experiment to settle controversial issues once and for all.If such a belief often foundered with apparently clear-cut simple issues, how can one hope that it will yield results on a piece of isotopically doped quench crystallized poly- ethylene as examined for low-angle neutron scattering ? Science advances not byA . KELLER 163 resolving but by bypassing the inappropriate questions ! As regards the issue under discussion, this is far from decided even as far as expectation of a single decision is appropriate. I believe we are only now at a stage that the relevant variables have been identified allowing a meaningful attack on the central issues to be planned. Having minimised the extent and magnitude of the conflicting issues at this point I reached a stage where what is left as controversial remains open ended: " it could go this way or that, let us wait and see ".I feel that in the interest of scientific objectivity this was my duty to do. Yet I realize that there is something intrinsically unsatisfactory in a totally non-committal attitude. Man is not purely a reasoning apparatus, (if nothing else the present controversies show this) but also has his convictions which guide him and which he is trying to impress on others. This applies to science as well as to other spheres, and within science even to the otherwise most objectively reasoned argumentation. Some of the most momentous advances in science, just as the most futile controversies, were punctuated by strong personal commitments-recall say Galileo and the Vatican, where the latter has shown more reason and objectivity than normally credited by the popular image, or closer to our times and topic, the events concerning the discovery of macromolecules.Arguments which lack this force of personal conviction remain unappealing and will in fact fail to leave their mark. Having done my duty of a comparatively impartial chronicler I feel that by now I have earned the licence to express also my own views. First, however, I wish to return to an aspect of factual information not yet touched upon, namely morphology. So far I endeavoured to give an essentially non-committal account. MORPHOLOGY For me, at any rate, direct visual observation has an exceptionally strong appeal, a persuasiveness stronger than perhaps any other mode of information, particularly in the field of structure studies.This remains so despite the pitfalls that numerous arte- facts can present, and despite the limitation that visual observation can hardly ever provide information on the molecular and atomic level at least in our subject. There are only two explicitly morphological papers in the present Discussion, but both of the highest quality and interest. The paper by Bassett and Hodge displays some astounding examples of morpholo- gical organization which crystallization can produce at least at low supercoolings. Quite evidently here we are far from the notion that nothing happens on crystalliza- tion. While direct molecular information may be lacking by the very nature of the technique, the observations make it clear that chains can move Over long distances (a point already referred to) and can organize themselves into regular textures in highly specific ways.With due respect to more direct molecular techniques, such as neutron scattering and the like, this is also part of the full truth which needs to be taken into account in a final evaluation. In fact I would go as far as to say that it is at this level of information where such an evaluation would best start. Implicitly this is already being done. Thus the acceptance of lamellae forms the starting point of all treat- ments that are being argued about at this meeting. Let us not forget that lamellae were first directly seen; their existence was neither predicted nor could it have been deduced in any unique manner otherwise. Having benefited in such a definitive way from direct visual observations in the past, let us not abandon or belittle this method of study thereafter.The most definitive morphological work, and possibly the most definitive one of the whole Discussion (within the obvious limitations of the technique involved) is in my opinion that by Kovacs and Straupe. This is a new instalment in a long series of164 CRYSTALLINE POLYMERS papers which form a uniquely personal exploration due to Kovacs and co-workers on the admittedly rather special materials of low molecular weight, highly monodis- perse poly(ethy1ene oxides). Amongst the features which strikes me most is the extent to which an optical microscope can be utilized in giving information which barely falls short of inferences about molecular features such as e,.g., popping out of individual folds.But most remarkable is perhaps the precision, to within 0.01 "C, by which a crystal seems to " know " as what to do. Within an interval of 0.03 "C in fact a whole story is infolding, metaphorically and literally, with strictly reproducible pre- cision : chains unfold, crystals change habit, melt and grow, sometimes simultaneously so in different crystal portions, etc. The clarity of the information, the reproducibi- lity of the phenomena, the precision of the measurements and copiousness of the documentation may well be unique in the field of crystal growth in general, here compounded to all the fascinating variants arising from the long-chain nature of the molecules. We could well stand back from our controversies and be pleased that the study of polymer crystallization could be brought onto this plane.It is to this point that I shall attach my final comments, my own credo. SOME PERSONAL REMARKS When becoming involved in polymer crystallization I was presented with the pic- ture of near total randomness with regions of localized order and nothing more. Ever since, my own scientific journey was one from chaos towards order. In a seem- ingly endless succession of surprises organizations of the most extraordinary kind made their appearance (fig. 15 and 16 should serve as two examples) impressing on me and colleagues engaged in such work that long chain molecules have the capability and the tendency to form organized entities which were far beyond what had been envisaged a priuri.Kovacs and Straupe's present contribution is yet another major signpost along this road. Before, however, attaching further significance to the latter I have to face the possible objection that they are very special samples indeed. It is in the nature of scientific discoveries that they start from the special cases. Scientific truth is not presented to us in its total generality as otherwise it would be there for everybody to see. The discovery of the singular nature of certain substances, materials and preparations had been indispensable for the recognition of phenomena of wide, sometimes universal generality. An ancient example is the " Magnesian " stone essential to the discovery of electromagnetism and later the element phosphorus which gave its name to all phenomena that shine in the dark (Bernal.41) In a11 these and in innumerable other instances it is the special which illuminates the general which otherwise would not be revealed in sufficient clarity to be recognized.I am asserting here that Kovacs' crystals are special only in this sense even if at present this may sound as a declaration of faith. With Kovacs' unique crystals we have to face up to the remarkable precision which governs the chain folding behaviour (I am referring to the various chain folding effects defined well within 0.01 "C) of those crystals. There is no room here for statistical groping; the chains seem to know exactly what to do and when! I do not suggest that there are new physical laws operative, merely that the behaviour of long chains is not yet sufficiently mastered so as to embrace situations of the kind quoted, not to speak of being able to predict them. If this holds for Kovacs' special crystals, I ven- ture to suggest, based on my belief declared above, that this should be pertinent to chain folding in the more general sense.The precision which governs the phenomena in Kovacs' crystals suggests corres- ponding perfection and regularity of the underlying organization and structure. AsFIG. 15.-Example of an unusually regular organization within a solution-grown crystal entity of poly(ethy1ene oxide). The consecutive terraces of a screw dislocation growth spiral within the square- shaped lamellae of poly(ethy1ene oxide) are rotated with respect to each other in a regular sequence.The material itself is unusual in as far as it is a two-block copolymer of poly(ethy1ene oxide) and polystyrene. The former crystallizes by chain folding while the latter is lying on the chain-folded surface in the form of a truly amorphous coating (Lotz et aZ.39). [To face page 164FIG. 16.--Example of a regular organization within a melt-crystallized polymer. The sample is a doubly oriented polyethylene ribbon where the orientation is such that not only the c (the chain direction) but also a and b have a unique orientation with respect to the macroscopic sample dimen- sions. In the present illustration c is vertical, a is horizontal and b normal to the plane of the print. The photograph reveals stacks of lamellae with two distinct lamellar orientation.(This lamellar arrangement has been predicted from preceding low-angle X-ray studies). Transmission electron micrograph of a stained section (Grubb et aZ.).40 [To face page 165A . KELLER 165 we know that this structure is, or at least can be, chain folded, this must apply to the folding mechanism and to the chain folded structure itself. That is to say, both folding and fold structure ought to be regular accordingly. As we do not see the folds we cannot be more specific as regards the explicit features of this regularity. It is possible that the re-entry positions are systematically one or two stems removed from each other, which itself would be a most remarkable effect, or there may be some other folding pattern nobody has thought of as yet.But I believe that there must be a pattern towards which the system is striving, and which it may only realize in a degenerate and defective manner in the case of polydisperse long chains crystallized under less well defined conditions than those pertaining to the Kovacs-Straupe crystals. All present evidence (including our own) on more conventional polymeric systems notwithstanding, I still find the case of predominantly adjacent re-entry as the most feasible and certainly modellingwise the most amenable pattern to govern the chain folding behaviour of polymers, the idealized situation from which the system may depart to varying extents as determined by circumstance. I realize that I may prove to be wrong in this last assertion, but this is my present conviction for what it is worth. However, my own opinion is of no real consequence for the present. What matters is that all the ingredients for a profitable discussion should be in front of you before we start, and this I endeavoured to achieve in the present Introduction. ’ J. Stejny, J. Dlugosz and A. Keller, J . Mater. Sci., 1979, 14, 1291. ’ A. J. Pennings, J. Polymer Sci., Polymer Symp., 1977, 59, 55. A. Keller in Ultrahigh Modulus Polymers, ed. A. Cifferi and 1. M. Ward (Applied Science Publ., Barking, 1979), p. 321. A. Keller, J . Polymer Sci., Polymer Symp., 1977, 58, 395. A. J. Pennings and K. E. Meihuizen in Ultrahigh Modulus Polymers, ed. A. Cifferi and I. M. Ward (Applied Science Publ., Barking, 1979), p. 117. M. J. Hill, P. J. Barham and A. Keller, Colloid PoIymer Sci., in press. M. Girolamo, A. Keller, K. K. Miyasaka and N. Overbergh, J . Polymer Sci., Polymer Phys. Ed., 1976, 14, 39. * R. Benson, J. Maxfield, D. E. Axelson and L. Mandelkern, J. Polymer Sci. Polymer Phys. Ed., 1978, 19, 1583. H. Berghmans, N. Overbergh and F. Gavearts, J. Polymer Sci. Polymer Phys. Ed., 1979, 17, 1251. D. C. Bassett, F. C. Frank and A. Keller, Phil. Mag., 1963, 8, 1753. lo A. Keller, Rep. Progr. Phys., 1968, 31, 623, ’’ D. T. Grubb and A. Keller, J . Polymer Sci, Polymer Phys. Ed., 1980, 18, 207. l3 D. Y. Yoon and P. J. Flory, Polymer, 1977, 18, 509. l4 P. Calvert, Nature, 1976, 263, 371. l5 J . 1. Lauritzen and J. D. Hoffman, J. Res. Nat. Bur. Stand., 1960, 64A, 73. F. C. Frank and M. Tosi, Proc. Roy. SOC. A , 1961, 263, 323. J. I. Lauritzen and J. D. Hoffman, J . Appl. Phys., 1973, 44,430. l8 A. Keller and A. O’Connor, Disc. Faraday Soc., 1958, 25, 114. l9 J. D. Hoffman, G. T. Davis and J. I. Lauritzen in Treatise on Solid State Chemistry, ed. N. B. ’ O J. Dlugosz, G. V. Fraser, D. Grubb, A. Keller, J. A. Ode11 and P. L. Goggin, Polymer, 1976, 21 M. M. Winram, D. T. Grubb and A. Keller, J. Mater. Sci., 1978, 13, 791. 22 A. I. Miiller, Helv. Chem. Acta, 1933, 16, 155. 23 R. D. Burbank and A. Keller, Be11 Laboratory Memorandum 60-1 12-1 19 (1960). 24 H. F. Kay and B. A. Newman, Acta Cryst., 1968, B24, 616. 25 G. R. Strobl and N. Miiller, J . Polymer Sci. A-2, 1973, 11, 1219. 26 C. G. Vonk, J. Appl. Cryst., 1973, 6, 81. ” K. H. Gardner, J. H. Magill and E. D. T. Atkins, Polymer, 1978, 19, 361. 28 A. J. Geddes, K. D. Parker, E. D. T. Atkins and E. Beighton, J. MoI. Biol., 1968,32, 343. 29 H. D. Keith, F. J. Padden and G. Giannoni, J. Mol. B i d , 1969, 43, 423. Hannay (Plenum Press, New York, 1976), vol. 3, chap. 7. 17,471.166 CRYSTALLINE POLYMERS 30 S. J. Spells, D. M. Sadler and A. Keller, Polymer, in press. 31 D. M. Sadler and A. Keller, Polymer, 1976, 17, 37. 32 D. M. Sadler and A. Keller, Macromolecules, 1977, 10, 1 1 28. 33 G. C. Summerfield, J. S. King and R. Ullman, J. Appl. Crysf., 1978, 11, 548. 34 D. M. Sadler and A. Keller, Science, 1979, 203, 263. 35 J. Schelten, D. G. H. Ballard, G. D. Wignall, G. Longman and W. Schmatz, Polymer, 1976, 17,751. J. D. Hoffman and J. J. Weeks, J . Res. Nat. Bur. Stand., 1962, A66, 13. 37 J. D. Hoffman and J. J. Weeks, J. Chem. Phys., 1965, 42,4301. 38 J. Rault, J. Physique Lettres, 1978, 39, L-411. 39 B. Lotz, A. J. Kovacs, G. A. Bassett and A. Keller, Kolloid-Z., 1966, 209, 115. 40 D. T. Grubb, J. Dlugosz and A. Keller, J. Mater. Sci., 1975, 10, 1826. 41 J. D. Bernal, Penghin Science Survey, 1961, 1 1 .

ISSN:0301-7249    

DOI:10.1039/DC9796800145

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

Reconsideration of Kinetic Theories of Polymer Crystal Growth with Chain Folding BY JEAN-JACQUES POINT Laboratoire de Chimie Physique et Thermodynamique, Universith de 1’Etat i Mons, 21, Avenue Maistriau, 7000 Mons, Belgium Received 30th April, 1979 When the elementary step in the formation of a surface nucleus is chosen to be the deposition of a full stem, the crystallization path is shown to be, in specific examples, energetically disfavourable. Moreover, the occurrence of a lateral interfacial free energy is, in this context, the sole reason for limi- tation of fold length. Avoidance of the blow-up problem results from questionable choices of expres- sions for the affinity of deposition of a stem. Lastly, for PEO oligomers, the thermal dependence of kTlnG (where G is the linear growth rate) is much larger than that of the affinity of deposition of the first stem and a consistent value cannot be found for the lateral interfacial free energy per unit area.Thus, it appears necessary to recall that the crystallizable entities are molecules made in the liquid state of joined stereoregular segments. The first consideration leads to a tentative interpretation of the PEO data. The second leads to a finer description of the process of molecular deposition, for- mulated as the result of reversible attachment of successive segments shorter than a stem, while allow- ing the molecule to fold back at every stage of its deposition. A new mechanism of limitation of fold length results. Such a model allows, in principle, consideration of all the crystallization paths.We give a brief outline of the classical kinetic theory of polymer crystal growth with chain folding and discuss the basic concepts and the approximations used. Then we give a tentative interpretation of the crystal growth data for oligomers of poly- oxyethylene. Finally we present an alternative explanation of the chain folding. 1. BRIEF OUTLINE OF THE THEORY The actual treatmentslP6 are all based on coherent surface nucleation and imply sharp molecular folds with adjacent re-entry. Only a brief account of the simplest4 of these treatments is given here : however, the basic assumptions and approximations to be discussed hereafter are emphasized and some insights into sophistications introduced in more complicated treatments are emphasised.The model is shown in fig. l(a). A surface nucleus composed of v stems of length 1, thickness b and width a forms on a substrate assumed to be even and smooth and spreads in the direction denoted g . The basic postulate (not retained in more sophis- ticated treatment^^*^*^) is that the first stem in each newly commencing strip on the edge of the crystal plate has a choice of length, but all subsequent stems have the same length. The process of formation of the secondary nucleus is formulated2 as proceeding through a denumerable sequence of stages (designated by suffixes 0, 1, 2 . , . ) and a range of configurations corresponding to the partial attachment of a stem are all considered to belong to one stage. Genuine physical nucleation problems are time- dependent, but we have chosen to consider the nucleation rate in the steady state.168 POLYMER CRYSTAL GROWTH ( a ) ( b ) ( C ) ( d ) (el FIG.1.-(a) Surface nucleus; (b) possible reaction paths (see para. 2.1.) On these bases, the calculation is straightforward. In an ensemble having Nv systems in the vth stage, the net transition rate between the vth and the (v + 1)th stage is Sv = AvNv - Bv+INv + 1 (1) where A , and Bv are the forward and backward transition rates from the vth stage. Provided that the condition A > B holds in the steady state and from the hypothesis : A , = A for v 1 and Bv = B (2) (3) we get Sv = NoAo(1 - B/A). From A/B = exp (abIAflkT - 2abae/kT), the necessary requirement for the growing nucleus to develop is written as I > 1, = 2ae/Af (4) where the quantity Afis the bulk free energy of fusion per unit volume and oe an ap- p r ~ p r i a t e ~ ~ ~ fold surface interfacial free energy.The average value of I, denoted ( I ) , is larger than I, ( I ) = I, + 61. ( 5 ) The only way to avoid 61 becoming infinite is to assume that the transition proba- bility A. is a decreasing function of the length of the stems. The expression for the transition probability was progressively adjusted '-' in order to account for new experi- mental data. From the most recent ver~ion,~ we have A. = p exp (-2bZalkT + yabIAykT) (4) where /? expresses the retardation due to the transport phenomena and the free energy term 2bIa corresponds to the creation of the new lateral surfaces [fig. l(a)]. The apportionating factor y, ranging between 0 and 1, has been introduced in order to increase the value of the critical undercooling AT, for which the quantity (20 - yaAf) is zero and 61 becomes infinite.This " 61 catastrophe " was never observed. Detailed comment on the nature of y is given in the literat~re.~.~ Assuming that possible values of I are increments of a unit length Zu, the total flux is approximated, if y = 0.5 by s(T> = Nop(aI/Q [a (Af )/40Iex~(abae/kT)ex~ [-4baael(Af PTI. (7) In a similar way, an explicit expression is obtained for 61.J . - J . POINT 169 2. DISCUSSION 2.1. CASES WHERE THE POSTULATE OF ADJACENT RE-ENTRY HOLDS We first establish that the steady state approximation holds. Then, we show that the assumption of persistence of stem length is very restrictive.Lastly, we conclude that an unbiased evaluation of the lateral surface energy reveals a basic inconsistency in the theory. (i) s T E A D Y s T A T E A P PR o x I MA TI o N this approximation, we solve the time-dependent equations In order to remove the repeatedly recalled3 uncertainty pertaining to the use of dNi/dt = AoNo - (A + B)N1 + BN2 i > l dNi/dt = AN,-1 - (A + B)Ni + BNi.1. The stationary solutions are linear combinations of the two particular solutions i > l Ni = 1 Ni = (A/B)I. (9) In the practical case where A > B, neither of these solutions can be attained in a finite period of time. With initial condition Ni = 0; i > 1 and boundary condition No = constant, the occupation number Nl and the flux are given by N,(z) = 2AoNo(AB)-1/2 [1,(22)/22] exp [-(X + l/X)z] dz (10) L Ilm [S(r) - S(4l/S(w) = (1 - 1/X [ u W / z l exp [-(X + 1 / m dz)/(l - 1/X) (1 1) where where 1' is the modified Bessel function of order 1.is that, as usually assumed, X = (A/B)'/' and z = t(AB)'I2 From these equations the result (12) Numerical estimates of time constants are obtained from values of p, O, oe . . . taken from ref. (3). They range from to s. Without solving the time-dependent equations in the more general situation where fluctuations6 of fold periods are allowed, the departure from steady state solutions sometimes assumed appears unlikely. limf+m S = 0 ifA < B; limf+m S = Ao(l - B/A) if A > B. (ii) REACTION PATHS The " 62 catastrophe " that occurs in the fluctuation theory was never f o ~ n d . ~ ~ ~ The avoidance of this event in the theory discussed here results frGm the unrealistic assumption of persistence of stem length.Two unsophisticated examples emphasize the very restrictive implications of this postulate. Consider, for instance, that the length of a nucleus is 1.12, and that the ratio o/oe is 0.15. The free energy of the new lateral surfaces of the first stem amounts to 2620. The net free energy gain pertaining to the attachment of the subsequent stems amounts to 2abae62/2,. As a result, the number of stems in a stable nucleus is greater than 2b202,/2aboe61 = 1.52/a. Along the chosen Both assumptions are plausible.170 POLYMER CRYSTAL GROWTH reaction path, the nucleus has to pass through a long sequence (for instance, several tens) of unstable states from which reorganization is expected.Let us now consider the secondary nucleation in isotactic polystyrene. Even at moderate undercooling nuclei made of two stems and of length >I, are supercritical. A subsequent growth of such a nucleus along the chain direction appears likely [fig. l(b)-(d)] and leads to a long nucleus. For such a long nucleus and along many reaction paths the energy barrier is much lower than that experienced along the usually considered path. (iii) DIFFICULTIES I N THE PREDICTION OF THE GROWTH RATE Comparison of experimental data from closely related systems illustrate these difficulties. The growth rates of single crystals of isotactic polystyrene lo from dilute solutions in good and poor solvents differ by three or more orders of magnitude.It is unlikely that such a large disparity could be accounted for by any realistic adjustment of the parameters involved in the theoretical expression for G. We discuss now, briefly, the exhaustive data obtained by Kovacs et al." on the growth from the melt of narrow hydroxy-terminated polyoxyethylene (PEO) fractions ranging between 2000 and 10 000 in the number average molecular weights. (A more cautious and more extensive discussion has been given elsewhere12 by Kovacs and myself .) Considering the growth rate, G, of extended chain crystals for two fractions (label- led 1 and 2) of number average degree of polymerization p1 and p2 and at two tem- peratures Tl and T2 such that [where T,( a) is the melting temperature of extended chain crystals of high molecular weight], we note that all the driving forces (except the lateral interfacial free energies 2b1,a and 2b12a) involved in the expression of A . and A have nearly the same value.Accordingly, we get from the classical kinetic theory the following reduction rule,12 which is well supported by the experimental data (fig. 2). '' The logarithmic growth rate branches of extended chain crystals obtained with low molecular weight PEO fractions plotted against the reduced undercooling 0 = p[T,( co) - T]/T are nearly superposable by means of vertical shifts, except in the immediate vicinity of the relevant melting temperature of the crystals." From the value of these shifts one can easily determine12 the apparent values of a. (In this presentation small corrections are ignored.) Assuming mononucleated growth, these values range from (1-3) x lo-'' J m-2 and increase by a factor of z 3 when the average length of the molecules is reduced by 2.Similar conclu- sions are obtained from the analysis of the growth rate of folded chain PEO crystals (in which, in view of the low molecular weight, adjacent re-entry is assumed). The apparent values of 2bZa are low and by no means proportional to 1, in formal contra- diction to the basic concept of coherent surface nucleation. 2.2. CRYSTALLIZATION FROM THE MELT OF HIGH MOLECULAR WEIGHT MATERIAL It is very likely that melt crystallization of high molecular weight material does not significantly alter the radius of gyration of the chains in the liquid state.13*14 Thus, the postulate of adjacent re-entry appears irrelevant when crystallization from theJ .- J . POINT 171 melt is considered. Nevertheless, it is usually assumed that the logarithm of the ratio of linear growth rate G to the transport factor p [see eqn (7)] goes linearly with bZ,a/kT = 2aae/(Af)kT.* In some instances impressive agreement between the values of a and a, obtained from this and other sources has been noted. On this basis, some modified form of the theory, usable when the postulate of adjacent re- entry does not hold, should be needed. L ' I I I 2 3 e I 1 I 1 I I I I 2 3 e FIG. 2.-Schematic representation of the vertical shifts between the growth rate curves of extended chain crystals for PEO fractions of degree of polymerization 43, 63 and 89. (a) calculated from 0 = 7 erg cm-2 and T,(co) = 341.5 K; (b) from experimental data of Kovacs." p = (i) 43, (ii) 63 and (iii) 89.We have however some words of caution. According to Hoffman, Davis and Lauritzen3 eqn (6) is to be regarded as the defining relation for a. More exactly, it is the defining relation for " 2ba ", the lateral interfacial energy per unit length of the stem. The difficulty pertaining to a choice of a reference interface between the first stem and the melt is clear. Thus, the comparison with the data obtained in a few cases l5 from homogeneous nucleation experiments is not conclusive. Moroever, if the thermal dependence of the lateral free energy of the system is felt to be the major reason for the thermal dependence of log G, the quantity 2b(Z)a/kTis perhaps to be considered instead of 2b2,alkT.The thermal variations of these two quantities are not alike in the often occurring case where the thickness of the lamellae are assumed16 or known1' to be temperature-independent. Even when the graph of log G against T is linear, dependence of its slope on the temperature or molecular weight is fre- quently observed. This makes extension of the theory to the case of crystallization from the melt unlikely. * In fact the theory shows that the full expression of log S does not go exactly linearly with 1 /(Af)kTwhen large temperature ranges are considered (especially when D and (ie are assumed tempera- ture-dependent). In this case, standard procedure used to derive the values of the physical parameters involved in the expression of B is not justified.172 POLYMER CRYSTAL GROWTH 3.ALTERNATIVE APPROACHES In view of these difficulties, we consider in the next sections new tentative ap- proaches to the problem. We first present a molecular nucleation mechanism which fits qualitatively the growth rate of PEO crystals data. Then, after a brief discussion of the merits of considering the attachment of a full stem as a single stage, we introduce another model where the attachment of the molecule involves sequential deposition of short chain segments while allowing them to fold at each elementary step of the crystallization process. 3.1. TENTATIVE INTERPRETATION OF CRYSTAL GROWTH OF OLIGOMERS From the results from neutron ~ ~ r k , ~ ~ * ~ ~ Fischer l4 proposed the " solidification model ".In this model the molecule precipitates first with a minimum of con- formational changes and then reorganizes. This model does not allow any detailed calculations. In this section the model is modified and used to give a very tentative interpretation9 of the thermal variation of the rate of growth of oligomeric PEO crystals. The slopes of the envelopes of the In G against AT/kT curves for the various PEO fractions studied by Kovacs and co-workers range from 70 to 100 % of the entropy of fusion of a whole molecule. This suggests the following (crude) model. (i) The molecules precipitate one by one on the edge of the lamella in such a shape as to minimize their free energy (this provides the difference from the " solidification model " and is reminiscent of the idea of molecular nucfeation18).If L is the length of the molecule and Z the length of the molecule shaped in such a way, we get a/al(2abl+ 2Lab(a,)/l) = 2ab - 2Lab(ae)/l2 = 0 (14) where (a,) is some kind of surface energy associated with the folds and ends in the molecule. The free energy pertaining to the newly created surface is OF POLYOXYETHYLENE 4(aaoe)1/2bL1/2 = CL1I2. (15) (ii) Then the molecule reorganizes in order to have the number of folds n appropri- ate to its degree of polymerization, to the temperature of crystallization and to the length of the substrate. The transition rates for the sequential deposition of the molecules obey In A = A . = (abLryAf - CL1I2)/kT In Ao/B = In A / B = [abLAf - 2ab(a,, + naef)]/kT (16) where aee and oef pertain, respectively, to the chain ends and folds.Fig. 3 shows the merits and deficiencies of such a crude model. Lack of extensive data on other similar systems makes further comments difficult. 3.2. FINER GRAINED MODE OF MOLECULE ATTACHMENT In the classical model, each stage of the sequential process considered is the attach- ment of a full stem and the appropriate expressions for the transition probabilities cannot be decided apriori. According to Frank and Tosi, we describe the building of a secondary nucleus as the result of the attachment of successive segments of length AZ. We denote by CC(CC~ if the first stem is considered) and y the forward and backward rate constants pertaining to the deposition of a small segment included in a stem andJ.-J. POINT 173 I I I I 1 I I 4 50 55 60 t /"C FIG.3.-Growth rate of PEO crystals calculated from para. 3.1. Curves are labelled by a letter [(b), (c) and (I)] which refers to the degree, p , of polymerization (60,83 and 180) and a number (1,2, 3 or 4) which is the number of folds in the molecule. The theory does not allow any prediction con- cerning the value of n. Experimental data (0) by courtesy of Prof. A. Kovacs. The assumed values of the parameters for the curves (b), (c) and (I) are: ly = 1.00; 0.85 and 0.72; Tm(co) = 341.53 K; by x and y the forward and backward rate constants pertaining to a small segment including a fold. The occupation numbers for the individual stages belonging to the attachment of a stem are designated by suffixes 1, 2, . . . i where i = l/AL aee/k = 50 K A-'; aeflk = 32 K A-'; C/k = 480.6 K All'.In steady state conditions, the occupation numbers are given by for the first stem for subsequent stems nj = C* + D*(cco/y)jj = 1, 2 . . ., i n j = C + D(m/y)j j = 1, 2, . . . , i. (17) The constants C, D, C*, D* and the net flux S obey the following equations S = C(tc - 7) = C*(CC~ - 7) = [C* + D*(cGJ~)']~ - [C + D(CC/~)]Y D = C ( R - Y + Y - x)lCx(a/r)' - Y(./Y)I. (18) We use the following expressions for the rate constants: tco = p exp (-2baAllkT + CabAlAflkT) tc = p exp (<abAlAf/kT) y = p exp [(C - l)abAlAflkT] x = p* exp (-2abaJkT + abAlAf/kT) y =p*. The results are that (i) the occupation numbers do not correspond to an equilibrium distribution; (ii) the fluxes do not depend (to an appreciable extent) on the apportion- ating factor < (which cannot be identified with the ty parameter); (iii) the ratio of the fluxes here computed to the fluxes calculated from eqn (7) (with y = 1) is nearly con- stant.This makes the usual approximation likely.174 POLYMER CRYSTAL GROWTH 3.3 ANOTHER MECHANISM OF FOLDING In the classical kinetic theory, the origin of the limitation of fold length is assigned to the imposition on the deposition of the first stem, of a lateral interfacial free energy. An alternative possibility is to assume that at each stage of the attachment of a molecule onto the crystal, the molecule has a finite probability of folding back. Similar argu- ments are used when discussing the shape and size of a linear macromolecule in solu- tion or in the melt. 0 50 118, 100 FIG.4.-Reactions paths drawn in a graph which give the free enthalpy A@ of a surface nucleus (in erg) against its width w and length 1. The assumed values of the parameters are (a) = 12.5 A; (b) = 5 A; Af = 1.5 x lo8 erg ~ m - ~ ; a, = 37.5 erg cm-2 and a = 7.5 erg cm-2 Considering19 the finer-grained means for attachment of the first stem of a newly commencing strip, we assume that, at the end of each stage of deposition, the molecule has the opportunity to fold back. For the sake of simplicity we conserve the Hoffman and Lauritzen postulate of persistence of stem length. We denote by y j the net rate of folding from the-jth stage (numerous arguments can be put forward to justify thatJ . - J . POINT 175 175~; y j is an increasing function ofj).We write the conservation equation of the occupa- tion number nj in steady state, (20) Before dealing with the resolution of the recurrence relation (20) we use a graph of A@ plotted against the length and the width of a two-dimensional nucleus to show the various reaction paths considered for the crystal growth. The undercooling is assumed larger than ATc. In fig. 4(a) we have drawn the reaction paths usually con- sidered. Growths along paths u, ZI . . . are not possible because negative values of A@ are never obtained. The other reaction paths x, y , . . . are possible and the “ 62 catastrophe ’’ comes from the fact that the larger the length of the stems, the larger the decrease in A@ (for all stages including the first). In fig. 4(b) we have drawn the reaction paths considered here.A decrease of the occupation numbers of the various states along the path x, y , z is expected, because of the advent of lateral growth from each of the intermediate states x, y , z . . . for which the length of the stem is higher than Zc. Whatever the value of (ao/?) may be and under the (fictitious) assumption that y j is a constant, one of the roots of the characteristic equation of the recurrence relation (20) is positive and less than unity. This ensures the existence of a steady state solution, where the nj are in a decreasing geometrical progression, and a finite value of ( I ) . When an appropriate expression for y j is chosen, the same conclusion is a fortiori obtained. The computation of the occupation numbers proceeds by iter- ation, and good fits of the experimental values of ( I ) and G are obtained (fig.5). The choice of the expression for y j and of the values of the physical parameters is not critical. aonj-1 - ( a 0 + y + yj)nj + ynj+t = 0. I I I I 0 150 125 100 125 100 75 I 50 I I I 50 100 150 B T / O C FIG. 5.-Thickness of polyethylene (PE) and polystyrene (PS) against AT. 0 are from the calcula- tion.‘O Curves are from the experimental data.**’ The assumed values of the parameters are: for polyethylene: a,lk = 70.8 K A-’; a/k = 6.4 K A-2; A1 = 12.8 A; for polystyrene: ae/k = 30.6 K A-’; a/k = 13.1 K A-2; A1 = 11.0 A. 4. CONCLUSIONS Because of the strict limitation of the authorized length of this report, many im- portant topics have not been discussed and references to works of major interest have been omitted or considered too briefly.However, we feel that a discussion of the role of the lateral interfacial free energy was the point to elucidate. Finally, we wish to emphasize that exhaustive data on closely related systems [see ref. (10) and (1 l)] are needed.176 POLYMER CRYSTAL GROWTH J. I. Lauritzen, Jr. and J. D. Hoffman, J . Res. Nut. Bur. Stand., 1960,64A, 73. F. C. Frank and M. Tosi, Proc. Roy. SOC. A, 1961,263, 323. J. D. Hoffman, G. T. Davis and J. I. Lauritzen, Jr, Treatise on Solid State Chemistry, ed. N. B. Hannay (Plenum Press, New York, 1976), vol. 3, chap. 7, pp. 497-614. J. I. Lauritzen, Jr. and J. D. Hoffman, J. Appl. Phys., 1973,44,4340. J. D. Hoffman, J. I. Lauritzen, Jr, E. Passaglia, G. S. Ross, L. J. Frolen and J. J. Weeks, Kolloid-Z., 1969, 231, 564. F. P. Price, J. Chem. Phys., 1961,35,1884; J. I. Lauritzen, Jr, E. A. DiMarzio and E. Passaglia, J . Chem. Phys., 1966, 45,4444. D. H. Jones, A. J. Latham, A. Keller and M. Girolamo, J. Polymer Sci., PoZymev Phys. Ed., 1973, 11, 1759. R. L. Miller, Kolloid-Z., 1968, 225, 62. ’ J.-J. Point, to be published. lo H. D. Keith, R. G. Vadimsky and F. J. Padden, Jr, J . Polymer Sci., Part A-2, 1070, 8,1687. l1 A. J. Kovacs, C . Straupe and A. Gonthier, J . Polymer Sci., Part C, 1977, 59, 31. l2 J.-J. Point and A. J. Kovacs, Macromolecules, to be published. l3 D. M. Sadler and A. Keller, Macromolecules, 1977, 10, 1128. l4 E. W. Fischer, to be published. l5 J. A. Koutsky, A. G. Walton and E. Baser, J. Appl. Phys., 1967,38, 1832. l6 J. D. Hoffman, G. S. Ross, L. Frolen and J. I. Lauritzen, Jr, J. Res. Nut. Bur. Stand., 1975,79A, l7 P. Dreyfuss and A. Keller, J. Macromol. Sci., 1970, B4, 81 1 . l8 B. Wunderlich, in Macromolecular Physics (Academic Press, N.Y., 1976), vol. 2, para. 5.3.4., l9 J.-J. Point, Macromolecules, to be published. 2o M. Dupire, Thesis (Fac. Sci. Mons University, 1977). 671. p. 98.

ISSN:0301-7249    

DOI:10.1039/DC9796800167

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

On the Problem of Crystallization of Polymers from the Melt with Chain Folding BY JOHN D. HOFFMAN,* CHARLES M. GUTTMAN AND EDMUND A. DIMARZIO National Measurement Laboratory, National Bureau of Standards, Washington, D.C. 20234, U.S.A. Received 19th July, 1979 Tt is shown that the " reptation " process proposed by de Gennes allows molecules to be reeled from the melt onto the crystal surface with chain folding by the force associated with crystallization at a rate that is comparable with that demanded by the observed crystallization kinetics for poIyethy- lene fractions n = number of C atoms = 1290-5310. Hence, the rate of transport in the melt is suffi- cient to permit a considerable amount of chain folding, and an objection due to Flory and Yoon is thereby countered for the range of n noted.The deductions of Yoon and Flory from the neutron scattering data of Schelten and co-workers on PEH + PED mixtures (nped E 3750) quench-crystallized from the melt are considered next. It is shown that Yoon and Flory's favoured pes = 0.3 model, which gives a probability of adjacent re-entry par close to zero, is deficient despite the good fit of the scattering data, since it exhibits a large density anomaly in the region between the crystal lamellae. This opposes their own view that the material in the interlamellar region has essentially normal amorphous state properties. A " central core '' model is proposed that does not possess a density anomaly, and which predicts the scattering curve, characteristic ratio and crystallinity with fair accuracy. This and certain other models give par z 0.65, indicating that the adjacent position is by a considerable margin the most probable site for re-entry, in contrast to the analysis of Yoon and Flory.The core model exhibits a mean throw distance of E 22 A for the non-adjacent re-entry loops. This is comparable with the mean " niche " distance calculated from nucleation theory. The number of ties between the lamellae is less than one per chain. Hence the connections of this type between the lamellae are less profuse than have sometimes been depicted. 1 . INTRODUCTION Theories predicting the rate of growth and thickness (fold period) of single crystals from solution and lamellae in the melt as a function of the undercooling AT are mostly based on a suitable modification of surface nucleation theory.l-1° It appears that only this type of theory can predict the existence of chain-folded crystals, give the temperature-dependence of the fold period, and simultaneously give the growth rate.In special cases, these theories can justify the constancy of the platelet thickness during the isothermal growth p r o c e ~ s . ~ ~ ~ In general, it was assumed that, once nucleated, the molecule was reeled5 onto the surface by the force of crystallization. Most of the theories use the approximation that the re-entry in the substrate completion pro- cess is of the adjacent type, though some deal with imperfections such as ciZia.598910 That adjacent re-entry was an approximation-though a very good one at low under- coolings, low to moderate molecular weight and low solution concentration-was of course clearly understood by those who advanced these treatments.There has been a question from the beginning concerning how much adjacent re-entry occurred in melt-crystallized material, since in this case there exists the maximum opportunity for disorder in the fold surface.178 CHAIN FOLDING In a recent review, Hoffman and co-workers' stated in connection with crystalliza- tion from the melt that the adjacent position is by a considerable margin the most prob- able site for re-entry. This remark was partly based on the concept that the adjacent site was highly favourable from an energetic standpoint, and that the molecule being reeled in had the greatest presence at that site. The statement was made with speci- mens of low and moderate molecular weight in mind, and with the understanding that some non-adjacent events, e.g., the intrusion of a " strange " molecule, must certainly occur to some extent.The foregoing is to be contrasted with the view of Flory and Yoon,ll*12 who state that adjacent re-entry in nzelt-crystallizedpolymer is an improbable event. The issue can be decided by a correct determination of the probability of adjacent re-entry, par. The value ofp,, will of course depend on the molecular weight, and the undercooling at which the specimen was prepared. The theoretical treatments of folded-chain systems generally aimed at simul- taneously predicting the initial fold period 1,' and the rate of growth G of the crystals. In this they may be deemed generally successful, including crystallization from the melt.The temperature range over which the formulae developed for G(T) apply is very large, and the fit of the data generally e ~ c e l l e n t . ~ ~ ~ ~ Meanwhile, adjunct theories give a good account of melting phenomena.' The work of chain folding q (or the fold surface free energy a,) obtained directly from G(T) at low undercoolings in crystal- lization from the melt is generally consistent not only with the value estimated inde- pendently from melting experiments,' but also with the detailed nature of the ~ h a i n . ~ * l ~ Though more work remains to be done, the kinetic theory of nucleation is not devoid of comment on the origin of the amorphous component that appears, especially in melt-crystallized material (see later).The conclusion of Flory and Yoon that whatever re-entry does occur in the same lamella is generally not at the site adjacent to the point of emergence from that lamella, is based in part on the belief that the polymer molecules cannot be withdrawn from the interpenetrated random coil melt fast enough to allow the substrate comple- tion process with a substantial degree of adjacent re-entry to take place.'' They indi- cate that the molecular motions in the liquid are several orders of magnitude too slow to allow substrate completion by the reeling process. They propose instead that on crystallization the overall topology of the molecules in the melt remains largely intact, the lamellae being formed by locally straightening out segments of the mole- cules; the latter process supposedly forces the entanglements in the melt into the amorphous zones between the lamellae.We do not challenge the concept that a polymer melt consists of interpenetrated random-coil molecules. In the first part (section 2) of this paper we shall, however, show for polyethylene that consideration of the force on the molecule caused by crystallization (which is a relatively large perturbation) taken together with the rather small friction coefficient characteristic of the " reptation " model of de Gennes,15?16 leads to a velocity that is quite adequate to allow molecules to be drawn from the random-coil melt onto the growth front with chain folding at a rate consistent with the substrate completion rate g obtained directly from the crystallization kinetics observed for polyethylene fractions n = 1290-53 10.The second major argument given by Flory and Yoon for believing that whatever re-entry that does occur is generally not adjacent to the point of emergence is based on neutron scattering experiments. They state that a detailed analysis of the scattering functions for a melt-crystallized PEH + PED mixture leads to the conclusion that adjacent re-entry occurs infrequently.11s12 This conclusion is not surprising, since in their Monte Carlo simulation, re-entry into an adjacent site with the stem in crystallo- graphic register (with an intervening short fold) was completely forbidden at the out-J . D . HOFFMAN, C. M.. GUTTMAN A N D E . A . DIMARZIO 179 set. They analysed the neutron scattering data of Schelten and CO-workers” for a PEH + PED sample with npED --”’ 3750 that was quench-crystallized in such a manner as to avoid segregation of the proto- and deutero-polyethylene.Guttman and co- workers 18*19 have shown that a difficulty exists in Yoon and Flory’s analysis that casts doubt on its validity: The Yoon-Flory model contains an “ interfacial ” layer com- prising over 20% of the disordered zone between the crystal lamellae that exhibits a large anomalous density (see later). Meanwhile Guttman et al. have shown from the same neutron scattering data for a number of models where adjacent re-entry was allowed and which had no density anomaly that the most probable event is in fact an adjacent re-entry. In the second part (section 3) of present paper, we summarize the results of some neutron scattering function calculations for the “central core ” model, which in many respects is generally illustrative, and which allows the introduction in an approximate manner of some effects of the energetics associated with the attachment of stems on the crystal substrate into the Monto Carlo calculations.The data of Schelten et aZ. give par x 0.65 with this model. Also included is a calculation of the niche separation on the substrate from nucleation theory, this separation being intimately connected with the presence of a surface amorphous zone consisting of short, non-adjacent re- entry loops. 2. SURFACE NUCLEATION A N D SUBSTRATE COMPLETION WITH REELING (REPTATION) I N CRYSTALLIZATION FROM THE MELT (i) ESTIMATE OF SUBSTRATE COMPLETION RATE g FROM EXPERIMENTAL DATA : POLYETHYLENE FRACTIONS In the particular case where Regime I and Regime I1 crystallization can be observed experimentally, it is possible to extract the velocity of the substrate completion rate g from the data.This will be done here for polyethylene. To accomplish this requires a discussion of the pre-exponential factors for Regime I and Regime I1 crystallization. The value of g so obtained will then be compared with that calculated from reptation theory using the data of Klein and Briscoe*O on the diffusion coefficient of polyethy- lene in the molten state, which gives the required value of the friction coefficient as a function of n, the number of -CH2- groups. According to the kinetic nucleation theory in slightly modified and recent form8v9 the growth front begins to propagate itself on a portion of the previously formed substrate when a stem attaches itself as an initial nucleus on that substrate.Such stems attach at a rate denoted i which has the units stems s-l cm-l. The nucleus then pulls in other segments that attach to the substrate in adjacent fashion, forming a surface patch at a spreading rate g . The overall process causes the crystal to grow at a rate G/cm s-l (fig. 1). The free energy of formation of such a surface patch is A9 = 2boaZ - aoboZ(Af) + (v - l)aob,[2ae - Z(Af)], where v = number of stems, a, = molecular width, b, = layer thickness, o = lateral surface free energy, oe = fold surface free energy, in erg cm-2 and A f g (Ah,) (AT)/TZ in erg ~ m - ~ .The term 2boa1 - a,b,Z (Af) is the net work of putting on the first stem. Eqn (2.1) describes the barrier system shown in fig. 1, where the A and B repre- sent the rate constants of the forward and backward reactions noted. By choosing the apportionment ty = 0, which is reasonable in the present application, and em-180 n CHAIN FOLDING 0 1 2 3 4 5 ‘3 FIG. 1 .-Upper diagram : Surface nucleation on substrate. Dangling molecule in tube represents “reeling ” or reptation. Lower diagram: Barrier system showing rate constants of substrate com- pletion process ( A = forward reaction, B = backward reaction). The symbol q represents the work of chain folding. ploying the flux in the form7 S = NoA,(A - B)/(A - B + B,) with No = Zn and j3 = Pg in the definition of the rate constant^,^ and calculating the surface nucleation rate from the integrated total flux ST as i = &/ao, one getss i = pi (Z/ao) exp[-4boaae/(Af)kT]. I = 1; = 2ae/(Af> + 61.(2.2) (2.3) The flux corresponds to a mean initial lamellar thickness in cm of Here Z = average number of -CH,- units in a stem, and pi is a retardation para- meter associated with the segmental jump rate4*’-’ in events s-’ to be given subse- quently. To an approximation sufficient for the present purpose ‘J-’ 61 GX kT/b,a. (2.4) This quantity is 9.2 x cm for polyethylene at 400 K (a = 14 erg cm-2, b, = 4.15 x Results that are in the practical sense identical to those given in eqn (2.2)-(2.4) are found if the apportionment yo = 1 is used for the first step, and ‘y, = 0 for the substrate completion process.The rate constants Ao, B,, A and B cm).J . D . HOFFMAN, C . M . GUTTMAN A N D E . A . DIMARZIO 181 used in the formula for S are given in the Appendix (section 4). Because the deriva- tion7 of S = N,A,(A - B)/(A - B + B,) is valid only for v > ca. 4, the expressions to be given for GI and GII are thereby restricted to cases where the molecule is long enough to exhibit at least several folds. We now note that by inserting eqn (2.3) into eqn (2.1) that Ayl = 2b,al,* - 2aoboae - vaobo(61)(Af). Notice that a finite positive 61 is required to allow an increase in substrate patch stabi- lity as v -+ v + 1, i.e., as stems are added. It will be seen shortly that the mean force pulling a molecule from the melt onto the substrate is proportional to a,b,(dZ)(Af).The spreading rate g in cm s-l is given to a sufficient approximation by9 g = a, ( A - m = a,P,{exp(-q/kT) - e x P [ - ~ a , ~ , ~ ( ~ f ~ / ~ T I l = aoP, exp(-qlkT), (2.6) where q = 2a,b,a, is the work of chain folding. tion step comes to As in previous work, the retardation parameter in events s-' for the initial nuclea- pi = ~ ( k T / h ) exp[- U*/R(T - Tm)]. (2.7) Pi is a segmental property, so the length of the molecule is not involved. The factor exp [- U*/R(T - T,)] is known experimentally to give the correct behaviour at low temperatures, and IC is a factor of the order of magnitude of unity that corrects the term in U* at high temperatures, and serves as a '' front factor '' for dealing with any orientation effects.The " universal "9 values U* = 1500 cal and T, = Tg - 30 "C will be used in the calculations for polyethylene to follow. We represent the retardation parameter for the molecular reeling process as pg = (K/n)(kT/h) exp[- U*/R(T - Tm)]. (2.8) The " reeling in " notion introduced many years ago is here explicity expressed by the factor l/n, and is clearly akin to the modern concept of reptation. The factor l/n is inserted to account for the fact that (in the ideal case) the entire molecule is drawn through the melt onto the substrate, the resistance being greater the longer the mole- cule (see later discussion of reptation). As an approximation, we take n to correspond to the length of the molecule, since reeling is most difficult for the longest dangling chain.Except for the factor I / n in eqn (2.8), the development given in this section is similar to previous We now must recognize that two regimes of crystallization are possible: (I) Regime I, where the nucleation rate i is such that one nucleus causes completion of the entire substrate of length L and (2) Regime I1 where a considerable number of multiple nucleation events occur (fig. 2).7-9921 For Regime I the growth rate in cm s-l is GI = b,iL so that GI = Go(I) exp[- U*/R(T - Tm)] exp[-4boaae/(Af)kT] (2.10) where Go(I) = boZ(kT/h)n,lc. (2.11) Here n, = L/a, = number of stems corresponding to the substrate length L. morphological considerations, L is estimated to be = 0.5 x to n, E 1.1 x lo3. Notice that g does not enter into either GocI> or G(I).From cm,22 corresponding182 CHAIN FOLDING For Regime I1 the growth rate is closely approximated by 10921923 GI1 = b0(id3 which gives where GII = Go(lI) exp[-- U*/R(T - T,)] exp[-22boaa,/(Af)kT] Go(11) = do(kT/h)(T/ln)t exp( -q/2kT). lateral surface, fl A I substrate lateral surf ace,^ s u bst rate T- fold Regime I ( z s. 0 .1) niche / - f o l d surface re - w e - w d L . (2.12) (2.13) (2.14) Regime I1 (221) FIG. 2.-Regime I and Regime II crystallization (schematic). Eqn (2.10) and (2.13) have found wide application in the analysis of growth-rate data of melt-crystallized polymers [see for example ref. (9), (13) and (24)]. The low AT portions of the data determine the product me, and the low temperature data give both U* and T,. As noted earlier, the value of ae usually turns out to give a work of chain folding q that is in reasonable agreement with independent e~timates.~ From eqn (2.6) and (2.8) it is seen that (2.15) Thus, an estimate of g can be obtained if K can be determined, since q is known and U* and T , can be estimated.Absolute values of the pre-exponential factors Go!I, and GO(II) are required for the analysis. The method for finding IC from the data will be given after introducing the expression below, which allows a cross-check on the whole procedure. According to Lauritzen2’ the criterion for the Regime I -+ Regime I1 transition occurs when 2 z 0.3 in the dimensionless parameter 2 = iL2/4g [see also ref. (8) and (9) for a further discussion]. Z = 0.3 = ~ z Z ( L / 2 a ~ ) ~ exp(q/kT) exp[--K,,,,/T(AT,)f] (2.16) g = (rc/n)a,(kT/h) exp(-q/kT) exp[- U*/R(T - Tm)].Then with the above expressions for i and g we getJ . D . HOFFMAN, C . M. GUTTMAN A N D E . A . DIMARZIO 183 where KgCI) = 4boao,/(Ahf)k, and ATt is the undercooling at which the Regime I -+ Regime I1 transition occurs. Thus, if AT,, Kg and q are known, L can be esti- mated in a manner that does not depend on K , U* or Tt. This value of L should be consistent with the experimental value of GocI, as calculated from eqn (2.1 1) with the the test value of K . Careful measurements have been made of the isothermal rate of growth of poly- ethylene crystals from the melt between - 123 and 131°C for good fractions from MW = 18 100 (n = 1290) to MW = 74 000 (n = 5310) where the Regime transition can be clearly seena8 Examples from the 11 fractions studied are shown in fig.3. The type of plots that give Kg(I), Kg,II), Go(I) and GOcII) are also shown. The Kg are the slopes and the Go are the intercepts of the plots of logloG + U*/2.303R(T - T,) against l/T(AT)f shown in the lower diagram in fig. 3. The transition from Regime I to Regime I1 in polyethylene always takes place at AT = 17.5 j-- 1"C8 The following input data are given: a, = 4.55 x lo-' cm, bo = 4.15 x lo-' crn, U* = 1500 cal, T , = 200 I<, Z = 158. The value of Kg(I) is 2.32 x lo5 K2, and q = 2.86 x erglfold or ~ 4 . 1 kcal mol-1.8 The experimental value of Gocr> for all 11 specimens averages to -1.4 x 1O'O cm s-l within a factor of about 2, and is essentially independent of n as predicted by eqn (2.1 1).The experimental value of Go(Il) for the same specimens clearly falls with increasing n, and can be expressed in the form of eqn (2.14) as Go(lI) EZ 1 .2 x 104/n1/2 within the experimental error, which is about a factor of two. cm (n, = 1.1 x lo3), which agrees with the lamella " fibril " width estimated from morphological considerations,22 we find from eqn (2.11) and (2.14) that the theoretical values of GocI, and Go(Ir) are 0.9 x lolo cm s-' and 2.1 x 104/rP2, respectively, for K = 0.2. This is satisfactory. We verify this result by using eqn (2.16) to calculate L with AT, = 17.5 "C, and find L = 0.55 x cm. Thus, K = 0.2 in eqn (2.7) and (2.8) allows the absolute growth rate G for all the fractions to be reproduced essentially within experimental error for both Re- gimes I and 11.Also, the value of L is consistent with morphology and the AT at which the Regime transition occurs, as well as with the absolute value of GotI,. This analysis is superior to one given earlier in which the factor l/n in eqn (2.8) was omit- teda8 The value of g computed with eqn (2.15) with K = 0.2, which is valid for the tem- perature range 123-1 3 1 "C for polyethylene fractions, is g 2.91~1 (2.17) By choosing L = 0.5 x which comes to 1 x cm s-l for n = 2860 (MW = 40 000). The reeling rate in the range indicated is r = (Zf/a,)g or r 130/n (2.18) which comes to 4.5 x cm s-' for n = 2860. We consider that eqn (2.17) and (2.18) are accurate to within a factor of about three. The quantities g and r given above may be regarded as " experimental " values, and are valid at T m 400 K.The activation energy for the motions in the melt found by Klein and Briscoe (70001RT) may be used instead of U*/R(T - T,) in the entire analysis, including the type of plot shown in the lower diagram in fig. 3, with the result that the " experimen- tal " value of g is found to be within about a factor of four of that given by eqn (2.17). The value of g given by eqn (2.17) reproduces the Regime transition at the observed undercooling, and is fully consistent within experimental error with the absolute values of the observed growth rates for the molecular weights and temperature range (For details see comments in General Discussion.)184 -5 h c I,,, - 6 - 5 \ Ls v s! - 7 - rn 0 d -8 -9 CHAIN FOLDING - I 3 - - - 74.4K (1.1 2) (1.39) 30.6K I I I I I I I I (1.19) I -4 I I I I I I I I I 1 I I 122 123 124 125 126 127 128 129 130 131 132 T I°C FIG.3.-Growth rate data and Regime transition for selected polyethylene fractions. Upper diagram: Examples of plot of log loG against T showing Regime I -+ Regime I1 transition. The numbers associated with the curves are the molecular weights (1 8.1 K = 18 100 MW), and the numbers in parentheses give MJM, for each fraction. Lower diagram: plot of log loG + U*/2.303 R(T-Tw) against l/T(AT)f with f = 2T/(T& + T ) showing change of slope of 2 predicted by Regime theory [see eqn (2.10 and (2.13)].J . D . HOFFMAN, C. M. GUTTMAN AND E . A . DIMARZIO 185 indicated. We must now ask if this result is comparable with the value of g that is estimated from reptation theory in the case where the driving force is the appropriate function of the free energy of crystallization.(ii) THE VELOCITY OF REPTATION: THEORETICAL ESTIMATES OF g Consider now the " reptation " model for diffusion in polymer melts proposed by In this model, the molecule evades entanglements by sliding lengthwise For centre-of-mass diffu- D, = Do/n2 (2.19) where Do is the value associated with a single -CH2- unit, This prediction has been convincingly verified experimentally for polyethylene melts by Klein and Briscoe 2o up to n = 1640. The value of Do is ~5 x cm2 s-l at 450 K, and we estimate using their activation energy that Do is E 1.5 x cm2 s-l at 400 K, which is the region of interest here. There was no evidence whatever of any change in the repta- tion process as a function of n for n > - 30.It was specifically pointed out by de Gennes that the friction coefficient [, associ- ated with reptation is proportional to n. The diffusion coefficient D, for reptation is related to D, by the relation de Gennes. as if in a relatively smooth tube along its contour length. sion de Gennes predicted that the diffusion coefficient D, is D, = 30, ( g 2 ) / { R 2 ) (2.20) where 9 is the contour length and R the end-to-end distance, so that for polyethylene D, = 3D,r~(l.27)~/(1.54)~ x 6.7 where 6.7 is the characteristic ratio. This leads to D, = 0.305Do/n. (2.21) (2.22) With D, = kT/c, = kT/con, we have c, = con = nkT/0.305Do. From Do = 1.5 x cm2 s-' we calculate co = 1.2 x lo-'' ergs cm-2 at 400 K.* A simple calculation will show that the rate at which molecules are pulled on to the substrate is not limited by viscous processes in the melt if reptation is assumed as the rate-determining step. We emphasize first the portion of the process involving stem completion while the chain is being added segment by segment into a niche, with no fold being formed.The fold can form first, and then the zippering down process can take place. Alternatively, the chain can wander into the niche from the pre- viously formed (vth) stem and zipper down, the fold being formed between the vth and (v + 1)th stem later in the process. During the zippering down niche-filling portion of the process, the force of crystal- lization is a maximum, and is given in erg cm-l by (2.23) The reptation velocity in cm s-l is therefore u, = f J C r = aobo(Af)/[on = 0.305Doaobo(Af)/nkT.(2.24) The velocity of the substrate completion process allowed by reptation only (with no fold energy included) is thus gr= (ao/lt)v, = (aibo/l$)(A f )/con = 0.305 D,(a~b,/l,*)AfjnkT. (2.25) * Note added in proof: A better vaIue of Do is given in a subsequent comment.186 CHAIN FOLDING By using Do = 1.5 x ( T r 400 K) and 1: = 200 x cm2 s-l, Af = 1.33 x lo8 erg for AT = 20 "C vr 2.1 x 103/n (2.26) cm, it is readily found that and g , G 47/11, (2.27) From a comparison of eqn (2.17) and (2.18) with eqn (2.26) and (2.27) it is evident that the reptation velocity is such that the substrate completion rate g , allowed by pure reptation is more than an order of magnitude larger than is required by the " experimental " estimate of g as given by eqn (2.17).This shows for the range of n under consideration that transport of molecular segments from the melt to the sub- strate is not the rate-determining step in the substrate completion mechanism. We complete the picture by estimating the mean velocity of the reeling rate rr,q and mean rate of substrate completion gr,q with the effect of the formation of chain folds included. It is readily shown that the mean force associated with crystallization that obtains during the substrate completion process is 24*25 (2.28) It is seen that the mean force on the molecule being reeled in is proportional to the gain in free energy as v -+ v + 1 in the substrate completion process [see fig. 1 and eqn (2.5)].[Eqn (2.28) is such that the free energy of crystallization is dissipated as heat in the liquid in the reeling process.] Accordingly, the velocity v ~ , ~ associated with the reeling process with the effect of folds included is (2.29) Vr,q =f',/Cr = aobo(Sl)(Af)/l~Con = 0.305 aoDo(A f )/lton and the corresponding substrate completion rate is gr,q = ao2bo(~l)(Af)/l,*2~on = 0.305 a; Do(A f )/Z:20n (2.30) where we have made use of 61 = kT/boo. A calculation for AT = 20°C correspond- ing to T G 400 K with CT = 14 erg cm-2 yields and (2.3 1) (2.32) These are remarkable results, since from a comparison of eqn (2.17) and (2.32) it is clear that, within the experimental error in g , the reeling process with the effect of folds included is of just the correct general magnitude to account for the experiment- ally estimated substrate completion rates.The result given in eqn (2.32) could, from a numerical standpoint, have been used with eqn (2.12)-(2.14) and eqn (2.16) to repro- duce the growth-rate data and regime transition within the experimental error. For the case of polyethylene in the temperature and molecular weight range cited, the foregoing treatment stands in contrast to the statement by Flory and Yoon that the molecular transport processes in the melt are several orders of magnitude too slow to allow a molecule to participate in substrate completion with chain folding.'' The belief that molecular transport in the liquid is much too slow to sustain crystallization with chain folding can be traced to their use of a long relaxation time associated with the Rouse model.The zeroth Rouse mode refers to a slow translational diffusion of the centre of friction of the whole random-coil molecule, and the first Rouse mode (which was apparently employed by Flory and Yoon) refers to a slow " breathing " motion of the molecule. Neither of these represents the type of motion that is inducedJ . D. HOFFMAN, C. M. GUTTMAN AND E. A . DIMARZIO 187 by pulling on the chain at one point, as does the force associated with cry~tallization.~ (See also remarks by DiMar~io.~') We observe in passing that there exists much evidence that polymer molecules can readily disentangle themselves from the melt during crystallization. One example : certain compatible blends that form true solutions in the molten state produce lamellar spherulites of one of the components on being ~ndercooled.~~*~* In the case of the compatible blend of PVF2 and PMMA studied by Wang and Nishi, the rate of growth of the PVFz spherulites obeys eqn (2.13) with considerable precision, and leads to a reasonable value of the work of chain folding.28 In the light of such evidence, it would seem difficult generally to uphold the view that polymer molecules cannot be separated from one another during crystallization from the melt.Reptation pro- vides a mechanism for the disentanglement that evidently takes place during the crystallization process. DiMarzi0~~3~~ has suggested a treatment where the molecule being reeled onto the surface can undergo lateral as well as reptation-like motions (" sea snake '' model).It is not clear at this juncture whether the lateral motions in this model would suffer from the effects of entanglements. For this reason, we have adhered to the reptation model in the main discussion. Our overall conclusion is that reptation is sufficiently rapid in polyethylene of low and moderate molecular weight to allow the reeling in of a molecule onto the substrate to take place during crystallization from the melt at a rate that is compatible with chain folding. While this in itself does not prove that adjacent re-entry occurs, it is clear that the transport processes that are present are rapid enough to permit a sub- stantial degree of adjacent re-entry. The results that we have obtained above are clearly consistent with the concept that reptation with considerable adjacent re-entry occurs at low and moderate chain lengths and undercoolings in polyethylene.A perturbation of the reptation mechanism resulting from entanglements may be expected at sufficiently high values of n. A change occurs in the nature of the crystal- lization kinetics at n % 7000 and another at n M 60 OO0.8 In the particular case of high undercoolings, reptation is still rapid enough to permit substrate completion with considerable chain folding, but another effect enters that will tend to decrease the amount of adjacent re-entry. Nucleation theory pre- dicts that, at high undercooling, the niches (fig. 2) get quite close together in Regime 11. This will cause an increase in non-adjacent re-entry and in the amorphous com- ponent associated with the lamellar surface.A calculation follows. (iii) NICHE THEORY AND NON-ADJACENT RE-ENTRY LOOPS : ORIGIN OF THE AMORPHOUS COMPONENT It is easily shown for Regime I1 that the number of niches per cm is given by Nk -- (i/g)* = ( 1/ao)(n2)* exp(ql2kT) exp[-22boaae/(Af)kT] (2.33) which for polyethylene becomes Nk = 1.26 X 10" exp[-1.1 X 105/T(AT)] (2.34) for n = 2850 (MW = 40000). It is emphasized that this is the initial value of the separation resulting from the generation of nuclei on the substrate before a considerable number of stems have been added to these nuclei. The quantity l/Nk gives the mean separation between the niches.188 CHAIN FOLDING A plot of Nk and the initial niche separation using eqn (2.34) is given in fig.4. It shows that as the undercooling is increased that the niches get quite close together. At AT = 27.5"C, they are only ~ 2 0 A apart. Considerable non-adjacent re-entry will then occur with the formation of short " loops " because of the proximity of the niches, and the energetically favourable character of the addition of a stem into a niche rather than a nearly flat site. (Addition of a stem in a niche gives a gain in free energy of aobo(S2)(Af), while addition on a flat site entails a net loss of [2b0a2z - aoboZ~(Af)], as shown by eqn (2.1) and (2.5). The latter quantity is always positive, since 2b0a2t is typically many times larger than aobo2g*(Af) because 209 a,(Af) at the undercoolings considered here.) 10 000 I I I I 1 A J= 17. 1 35 30 25 20 AJ/"C w L Y d ul 3 v) n 10 g u! 0 c 0 m Q) 2 0 100 *E + 0 Q) L n 5 1000 = FIG.4.--Initial niche separation and Nk as a function of undercooling for PE (n = 2850). (a) Regime I : AT < 17.5"C; (b) Regime 11: AT > 17.5"C. Polyethylene specimens crystallized from the melt at about this undercooling have been used in neutron scattering studies, the " quench " crystallization technique being used to discourage segregation of the two isotopic species. It will emerge later that these exhibit a mean non-adjacent re-entry throw distance of z22 A, which is com- parable with the niche separation calculated above. The " loops " will make a considerable contribution to the amorphous component. The nature of this effect is shown in fig. 5(A). By making rough estimates of the number of segments in a loop whose ends are 20 A apart, it is a simple matter to estimate that a 1525% amorphous component will appear in quench-crystallized polyethylene because of this phenomenon; the remainder of the amorphous com- ponent is associated with the few but quite long tie molecules (see later).Observe from eqn (2.33) that the niche separation l/Nk varies as l/&. This leads to the pre- diction that a low molecular-weight sample will have fewer loops and a smaller surface amorphous component than one of high molecular weight crystallized at the sameJ . D. HOFFMAN, C. M. GUTTMAN AND E . A . DIMARZIO 189 AT. (The effect of the niches being close together can cause some non-adjacent re- entry in crystallization from dilute solutions at sufficiently high undercoolings.) A smaller amorphous component resulting from loops and a higher fraction of adjacent re-entry is expected at low undercoolings.However, it should be understood that the actual niche separation at the smaller undercoolings in Regime I1 (where the initial ones are quite far apart) can actually be considerably less than the initial value because of the addition of stems that will naturally take place at the rate g on the substrate. Consequently, the effective niche separation will be less, and non-adjacent re-entry resulting from the " niche " effect, while diminishing, will not catastrophic- ally disappear as AT is lowered in Regime 11. I-' c,-; /loop ,, {/niche /'/ I < . \ I 4 niche separation FIG. 5.--Non-adjacent re-entry loops (schematic).Upper diagram (A) : non-adjacent re-entry caused by low niche separation at high AT. Lower diagram (Bl): forbidden types of loop structures. Short vertical wavy lines show amorphous space-filling emergent stems; solid horizontal lines show excess segments. Lower diagram (B2): allowed type of short loop structure. The treatment outlined above dispels the belief that the existence of an amorphous zone that is associated with the lamellar surface is incompatible with the kinetic theory of chain folding. The best crystals with the lowest amorphous component will be formed at low undercoolings from polymers of low molecular weight. There is an interesting restriction concerning loops that has been analysed by DiMarzio and G~ttman.'~ Non-adjacent re-entry loops must be accompanied by some tight folds.This is illustrated schematically in fig. 5(B) (" wicket " model). Here the vertical wavy lines represent emergent stems. These are " amorphous " and space filling. The horizontal solid lines represent the traverse to a non-adjacent site. The segments represented by the horizontal solid lines in fig. 5(B1) then ac- tually overfill the space, creating a serious density anomaly in the amorphous zone in which p B pa. Such structures are forbidden because of this anomaly. The difficulty can be mitigated by interspersing tight folds between (or adjacent to) the190 CHAIN FOLDING points where the loop emerges from and then re-enters the lamella [fig. 5(B2)]. When the idealized loops are allowed to be more random, even more adjacent folds are required.In practice, one would expect at least one pair of adjacent re-entry stems for every emergent stem involved in a “ loop ”. We do not attempt here any further theoretical discussion of the problem of non- adjacent re-entry. Intervention by a “strange ” molecule in the reeling process creating a non-adjacent re-entry is bound to occur to some extent during crystallization from melt. Rather than speculate on the theory of how this particular process occurs and on the details of what might limit its frequency, it seems more appropriate to go directly to a discussion of the neutron scattering results for polyethylene, which leads to an estimate of the probability of adjacent and non-adjacent re-entry. From this it will emerge that it is likely that non-adjacent re-entry is nowhere near as prevalent as has been heretofore supposed even in quench-crystallized specimens, which treat- ment tends to maximize it.3. NEUTRON SCATTERING ON QUENCH-CRYSTALLIZED PEH + PED The basic challenge in dealing with a model that is used to predict a neutron scat- tering curve lies in simultaneously meeting a number of criteria, some of which are as follows : (1) the observed radius of gyration (or characteristic ratio) from low-angle data should be predicted correctly; (2) the shape and absolute value of the observed scattering function Fn(p) or Q at moderate and high angles should be matched within experimental error; (3) the degree of crystallinity consistent with the model should match the experimental value and (4) the model must not show gross density anoma- lies, i.e., large volume elements with either many extra or missing segments in the crystalline or amorphous zones, and the computed densities of the amorphous and crystalline zones should correspond approximately to the experimental estimates for We shall refer here to the data of Schelten et uL1’ on a specimen where the deuterated species correspond to n = 3750 that was crystallized at AT x 27.5 + 3.5 OC.12 This is well within Regime I1 where the niches are rather close together.Crystallization at this undercooling is very rapid, and fortunately discourages both isotopic segregation and lamellar thickening. Consider now the analysis of these data by Yoon and Flory.12 They treated a number of models, and settled on one denotedp,, = 0.3 as providing the best overall fit of the data.They assumed crystalline lamellae 160 A thick with an intervening disordered zone 90 A thick. This disordered zone contained two “ interfacial ’’ zones, each 10 A thick, in juxtaposition to the crystal lamellae, and a 70 A thick “ amorphous ” zone was interposed between the two interfacial zones. Thus, the two interfacial layers comprised >20% of the disordered zone between the lamellae. In their Monte Carlo simulation, a chain was allowed to emanate from the crystal into the interfacial layer, but an immediate return in a crystallographic adjacent posi- tion was not allowed. When a chain in a random flight reached the boundary be- tween the interfacial and amorphous zone, it was allowed to escape into the amorphous zone with a probability of 0.3 (hence pes = 0.3), and was turned back toward the lamella of origin with a probability of 0.7.Thus, a semi-reflecting boundary was used. The chain was allowed to re-enter the lamella whenever in its random pere- grinations in the interfacial zone it contacted the lamella. The events noted above were allowed to occur without regard for any energetic considerations associated with P a and P C .J . D . HOFFMAN, C . M. GUTTMAN AND E . A . DIMARZIO 191 the attachment of the stem to the substrate. Thus, the placement of the stems in the crystal is determined principally by liquid-state configurations. Yoon and Flory achieved good agreement with the neutron scattering data (fig. 6). Guttman et aZ.18319 have repeated the calculations of Yoon and Flory for the pes = 0.3 model, and generally confirm their fit of the scattering function shown in fig.6 . Guttman et al. also calculated the characteristic ratio C,, and the degree of crystallinity x for this model (table 1) for n = 3500 and their values do not differ greatly from those reported by Yoon and Flory. Thep,, = 0.3 model with n = 3500 gives values of x and C,i that each differ from the experimental value by 3 14%. 1.2 1.0 0.8 0.6 \ 4- 5 0 *4 0.2. 0 I I 0 I 1 1 1 0.04 0.08 0.12 0.16 p = (4 n / ~ ) sin ~2 in A-' FIG. 6.-Neutron scattering function for quench-crystallized PED (AT g 27.5 f 3.5 "C, n z 3750). Solid circles: F&) calculated from data of Schelten et a/." Solid lines: Calculated scattering functions for Yoon-Flory pes = 0.3 model for n = 2500 and Guttman ef a/.core model for various y for n = 3500. (a) y = 28, x = 1 ; (b) y = 8, x = 0.62; (c) y = 3, x = 0.52; ( d ) pes = 0.3, x = 0.57. The inset depicts the mean density profile for (e) y = 8 core model and (f) thep,, = 0.3 model in the interlamellar region. The experimental degree of crystallinity x is 0.65.192 CHAIN FOLDING Also shown in table 1 are some other properties of thep,, = 0.3 model obtained by Guttman et al. It was noted that the density of segments in the " interfacial " zone, which makes up 20% of the disordered zone, was about twice that of the crystal (see inset in fig. 6). This was found for n = 2500 and n = 3500. Thus, this model does not fulfil condition (4) above. This feature is at variance with the statement TABLE 1 .-ANALYSIS OF NEUTRON SCATTERING DATA ON QUENCH-CRYSTALLIZED POLYETHYLENE [DATA FROM REF.(1 7)] property Yoon and Flory Guttman et at. experimental (pes = 0.3 model (central core model, value n = 3500) y = 8, II = 3500) characteristic ratio, C, 8.7 10 tie chains per molecule - 1.0 f 0.2 number of loops per chain average loop size (segments) - average throw distance of loops - x12A average number of adjacent stems per cluster - probability of adjacent re-entry, par - density degree of crystallinity, x 0.65 0.57 -15 78 - 1.3 0" pc = 1.00 g cm-3; p m 2pc in interfacial P a = 0.85 g ~ m - ~ . zone; p < pa in amorphous zone. 9.4 0.62 = 0.8 6 200 x22 A 2.7 0.65b p s p a in entire amorphous zone; p E pc in crystal. ~~ ~~ ~ ~ _ _ _ _ Strictly crystallographic adjacent re-entry is forbidden as an elementary process in this model.If we modify the definition to say that any chain which fell within 7.5 8( of its point of emergence represented an adjacent re-entry, then par E 0.23. * For the core models, par represents the prob- ability that a short adjacent re-entry type fold will occur during the substate completion process. by Yoon and Flory that the material comprising the interlamellar layers has proper- ties, including the density, which closely match those of the bulk amorphous poly- mer." The pes = 0.3 model cannot be regarded as satisfactory even though the neutron scattering curve was accurately reproduced. The high density of segments in the interfacial layer can be traced to an excess density of loops that resembles the situation discussed in connection with fig.5(B1). In dealing with models for the analysis of the same neutron scattering data as were employed by Yoon and Flory, we required with regard to criteria (1)-(3) above that the overall fitf' be minimized according to where W = percentage error in x, X = percentage error in C,, and Y = average percentage error in the fit of the neutron scattering function at high angles. The percentage error was calculated using the experimental values as a base. The average percentage error of the fit of the scattering function at high angles (p = 0.03-0.13) was calculated at intervals of 0.01 p using fi = [(W2 + X 2 + Y2)/'3]' (3.1) 2 3 [Fcak(pi) - Fobs(kl)/Fobs(~d] } (3.2)J . D .HOFFMAN, C . M . GUTTMAN A N D E . A . DIMARZIO 193 Eqn (3.1) provides a systematic basis for selecting a model from a set. After making such a selection, criterion (4) was applied, and the model accepted as plausible if this test was met. Although many models were tried, we discuss here only one type, the " central core " model suggested by in another connection. This has certain interesting features, and the results are generally illustrative. Other models have been discussed elsewhere by Guttman et aZ.18*19 In the core model, the substrate completion process is begun by first putting down y adjacent stems. This was done on reflection of the point that reptation following the initial surface nucleation act would allow some " reeling " with its attendant adjacent re-entry, before an interruption or a " mistake " occurred.This is justified on a trial basis by our earlier demonstration that reptation is a physically tenable concept at the molecular length (n = 3750) under consideration. The central core model is thus generally consistent with the picture of crystallization kinetics given in section 2. After the central core was laid down, random flights of the remaining ends were allowed. Both adjacent and non-adjacent re-entry were permitted. Any short random-flight excursion of 20 -CD,- units or less that re- turned to the same lamella was taken to mean adjacent re-entry with a short fold. This is justified by the increase of stability of aobo(SZ)(Af) gained by crystallizing on an adjacent niche; a non-adjacent re-entry on a nearby flat site would induce a decrease of stability of 2boaZr -aoboZz(Af) when the stem was completed.A random flight that was longer than 20 -CD,- units was allowed to re-enter the lamella of origin (or another one) at the point of contact. When introduced into the Monte Carlo calculations, these restrictions led to a mean throw distance for the non-adjacent loops of w22 A, which is comparable with the mean niche separation derived from nucleation theory for AT w27.5 "C. It is these flights that lead to the correct radius of gyration (or C,) and degree of crystallinity, and which greatly lower the scattering curves at high angles, even though the molecule possesses a high proportion of adja- cent re-entry folds. It is evident from the foregoing that we adhere to the view that the question of adjacent re-entry involves the energetics of crystallization on the substrate as well as the energetics involved in determining proper liquid-state con- figurations.Various values of y were tried for the core model, and it was found that y z 8 gave the best overall fit according to eqn (3.1) as shown in table 2. Note the rapid drop of F,@) at p > 0.03 in fig. 6 as y falls from the case of perfect chain folding ( y = 28) to lower values. Criterion (4) is fully met by any central core model where x is close to the experimental value (see fig. 6). It is seen from table 2 thatp,, z 0.65 for the PED sample studied as analysed with the central core model. The values of C,, x, and the density in the amorphous and crystalline zones for y = 8 are close to being correct (table l), but the fit of the observed neutron scattering curve, while acceptable, is not as good as that given by Yoon and Flory (fig.6). In deeming the fit with y % 8 acceptable, we have taken into account the fact that the theoretical scattering functions with 100 to 160 molecules exhibit a scatter of z 10% at high angles, and have assumed that the experimental scattering functions at high angles are accurate to w 10-15%. The absolute accuracy of the F,(p) data is difficult to estimate from the information in the literature. We have carried out calculations on some rather different models that give a good overall fit according to eqn (3.1) and criterion (4). These give results for par, the num- ber of stems per cluster, the average throw distance for non-adjacent loops and the number of tie molecules per chain that are quite similar to those shown in table 1 for the y = 8 core m 0 d e 1 .l ~ ~ ~ ~ We consider that it is premature to select a final " best " model at this juncture, since certain phenomena, such as the fold surface roughness194 CHAIN FOLDING that is predicted by nucleation theory,6 and PED concentration effects, have not been included. Meanwhile, it is possible that the accuracy of the F,@) data needs further consideration. Nevertheless, the studies cited provide strong support for the view that adjacent re-entry was by a considerable margin the most probable event that occurred at the surface during the substrate completion act during formation of the PED specimen investigated.Considering all the models tested, the value par x 0.65 may be taken as a reasonable and even conservative estimate of the probability of adjacent re-entry for the system considered. The '' central core " model and " vari- able cluster " model of Guttman et al. are particularly attractive. TABLE 2. PROPERTIES OF CENTRAL CORE MODEL CALCULATED FOR VARIOUS y VALUES (n = 3500) fit of scattering X C" curve overall fit, Y ( X expt. = 0.65) (Cn expt. = 8.7) p = from 0.03 to 0.13" fib.c P a r r- m 7- value W = error (%) value 3 0.52 (25) 11.9 4 0.54 (20) 12.0 6 0.56 (16) 12.0 7 0.60 (8.3) 9.6 8 0.62 (4.8) 9.4 9 0.64 (1 .a 9.8 11 0.66 (1.6) 9.1 error (%) 0.51 (27) 25) 0.58 (26) 0.60 (14.2) 0.68 (13.3) 0.65 (17.2) 0.71 (19.9) 0.78 Calculated in intervals of 0.01 in ,u according to eqn (3.2).Calculated using eqn (3.1). The pes = 0.3 model with rt = 3500 gives an overall fit of 13% when treated in a manner entirely analogous to the core models ( W = 14%, X = 14%, Y = 11%). Some additional points emerge from considerations based on the neutron scatter- ing analysis. The first-and perhaps most surprising-point is that the PED specimen evidently had less than one tie chain between the lamellae per molecule (table 1). It is clear that the number of tie chains for n % 3750 is far less than has been implied in some pictorial representations.ll Our Monte Carlo simulations indicate that, while small in number, the tie chains are long and space-filling random coils that contribute substantially to the amorphous component.This finding may be of importance in dealing with criticisms l1 that concern the behaviour of lamellar systems under deform- ation. A sketch of two typical trajectories for the y = 8 core model and the pes = 0.3 model are shown in fig. 7. It should be recalled that these depictions refer to quench- crystallized material. Even so, it is difficult to understand how a distinctly lamellar entity could form with the randomness demanded by pes = 0.3. The larger number of adjacent re-entry folds in the y = 8 core model and other models with a similar par would appear to be more consonant with the decidedly lamellar habit exhibited by polyethylene in the molecular weight range considered here. It is to be anticipated from the developments noted in this work that a higher degree of adjacent re-entry should appear in polyethylene of n % 2000-4000 if lower undercoolings than AT x 27.5 "C could be employed in preparing the PEH + PED specimens for neutron scattering experiments. This has been impossible up to the present time as a result of isotope segregation effects.Were this problem somehow circumvented, a difficulty would still remain: the isothermal thickening that is knownJ . D . HOFFMAN, C. M . GUTTMAN AND E . A . DIMARZIO 195 to occur to some extent in Regime I1 near ATt and to a much greater extent in Regime I would modify the fold morphology that was originally put down. As a conse- quence, neutron scattering for PED specimens formed at the lower undercoolings is apt to reveal more about annealing mechanisms than it does about the initial struc- tures that were produced. J t is to be expected that changes in the radius of gyration resulting from penetration by cilia or folds from one lamella into adjacent ones will be amorphous zone semi- reflecting boundary interfacial zone (IoA) A FIG.7.--Schematic representation of y = 8 core model (upper) and pes = 0.3 model (lower) for quench-crystallized polyethylene (n = 3500). Two typical molecules are shown in each case. The core model has somewhat less than one tie between the lamellae per polymer molecule. The number of ties is N” one per molecule for the pes = 0.3 model. The stems have been drawn z 10 times further apart than in the actual crystal. found early in the annealing process ; such effects probably represent the first stages of thickening.The fact that par z 0.65 for quench-crystallized PED allows one to surmise that simple reptation with adjacent re-entry was involved in about two-thirds of the stems that were added to the crystal. This is consistent with our earlier finding that crystal- lization at lower undercoolings in polyethylene fractions of similar n, involved repta- tion in the substrate completion mechanism. The reeling process is not perfect, and interruptions and ‘‘ mistakes ” occur, but our proposed mechanism seems more plausible for the molecular weights considered than models which hold that the lamellae are formed in a virtually transportless collapse of the liquid state with no196 CHAIN FOLDING significant adjacent re-entry. The kinetic nucleation theory of chain folding un- doubtedly needs extension and improvement especially with regard to the details of the interruptions which give rise to the amorphous component, but any proposal to abandon it requires careful examination. 4.APPENDIX The rate constants noted in the text and fig. 1 are B = P g exp - aobo@f )/kTI (4.4) where q = 2aoboa,, and pP, which varies as l/n because of reptation, is given by eqn (2.8). As required, the ratios Ao/B, and A/B obey the principle of detailed balance. Eqn (4.3) and (4.4) are given for the case ‘y, = 0, i.e., where the activation barrier in the forward reaction A for substrate completion is the work of chain folding q, and where the activation barrier for the backward reaction B is the work of converting the stem to the liquid state.We consider this a reasonable first-approximation apportion- ment for the substrate processes. The apportionment ly0 = 0 for the first step has the advantage of making B, = B with the result that the barrier to stripping off the first stem is then physically similar to stripping off one of the later stems. The nucleation rate i is calculated as where Zn = No and the mean value theorem is used to deal with 2. thickness is found using The initial lamellar With the approximations noted here and el~ewhere,~ and recalling that Pi = npg, eqn (2.2) and (2.3) are readily derived. J. I. Lauritzen Jr and J. D. Hoffman, J. Res. Nat. Bur. Stand., 1960, 64A, 73. F. P. Price, J. Polymer Sci., 1960, 42, 49. F. C. Frank and M. Tosi, Proc. Roy. Soc. A, 1961, 263, 323. J. D. Hoffman and J. J. Weeks, J. Chem. Phys., 1962,37, 1723. J. D. Hoffman, S.P.E. Trans., 1964, 4, 315. J. I. Lauritzen’ Jr and E. Passaglia, J. Res. Nat. Bur. Stand., 1967,71A, 261. J. D. Hoffman, L. J. Frolen, G . S. Ross and J. I. Lauritzen Jr, J. Res. Nat. Bur. Stand., 1975, 79A, 671. J. D. Hoffman, G. T. Davis and J. I. Lauritzen Jr, in Treatise on Solid State Chemistry, ed. N . B. Hannay (Plenum Press, New York, 1976), vol. 3, chap. 7. lo I. C. Sanchez and E. A. DiMarzio, Macromolecules, 1971, 4, 677. P. J. Flory and D. Y. Yoon, Nature, 1978, 272, 226. l2 D. Y. Yoon and P. J. Flory, Polymer, 1977, 18, 509. l3 R. L. Miller, Status of the Analysis of Crystallization Kinetic Data, in Flow-Induced Crystalliza- ’ J. I. Lauritzen Jr and J. D. Hoffman, J. Appl. Phys., 1973, 44, 4340. tion (Gordon and Breach, N.Y., 1979).J . D . HOFFMAN, C . M. GUTTMAN A N D E . A . DIMARZIO 197 l4 R. L. Miller and R. F. Boyer, J. Polymer Sci., Polymer Phys. Ed., 1978, 16, 371. l5 P. G. de Gennes, J. Chem. Phys., 1971, 55, 572. l6 P. G. de Gennes, Macromolecules, 1976, 9, 591. l7 J. Schelten, D. G. H. Ballard, G. D. Wignall, G. Longman and W. Schmatz, Polymer, 1976, 17, 751. C. M. Guttman, J. D. Hoffman and E. A. DiMarzio, Faruduy Disc. Chem. Soc., 1979,68,297. l9 C. M. Guttman, J. D. Hoffman and E. A. DiMarzio, manuscript in preparation. ’O J. Klein and B. J. Briscoe, Proc. Roy. Soc. A , 1979, 365, 53. 21 J. I. Lauritzen Jr, J . Appl. Phys., 1973, 44, 4353. ’’ H. D. Keith and F. J. Padden, Jr, J . Appl. Phys., 1964, 35, 1270. 23 F. C. Frank, J . Crystal Growth, 1974, 22, 233. 24 T. Suzuki and A. Kovacs, Polymer, 1970, 1, 82. 2s E. A. DiMarzio, C . M. Guttman and J. D. Hoffman, Faraduy Disc. Chem. Soc., 1979, 68,210. 26 E. A. DiMarzio, C. M. Guttman and J. D. Hoffman, manuscript in preparation. 27 W. J. MacKnight, F. E. Karasz and J. R. Fried, Polymer Blends, ed. D. R. Paul and S. Newman 28 T. T. Wang and T. Nishi, Macromolecules, 1977, 10, 42 1 . 29 E. A. DiMarzio and C . M. Guttman, Polymer, 1980, in press. 30 R. J. Roe, J. Chem. Phys., 1973, 53, 3026. (Academic Press, N.Y., 1976), vol. 1, chap. 5.

ISSN:0301-7249    

DOI:10.1039/DC9796800177

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

Kinetic and Topological Limits on Melt Cry stallisation in Polyethylene BY JACOB KLEIN Polymer Department, Weizmann Institute of Science, Rehovot, Israel AND ROBIN BALL The Cavendish Laboratory, Cambridge Receiued 10th May, 1979 The rates at which molecular sequences may deposit onto growing lamellae in a crystallising polyethylene melt are examined on the basis of the results of recent self-diffusion experiments in such melts, in conjunction with theories of molecular dynamics in polymer melts based on the reptation picture. The results are compared with rates of sequence deposition in polyethylene melts as esti- mated from experimentally measured growth rates. This comparison indicates that, purely from a kinetic point of view, some regular folding of molecular trajectories at lamellar surfaces is not in- compatible with experiment.The organisation of polymer molecules from the melt into the lamellar morphology associated with semi-crystalline polymers generally takes place under conditions which are far from true thermodynamic equilibrium ; in consequence, such organisation is to a large extent controlled by kinetic and topological factors."-' In order to evaluate the limits thus set on patterns of molecular ordering during crystallisation, it is neces- sary to know both the mobility of the polymer molecules and the constraints imposed on their motion by entanglements. Recent measurements 2-4 of self-diffusion in linear polyethylene melts have provided direct information on the molecular mobility in such melts; within the range of experimental parameters de~cribed,~ the results also strongly support de Gennes' suggestion5 that the effect of topological constraints on polymer molecules in such systems is to cause the longest molecular relaxations, in particular the translational self-diffusion, to proceed by reptation, or snake-li ke motion. We use this informa- tion, in conjunction with theoretical models of molecular dynamics in entangled polymer systems which are based on the reptation concept, to estimate the limiting rates at which molecular sequences may deposit onto growing lamellae.Our results are examined in the light of experimental data on lamellar growth rates in crystallising polyethylene; in addition, we discuss (purely from a kinetic point of view) whether regular adjacent-re-entry folding of molecular trajectories in the lamel- lae is feasible under normal circumstances.MOLECULAR DYNAMICS I N POLYETHYLENE MELTS The diffusion coefficients D of five deuterated polyethylene fractions (3600 < &fw < 23 000) diffusing in a high molecular weight protonated polyethylene melt (&fw N 1.6 x lo5, MW/i@" 21 15) at 176 "C have been previously mea~ured.~'~ The results, corrected for diffusant polydispersity and isotope effect, show that, for a diffusant molecular weight M D = 0.26 x M-2*0f0*1 cm2 s-l. (1)J . KLEIN AND R. C . BALL 199 The activation energy Q,, for such self-diffusion is independent of A4 and measured3 as: More recently D for two deuterated polyethylene fractions (a, = 3600, 23 000) diffusing in several protonated polyethylene melts of different molecular weights Mm(104 < M , 2< 1.6 x lo5) and polydispersities has been mea~ured.~ The results show D for these fractions to be independent of Mm [and to be equal to its value in Within the range of experimental parameters described, these results strongly support2 De Gennes' proposal that the long range molecular relaxations (in particular the translational self-diffusion) in entangled polymer melts are constrained to take place by curvilinear motion, or reptation.In his original treatment' De Gennes considered the motion of a single flexible chain within a " tube " defined by $xed obstacles within which the chain was moving: motion along the " tube " took place by random back-and-forth propagation of length " defects ", leading to overall trans- lation within the " tube ".The constraints about a given polymer molecule in a melt due to its neighbours may also be viewed in terms of a " mean-field tube " picture6 (originally proposed by Edwards). Very recently Doi and Edwards (DE) have presented a molecular theory for dynamics of a polymer melt based on this mean-field tube picture; our subsequent discussion will be largely based on these two appr~aches.~* The essential features of our model (following DE) ' are schematically illustrated in fig. l(a). A given molecule with N freely-linked monomers, each of size b, is con- Q, = 7.0 & 0.4 kcal mol-l. (2) eqn (1)1* (a 1 (b) FIG. 1 .-(a) A molecule in a melt may be considered as enclosed by a " tube ", indicated as a broken line.The " tube " radius a indicates the extent of lateral freedom of motion (normal to the " tube " axis) which the chain has, while carrying neighbouring chain segments along with it (black dots represent, schematically, instantaneous sections through neighbouring segments). (b) Curvilinear motion within a " tube " takes place via random motion of chain segments, which result in an effective back and forth propagation of " stored length " or " slack " [see also ref. ( 5 ) ] . fined laterally within a series of contiguous " cages " of dimension a, which form a " tube " of length L and diameter a. Curvilinear motion, i.e., reptation, along the tube is permitted. The tube represents (in a mean field sense) the effect of the topological constraints about the molecule due to neighbouring molecules : it is appropriate in the present context to examine briefly the nature of the tube constraint.Even in a very closely packed system such as a polymer melt one expects the poly- mer chains to have a certain degree of freedom normal to their contour direction. For small lateral movement of a given chain, other chains would respond by a local rearrangement of their position, without the need for disentanglements to take place : i.e., they would respond as a normal viscous l i q ~ i d . ~ This is suggested by various experimental observations and is also necessary, for instance, for the propagation of length-transporting defects which result in the net curvilinear motion along the200 KINETIC AND TOPOLOGICAL LIMITS ON MELT CRYSTALLISATION tube.5 The tube diameter a then represents the extent of freedom a chain has in moving laterally (in a direction perpendicular to its axis) while dragging other chains along, without di~entangling.~ a is an average measure of lateral chain freedom and not the instantaneous segment-to-segment separation, which in a poly- mer melt must be of the order of a monomer size [fig.l(a)]. A more detailed dis- cussion is given in ref. (7). Our model for the propagation of a free chain within a tube is illustrated in fig. 1(b). Following de Gennes’ we consider propagation to take place by random back and forth motion of stored-length “defects” along the chain. We postulate p defects per unit tube length and a stored length v associated with each. The total stored length per unit tube length C is then: or, at eq~ilibrium,~ c = pv co = Po v (there will be a distribution of v values, but, as pointed out by de Genne~,~ inclusion of this leads to no significant change in the results of the reptation model).Since the defect motion essentially takes place as a result of lateral motion of chain segments within the tube, the total stored length CoL of chain defects in the tube may be identi- fied with the “ slack ” of chain within the tube. We may estimate this slack as follows: the end-to-end vectors of the “ tube ” and the enclosed chain are identical and denoted by R. Regarding the “ tube ” as (L/a) freely connected segments each of size a,7 we have: (L/a)a2 = Nb2 = (R2). Co L = (Nb - L) (4) (5) Now the slack of chain in such a tube, Co L, is given by: which is the actual stretched chain length less the tube length.from eqn (4) gives Substituting for L c o = (; - 1). (6) Putting A as the defect diffusion coefficient, it may readily be shown [see, for example, also ref. (5)] that (7) ACo v D, = - L where D, is the curvilinear diffusion coefficient of the chain along the tube. A will be characteristic of local jump processes and independent of chain lengthq5 We may also relate D, to the translational diffusion coefficient D [as given, e.g., by eqn ( 1 ) for polyethylene]. If the renewal time for a chain (the time it takes to reptate along a tube length) is z ~ ~ ~ , then 6Dqep = (R2) = La (8) from eqn (4), the mean square centre of mass displacement being (R2), Also giving from eqn (4).2DC2,,, = L2, D, = 3D(L/a) = 3 D((R2)/a2)J . KLEIN AND R. C . BALL 201 Graessley has very recently8 calculated some of the phenomenological consequences of the Doi-Edwards t h e ~ r y . ~ On the basis of their theory (and mechanical data) he estimates a N 30 A in a polythylene melt; he also finds that, for a polyethylene melt of molecular weight A4 at 176 "C, the theory predicts D = 0.34 M'2 (1 1) in remarkable agreement with the experimental result in eqn (1). Both the de Gennes and the Doi-Edwards models assume motion within a tube whose configuration is essentially fixed. However, since the tube is defined by the locus of intersections of a given molecule with its mobile neighbours (as in fig. 2) it will also renew its configuration with time. Thus, in fig.2, a real change in tube 0 FIG. 2.-" Mean-field tube " about the molecule C [as in fig. l(a)] will undergo a real topological change whenever an adjacent constraining molecule, as Cl-C4 diffuses past so that one of its ends crosses the tube position. This process leads to a renewal of tube configuration, but in a free melt is very slow relative to the curvilinear motion of C within the tube. topology (as opposed to local fluctuations of size w a about a mean position) will take place whenever an end of one of the constraining chains (as C1-C4) reptates past the tube p o s i t i ~ n . ~ ? ~ The overall motion of a molecule (as C ) has been considered in terms of reptation within a tube which is itself renewing its configuration:6*9 it has been shown6 that in entangled polymer systems the characteristic time for con- figurational rearrangement of a tube as a result of the diffusing away of neighbouring molecules is given by Thus for high N, rtube % z,,, and molecules move within essentially fixed surroundings.In this way, a self-consistent picture of reptative motion is possible. LAMELLAR GROWTH I N POLYETHYLENE MELTS The details of lamellar morphology in semi-crystalline polymers crystallised from the melt have been extensively studied.l0-l2 The lamellae are ordered, ribbon-like regions of thickness I x 100-400 A and width of several pm. Their lengths may be up to many tens of pm. The orientation of the polymer chains within the lamellae202 KINETIC AND TOPOLOGICAL LIMITS ON MELT CRYSTALLISATION is parallel to the thin dimension: the lamellae thus consist of ordered arrays of straight molecular sequences, each sequence being of length 1.The lamellae are stacked with respect to each other, the interlamellar regions consisting of disordered polymer ; they (the lamellae) may comprise 60 % or more of the polymer bulk and are often part of a superlamellar, spherulitic structure. In this section we estimate the rates at which molecular segments may incorporate onto growing lamellae in a crystallising melt and the limits set on these rates by the entangled nature of the polymers. Our calculations are based on the model outlined in the previous section. A growing lamella in a polymer melt is depicted schematically in fig. 3. This Ow FIG. 3.-Scherna$ic illustraiion of part of a growing lamella in a polymer melt, about to encounter an otherwise unattached molecule (drawn in isolation for the sake of clarity).Molecular sequences deposit parallel to the thin lamellar dimension, as indicated (for two of the sequences at the growing surface) by thicker zig-zagged lines. Details of exit from, or entry of the molecular trajectories into the lamella are omitted. G and g represent lamellar and sequence growth rates. Lamella and molecule dimensions are approximately to scale for a polyethylene melt of M N lo5. shows a lamellar growth surface approaching a molecule, which for the present we assume is unattached to any other lamella; i.e., it is about to deposit its first sequence on the approaching lamellar surface. G and g represent lamellar growth and sequence deposition rates as indicated.Although, for clarity, other melt molecules have been omitted from fig. 3, they are of course present and constrain the motion of the chain of interest. Once a segment of the chain has begun to deposit as a straight sequence, its subsequent motion must take such constraints into account. In terms of our model, this may be done as follows : (a) short range rearrangements, (on the scale of a) which do not involve disntanglements, (b) motion within a tube, as indicated schematically in fig. 4, (c) topological rearrangement of the tube itself as briefly indicated at the end of the section on molecular dynamics (fig. 2). A. SEQUENCE DEPOSITION BY SHORT-RANGE REARRANGEMENTS This involves the short-range lateral motion which segments may undergo before they are constrained by the -tube.The length of molecule implicated is that corres- ponding to a region of size a. Using Graessley's estimate* (based on DE7) of a 21 30 A, the segment of polyethylene (PE) implicated contains 50-100 monomer (-CH,-) Thus, the length of PE molecule involved in this deposition stepJ . KLEIN A N D R . C. BALL 203 is typically of the order of one sequence length or less. The characteristic relaxation time 2, of a PE segment with this number of units (50-100) may be estimated from data on linear molecules, with a (CH,),-like structure, diffusing in a polymer melt.3 The translational diffusion coefficient D' of such a molecule in a polyethylene melt at 120 "C is giving for PE segment with 50-100 (-CH2-) units.The actual time for deposition of such a segment may be shorter, as a result of the crystallisation process (i.e., the short range co-operative effects in the immediate vicinity of the lamellar surface). No disentangling (in the r e p t a t i ~ n ~ - ~ or " tube-renewal " 6 sense) takes place in this short range rearrangement. One expects, rather, that over the dimensions in- volved (50-100 A) deposition of a sequence may take place by the " pushing " of adjacent segments (with which the depositing sequence is entangled) away from the deposition site in the direction of the disordered, interlamellar region (in a manner reminiscent of zone-refining of impurities in conventional crystals), The overall topological relationships between the depositing molecule and its neighbours remain essentially unchanged.D' 2i 5 x cm2 s-' z, z 10-6-10-7 s (1 3) B. SEQUENCE DEPOSITION via MOTION WITHIN A TUBE (FIG. 4) We consider sequence deposition from an otherwise unattached molecule. Once initial deposition (as described above) takes place, each of the tails Ni(i = 1,2, fig. 4) (a) (6) FIG. 4.-Schematically illustrating how free " tails " of a depositing molecule may be reeled-in along their tubes to deposit a straight sequence about a crystallisation site. Further reeling-in may result in deposition of adjacent (hence regularly folded) sequences belonging to the same molecule.204 KINETIC AND TOPOLOGICAL LIMITS ON MELT CRYSTALLISATION may be “ reeled-in ” by the crystallisation process. We express this in terms of a “ sink ”, at the crystallisation site, for the length transporting defects.Fig. 5 indicates schematically the subsequent motion. lamella surface V 0 X FIG. 5.-(a) A free “ tail ” about to start deposition at the lamella surface (top), indicating schemati- cally the uniform “ slack ” along the tail. The lower part of the figure shows the distribution of Cat t = 0. The “ sink ” (deposition site) is at x = 0. (b) At time t < r d later, indicating schemati- cally the changes in “ slack ” and in C. (c) At t + rd. Steady state has been reached and defects propagate down the “ slack-gradient ” C0/(L’/2). If F is the flux of chain length along the tube due to motion of stored-length de- fects, we have aF- aP -vat ax ax at - _ or, from eqn (3), (14) aF aC - = - - where x is the curvilinear tube axis co-ordinate, C as before being the stored-length/ unit length of chain within the tube.Also giving a2 C at (where A is assumed constant). To solve for the motion where there is a sink at x = 0, for a tube occupying the region 0 < x < L, we solve the more general case of a free chain simultaneously starting to crystallise at its two ends. We make the following assumptions, which give us our boundary conditions : (i) immediately prior to deposition (at t = 0) the chain is in equilibrium, i.e., C(X, 0) = co, 0 < x < L. C(0, t ) = C(L, t ) = 0. (ii) The “ defect sinks ” at = 0, L are “ perfect ”, i.e.,J . KLEIN AND R . C . BALL 205 The solution of eqn ( obtains C(X, t ) 6 ) subject to (i) and (ii) above is given in the appendix.One The solution eqn (17) is for the case of a molecule being reeled-in at both ends simultaneously, as for the case of simultaneous deposition in two lamellae widely separated along the molecular trajectory. However, for t 2( zd, where we find ix., the effects of reeling-in a t one of the chain ends have little sensible effect on the stored-length concentration at the chain centre and hence on the motion at the other end. Thus, for t < zd the solution eqn (17) holds also for a free tail initially in the tube 0 < x < L/2 or L/2 < x < L. If we make the assumption that at a free chain end the value of C attains the equilibrium value Co very rapidly (over a time t < 7,) then for a free tail, i.e., one crystallising at one end only, as in fig.5 , we attain a steady flow condition for t $ z d , with C varying linearly as in fig. 5(c). We term the crystallisation at times t 6 zd the transient regime [fig. 5(b)] and at t We now evaluate the rate of chain deposition at the lamella surface (x = 0), S, where c(L/2, t ) 21 CO 7 t < z d [fig. 5(b)i zd the steady state regime [fig. 5(c)]. from eqn (15). (a) TRANSIENT REGIME, t < zd. Eqn (17) holds, giving from eqn (17) and (18). limit For t < zd we approximate eqn (20) by the continuous Because of our assumption of a " perfect " defect-sink we have 3 = 00 at t = 0. We should not, however, use this solution for t ,< z, [eqn (13)] since in our picture the initial deposition event takes place as in section A above, over a time z,. This, the initial rate of sequence deposition Si = St=,,, is given by206 KINETIC AND TOPOLOGICAL LIMITS ON MELT CRYSTALLISATION [we shall later see that for cases of interest z, < z d , justifying the approximation (21)].Eqn (22) may also be understood by reference to fig. 5(b). Over a time t the " slack- depleted " front (C < C,) has moved to x N (At)* [as indicated in fig. 5(b)] corres- ponding to a chain slack z&Cox z Co(At)+ being reeled-in at the lamella surface. The mean rate of deposition is then approximately - 1' = co (+) ', as in eqn (22). The results for this regime also hold for a chain simultaneously crystallising at both ends (for t < rd), as in the case of a molecule simultaneously depositing in more than one lamella (for deposition sites not too close together, i.e., L % a).t (b) STEADY STATE REGIME (FREE TAIL), t 9 z, In this case [see fig. 5(c)] we have where the prime indicates that the original free tail tube (L/2) which we had at the beginning of the transient regime may be shorter due to the crystallisation process reeling-in the chain. By the same token Si in this regime will increase as L' decreases. c. SEQUENCE DEPOSITION BY LARGE-SCALE TUBE- REARRANGEMENT^ As indicated in eqn (12) the characteristic time for such " tube " renewal (for high N ) is much longer than zre,,, the reptative renewal time, and thus very much longer than zd (the respective chain length dependences being N5, N3 and N 2 [ref. ( 5 ) , (6)]). It turns out that the rearrangement of even small portions of the " tube " (of the order of a sequence length I ) is a relatively slow process, which requires times that are many orders of magnitude longer than the experimentally measured times for sequence deposition.In the present paper, therefore, we shall no longer consider this mode as contributing to processes of interest and assume that " tubes " are essentially fixed (within a) over the relevant time scales. COMPARISON WITH EXPERIMENT The most comprehensive results on lamellar growth rates G (fig. 2) in polyethylene are those of Hoffman et Following ref, (1) we consider their data14 for a poly- ethylene melt of M N lo5 crystallising isothermally at 120 "C (or some 25 "C below the melting point). In this case G z 1 pm s-l and I 2: 200 A. The rate of sequence deposition g in these circumstances, as estimatedl from the results of Hoffman et for multiple nucleation g r o ~ t h ' ~ (regime 11), is equivalent to 50-500 pm s-l, or 105-106 consecutive se-quences per second.This gives, for the experimental sequence de- position rate Sex,, Sex,, z 0.1 - 1 cm s-I (25) and the time per sequence rexp z 10-5-10-6 s. To this order of accuracy we make the following identifications: (i) Following the calculations by Graessley,8 we take a 2: 30 A in molten PE. (ii) We assume an effective mean " stored-length defect " size to be of the order of the tube diameter a (this assumption is not critical), giving a stored length Y per defect v N Coa. TheJ . KLEIN A N D R . C . BALL 207 effective " free-link " length for a PE molecule is b 21 15 A giving [from eqn (6)] C, N 1 and hence v N 30 A.The root mean square end-to-end distance for PE of M N lo5 is (A2)* N 340 A. For PE melt of M 2: lo5, at 120 "C, we have from eqn (1) and (2), D N 1 x lo-'' cm2 s-l, so that from eqn (4), (7) and (10) we obtain A N 5 x cm2 s-l [we have an independent check on this value from the results of ref. (3), where the measured value of the diffusion coefficient of a linear molecule of size corresponding to the " propagating defect '' size, i.e., x 50 (-CH,-) units, diffusing in a PE melt at 120 "C is closely similar to that estimated for A above]. From above and eqn (1 8) and (4) we have rd N 2 x s so that z, < z d as stated earlier. We may now evaluate the initial sequence deposi- tion rate from eqn (23) Si x 0.1 - 1 cm s-l .This initial rate is comparable with that estimated from experiment [eqn (25)]. The implication of this is that the deposition of consecutive sequences at a growing lamellar surface by a single crystallising molecule, an essential condition for adjacent- re-entry regular folding of the sequences, may be possible on purely kinetic grounds. It is necessary, however, to examine this in greater detail. The length of molecule S which may be deposited in a time z is given by from eqn (22). With reference to fig. 4, suppose that an otherwise unattached PE molecule (M N lo5) in the melt at 120 "C starts to deposit at its centre (N, = Nz). Then in the transient regime (for either of the free tails Ni) we may apply eqn (26). Putting, for either tail, z x rd z S z 800 A s, we have the deposited length from eqn (26).This is equivalent to deposition of some 4 sequences in s, which is a little lower than the deposition rate estimated from experirnent.'~~~ Note that the " slack " associated with such a tail (curvilinear tail length w 5000 A; slack within the " tube ", around 3000 A) is easily sufficient to account for the length of molecule deposited. At time t zd the rate of deposition Si is determined by the steady-state motion, eqn (24), and is independent oft. For a free tail (in this regime) of M N lo4, we find [from eqn (24)] S x 0.1 cm s-l, which is comparable with the value estimated from experiment [eqn (25)]. We note that some five consecutive sequences would be involved in the crystallisation of such a tail. DISCUSSION AND CONCLUSIONS The dynamics of polymer molecules crystallising from a melt have been considered in terms of a model based on the lateral confinement of molecules within tubes; the motion normal to the tube axis is confined within an effective tube diameter and motion along the tube proceeds via propagation of defects.In evaluating the208 KINETIC AND TOPOLOGICAL LIMITS O N MELT CRYSTALLISATION deposition rate of crystallising molecules we have assumed a perfect " defect-sink " at the site of crystallisation: this assumption is probably not too bad, since after an initial deposition event (over a time z,) involving many tens of monomer units, the likelihood of " desorption " of the chain decreases very strongly (as indicated, for example, by the tenacious nature of polymer adsorption at surfaces).An important parameter in our treatment is the tube diameter a. This has not yet been calculated7 from first principles;* the crucial idea, however, is that of some lateral freedom of a chain (with unlimited curvilinear freedom for a free chain) over and above the instantaneous segment-segment separation. This leads to the concept of slack within a tube, which is capable of being reeled in as segments of a molecule straighten out to form sequences in the lamellae. (It is interesting that the amount of slack of a polyethylene molecule in the melt, of the order of a half of the stretched molecular length, is comparable with the degree of crystallinity in the melt-crystallised polymer). In any case, Graessley's estimate' of a on the basis of DE7 is acceptable, to the order of accuracy of our present discussion.Comparison of our results with experimental data for a particular case1J4 (iso- thermal crystallisation of a PE melt, undercooling ~ 2 5 "C, M 21 lo5) indicates the following : (i) The time z, associated with short range rearrangement of molecular segments (for a molecule commencing deposition at a crystallisation site) within the range of lateral freedom a, is short enough to be consistent with the experimental data. The segmental length associated with this short range mode is of the order of one sequence length I and so cannot involve the crystallisation of more than about one sequence: this mode is then consistent with the random re-entry picture' of molecular trajec- tories within a lamella.(ii) Subsequent deposition, t > z,, if it is to involve the same molecule at the same deposition site, takes place in two stages: (a) A so-called transient regime, t 2< zd where " slack " is taken up (fig. 5b) but molecular segments distant from the deposi- tion site are unaffected. The rate of deposition Si in this regime is comparable with the values estimated from experiment Sexp and not dependent on melt molecular weight. For the case of a PE melt considered this regime may involve consecutive deposition of a small number (< 5) of adjacent sequences. (b) A steady state regime, applying only to free " tails ", at t $- zd. The rate of deposition depends here on the length of free " tail ". For a " tail '' length equivalent to up to x 10 sequences, the time for deposition of the entire tail, in consecutive, regularly folded adjacent se- quences, is comparable with that estimated from experiment.We have limited our discussion to a consideration of the rates of crystallisation of molecules in a PE melt ; these rates are limited by the entanglements between molecules (represented by a " tube " constraint) and their consequently reduced freedom of motion. Although we have compared our results with experiment for a particular case, the important features of our findings are relatively independent of melt molecu- lar weight or even degree of supercooling (for supercoolings of order 25 "C or less). This is because of the moderate dependence of g (sequence deposition rate) on the degree of super~ooling~~ and the small temperature dependence of the molecular m~bilities.~ We, therefore, expect our conclusions to have relevance beyond the particular use considered.In the context of the current discussionlupb concerning the configuration of molecu- 1 ar trajectories within lamellae in semi-crystalline polymers, the present analysis indi- cates that some regular folding of consecutive sequences in a lamella by deposition tanglement couplings ", as in the earlier theories of entangled polymers. * In the Doi-Edwards model, for example, a is related to the critical length M, between " en-J . KLEIN AND R. C . BALL 209 from a given molecule in a PE melt is not incompatible with the available data14 on rates of lamellar growth in such a melt. We are grateful to Professors A. Brandt and A. Silberberg for fruitful discussions and to Dr. P. Castle for his help during the preparation of the manuscript. APPENDIX We wish to solve subject to Let -- aC-*- a2c at ax2 C(x, 0) = c, C(0, t ) = C(L, t ) = 0. Then, from eqn (Al) and (A2a) C(X, 0) = 2 a, n odd ~ ( x , t ) = 2 a, sin n odd Multiply both sides of eqn (A3) by sin (".") - and integrate, giving Po sin r9) dx = [a, cos2 PF) dx 4G a, = - mn which on substitution in eqn (A4) yields eqn (17). (a) P. J. Flory and D. Y. Yoon, Nature, 1978,272,226; (b) P. Calvert, Nature, 1976, 263,371 ; (c) D. Aitken, M. Glotin, P. J. Hendra, H. Jobic and E. Marsden, J. Polymer Sci., Polymer Letters, 1975, 14, 6A. J. Klein, Nature, 1978, 271, 143. J. Klein and B. J. Briscoe, Proc. Roy. SOC. A , 1979,365, 53. J. Klein, to be published. P. G. De Gennes, J. Chem. Phys., 1971,55, 572. J. Klein, Macromolecules, 1978, 11, 852. ' M. Doi and S. F. Edwards, J.C.S. Faraday 11, 1978,74, 1789, 1802, 1818. * W. W. Graessley, J. Polymer Sci., Polymer Phys. Ed., in press. P. G. de Gennes, Macromolecules, 1976, 9, 587. lo L. Mandelkern, Crystallization of Polymers (McGraw-Hill, New York, 1964). l1 P. H. Geil, Polymer SingZe Crystah (Interscience Publishers, New York, 1963) l3 P. J. Flory, Statistical Mechanics of Chain Molecules (Interscience Publishers, New York, B. Wunderlich, Macromolecular Physics (Academic Press, New York, 1973), vol. I. 1 969). l4 J. Di Hoffmann, L. J. Frolen, G. S. Ross and J. I. Lauritzen, J. Res. Nut. Bur. Stand., 1975, 79A, 671. l5 J. 1.-Lauritzen, J. Appl. Phys., 1973, 44, 4363

ISSN:0301-7249    

DOI:10.1039/DC9796800198

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

Is Crystallization from the Melt Controlled by Melt Viscosity and Entanglement Effects ? BY EDMUND A. DIMARZIO, CHARLES M. GUTTMAN AND JOHN D. HOFFMAN National Measurement Laboratory, National Bureau of Standards, Washington, D.C. 20234, U.S.A. Received 9th July, 1979 An estimate is made of the time required to reel in a polymer molecule from the melt onto the growing crystal surface. Two models, one a reptation model involving transport within a worm-hole (tube-flow), one a more conventional model, both yield reeling-in times which are orders of magnitude faster than a recent estimate by Flory and Yoon. These times are shown to be consistent with crystal growth rate data. Experimental and theoretical evidence is adduced to show that polymer chains disentangle during crystallization. 1 .INTRODUCTION In a recent article Flow and Yoon argued that polymer molecules in the melt cannot disentangle from each other during the time scale that it takes for the crystal- lization front to advance across these self same molecules.' This paper constitutes a response to this objection. There are three parts to this response. In the first part a theory of reeling-in from the melt is developed. The friction coefficient 5 for pulling in a molecule from one end onto the crystal is calculated for two models. Knowledge of plus the driving force f due to crystallization enable us to calculate the rate of reeling-in dL/dt. cf = 5 dL/dt, where L is the contour length of the molecule.) The reeling-in rate dL/dt is shown to be consistent with the experimental facts of crystallization.In the second part, known experimental facts are adduced which show that molecules fractionate (and, therefore, disentangle) during crystallization. In the third part a simple objection to the calculation of Flory and Yoon is made. It is shown that disentanglement times are two to five orders of magnitude faster than the value quoted by Flory and Yoon. 2. CRYSTALLIZATION OF A POLYMER BY THE REELING-IN PROCESS 2.1. CALCULATION OF THE RATE OF REELING-IN; dL/dt Let the frictional resistance of the monomer unit be c0 and let the chain length be L = Nl where N is the number of monomer units and 1 the length of a monomer unit. We imagine the chain being pulled by one end through a small hole in a surface with a forcef,. Before the chain is pulled through the hole the characteristic dimen- sions of the end segment are2s3 (x) = ( y ) = 0, (2) = d m 1 N 3 <x2) = <y2) = 12N/3, (2') = 212N/3.E .A . DIMARZIO, C . M. GUTTMAN AND J . D. HOFFMAN 21 1 After a piece of chain of length dL is pulled through the hole the part remaining in the liquid has dimensions The changes in these quantities are (dx) = (dy) = 0, (dz) = ( ~ z N ) - ~ dL dL (dX2) = (dy2) = 3' (dz2) 1 22L/3. We shall assume that segment i in the interior of the chain behaves as the end segment in a chain of length i, so that (hi) = 2/lj6ni-* dL. The z component of the tension in the bond between the ith and the (i - 1)th bead is denoted byh-,. Summing over i we obtain dL = lo 1/2/3n N3 dt -- fo = lo 5 l = i which defines the effective friction coefficient as (2.4) Had we used ( z ) = 1/<2'> rather than the Rubin result for ( z } we would have 0.816 rather than 0.46 in eqn (2.6).Values of the monomeric friction coefficient lo are tabulated by Ferry.4 Although eqn (2.6) was derived for slow processes it can be shown on physical grounds that the square root dependence must hold aside from entanglement problems even for large tugs. To see this, follow the chain from its point of attachment with the surface to the first place the tangent to the chain (which initially pointed away from the surface) turns towards the surface. The contour length of this " loop " is proportional to the Kratky-Porod persistence length. Pulling on such a loop will result in the motion of the loop but not the remainder of the chain since there is no way to transfer tension to the remainder of the chain until this loop is straightened.Thus, instantaneously, the resistance is independent of N. Intuitively, the property that results in mdependence resides in the fact that a plane passed through the molecule parallel to the surface, but out a distance z from the surface will cut the polymer at 1 / N p l a ~ e s ~ ~ ~ (actually proportional to dN). If we are pulling on one of the chain segments that pass through this plane, we can hardly imagine that the other (dr- 1) chain segments are affected by the pull. The average number of mono- mer units between cuts is %% Thus, = Bl,N3 no matter how strong the reeling- in force is. Another observation of significance is that if we allow the friction coefficient for the molecule to be 5 = CON (proportional to N ) but allow the forcef, to act for the212 CRYSTALLIZATION KINETICS time the molecule moves a distance d2/37t Iz/N, which seems reasonable since the molecule has such dimensions, then the time required to reel-in the whole molecule t, = d2/37t I d N - is of the same order as if we use eqn (2.6) for a contour distance - -1% L.The above model is not a reptation model; we shall call it the sea snake model to emphasize that motion of the chain is not constrained to be along the tangent direction of the chain. If we use the reptation model of De Gennes, the friction coefficient for pulling the molecule through its worm-hole (tube-flow) would be5 where r denotes reptation. We have subscripted < since the monomeric friction co- efficient is model dependent.The question as to which of the two models is the better model for real chains cannot be answered without further work. One might expect the sea snake model to be useful for dilute solutions and the reptation model to be useful for bulk polymer. Fortunately, the models give similar results in the molecular weight range of interest (M, = 104-105, see subsequent discussion). We now use eqn (2.6) and (2.7) to calculate dL/dt for each of the two models. fo is obtained from the relation f o dL = d(free energy). (2.8) The right-hand side of eqn (2.8) represents the free energy change in crystallizing a chain of length dL. Notice that if we divide eqn (2.8) by dt, then the left-hand side represents the frictional power dissipated in the melt by pulling on the chain and the right-hand side is the source of this power: fo is thus the free energy of crystalliza- tion per unit length of polymer reeled-in.A quantitative estimate can be obtained from the work of Hoffman et aL6 fo = aobo {T AhAT - 20, z] = 9 (i;Af - 2oe}. It consists of a bulk free energy part Af= AhAT/T, and a surface free energy part, 2a,/l*. The notation is the same as in ref. (6) (see Section 2.3): fo is an average force. The maximum value of the force occurs during the zippering down of the segments of the stem and has the value aoboAf. Thus, we can expect that instantaneously the reel- ing-in velocity can be considerably larger than that obtained fromf,. Use of eqn (2.8) and eqn (2.6) and (2.7) immediately gives a, dL a~bo(l~AhAT/Tm - 20,) Ig dt 0.46 <oN31i2 g s = * - = a.dL - aib,(l~AhAT/T, - 20~) gr=--T.-- I, dt c"2 (2.10) sea-snake model (2.11) reptation model where g is the rate of lateral strip growth.E. A . DIMARZIO, C. M. GUTTMAN AND J . D. HOFFMAN 213 2.2. RELATION BETWEEN g (THE RATE OF LATERAL STRIP GROWTH) AND G (THE CRYSTAL GROWTH RATE) The primary piece of experimental information on crystal growth rates is G, the rate in cm s-l with which the edge of a growing polymer crystal propagates into the melt. Fig. 1 serves to establish the geometry of the growth and to define variables. L, is not the external crystal dimension but a smaller number. The experimental 4 2 4 FIG. 1.-Total number of niches that exist per cm of lateral length is n.The numbers in the figure count niches. g represents the lateral growth rate of each nich in cm s-l and G is the rate at which the whole crystal face advances in cm s-l. ao, bo are stem thicknesses and I* (not shown) is the stem length. fact that the growth rate G is not exponential in the linear dimensions of the crystal means that there exists a characteristic L, beyond which the growth does not propa- gate.7 L, can be due to cracks in the crystal, impurities within the crystallizing chain (a section of copolymer for example) or other poisons that act as barriers to lateral propagation. A fundamental relation connecting g and G is G = b,gn (2.12) where n is the number of niches per cm of lateral length. The general relation* con- necting G to both g and i, the rate of stem nucleation, is an unwieldly expression, although simple and useful limiting forms exist (G = boLi regime I; G = b0(2ig)+ regime II).6 Fortunately, we shall need only eqn (2.12) to establish that our value for g is reasonable.2.3. NUMERICAL CALCULATIONS We use the following experimental values for polyethylene (M.W. = 10'): the undercooling at AT = 20°C, the melting temperature T, = 420 K, the heat of fusion Ah = 2.8 x lo9 erg ~ m - ~ , the end surface free energy oe = 93 erg cm-2. The stem dimensions are (see fig. 1) a, = 4.55 x cm, Zi = 1.6 x cm. Also we have To = lom8 dyn s cm-I,* [, = 1.2 x 10-lo..F Eqn (2.10) and (2.11) yield g , = 2.3 x cm s-l. Thus, the result is rather insensitive to model. Since To and T, can conceivably be as much as an order of magnitude different from our figures and since eqn (2.9) is a difference between two similar quantities, g, and g, should be viewed as order of magnitude estimates only.cm s - ~ . ~ cm, b, = 4.15 x cm s-l and g , = 1.1 x The product ng is obtained from eqn (2.12) and the use of G = * This estimate is made from table 12-111 of ref. (4). t From eqn (4.5) and (2.7) and the relation D, = kT/&.214 CRYSTALLIZATION KINETICS We obtain ng = 24 s-'. We now ask (using g = 2 x whether n = 1.2 x lo4 cm-l is a reasonable value. This works out to be one niche per 8300 A. If we accept the idea that the number of niches is > 1.2 x lo4 cm-', then the actual value of g is correspondingly smaller. Eqn (2.10) and (2.11) give upper bounds to the experi- mental values of g .Existing kinetic theories of crystal growth must not exceed these values; however, they can be considerably smaller. In the Appendix we discuss the extent to which an entanglement prevents the reeling-in of polymer chains. Our conclusion is that there is no barrier to reeling-in of polymer due to entanglements except when different parts of the molecule are simultaneously incorporating into niches. 3. EXPERIMENTAL ARGUMENTS There is a wealth of evidence that polymer chains fractionate during crystallization of polydisperse systems." Also, compatible polymer blends exist that form true solutions and whose components separate out during crystallization.'' The existence of any kind of phase separation in polymer blends argues for disentanglement of the two kinds of molecules.Transitions near the lower critical solution temperature involve motion on the order of microns in minutes. Finally, fractionation has been observed during crystallization of mixtures of deuterated and protonated polyethyl- ene.I2 In fact, the neutron scattering community has gone to great lengths to avoid fractionation since it complicates the interpretation of experiments. They are able to avoid fractionation only by using large supercoolings. The above examples provide unambiguous proof that chains indeed disentangle during crystallization. This means that at a molecular level there is a disentanglement mechanism operating. Thus, even if the disentanglement mechanisms described in this paper (in Section 2 and the Appendix) were incorrect, we would be forced by the experiments to invent others.4. DISCUSSION OF THE FLORY-YOON ESTIMATE FOR DISENTANGLEMENT TIME Flory and Yoon give 1 s as an estimate of the disentanglement time in the melt which they identified with the longest relaxation time in Rouse-Bueche theory.' The Rouse and Bueche theories of relaxation give for the longest relaxation time r1 r1 = 6vM/n2~RT (4.1) where eqn (4.1) reproduces eqn (59) of chapter 9 of ref. (4). There is a fundamental inconsistency in the use of eqn (4.1) above the entangle- ment point (M, 21 3800). Above the critical molecular weight Rouse-Zimm- Bueche theory breaks down precisely because bulk viscosity is determined by entangle- ment effects above M,. Eqn (4.1) is valid only below the critical molecular weight.Consequently, we do not believe it is appropriate to use Rouse-Zimm-Bueche theory to estimate disentanglement times. One can get a more meaningful estimate of the relaxation time for disentanglement by estimating the time for a molecule to reptate a distance proportional to its end- to-end length.5 Obviously, after transport of such a distance, the chain has dis- entangled itself. We obtain (R2) = 6D,t, t = 6.6 x s (4.2)E . A . D I M A R Z I O , C. M . GUTTMAN A N D J . D. HOFFMAN 21 5 where we used an end-to-end length of 340 A and D, = 2.94 x value of D, was obtained by use of the equation cm2 s-l. The D, = 1.5 x 1 0 - 3 1 ~ 2 (4.3) which is our best estimate of the curve fitting the data of fig. 12 of the paper by Klein and Briscoe.13 One obtains the same estimate by asking for the time required for the chain to reptate its full contour length within a worm-hole.One simply uses (L2) = 2D,t (4-4) where D,, which is the diffusion coefficient for reptation, is defined so that the time required to diffuse a contour length L is the same as that obtained from eqn (4.2). Obviously D, = 3D,(L2)/(R2). (4.5) Eqn (4.2) and (4.4) do not represent independent estimates of the disentanglement time. They are equivalent. Eqn (4.2) and (4.4) give the time scale for disentanglement under diffusion. If one applies a steady pull, one can move a distance L in the worm-hole in a much shorter time. The situation is exactly the same as a drunk randomly walking on a street compared to a sober man who presses forward always in the same direction.Our crystallization force provides a steady pull that reels in the chain along its worm- hole onto the crystal. Thus, a time scale which is even more meaningful is an esti- mate of the time required to reel-in a chain of length 9 x 103 A (M = lo5). Use of g, = 1.1 x cm s-l. This value of dL/dt in turn results in a time of 1.2 x s to reel-in the whole mole- cule. The use of eqn (2.6) gives an even shorter time (5.5 x These numbers represent the time to fold the molecule of M,,, = lo5 completely (approximately 45 stems). If we were content to fold only 4 or 5 of these stems, an order of magnitude less time would be required. In fact, because of stored length (slack), the initial stems would be reeled-in even faster than the above calculations would indicate.Finally, eqn (2.10) and (2.11) can be written as cm s-l implies, uiag, = (a, dL/dt)/li, a dL/dt of 3.8 x dL c1 =L* - dt dL C , = L - dt (4-7) which show by simple quadrature that the time required to reel-in a molecule varies in one case as L% and in the other case as L2. Thus, shorter molecules require even less time. We conclude that the characteristic times implied by the two reeling-in processes (the sea snake model and the reptation model) are on the order of three orders of magnitude smaller than the characteristic time calculated by Flory and Yoon. CONCLUSIONS Our estimate of the time scale for disentanglement of polymers from the melt in the process of crystallization is about three orders of magnitude faster than the estimate by Flory and Yoon.One is the reptation model, in which a molecule is imagined to move only within its worm-hole The other model, called the sea snake model, allows motion perpendicular to the worm-hole, as well as along it. Both experimental and theoretical evidence was adduced to show that there is no The estimate was made with two models.216 CRYSTALLIZATION KINETICS difference in the disentanglement mechanism above and below the accepted entangle- ment point for polyethylene (see Appendix). It was observed that definitive experimental evidence for disentanglement during crystallization exists. They are (1) fractionation of heterogeneous molecular weight polymers during crystallization, (2) separation during crystallization of polymer blends and (3) separation of hydrogenated from deuterated polyethylene during crystallization. We conclude that the kinetics of disentanglement from the melt do not force the switchboard model and are consistent with regular chain folding. Chain folding is neither proved nor disproved by kinetic considerations.APPENDIX THE QUESTION OF ENTANGLEMENTS The problem of entanglements is nowhere near being solved because the required However, we wish to offer the following two mathematics simply does not exist. insights that bear on the problem: INSIGHT 1 Consider a polymer in a hollow tube of radius r [see fig. 2(a)]. We can write fo = (C,N)v and this formula should be independent of how the tube is bent. The physics is simply that the Brownian motion of the beads is sufficient to prevent the chain from being hung up on the tube wall.Thus to the extent that one has tube- flow (reptation) we expect that entanglements are not an impediment to the separation of chains from each other. The recent experimental work of Klein and BriscoeI3 is in accord with the view that entanglements do not affect the reptation process. They have measured the self diffusion coefficient of polyethylene as a function of molecular weight and find that (A) the molecular weight dependence is D, = Do/N2 in accord with the prediction of De Gennes for the reptation process and (B) there is no effect of entanglements on D,! The diffusion coefficient varies smoothly through the point N = 271 which is the accepted location of the entanglement point. Thus, the method of disengagement of a polymer molecule from the melt is no different above the entanglement point than below it.c.ccI FIG. 2.-The frictional resistance to a polymer being pulled through a tube is independent of how the tube is bent [fig. 2(a)]. Brownian motion will keep the chain segments far from the post provided that the forcefo is small. There will thus be no frictional resistance due to the wrapping about the post forfo small [fig. 2(b)].E. A. DIMARZIO, C. M. GUTTMAN AND J. D. HOFFMAN 217 The connection between reptation which describes diffusion of a polymer molecule along its worm-hole and tube-flow which describes the motion of a polymer molecule along its worm-hole under the influence of an applied force is immediately given by the fluctuation-dissipation theore111.l~ All this means is that the diffusion coefficient D, is related to the friction coefficient by D, = kT/l,.INSIGHT 2 Consider a chain wrapped around a fixed post as in fig. 2(b). Presumably if f o were large enough one would wrap the chain tightly on the post and there then might be a resistance to flow of the polymer around the post. However, one can always let the force be sufficiently small that the chain is distant from the post. To see this, consider the quantity exp [-271(R - Ro)f,/kT]. (Al) The numerator in the exponent is a potential energy and represents the energy needed to expand the ring of particles surrounding the post. When this number is close to kT we expect a steep spatial variation in bead density and the probability of the wrap- ping being tight is large.Thus 2 4 R - Ro)fo/kT I 1 (A2) is a condition for loose wrapping on the post and a consequent lack of constraint by the post on the motion of the chain. When eqn (A2) is satisfied, the chain easily slides around the post. For R - Ro = 5 x 1.8 x lo-' dyn. The crystallization force for 20 K supercooling is less than this (fo = 3.2 x lo-' dyn). Furthermore, we have shown in the body of the text that the actual velocity resulting from this driving force is determined by thermodynamics of growth and can be considerably less than that determined from eqn (2.9). This lower velocity occurs because the time required to surmount the free energy barrier to folding within the crystal is large. During this large " waiting time " the loop around the post has no tension on it and enlarges due to entropy effects. We conclude that polymer chains readily disentangle from one another as they are being reeled into the crystal from the melt from one end only. However, if they are being incorporated into the crystal simultaneously at different points along their contour length then entanglements will not be relieved. cm and T = 400 K we have f o P. J. Flory and D. Y. Yoon, Nature, 1978,272,226. R. J. Rubin, J . Chem. Phys., 1965, 43, 2392. J. D. Ferry, Viscoelastic Properties of Polymers, (J. Wiley, N.Y., 2nd edn, 1970). P. G. De Gennes, J. Chem. Phys., 1971, 55, 572. J. D. Hoffman, G. T. Davis and J. I. Lauritzen, Jr, Treatise on Solid State Chemistry, ed. Bruce Hannay (Plenum Press, N.Y., 1976), vol. 3, chap. 7. F. C . Frank, J . Crystal Growth, 1974, 22, 233. J. D. Hoffman, L. Frolen, G. S. Ross and J. I. Lauritzen, Jr, J . Res. N.B.S., 1975, 79A, 671. lo I. C. Sanchez and E. A. DiMarzio, J. Res. N.B.S., 1972, 76A, 214; B. Wunderlich, Macro- molecular Physics, Vol. 2, Crystal Nucleation, Growth, Annealing (Academic Press, N.Y., 1976). W. J. MacKnight, F. E. Karasz and J. R. Fried, Polymer Blends, ed. D. R. Paul and S. Newman (Academic Press, New York, 1978), vol. 1, chap. 5 . l2 J. Schelten, D. G . Ballard, G. D. Wignall, G. Longman and W. Schmatz, Polymer, 1976, 17, 751. l3 J. Klein and B. J. Briscoe, Proc. Roy. Soc. A, 1979, 365, 53. l4 R. Kubo, Statistical Mechanics (North Holland, London, 1971). ' E. A. DiMarzio and F. L. McCrackin, J . Chem. Phys., 1965,43, 539. ' I. C. Sanchez and E. A. DiMarzio, J . Chern. Phys., 1971,55, 893.

ISSN:0301-7249    

DOI:10.1039/DC9796800210

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

Lamellar Morphologies in Melt-crystallized Polyethylene BY D. C . BASSETT, A. M. HODGE AND R. H. OLLEY J. J. Thomson Laboratory, University of Reading, Whiteknights, Reading Received 1st May, 1979 The lamellar morphologies of linear polyethylene crystallized from the melt in uacuo have been surveyed. It is shown that spherulites form by the outward growth of dominant lamellae along 6, with low angle branching, with the intervening spaces subsequently filled by subsidiary lamellae. There are three principal habits of dominant lamellae: ridged sheets of alternating (201) facets, planar (201) sheets and S- or C-shaped sheets which can be derived from (201) sheets by suitable shear. These occur in increasing order of growth rate, caused either by increasing molecular mass or decreasing crystallization temperature.The most widespread morphology is one of S-shaped dominant lamellae with narrow (201) subsidiary platelets; these are found, e.g., in banded spherulites. It can be shown, at least in certain circumstances, that longer molecules tend to form the dominant lamellae and shorter ones the subsidiary. Even in quenched samples the lamellar texture is not homogeneous. Here and elsewhere it has a lateral scale which can be measured by the widths of dominant lamellae, but this varies much less than the Keith and Padden parameter 6 to which it has been thought to be related. Since 1957 we have become accustomed to the concept of polymer morphology, i.e., that crystalline polymers possess a (lamellar) microstructure, whose details are both a record of a sample’s past and a determinant of its properties.A succession of studies has elucidated this microstructure for solution-crystallized specimens, always confirming and elaborating the remarkable phenomenon of molecular chain-folding underlying the lamellar habits. For melt-crystallized polymers, the situation is less clear, primarily because it had not proved technically possible to examine them, to the same extent as their solution-grown counterparts, with the electron microscope. Nevertheless, the comparison of solution- and melt-grown polymers from their crystallization behaviour to their thermal, mechanical and other properties, has built up confidence in the related hypotheses (i) that melt-crystallized polymers also are lamellar and (ii) that there is molecular chain-folding within the layers.This is not to imply that such samples are wholly lamellar: evidently they are not and the nature and extent of interlamellar material can be very important. Nor does it necessarily imply that chain-folding is universal and highly regular: it is unreasonable to expect the same quality of ordering from molecules crystallizing cheek by jowl from the melt as when they add, more or less independently, to lamellae from dilute solution. It has seemed to many, therefore, that such differences as do exist between solution- and melt-grown morphologies, tend to be of degree rather than of kind. Others, however, have taken issue, particularly concerning the possibility of chain-folding and its regularity. The purpose of the present paper is to introduce into the debate basic facts on the lamellar morphologies encountered within melt-crystallized poly- ethylene which have been revealed using the new electron-microscopic technique of permanganic etching.It may be stated further that morphologies of other systems investigated in this laboratory, viz. polyethylene crystallized anabarically, i.e., as the disordered hexagonal phase at high pressures, in a comprehensive study, as well asFIG. 1.-Replica of an etched cut surface prepared from a polyethylene sample having I@,,, = 2 lo4, arn/&fn = 1.7, crystallized at 130.4 "C for 27 days. The ridge lamellae radiate from the ce of the spherulite at the top left of the micrograph. FIG. 2.-Enlargement of detail in an area adjacent to fig.1 showing small-angle branching of some of the ridged lamellae. [To face page 218FIG. 3.-Enlargement of an area adjacent to fig. 1 in which lamellae grew out of the plane of the photograph, making their ridged profile apparent. FIG. 4.-Electron micrograph of another area of the same etched cut surface as in fig. 1, in which a few ridged lamellae, viewed down the b axis (spherulite radius), are isolated from each other by thin lamellae formed on quenching. [To face page 219D . C. BASSETT, A . M . HODGE A N D R . H. OLLEY 219 preliminary surveys of polyethylene copolymers, isotactic polypropylene formed in both monoclinic and hexagonal structures and isotactic poly(4-methylpent-1 -ene) are also composed of well-defined lamellae. The scope of the paper concerns lamellae, their shapes, crystallography and organization within spherulitic textures, together with the conclusions which may be drawn concerning the nature of the lamellae and the crystallization processes.EXPERIMENTAL MATERIALS A N D TECHNIQUES The work described is selected from a wide survey of linear polyethylenes, both fraction- ated and whole polymers, crystallized from the melt in uac~cu.~ For the most part these were homopolymers of the Rigidex series (B.P. Chemicals), or of fractions separated from them by selective dissolution using procedures similar to those previously described.2 Molecular lengths have been measured by gel permeation chromatography (g.p.c.) using o-dichloro- benzene at 130 "C and calibration against polystyrene standards.For crystallization, samples in sealed glass tubes were melted at 160 "C for 1 h, then held at the chosen crystal- lization temperature (1t0.2 K) for controlled times and, finally, quenched in ice-water. The products have all been characterized by their melting endotherms (which indicate the different lamellar populations present and their amounts) and by g.p.c. analysis following digestion with fuming nitric acid for 72 h at 60 "C. This gives an independent estimate of the distribution and quantity of populations and also measures the respective lamellar thicknesses.* It is possible to reveal random views of the morphology of such samples following permanganic etching of arbitrary surfaces exposed by cutting with the glass knife of a microtome at temperatures between ambient and -20 "C.The etching in a 7 solution of potassium permanganate in sulphuric acid was for 15 min at 60 "C following procedures des- cribed el~ewhere.~ This removes thicknesses of order 1 ym (less than typical lamellar widths, fig. 12) from surfaces selectively, making the lamellar textures apparent. The various micro- graphs illustrated are of two-stage carbon replicas of such surfaces, with metal shadow applied to the first-stage impression. The appearance of relief in the micrographs alters with the viewing direction; the attempt has been made to align the micrographs with the text so that the correct impression of the relief is observed. Although permanganic etching is a new technique, there is no reason to doubt that microstructures it exposes are authentic.In many cases the same morphologies have been seen in comparisons with the quite different new method of chlorosulphonation5 on the same samples. There is also consistency with the results of fracture-surface studies (especially on anabaric polyethylenes) and agreement with the proportions and dimensions of various lamellar populations inferred from thermal and nitrat ion/g. p .c. measurements. 1,4 RESULTS AND DISCUSSION It is convenient to begin the survey with the most regular melt-crystallized poly- ethylene morphologies, that is those grown very slowly, over three weeks, at 130 "C from fractionated polymer of average molecular mass \< ~3 x lo4. The lamellae thus formed approach 100 nm in thickness and, as the nitration/g.p.c. evidence following previous work2 suggests that chain-ends are excluded from lamellae, can be expected to have two folds and three stems per average molecule.The habits and organization of such lamellae have previously been described in detail6 and provide evidence of sectorization of a type similar to that used to infer regular folding in solu- tion-grown crystals. They form ridged sheets, of about six facets each z 1 ,um wide, of (201) type growing outwards along the b axis, which is always the radial direction of mature spherulites in polyethylene. Frequently, however, and practically always220 MELT-CRYSTALLIZED POLYETHYLENE at the higher growth temperatures, the growing entities do not become large enough to achieve spherical envelopes; instead they adopt sheaflike or other shapes which we refer to collectively as immature spherulites.On a gross level the various outlines of such objects, which alter with changing growth conditions and molecular mass, give varying small-angle light scattering pattern^,^ but these are not reflected in corre- sponding changes in the basic lamellar habits which number only three: there is no close correspondence between the growth envelope and the shape of the constituent lamellae. Fig. 1 shows radiating microstructure, in a fraction with am = 2.1 x lo4, nrn/nn = 1.7 grown at 130.4 "C for 27 days, resulting in 40% of lamellae 102 nm thick (mass average) and the remainder 17 nm thick. In this, and the enlarged detail of fig. 2, it can be seen that lamellar units (which are the ridged sheets described above, seen in various orientations about the radius) grow outwards along what has been identified as the b axis.In places continuity can be clearly seen to extend over lengths of z30 pm, but there is also evident small-angle branching as the radii lengthen which is physically necessary to fill space. On a lamellar level this has been seen to be by incorporation of additional lamellae one at a time.6 In terms of ridges, new corruga- tions displaced laterally and usually growing in slightly rotated directions, appear to arise by a change in dominance among the outward-growing lamellae. The concept of dominance is helpful in the description of spherulitic growth and may be introduced using fig. 3 showing, in further detail of fig. 1, the profile of the ridged sheets viewed at an angle to the growth direction b.In this it is clear from the lateral continuity of individual sheets that the larger ones must have grown first, leaving intervening cavities to be filled in by later-forming narrower laminae. The former we term dominant, the latter subsidiary lamellae. It is the dominant lamellae which will determine the growth envelope. In the samples so far discussed there is no obvious difference in the constitution of dominant and subsidiary platelets, but in other samples it will be demonstrated that there is fractionation which tends to place shorter molecules in the later-forming subsidiary crystals. Before this, it is necessary to describe the three basic lamellar habits found in melt- crystallized polyethylene.For growth at 130 "C, fractions of molecular mass 6 3 x lo4 give dominant ridged (201) sheets as already described (fig. 4), masses between 3 x lo4 and %lo6 give dominant planar or slightly curved (201) sheets, while still longer molecules give a distortion of the (201) geometry resulting in lamellae whose profile viewed down b is a single shallow S, fig. 5. This order is that of increasing growth rate. The same sequence is seen following growth at successively lower tem- peratures. Fig. 6, which includes minor differences for the best comparison with small-angle light scattering, summarises the position. The crystallography of all the shapes is sketched in fig. 7 and results from (i) knowledge that b is radial and (ii) that the c axis can be identified, in places chosen so that they are normal to b, as parallel to a fracture-induced striation in the replicas.(This is a feature which has been thoroughly explored and confirmed for anabaric polyethylene^.^^^ While permanganic etching removes any such initial striations, others can be introduced, if desired, by suitable preparation of the replicas). The ascription of Miller indices then depends solely on the angle between this c striation and the lamellar surface; (201) is the closest low-angle plane to the mean orientation but the statistics give standard deviations of & l o for ridges and &5' for planar sheets and S's. It is not certain that this represents the true spread, as fine serrulation of the profiles undoubtedly increases the measured variation in some instances.6 In any event, the spread around the precise low-index angle is not very different from that found in solution-grown hollow pyramids.1° The lamellae in fig.4 and 5 are dominant lamellae, revealed (fig. 5) by quenchingFIG. 5.-Replica of an etched surface of polyethylene with A&, = 4.4 x lo5, A?fm/n,, = 2.0 crystallized at 128.1 "C for 1 h. The two dominant lamellae have an S-shaped profile, deduced to be that of the lamellae viewed down the spherulite radii. The majority of the sample crystallized on quenching and then formed thin lamellae around the S's. [To face page 220FIG. 8.-Electron micrograph of a replica of an etched cut surface of the polyethylene used also for fig, 5 , but now crystallized almost entirely at 128.1 "C.The infilling lamellae appear not to be organized with respect to each other or the S's. [To facepage 221D. C . BASSETT, A . M. HODGE AND R . H. OLLEY 22 1 0 \ !! 130 z +- 128 E + c 0 N CI VI .s 125 .- k 4 Y ? 120 quenched 1 o4 1 o5 lo6 molecular mass 1 o7 FIG. 6.-Schematic of the observed morphology in linear polyethylene fractions as a function of molecular mass and crystallization temperature. The numerals refer to the following morphologies : (i) Dominant ridged lamellae organized into large spherulites or sheaves. (ii) Planar sheets arranged in smaller spherulites or sheaves. (iv) S- shaped sheets and subsidiary planar sheets in irregular sheaves. (v) S’s and infilling lamellae, occasionally arranged into parts of banded spherulites. (vi) Randomly arranged S’s and planar sheets.(vii) Relatively complete banded spherulites containing S-shaped and infilling lamellae. (iii) Curved sheets assembled into birefringent units. C FIG. 7.-Sketches to indicate the crystallography of the various lamellar shapes, as viewed down the spherulite radius (b axis), (a) ridges, (b) planar sheets and (c) S’s. ( d ) represents the organization of the infilling lamellae with respect to an S in, for example, a banded spherulite. growth at an eady stage before subsidiary ones had begun to form. In both cases the coherence of the several wave-forms of the profiles strongly suggests an origin from a single precursor which has multiplied by branching. Subsidiary lamellae will even- tually form between these, illustrated by fig. 8 which is of the polymer in fig.5 crystal- lized for a longer period. The infilling lamellae in this area are apparently not organized with respect to each other or their enclosing S, whereas in banded spherulites, for example, a number of parallel subsidiary platelets will be arranged such that they222 MELT-CRYSTALLIZED POLYETHYLENE are (201) if the associated dominant S is (201) at the centIe of its profile, as indicated in fig. 7(d). This organization of S's and associated narrow planar platelets prevails over most of the accessible growth conditions, notably those found when quenching or rapid growth has been involved. It is certainly present in the banded spherulites where the average molecular orientation is known to rotate around 6, moving along a radius.Some aspects of their underlying morphology have now become clearer. The asym- metry of the S is related to the twist in such a way that in travelling outwards the S would rotate so as to appear to scoop up the melt. The dominant S-lamellae (and, by inference, their associated subsidiary platelets) maintain essentially the same c-axis orientation over distances of order one-third of the band period. Then one can often see an individual S split into two or three daughters with rotations producing large changes in the corresponding c-axis orientation. The points which still need clarifi- cation are the precise way in which an individual S continues to grow and its lateral relationships to its neighbours. There is, however, no support for the familiar model of an array of continuously twisted helicoidal ribb0ns.l' Further examination of morphological detail shows that there is fractionation of shorter molecules into the melt between the dominant lamellae and that, at least in some instances, the subsidiary lamellae which form from this melt also consist of lower molecular mass polymer than do the dominant lamellae.On the first point, it is inevitable, since dominant lamellae form first and ultimately penetrate to the limits of a spherulite, that any uncrystallized material must be located in the intervening channels, as can be seen directly following quenching (fig. 9). At high crystallization temperatures, a study of such changing morphologies with time as a function of molecu- lar mass leaves no doubt that residual uncrystallizable material in linear polyethylene contains the shortest molecules.This has indeed been shown directly by selective dissolution of such populations and determinations of the molecular mass.12 A similar situation is that familiar in the anabaric crystallization of polyethylene when short molecules (< z lo4 at 5 kbar) are unable to enter the high-pressure disordered hexagonal phase and eventually crystallize as a separate population of thin ortho- rhombic lamellae.9 For the second point, there is the evidence of fig. 10 in which a fraction &fm = 3.1 x lo4, = 1.3 has crystallized at 130.3 "C for 27 days as dominant planar sheets interspersed with ridged subsidiary lamellae. This difference in habit can be related to differences in molecular mass using knowledge of the crystal- lization of other fractions at 130 "C which only produce ridged sheets for masses of 3 x lo4 or less, but give planar sheets for higher masses to z lo6.More polydisperse samples tend to give a mixture of habits. We may thus infer that dominant sheets in this sample contain the longer molecules and the subsidiary lamellae the shorter ones. Extension of this conclusion to other crystallization conditions cannot yet strictly be made because only at high temperatures has the correlation between ridged habits and molecular masses been made. Nevertheless localized areas of ridged crystals do appear even in quenched polyethylenes, suggesting strongly that there may be a general tendency to incorporate shorter molecules in subsidiary lamellae. For example, fig.1 1, which is of the whole polymer Rigidex 50 crystallized at 1 19.8 "C, has all three lamel- lar profiles adjacent. Such inhomogeneities, obtained in this instance for crystalliza- tion which would have been complete within a few minutes, and similar features found in quenched materials, are evidence for the maintained subtlety of the processes of spherulitic growth, even at very rapid rates, rather than retaining molecular conformations roughly as they were in the melt. Attempts have been made to investigate whether dominant and subsidiary lamel- lae can be distinguished in their properties by studying the morphological changesFIG. 9.-Replica of an etched cut surface showing thin lamellae formed on quenching from the residual melt, located in the interstices between adjacent ridged sheets.The sample was polyethylene having I$T, = 2.1 x lo4, = 1.7 crystallized at 130.4 "C for 27 days. FIG. lO.-Replica of an etched cut surface in which planar sheets surround ridged sheets, providing evidence for fractionation of molecules according to their length. The average molecular mass (M,) of the polyethylene was 3.1 x lo4 with Mm,/I$,, = 1.3 and the sample was crystallized at 130.4 "C for 27 days. [To face page 222FIG. 11 .-Electron micrograph showing ridged, planar and S-shaped lamellae in the whole polymer Rigidex 50 (am = 6.8 x lo4, &$,,,/A& = 5.9) crystallized at 119.8 "C, indicating the inhomogeneity of the structure formed even during rapid crystallization. [To face page 223D .C . BASSETT, A . M. HODGE AND R. H . OLLEY 223 '7 6 - ' 5 - 5 E E 3 4 - 6 d d 5 3 - d 2 - 1 - resulting from annealing treatments at 130 "C and lower temperatures. The results show that subsidiary and dominant lamellae are both increased in thickness possibly with marginal differences between the two, though these have still to be shown to be statistically significant. It is pertinent to compare the lamellar morphologies described here with the theory of spherulitic growth proposed by Keith and Padden13 which is able to account semi- quantitatively for optical observations especially on polystyrene and polypropylene - + + . 0 4- + X + 8 + + 0 + 0 A X X 0 0 + 0 X 0 + + 4- X 0 f 0 A 01 I I J l o 4 lo5 106 1 o7 molecular mass FIG. 12.-Graph showing the variation of lamellar width, measured in etched cut surfaces, as a func- tion of molecular mass for polyethylenes crystallized at different temperatures : + , 130; 0 , 128 ; x , 125 ; 0 120 "C and A, quenched from the melt.spherulites. Qualitatively there is general accord. Their fundamental assumption that there is lateral segregation of rejected molecular species during spherulitic growth is undoubtedly true. We have now, however, the means of measuring the lateral scale of the texture directly, as the distance between the channels of segregated polymer, i.e., the locations of subsidiary lamellae. As Keith and Padden suggestedl4 this is approximately the width of the dominant lamellae which, moreover, is predicted to be of the order of 6 = diffusion coefficient/growth rate.On this last point our ob- servations provide no support for 6 being the scale of the texture in polyethylene spherulites. It has previously been pointed out6 that, for ridged crystals grown at 130 "C, the facet width of w 1 pm compares with anticipated values of 6 of 10-100 cm. Fig. 12 shows that the width of dominant lamellae in the whole range of polyethylenes examined decreases only slightly with temperature. On the other hand 6 should decrease by orders of magnitude because of increases in growth rate (with relatively constant diffusion coefficient). CONCLUSIONS The several conclusions arising from this work include: (1) Melt-crystallized poly- ethylene is composed of lamellae. The highly regular ridged habit formed under optimum growth conditions suggests correspondingly regular chain-folding. (2) Spherulitic textures are formed by the growth of dominant lamellae, with low-angle224 MELT-CRYSTALLIZED POLYETHYLENE branching, the intervening spaces being filled in by subsidiary lamellae.(3) At least for growth at high temperatures, longer molecules form dominant lamellae, shorter ones subsidiary lamellae. (4) The inhomogeneities represented by dominant and subsidiary lamellae as well as the segregation, probably of very short molecules, into ridged lamellae obtains for all crystallization conditions examined. (5) The dominant lamellae have widths of w 1 pm or a little more, decreasing only a little with crystal- lization temperature and not by orders of magnitude as would be expected for the parameter 6. A. M. H. and R. H. 0. are indebted to the S.R.C. for financial support. A. M. Hodge, Ph.D. Thesis (University of Reading, 1978). R. H. Olley and D. C. Bassett, J. Polymer Sci., Phys. Ed., 1977, 15, 1011. D. C. Bassett, B. A. Khalifa and R. H. Olley, J. Polymer Sci., Phys. Ed., 1977, 15, 995. R. H. Olley, A. M. Hodge and D. C. Bassett, J. Polymer Sci., Phys. Ed., 1979, 17, 627. A. M. Hodge and D. C. Bassett, J. Mater. Sci., 1977, 12, 2065. D. C. Bassett and A. M. Hodge, Proc. Roy. Soc. A , 1978,359, 121. ' J. Maxfield and.L. Mandelkern, Macromolecules, 1977, 10, 1141. * D. C. Bassett, High Temp. High Press., 1977, 9, 553. D. C. Bassett, Polymer, 1976, 17, 460. lo D. M. Sadler, Ph.D. Thesis (University of Bristol, 1969). l1 D. C. Bassett and A. M. Hodge, Polymer, 1978, 19, 469. l2 A. Mehta and B. Wunderlich, Colloid Polymer Sci., 1975, 253, 193. l3 H. D. Keith and F. J. Padden Jr, J. Appl. Phys., 1963,34, 2409. l4 H. D. Kcith and F. J. Padden Jr, J. Appl. Phys., 1964, 35, 1270.

ISSN:0301-7249    

DOI:10.1039/DC9796800218

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

Isothermal Growth, Thickening and Melting of Poly(Ethy1ene Oxide) Single Crystals in the Bulk Part 4.-Dependence of Pathological Crystal Habits on Temperature and Thermal History BY AND& J. KOVACS AND CHRISTINE STRAUPE Centre de Recherches sur les Macromoltcules, C.N.R.S.-U.L.P., 67083 - Strasbourg, France Received 15th May, 1979 Characteristic features of isothermal growth, thickening and melting behaviour of melt grown single crystals of low molecular weight poly(ethy1ene oxide) fractions are described and discussed in terms of their relevance to basic concepts of polymer crystal growth. In the narrow temperature interval where transition from once folded to extended chain growth occurs, the crystal morphology displays some spectacular modifications. The dependence of the relevant crystal habits on tempera- ture and on thermal history are analysed in terms of the probabilities of chain deposition in the oncefolded and the fully-extended conformation, while defining a series of precisely determined transition temperatures at which these probabilities are equal.It will be concluded that in these systems crystal growth proceeds with regular chain folding, determined by the free energy balance relevant to the local environment of the depositing chains. Low molecular weight poly(ethy1ene oxide), (PEO), fractions crystallize from the undercooled melt in the form of lamellar single crystals, the thickness of which is an integer submultiple1*2 of the total chain length L (in the crystal lattice). This implies that the chains are either folded an integral number (n 2 1) of times or fully extended (n = 0); in both cases the chain ends are located in the surface layers of the lamellae.Hence for chains composed of p monomer units, the lamellar thickness : Z(n, p ) = L(l + n)-l = pZu(l + n)-l (1) depends on two independent molecular parameters, p and n, Zu (= 0.2783 nm) being the length of one monomer unit along the helical chain axis, parallel to the c axis of the PEO subcelL3 Folded chain crystals are metastable with respect to extended chain crystals and, for a given fraction, the number (n) of folds per chain molecule depends not only on crystallization temperature (T,) but also on crystallization time (tc). In fact, as T, or t, increases, the lamellar thickness increases in a stepwise manner, due to the quantized reduction of n [cf.eqn (l)] until full chain exten~ion.~,~ Such crystals are therefore suitable models for investigating growth, thickening and melting behaviour of polymer crystals as a function of the two independent parameters, p and n, characterizing the number average chain length and the overall chain conformation in the crystal, respectively. In previous work six sharp hydroxy-terminated PEO fractions (to be referred to as standard materials) have been investigated 4-8 ranging between 2000 and 10 000 in the number average molecular weight, M,,. More recently, the behaviour of a sample composed of diphenyl-terminated chains at one end has been compared with that of a standard fraction of similar chain length.9 Some conclusions of these investigations226 MELT GROWN PEO SINGLE CRYSTALS will be briefly recalled here and supplemented with new observations made on a standard fraction [ S , in ref.(9)] of molecular weight M , 2: 6200, comparable with that of another fraction ( S , ; M, 2: 6000) investigated The peculiarity of sample S2 is that it gives rise to bilayer crystals (in addition to monolayers) when n 2 1, whereas S , crystals grown in the same conditions from the melt are composed exclusively of single lamellae (disregarding spiral terraces which develop in both). In addition the thickening and melting behaviour of these two fractions displays some significant differences which will be discussed below. These dissimilarities presumably arise from some slight difference in the dispersity of these two fractions which, how- ever, cannot be determined accurately by the usual characterization techniques, since the ratio of the weight and number average molecular weights (MJM,) for both materials is FZ 1.1.PREPARATION TECHNIQUES AND CRYSTALLOGRAPHY Films E 10 pm thick, sandwiched between cover slides, are isothermally crystallized (in uacuo) after self seeding4l5 with tiny extended chain crystals. The specimens are then quenced at increasing crystallization times in order to arrest growth and to delineate the edges of the lamellae for observation under the optical microscope (between crossed polarizers or in phase contrast). In addition, fast quenching gives rise to a selective self decoration of the large surfaces of the lamellae, depending on whether the chains are folded (n 2 1) or fully extended (n = 0).When both chain conformations are present in the same monolayer crystal, as in fig. 1, self decoration thus enables one to delinate the extended chain portion of the lamella, which remains essentially undecorated, whereas the folded chain region is uniformly speckled by closely packed spherulitic overgrowths displaying positive birefringen~e.~ For all fractions the crystals have an overall hexagonal habit which can be charac- terized by the ratio of the diagonals H and W along the two mirror symmetry planes (fig. 1) parallel to the b and a* axes of the monoclinic PEO ~ubcell,~ respectively, whereas the helical chain axis, parallel to c, is normal to the lamella.5 Accordingly, the growth faces involve two (100) and four (140) prism faces.Depending on T,, however, the latter are often truncated by two additional (010) facets, or else the prism faces become roof shaped or rounded. In a given specimen, the crystals have uniform shape and size because of self seeding. During isothermal growth the aspect ratio (H/W) of the crystals is inde- pendent of time, whereas the crystal habit displays a systematic variation with T, for all fractions, as shown in fig. 2. In addition, in the narrow temperature interval ( ~ 0 . 1 K) where transition from once folded to extended chain growth occurs, the morphology of monolayer crystals displays some spectacular modifications [patho- logical crystals; CJ fig. 2(c) and (d)] which will be further documented below and interpreted in terms of the difference between the growth rates of folded and ex- tended lamellae along the same crystallographic direction at the same T'.GROWTH Fig. 3 summarizes for the sample S2 the temperature dependence of the radial growth rate, G, (along the b axis), that of full chain extension, Gd, around an extended chain nucleus (or seed) protruding from folded chain monolayer crystals and the negative melting rates, eH and GH, to be discussed below. The notched appearance of the log G, curve clearly resats from the juxtaposition of independent growthFIG. 1 .-Typical aspect of self-seeded and self-decorated monolayer single crystals of PEO 6000 (Sl), as observed under the optical microscope using phase contrast. The crystals grew at 58.5 "C (tc = 17 h) in the once folded chain conformatkon, while their central part (4) thickened by full chain exten- sion around the original extended chain seed.The H and W diagonals along the mirror symmetry planes are parallel to (100) and (OlO), respectively. Scaling bar: 20 pm. [To .face page 226(e 1 ( f ) FIG. 2.-Dependence of the morphology of Sz monolayers on crystallization temperature Tc : (a) 56.10 "C, ( t c = 1 h); (6) 59.45 "C (48 h); (c) 59.52 "C (72 h); ( d ) 59.58 "C (48 h); (e) 59.65 "C (48 h); Crossed polars, polarizer vertical. [To face page 227 ( f ) 61.52 "C (240 h). Scaling bars: 20 pm.A . J . KOVACS AND C. STRAUPE 227 branches GH(n, T), each characterized by the relevant value of n. As GH(n, T ) -+ 0, these branches approach vertical asymptotes at various temperatures Tm(n, p ) which thus define the melting temperatures of n-times folded chain crystals.Furthermore, these branches intersect at rather precisely defined (AO.01 K) growth transition tem- peratures, T&), at which d log GH/dTc (<O) displays a discontinuous increase with T, as the number of folds decreases from n + 1 to n, as indicated in fig. 3. In the lowest temperature interval (T, < 52.65 "C) where spherulitic growth prevails (charac- 1 I I I I I I, 1 48 52 56 60 64 Tc / "C FIG. 3.-Temperature dependence of the growth (G, or GR), thickening (Gd) and melting (GH# or zH) rates of sample SZ and that of the aspect ratio (H/ W) of the single crystals. Each data point represenis the average of M 100 crystal size measurements. Growth transition temperaLures Tf";(n) are indicated by vertical dashed lines. 0, GR; V, V, GH; 0, G4; A, A, GH; A, terized by the rate GR 21 GH), the value of n could only be bounded.Crystals grow- ing in this range are so unstable that they readily transform into the next nearest meta- stable form7p8 involving the largest integer value of n compatible with the chain length. In the present case nmax = 2. Fig. 2 shows, in the relevant temperature ranges, the typical modifications of the habit and morphology displayed by monolayer crystals of sample S2 and other stand- ard fraction^.^ These modifications are gradual, as illustrated by the smooth varia- tion of aspect ratio H/ W, except in the narrow temperature interval in which transition from once folded to extended chain crystal growth occurs (see below) and where H/ Wdisplays an abrupt decrease (cf.fig. 3) when n decreases from 1 to 0. Note also that the growth branch of once folded chain crystals extends above TA(0). This extension has been achieved by seeding the melt with once folded chain crystals (obtained at 59.0 "C) rather than by extended chain crystals. In fact extended chains cannot deposit onto a once folded chain substrate and such seed crystals keep on grow- ing with the once folded chain conformation, provided that T, < Tm(l, p), although228 MELT GROWN PEO SINGLE CRYSTALS in the relevant temperature interval [TG(O, p ) < T < Tm(l, p ) ] the growth rate of extended chain crystals is much greater. The data shown in fig. 3 together with the above observations suggest that at any temperature the chains deposit in that conformation which involves the largest growth rate, provided that the substrate is large enough to accommodate the chains in the relevant conformation.Therefore, chain conformation and crystal growth appear to be determined essentially by kinetics ; kinetic criteria may, however, be invalidated by the insufficient substrate length along the direction of the chain axis. 1 I f 0 0 0 / 0 0 FIG. 4.-Variation of the most probable lamellar thickness l*(n, p ) with the reciprocal of the under- cooling AT&, p) = Tm(oo) - T&, p ) . Solid lines refer to the values at constant p and dashed lines to those at fixed n, as indicated. Data relevant to the previously investigated8 and the present (SJ standard PEO fractions.The extended chain length, L, of each fraction corresponds to the One can also establish a correlation between the most probable lamellar thickness, Z*(n, p ) , involving the largest growth rate just above the growth transition tempera- tures, G ( n , p ) , and the relevant undercooling, AT*(n, p ) = Tm(m) - Ti(n, p ) , referred to the melting temperature, Tm(oo) = 68.9 oC,6 of a large and perfect PEO crystal including neither chain folds nor chain ends. In this respect, fig. 4 represents the variations of Z*(n, p ) as a function of the reciprocal undercooling, [ATH@, p ) ] - I , as determined from the singularities in the temperature dependence of the crystal growth rate of the previously and presently investigated (fig. 3) standard PEO fractions.This figure shows that, at constant p , Z*(n) rapidly increases with (AT*)-' (solid lines), whereas at constant n, I*@) is approximately proportional to (AT*)-' (see the dashed lines connecting the data points referring to fixed values of n). Further- more, the slope [ aZ*(p)/ 8(AT*)-'],, decreases and approaches a limiting value as n ordinate Z*(O, p ) .(c 1 (d 1 FIG. 5.-Modifications in the crystal habit of once folded chain S2 monolayers, grown at Tc,2 = 59.45 "C upon extended chain seed crystals (a), obtained at Tc,l = 60.0 "C; (tc,l = 17 h), during increasing Scaling bar: 20 pm, common for all crystals. crystallization times tcY2: (b) 29 h, (c) 48 h, ( d ) 58 h (see fig. 6). Crossed polars. [To face page 228FIG. &-Once folded chain bilayer crystals of Sz, grown at 59.0 "C ( t c = 17 h).Arrows indicate the separate appearance of the prism faces. Note the monolayer overgrowth (displaying a central thickened step) on one of the bilayers. Crossed polars. Scaling bar: 20 pm. [To face page 229A . J . KOVACS AND C . STRAUPE 229 increases, suggesting that the product Z*(p)AT* depends on n alone, similar to the average surface free energy a,(n) of the relevant cry~tals.~-~ These findings are ap- parently consistent with the prediction of kinetic theories of polymer crystal growth based on coherent surface nucleation.1° At temperatures other than T*(n, p ) this agreement obviously breaks down, since Z(n, p ) is invariant within each temperature interval where n is constant. Actually it has been shown8 that the growth branches of the various PEO fractions involving the same integer value of n cannot be described by the present formulation of kinetic theories.Detailed analysis of these growth branches reveals, furthermore, that the fundamental concept of coherent surface nucleation is in contradiction with the experimental data." ISOTHERMAL THICKENING In folded chain lamellae the chains unfold during isothermal growth and subsequent annealing. This process gives rise to some typical morphological effects, especially in monolayer crystals, in which unfolding of chains results necessarily in a stepwise increase of the lamellar thickness [cf. eqn (l)]. When the thickened portion consists of extended chains, its outline becomes decorated on quenching while its surface remains essentially undecorated, as shown in fig.5 . The crystals shown in this figure were grown at Tc,2 = 59.45 "C from extended chain seed crystals (obtained at Tc,l = 60.0 "C) and the relevant growth isotherm is represented in fig. 6 as a function of the crystallization time. Clearly, at Tc,2 the extended chain seed continues to grow with once folded chains, which deposit faster, 100 75 I-'m 50 25 0 -60.0 'C- 0 17' 0 20 40 60 f c , ~ / h tc,2 /h FIG. 6.-Time dependence of the average dimensions Hand W along the mirror symmetry planes and that of 4 (cf. fig. 1) of Sz monolayers shown in fig. 5 , as determined by at least 20 measurements at each t,.230 MELT GROWN PEO SINGLE CRYSTALS A and the aspect ratio H/ W = GH/Gw ( N 1, initially) becomes greater than unity (cf.fig. 3). In addition, the central extended-chain portion of the crystals continues to expand with a radial rate Gd, which is about half the value of the growth rate of the initial seed (fig. 6). The thermal variation of Gd is represented in fig. 3, which shows that d log Gd/dT, < 0, suggesting that full chain extension is nucleation controlled. The unfolding process obviously implies the migration of one chain end across the crystal lattice, while the lattice vacancy left is filled by another molecule extracted from the surrounding melt,5 as depicted schematically in fig. 7. In fact, depletion of the / I I I I I I I I I I I I I I I I I I I I I I I I I I I I t I I 1 I I I I T I I I I I I I I I I I I I I I I L FIG. 7.-Lattice model for unfolding of once folded chains along an extended chain substrate.melt stops the unfolding of the chains, implying that bilayer crystals and closely stacked multilayer terraces cannot thicken, at least in the regular way shown in fig. 5 and 6. This unfolding mechanism is, of course, independent of the size of the initial extended chain seed crystal. When the seed consists of folded chains, however, thickening does not start simultaneously with growth, as in the case of fig. 6, but after a well defined incubation period, z, necessary to produce the first extended chain nucleus at the centre of the folded chain lamella. This phenomenon has been described and analysed in previous work5 and will not be documented further, since for sample S2 the incubation time around TA(0) is certainly longer than 6 days and could not be determined.In comparison, for the previously investigated S1 fraction, z is of the order of one day in the same temperature range [see fig. 6 in ref. ( S ) ] . BILAYER CRYSTALS Folded chain bilayer crystals growing from the same extended chain seed can be identified by the appearance of doubled edges at some of the prism faces (fig. S),( b ' ) FIG. 9.-Morphological modifications on melting, at 61.2 "C, of mono- and bilayer crystals [grown at 59.0 "C (a) with once folded chain conformation] at increasing melting times t-: (b) 3 h, (c) 8 h, (d) 12 h. Note the emergence of non-central thickened islands in the adsorbed layers, at t , = 12 h. [To face page 230 Crossed polars. Scaling bar: 20 pm, common for all crystals.(C) (C') (C") FIG.12.-Normal and pathological crystals of Sl, grown in the lower transition interval, at 59.60 "C during increasing times t , : (a) 45, (b) 72 and (c) 96 h. Note the close vicinity of all three crystal types in (a). Crossed polars. Scaling bar: 20 pm, common for all crystals. [To face page 23 1A. J . KOVACS AND C. STRAUPE 23 1 provided that they are separated by more than % l pm, the resolution power of the edge decoration. In addition, such crystals never display any edge decoration of the central extended chain seed (such as shown by monolayers; fig. l), since the thickness of the latter is nearly equal to that of two superposed, once folded chain monolayers. The absence of this decoration thus enables one to recognize bilayer crystals in an unambiguous manner, even when all the prism faces appear in coincidence under the optical microscope.The growth rate of bilayer crystals is slightly lower (x 5 %) than that of mon01ayers.~ Chain unfolding in bilayers is, however, much more restricted, since the single sided contact of each of the two lamellae with the melt reduces the probability of penetra- tion of the molten chains inside the crystal lattice (fig. 7) by a factor of at least two. In the growth transition interval, however, one of the layers may display thickening features similar to those shown by monolayers. The dissimilarity between the two layers also becomes apparent in the melting behaviour of bilayers, as will be docu- mented in the next section. ISOTHERMAL MELTING When folded chain lamellae, grown at Tc,l < Tm(l,p), are suddenly heated to T2 > T,(l,p), the size of the initial crystals decreases isothermally, starting at the corner^.^ This decrease is proportional to (or becomes linear with) the melting time period, involving constant melting rates, G, and G,w along the two mirror symmetry planes of the lamellae (fig.1). The same situation prevails for extended chain crystals when heated above T,(O,p). Fig. 3 shows that the relevant melting rate G,(n, T ) increases exponentially with the degree of superheating, T2 - T,(n, p ) , for bothn = 1 and 0. The slope d log e,/dT, relevant to extended chain crystals, is, however, about twice as large as that for once folded chain lamellae, suggesting the activation barrier for melting to be proportional to the lamellar thickness, as already noted previou~ly.~ Isothermal melting behaviour of monolayers has been described and analysed in previous leading to the conclusion that melting, like growth and thickening, is nucleation controlled.It has also been shown that folded chain mono- and bilayer crystals display much lower melting rates when they are adsorbed on the cover slides of the specimen.' Fig. 9 further illustrates the modifications in the crystal habit on melting (of once folded chain lamellae of S2, grown at 59.0 "C) with particular distinction between the features displayed by mono- and bilayers found in the same specimen, while fig. 10 represents the relevant growth and melting isotherms, as measured along the H diagonal at increasing melting times, t , (at T2 = 61.20 "C).A similar situation prevails along W, not shown for clarity. Clearly, bilayer crystals (see left column in fig. 9) display two melting rates, the larger of which (GH#, in fig. 10) being practically equal to that (cH) of non-adsorbed monolayers (see the right-hand column in fig. 9). This implies that the interaction between closely stacked lamellae is negligibly small. On the other hand, the ad- sorbed lamella in bilayers and adsorbed monolayers (middle column in fig. 9) both melt much more slowly and involve approximately the same melting rate eH = GH (@. fig. 10). The temperature coefficient of the latter is nearly equal to that of GH 21 GH#, (cf. fig. 3), consistent with the statement made above about the activation barrier formelting. During melting of the once folded chain portion of monolayers, their extended chain centre still expands, at a rate Gd, and finally grows (at a rate determined by T2 alone) when the lateral contact with the melt is established. On the other hand, in - - -232 MELT GROWN PEO SINGLE CRYSTALS bilayers, melting of the less stable lamella exposes the extended chain islands emerging from the adsorbed layer, in particular the common extended chain seed, at the crystal centre.' The size (+') of the latter indicates that during growth and subsequent annealing some chain unfolding still occurs in bilayers (by migration of chain ends from one layer to the other), yet the relevant rate is about twice smaller than Gd in monolayers (cf.fig.lo). 59.0oc 4 75 r tc /h I I -6l.2O0C + I I I 0 5 10 15 20 25 t,/h FIG. 10.-Growth and melting isotherms (along H) of mono- and bilayer crystals of S2, shown in fig. 9, indicating the relevant symbols. Note the slight difference in size of these two types of crystals prior to melting and also the central thickened portion (4') which becomes apparent in bilayers at t , > 17 h. PATHOLOGICAL CRYSTALS The most spectacular and significant morphological features displayed by PEO single crystals have been observed in the narrow temperature interval where transition from once folded to extended chain crystal growth O C C U ~ S . ~ Since these phenomena are extremely sensitive to small changes in Tc and humidity, the experiments described in this section were performed on a much more thoroughly dried Sz sample (to be referred to hereafter as S;), in order to minimize the fluctuations in the water content ( z of the specimens.This results in a shift of the growth rate curves of S2 (fig. 3) towards higher temperatures and growth rates, by an amount of about ATc 'v 0.07 K and A log G 2: 0.02, respectively. GROWTH TRANSITION TEMPERATURES Fig. 11 represents on an enlarged scale the critical growth transition range (n = 0 ++ 1) for sample S;, while plotting the measured growth rates of the (100) and (140) prism faces? of folded chain crystals and those of the (100) and (010) faces of 7 which grow the slowest. Note also that GldO(l) = G,(1) cos (b 2: 0.894 GH(l) since, in this T, range, once folded chain single crystals display a sharp apex along H, limited by 140 and 140 (see fig.2 and 3, the apex angle being n - 24, with '4 N tan-' (1/2) 2: 26.6". In previous work GH(l) was identified with Golo(l) [see fig. 18 in ref. ( 5 ) ] which is erroneous, since in such crystals the (010) faces do not show up, thus GH < GOIO.A . J . KOVACS AND C. STRAUBE 233 extended-chain crystals. The dashed lines also show for the former the growth rates of the (010) and (120) prism faces (as estimated from indirect evidence) which grow faster than (140) and thus do not develop in pormal conditions, according to first principles of single crystal faceting.I2 Owing to the anisometry of the crystals in this temperature range and to the abrupt decrease of their aspect ratio (cf. fig. 3) when n decreases from 1 to zero, the intersection of the individual growth branches Gi(1, T ) and G,(O, T) define for each hkO (=i) face a critical temperature Tl(O), at which the -0.6 -0.8 h s -1.0 ci- u m 0 d - 1 .2 I 1 I I I 1 59.4 59.5 59.6 59.7 59.8 T, / O C FIG. 11 .-Expanded detail of the growth map G&, T) and G4 of S; crystals in the transition range with indication of the relevant (hkO) growth faces. Open symbols: n = 1, closed symbols: n = 0. Open symbols with dots: crystals grown from once folded chain seed crystals, obtained at 59.0 "C, (t, = 6 h). rates of once folded and extended chain deposition are equal. The situation is simplified by the almost circular habit of the extended chain crystals in this critical T, range (cf. fig. 2), a general feature observed for all standard fraction^.^*^ Accordingly, one can define the following growth transition temperatures for sample S; (fig.11): G o o ( 0 ) 21 59.56 O C } lower interval T;40(0) 2: 59.62 "C (2) T,*,,(O) N 59.68 ' C } upper interval and consider the relevant intervals T;40 - T;oo (210.06 K) and T& - T;40( -0.06 K), to be referred to hereafter as the lower and the upper one, respectively. The importance of these intervals is obvious considering the kinetic postulate given above, according to which growth proceeds (from an extended chain seed) in that chain conformation which implies the largest rate. One can thus expect the (100) faces to grow with extended chains in the lower interval, whereas in the upper one both the234 MELT GROWN PEO SINGLE CRYSTALS (100) and (140) faces should grow with chains depositing in the extended conforma- tion.In both cases, however, growth faces other than (100) and (140) may develop involving faster deposition of folded chains than extended ones (cf. fig. 11). The unusual crystal habits (cf. fig. 2) observed in the transition range fully substantiate this expectation and thus give further support to the kinetic concept of polymer crystal growth. BASIC PATHOLOGICAL HABITS The pictures shown in fig. 12 represent the characteristic crystal morphologies obtained in the lower transition interval. Besides the " normal " habit, the crystals display a " pathological " outline associated with a diamond shaped thickened interior, emerging in the middle of one or both (100) growth faces, as implied by the faster deposition of extended chains along a* in this temperature interval (fig.11). In ideal conditions the extended chains would emerge symmetrically in both (100) faces, as shown in the right-hand column in fig. 12. Although such crystals are the most frequently observed ones (and their relative proportion increases with T,), due to the slight inhomogeneity of the specimens and to the temperature fluctuations (of the order of & 0.02 K, to be commented on below), one or even both (100) faces of the tiny extended chain seeds may be accidentally covered, during the early stage of growth, by folded chains which prevent further deposition of extended chains along a*. In fact, as noticed above, the latter cannot deposit on a folded chain substrate, an abso- lute rule which applies without restriction.Thus folded chain seeds never give rise to pathological habits and the number of extended chain branches emerging in the latter can only decrease in an irreversible manner, at least in monolayers (see below). The diamond shape of the thickened portion merely results from the subsequent chain unfolding (at a rate Gd; cf. fig. 5) normal to the extended chain lath, growing along a* at a rate Gloo(0). Therefore, the apex angle, 0, of the arrowhead tip emerg- ing in (100) is uniquely determined by the ratio G4/Gloo(0) = tan (0/2), which depends only slightly upon T, (fig. 11). Furthermore, this tip retains its tiny initial dimension, rather than developing a complete (100) sector, as one would expect from kinetic considerations, while the continuity with the neighbouring (140) sectors is realized by two roof-shaped folded chain prism faces (fig.12), involving high order Miller indexes and growing faster than (100). When growth is initiated in this lower transition interval by a large extended chain seed crystal, as in fig. 5, the width of the initial extended chain (100) sector decreases and reduces eventually to an arrowhead tip, as in fig. 12. During this process, the apex angle 0 is no longer uniquely determined by the G~/G,,,(O) ratio, but it also depends on the respective probabilities of once folded and extended chain deposition at the specific corners at which the frontier between these two distinct chain conformation abuts at the edge of the crystal [see fig. 20, in ref.(S)]. As T, is increased, one observes, however, a gradual opening of the extended chain (100) sector, the central angle, w, of which rapidly increases for T, > T*140(0) approaching 4 2 at T*120(0), (cf. fig. 11, and see below). In this range, the value of co depends on T, alone and is uniquely determined by the respective probabilities of extended and once-folded chain deposition at the specific corners defined above. The dramatic increase of co with T, thus provides a critical test for any sound theoreti- cal treatment of chain folding. These observations and their interpretation are further supported by the drastic modifications in the morphology of pathological crystals growing in the upper transi-FIG. 13.-Morphological modifications of six branched pathological (S,) crystals, grown in the upper transition interval during the same time (48 h) but at different temperatures T,: (a) 59.64, (b) 59.66, (c) 59.68 and ( d ) 59.70 "C.Note the sharp apex along H in (a) and its rounding at increasing T,, giving rise to (010) prism faces with deposition of folded chains in a gradually decreasing sector. Note also in (b) the opening of (100) extended chain sectors and the subsequent appearance in (c) of two small folded chain sectors in symmetrical positions. The ultimate folded chain growth faces in ( d ) appear parallel to {120) (cf. fig. 11). Crossed polars. Scaling bar: 20 pm, common for all crystals [To face page 234FIG. 14.-Pathological growth spirals grown in thin Ss film at 59.39 "C. Electron micrograph.Pt-C shadowed replica (courtesy of B. Lotz). Scaling bar: 5 ,urn. [To face page 235A . J . KOVACS AND C . STRAUPE 235 tion interval, where the rate of deposition of extended chains onto the (140) prism faces also becomes larger than that of once folded chains (cf. fig. 11). In these condi- tions, besides the extended chain lath developing along a*, four other extended chain tips emerge normal to {140}, thus giving rise to a six branched, star-like thickened portion of the once folded chain lamella [see fig. 2(d) and 13(a)]. Again, when growth is initiated by a tiny extended chain seed, the apex angle (13) of the (140) tips, as deter- mined by Gd/G140(O) = tan (I3’/2), differs only slightly from @, since G14,,(0) = Gloo(0) When T, increases, the tips emerging in (140) and (100) undergo a rather dramatic opening of the extended chain sectors, as depicted in fig. 13, giving rise eventually to fully extended chain crystals above T;,,(O) > TElO(O).In fact, the last once folded chain prism faces which persist at the highest temperature appear to be (120) [see fig. 13(d), and fig. 111. Unlike (loo), the opening of (140) extended chain sectors is asymmetric, since it results from the gradual closing-down of the folded chain (010) sectors around the H diagonal. Similar modifications are observed in pathological spirals grown in thin films from screw dislocations, occurring in the extended chain region of pathological crystals, such as shown in fig. 14. Clearly, each layer displays an extended chain portion, which in this case first emerges at (100) and later at (140}, while finally only extended chain terraces grow, without any folded chain overgrowth.The progressive variation of the lamellar morphology must be attributed to the gradual decrease of the effective undercooling, since T, is kept constant. This results essentially from some fractiona- tion of the sample during crystallization, which gradually depresses its melting tem- peratures T,(n, p ) and concomitantly its growth transition temperatures T;(O). In fact, unlike crystals embedded in a large amount of melt, in thin films the composition of the melt changes appreciably before its depletion, due to the rejection of the shortest chains by the growth process. Hence the effect is similar to that which would result from a gradual increase of T,, beyond TiZ0(0). Note also that in such spirals (fig.14) the thickening of the individual layers is restricted by the screening effect of successive terraces, preventing contact with the melt, which stops the chain unfolding process (cf. fig. 7). Returning to fig. 13, one notices that the actual temperatures (T,) indicated in the legend exceed, by ~ 0 . 0 2 K, those which would be strictly expected from fig. 11. In fact, the growth rates plotted in this figure are essentially determined by the average values of T,, (maintained invariant within 0.01 K), whereas the morphology of the crystals critically depends on the lowest limit of the fluctuating T,, at which chains may still preferentially deposit in the once folded chain conformation along (010) or (120) and possibly in other prism faces of neighbouring orientations, involving high order Miller indices. The truncation of one or both extended chain branches of the crystals shown in fig.12 results presumably from the same effect, or equivalently, from some gradient in the composition of the specimen determining the effective undercooling of the melt. Similarly, in crystals growing in the upper transition interval, some of the four extended chain branches emerging in (140), or even all of them, may also disappear when their growth tip becomes accidentally covered by folded chains, preventing further extended chain growth. Accordingly, pathological crystals grown above T;40(0) may display eight different morphological varieties. These are shown in fig.15 for the crystals of the type (c) depicted in fig. 13. [Similar features displayed by the simplest (a) type crystals in fig. 13 have been reported previously, see fig. 21, in ref. (5)]. On the other hand, the crystals shown in fig. 15 clearly experienced a decrease of T, below T;40(0), as revealed by the doubled edge decoration resulting from deposition (cf. fig. 11).236 MELT GROWN PEO SINGLE CRYSTALS of folded chains up011 the initial (140) extended chain sectors which no longer emerge in the relevant growth faces. In addition, one or two (symmetrical) small folded chain sectors may also appear, in equivalent positions, upon the rather largely opened initial (100) extended chain sectors, subdividing the latter into two or three branches.On further growth, these features give rise to more involved morphologies, to be described in the next section. Finally, the crystal depicted in fig. 16, grown at 59.66 "C, reveals some interesting features with respect to chain unfolding in bilayers. In fact, the optical contrast clearly delineates the extended chain regions and shows that they participate in both layers and are fully developed along a* (displaying a slight sector opening), while the (140) sectors were closed at the early stage of growth. Furthermore, the two layers display different habits : the normal and the two branched pathological one. Chain unfolding subsequent to growth is restricted in the overlapping region and becomes only operative outside, presumably giving rise to the opening of the common (100) extended chain sectors.Apparently the specific morphology of this type of bilayers is essentially due to the faster growth along a* of the pathological layer, whereas the other plays only a passive role restraining the former to thicken in the overlapping region. The extended chain crystal halves developing along a* presumably result from fractionation, due to the depletion of the melt. DEPENDENCE ON THERMAL HISTORY Clearly, the modifications in the basic pathological morphologies are extremely sensitive to small changes in temperature and/or composition. Since these modifica- tions are rather spectacular and occur within presumably <0.01 K, they provide accurate temperature standards, which is unusual for polymer systems. The very sensitive temperature dependence of pathological morphologies can further be illustrated by the modifications displayed by the crystal habit when the specimen is deliberately subjected during growth to small T-jumps and kept at the successive values of T, isothermally.The relevant observations will now be illustrated in a self-explanatory manner by a few examples of increasing complexity. (a) The effect of varying T, is shown in fig. 17, for the six-branched, star-like crystals (grown at = 59.64 "C, t, = 44 h) such as the one depicted in fig. 13(a). The specimen was then either cooled [fig. 17(a)] or heated [fig. 17(b)] to Tc,2 = Tc,l F0.02 K, respectively and further crystallized for 28 h (t, = 72 h). Cooling (to 59.62 "C) results here in passing into the lower transition interval, thus in covering the {140) extended chain tips with folded chains, yet still allowing ex- tended chain growth to proceed along a* (fig.11). The initial positions of the four extended chain (140) tips, prior to cooling, can easily be located in the crystal shown in fig. 17(a), since they define the centres of the circular arcs, delineating its thickened central portion, which result from subsequent chain unfolding. On cooling below 7&(0), the extended chain (100) tips would also be covered by folded chains, thus becoming rounded on further growth. In contrast, heating to Tc,2 = 59.66 "C preserves the six-branched morphology and merely results in opening all four {140} extended chain sectors towards the b axis direction. Concomitantly, the (100) sectors display a larger opening, similar to that shown by the crystal (b) in fig.13, grown at nearly the same T, as Tc,2. A slight addi- tional increase of T, (or a larger initial increase) would clearly give rise to a further enlargement of these extended chain sectors, possibly leaving behind them six folded chain islands, completely surrounded (at least temporarily) by extended chains, since Gi(0) 3 G4 (fig. 11).(4) ( h 1 FIG. 15.-Truncated varieties of six branched pathological crystals (of the type intermediate between (b) and (c) in fig. 13) found in the same specimen crystallized at 59.67 "C, f, = 43 h, and then at 59.62 "C for 5 h, (see text below). Note the lack of two-fold mirror symmetry in all crystals except (b) and (A). Only the four branched crystals can display more than one variety ( d ) - ( f ) , since the 1140) branches are truncated preferentially with respect to the (100) ones, due to GId0(1) > Glo,,(l); cf.fig. 11. Crossed polars. Scaling bar: 20 pm, common for all crystals. [To face page 236FIG. 16.-Bilayer crystal grown in the upper transition interval from thin molten film. Darkest con- trast indicates overlap of the two once folded chain monolayers. Intermediate contrast denotes the extended chain portion, common to both monolayers in the overlapping region. Phase contrast. Scaling bar: 20 ,um. (a 1 (6) FIG. 17.-Modified pathological crystal habits obtained on cooling (a) and heating (6) of six branched starlike crystals shown in fig. 13(a) Crossed polars. Scaling bar: 20 ,urn, common for both crystals.[l'o facepage 237A. J . KOVACS AND C. STRAUPE 237 The two crystals depicted in fig. 18 were grown in similar conditions (see the legend) from thin films. The extended chain crystal halves emerging from the (100) and (140) sectors result here from the increase of T, above T*120(0). (b) In the second example illustrated in fig. 19, the initial crystal, grown at 59.68 "C (t, = 45 h), is similar to that shown in fig, 13(c), displays rather large and (140) and (100) extended chain sectors. On cooling to 59.62 "C, the former are completely covered by folded chains, whereas the latter are only partly, similar to the crystals shown in fig. 15 and described above. On final reheating (at t , = 48 h) to 59.66 "C, both original extended chain (100) sectors split into three branches and develop one (100) and two (140) tips on each side of the crystal (fig.19). Concomitantly, the original adjacent (140) sectors merge along the b axis direction and give rise to the rectangular thickened portions in the crystal interior. For the truncated crystal varieties, such as those shown in fig. 15, the relevant extended chain sectors display the same modifications. (c) Starting with crystals, grown at 59.66 "C, of the type depicted in fig. 13(b), but now increasing T, (after 10 h) to 59.68 "C, to open the (100) and (140) sectors [cf. fig. 13(c)], the specimen is cooled (t, = 36 h) to 59.67 "C and kept at this T, until final quenching at t, = 54 h. Fig. 20 depicts the typical crystal habit obtained after this thermal treatment t (for the six branched variety) displaying four (140) extended- chain tips, in addition to those resulting from the splitting of the large initial (100) sectors, as in fig.19, thus giving finally rise to ten extended chain branches. ( d ) In a similar treatment, (see the legend to fig. 21), but now heating to 59.69 "C in order to open very large (100) and (140) sectors, resulting in a four-leaved clover shaped thickened portion [intermediate between those shown in fig. 13(c) and 13(d)], the specimen is cooled again to 59.67 "C (at t, = 48 h) and finally quenched at t, = 66.5 h. Fig. 21 illustrates four of the crystal varieties obtained, displaying 2, 3, 4 or 6 of the initial (100) and (140) branches [cf. fig. 14(b), (c), (e) and (h)]. (The four others were also observed).These show, in addition to the (100) and (140) sectors displayed by the crystal in fig. 20, an extraneous extended chain tip emerging, near to the (120) oriented growth faces, in each quadrant (between a* and 6) where the (140) sectors were initially present. Therefore, the original six branched variety [cf. fig. 15(h)] gives rise to 14 extended chain sectors [fig. 21(d)], whereas in the other crystals some of these were truncated, according to the selection rule described above (fig. 15). Though the origin of the extra extended chain tip cannot be interpreted unambigu- ously at present, there is some suggestion that it results, similarly to (100) and (140}, from the emergence of an (hkO) prism face which grows more rapidly in the extended- chain conformation than the neighbouring ones in the folded-chain conformation.If this is the case, one should be able to produce in a single crystallization step a new type of basic pathological habit, displaying a ten branched thickened interior and possibly its truncated varieties, presumably at least 13.: The complexity of pathological morphologies increases, of course, with that of the thermal history. Nevertheless, the various crystal habits can be rather precisely predicted by simply accounting for the basic habits and the relevant growth rates involved. Conversely, one can also extract from the various morphologies the simp- t Note that starting at 59.68 "C and subsequent cooling (at 36 h) to 59.67 "C would give rise to a quite similar morphology, but to a smaller proportion of the truncated crystal varieties (not shown in fig.20). 1 Note added inpoof: Such crystals (similar to that shown in fig. 20) have indeed been obtained recently in a single crystallization step by a more precise control of T, (f 0.003 K) in the range 59.675-59.695 "C.238 MELT GROWN PEO SINGLE CRYSTALS lest thermal treatment required to produce them, though such a deconvolution may not be unique, since the temperature changes involved are of the order of 0.01 K. CONCLUDING REMARKS The previous and present investigations provide an unprecedentedly direct and detailed insight in the way polymer chains fold, unfold and melt. They further reveal, in addition to T,(n, p ) , a series of precisely defined growth transition temperatures, Tr(n,p), at which in a given growth face (i) the number of folds per chain abruptly varies by one unit.In this respect, the features described above clearly show that on crystallization short polymer chains select their conformation in a unique manner, determined by the free energy balance relevant to their immediate environment, with the proviso that the time allowed is long enough to approach dynamic equilibrium between the various conformations. (Note that in the transition interval deposition of a monomolecular layer lasts w 5 s, whereas at room temperature NN lo6 times less; cf. fig. 3). In this respect the present system is certainly not unique, its main peculiarity is merely that changes in chain conformation produce large and easily detectable effects. The data reported in this work thus provide a challenging framework for theoretical speculations about polymer crystal growth.Of course, at large undercoolings, or equivalently for longer chains, there is not enough time to approach the relevant dy- namic equilibria since other more rapid processes become operative. The latter compromise the former and lead to unstable chain conformations rather than to regu- lar chain folding which is thought to be the case with the present system, at least when n is an integer. Although no explicit information is presently available about the origin and precise structure of the folds, the observations made above imply that chain folding is a highly systematic phenomenon in polymer crystallization, even when the latter is performed from the melt. The authors are indebted to Dr B. Lotz for enlightening discussions during the They are also grateful to Dr A. Schierer for the quality of evolution of this paper. photographic work. J. P. Arlie, P. Spegt and A. Skoulios, Macromol. Chem., 1966, 99, 160; 1967, 104, 212. P. Spegt, Macromol. Chem., 1970, 140, 167. Y. Takahashi and H. Tadokoro, Macromolecules, 1973, 6, 672. A. J. Kovacs, A. Gonthier and C. Straupe, J. PoZymer Sci., Part C, 1975,50,283. C . P. Buckley and A. J. Kovacs, Progr. Colloid Polymer Sci., 1975, 58,44. C . P. Buckley and A. J. Kovacs, Colloid Polymer Sci., 1976, 254, 695. A. J. Kovacs, C. Straupe and A. Gonthier, J . Polymer Sci., Part C, 1977,59, 31. A. J. Kovacs and C. Straupe, J. Crystal Growth, 1980, in press. ed. N. B. Hannay (Plenum, New York, 1976), vol. 3, chap. 6. * A. J. Kovacs and A. Gonthier, Kolloid-Z., 1972,250, 530. lo J. D. Hoffman, G. T. Davies and J. I. Lauritzen, Jr, in Treatise on Solid State Chemistry, l1 J.-J. Point and A. J. Kovacs, Macromolecules, submitted. l2 B. Lotz and A. J. Kovacs, Kolloid-Z., 1966, 209, 97.FIG. 18.-As in fig. 17, but using the following thermal treatments (a) Tc,l = 59.66 "C (tC,1 = 19 h) 59.80 "C ( t c , 2 = 18 h). -+ Tc,2 = 59.62 "C ( t c , 2 = 19 h) -+ Tc,3= 59.72 "C; (b) Tc,l = 59.66 "C ( t c , l = 48 h) + Tc,z = Phase contrast. Scaling bar: 20 ,urny common for both crystals. ( a ) (b 1 FIG. 19.-Crystals grown at three consecutive temperatures: Tc,l = 59.68 "C (tc,l = 45 h) + T S , ~ = 59.62 "C (t,,. = 3 h) + Tc,3 = 59.66 "C [to3 = 24 h for crystal (a) and 44 h for (b)]. Crossed polars. Scaling bar: 20 pm, common for both crystals. [To face page 238FIG. 20.-Thermal history: Tc,l = 59.66 "C (tc.l = 10 h) -+ TC,* = 59.68 "C ( t c , 2 = 26 h) 4 Tc,3 = 59.67 "C ( t c , s = 18 h). Crossed polars : Scaling bar 20 pm. ( t 1 (d 1 FIG. 21 .-Pathological crystal varieties obtained after the following thermal treatment : Tc,l = 59.66 "C (tc,l = 24 h) + TC,* = 59.69 "C (tC,* = 24 h) -+ Tc,3 = 59.67 "C (tc,3 = 18.5 h). Note that the lack of symmetry with respect to (100) in the 3 and 4 branched crystals [(b) and (c)], merely arises from the truncation of the extra (hkO) tips. Crossed polars. Scaling bar: 20 pm, common for all crystals. [To face page 239

ISSN:0301-7249    

DOI:10.1039/DC9796800225

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

Molecular Nucleation and Segregation BY BERNHARD WUNDERLICH Department of Chemistry, Rensselaer Polytechnic Institute, Troy, New York 121 81, U.S.A. Received 2nd May, 1979 The possibility of large scale mobility of flexible linear macromolecules is discussed with examples of quantitative studies of crystallization and melting kinetics, the segregation of complete molecules on crystallization and the direct observation of molecular diffusion. The organization of macromolecules in the condensed phases may be characterized by their macroconformations. The term macroconformation was coined to describe the overall shape of a macromolecule without specific reference to the detailed suc- cessions of rotational states along the chain. One can distinguish three limiting macroconformations : random coil, folded chain and extended chain.An inter- mediate macroconformation, which contains elements of all three, is the fringed micelle.2 In the molten and glassy states the random coil is a rather open macro- conformation with an average chain atom density similar to that of a gas; considerable interpenetration and entanglement must exist to build-up the observed condensed phase density. One of the key questions for the understanding of ordering on crystal- lization is the degree of disentanglement and segregation of the molecules. In this discussion evidence for the broad variation in the degree of disentanglement and segregation is presented. KINETICS OF CRYSTALLIZATION A N D MELTING Crystallization after primary nucleation can be measured quantitatively by the linear crystal growth rate (v).Crystal growth rates of flexible linear macromolecules range from mm min-l to nm min-1.3 Qualitatively an even larger range is observable. This broad time scale suggests different degrees of disentanglement and segregation in the crystallization steps, although no noticeable discontinuity exists in crystalliza- tion-supercooling curves. Models have been devised for the description of various degrees of disentanglement during crystallization. The limit of complete absence of disentanglement has been called cold crystalliza- t i ~ n . ~ The size of the resulting small crystals has been estimated from statistical considerations by assessing copolymer units, chain entanglements, loops and chain ends as non-cry~tallizable.~ A one parameter description could be achieved for this simplest case.Copolymers quenched for crystallization seem to follow this model. The influence of increasing molecular mobility on homopolymer crystallization was discussed by Ewers et aL6 The probability that a newly crystallized sequence of chain atoms is from a previously uncrystallized molecule is treated as adjustable parameter PI. The surface structure could be calculated from such model. Changing the parameter PI by nine orders of magnitude, the macroconformation changed from a240 MOLECULAR NUCLEATION AND SEGREGATION fringed micelle type of interpenetrating molecules to a folded chain type of well separated molecules. The limit of complete disentanglement and segregation can be described through thermodynamic argument^.^ A discussion of the entropy at the interface crystal-melt normal to the molecular chain direction led to the conclusion that in the case that crystallization is slow rela- tive to the time needed to reach equilibrium between various conformations, folding is preferred .s A survey of morphological evidence on many macromolecules crystallized from solution, but also from the melt has led to the formulation of the chain folding princi- ple : “ A sufficiently regular, flexible linear macromolecule crystallized from the mobile random state will always crystallize first in a chain-folded macroconformation.” As the mobility decreases, the fringed micellar macroconformation with decreasing number of folds should become more prominent.Of interest to the present discussion is the evidence for mobility necessary for large scale disentanglement and segregation and in the end also for chain folding.A comparison of the crystallization and melting kinetics may reveal any particular differ- ence between the separation process of entangled molecules and the mixing after melt i ng . The melting kinetics have been studied much less than lo the crystallization kinetics. The main reason lies in the smallness of fringed micellar crystals and also of thin chain folded chain lamellae. The melting of such small crystals is so fast that the limiting factor is the conduction of heat to the interface. Reorganization and re- crystallization, as well as relaxation of strained tie molecules during heating, further obscure the melting process.Well crystallized macroscopic extended chain crystals of flexible linear macro- molecules melt slowly enough so that the melting kinetics can be followed. Fig. 1 shows data for two model compounds, selenium 11,12 and polyethy1ene.l3*l4 The melting and crystallization processes are clearly discontinuous at the equilibrium melting temperature. It requires a much larger supercooling to reach a crystallization rate identical to the melting rate at a given superheating. The abnormally high free enthalpy barrier to crystallization was originally linked to secondary (surface) nucleation because of its functional correspondence to an exp (- l/AT) dependence. Crystallization from the gas phase, in contrast, is com- monly AT2 dependent [see fig.l(a), dotted curve]. Analysis of surface nucleation indicates, however, that molecules do not make use of surface steps to enhance crystal growth.” The solution to this puzzle is the need of molecular nucleation for crystal growth.16 At the lowest supercooling, no crystal growth is observed because of a nucleation barrier to add a new molecule to the crystal surface. This nucleation step will be shown next to be the major cause of segregation. SEGREGATION ON CRYSTALLIZATION A study of tfie segregation of molecular weights on crystallization from the melt17 permits a judgment of the mobility of molecules during crystallization. The tech- nique involves fractional dissolution of lower melting crystals and separation by filtration. Only if the molecules are completely separated from other, higher melting crystals is such separation possible.As soon as tie molecules exist between crystals of different stability, the lower melting portion of the molecule can be dissolved, but not removed from the sample by filtration. The formation of such tie moleculesB . WUNDERLICH 30 20 241 - - -0 0. 160 Pa **. I 2 . 5 1 4 0 '\ 7 ~ 1 0 - ~ oo.-o 3 xlO-' 5 x ~ O - ~ \ (b) \ O\ 0 I I I I I ' I 100 80 60 40 20 0 20 I I I I I . 20 15 10 5 0 5 -30 A T I K A T 1 K FIG. 1 .-Linear melt crystallization and crystal melting rates of selenium (a) and polyethylene (6). The crystals were of the extended chain type. Melting rates at right angles to the chain direction. Equilibrium melting temperatures: selenium 494.2 K, polyethylene 414.6 K.The dotted line indi- cates vapour phase crystal growth of selenium which occurs by crystallization during polymerization of Se2 and shows no molecular nucleation barrier to crystal growth needed for flexible linear macro- molecules. could be shown to increase with molecular weight and supercooling.18 This expected increase in tie molecules is an indication of the limits to molecular mobility. As soon as a molecule participates in one or more crystals it cannot be rejected as a molecule. Quantitative segregation results for a broad molecular weight distribution poly- ethylene are listed in table 1. These results show clearly that for low degrees of super- cooling, large molecules are segregated, i.e., considerable motion unhindered by tie molecules must be possible.A comparison of the last two columns shows, further- more, that the process of segregation is not governed by equilibrium but rather it is a segregation due to molecular n~cleation.~ Similar segregation was also observed for mixtures of polyethylene and deutero- polyethylene. On slow crystallization considerable segregation occurs, while on quenching a more homogeneous mixed crystallization is p0ssib1e.l~ The reverse process of mixing on melting could also be shown to be fast enough on slow heating to approach equilibrium conditions. Extended chain crystals of poly- ethylene could be dissolved into a melt of various molecular weights with the predicted change in melting temperature.20 On these slow melting experiments (2 K h-l) complete mixing on a molecular scale is necessary to account for the results.242 MOLECULAR NUCLEATION AND SEGREGATION Segregation on a less than molecular scale are common in the crystallization of A frequent observation is in these cases a change in the fraction of copolymer content in the crystalline phase with crystallization conditions.This may also be taken as evidence of the changing time scale for segregation with crystalli- zation rate. TABLE 1 .-VARIATION OF THE CRITICAL MOLECULAR WEIGHT WITH CRYSTALLIZATION TEMPERATURE FOR MELT CRYSTALLIZED POLYETHYLENEa experimental equilibrium weight* weight" temperature/K critical molecular critical molecular 373.2 383.2 388.2 393.2 398.2 400.2 402.2 600 940 1100 1800 3100 2200 3700 2900 4400 3800 7300 4500 22 300 5200 ~~ (I Data from ref. (17), extraction with g-xylene, checked for completeness by scanning calorimetry. The critical molecular weight is defined as the highest molecular weight which is separated to 90 % The equilibrium critical molecular weight was calculated using the Flory-Huggins or better.equation, assuming x = 0. DIRECT OBSERVATION OF MOLECULAR DIFFUSION Direct observation of molecular diffusion is possible by a study of crystallization in thin 1a~ers.l~ Fig. 2 shows the surface of an extended chain crystal of polyethylene on which folded chain lamellae were grown. Crystallization at 403.2 K led to a lamel- lar spacing of 67 nm. Reduction in crystallization temperatures to 393.2, 388.2 and 373 K reduced the lamellar spacings successively to 33, 25 and 20 nm. This large scale motion must have occurred in the time scale of crystallization (see fig.2). Other direct evidence for long distance motion of macromolecules was presented by Nachtrab and Zachmann2' and Johnson et aZ.22 who crystallized ethylene-vinyl acetate copolymers. The linear crystallization rates showed a decrease whenever neighbouring spherulites approached to within 20 pm. The slowing down of crystal- lization must mean that there is a segregation on a molecular scale. At lower crystallization temperatures the effect decreases as one would expect. In both cases the observed molecular motion is larger than the typical radius of gyration of a macromolecule and must involve disentanglements of thousands of molecules. CONCLUSIONS The selected examples discussed above show clearly that gross changes in the spatial entanglement in advance of the crystal surface can take place, provided the molecules remain sufficiently mobile.The mobility is to be judged in the time frame set by the crystallization rate which may change by more than six orders of magnitude. Polyethylene of over 20 000 molecular weight could be shown to separate fully and practically completely from higher molecular weights at 130 "C. This must be taken as evidence that assumptions to the contraryz3 are not supported by experiments.FIG. 2.-Electron micrograph of a replica of a fracture surface of polyethylene extended chain crystals which served as substrate for crystal growth at 403.2 K. The newly grown lamellae can be seen to be independent of the substrate surface structure except for parallel alignment of the crystallographic c-axis.Micrograph by Melillo. Scale bar 1 pm. (Molecular weight M,, = 8000, polydispersity 20, extended chain crystals grown at 500 K and 450 MPa.) [To face page 242B . WUNDERLICH 243 It was not the purpose of this discussion to point out the evidence for the cases where crystallization is fast relative to molecular mobility. Naturally they exist frequently and can be documented just as c o n v i n ~ i n g l y . ~ ~ ~ ~ ~ * The special goal for the future must be the quantitative evaluation of partial segregation, disentanglement and chain folding rather than the proof or disproof of the two limiting cases. Special hope for such results is contained in well devised neutron scattering experiments presented in other places of this discussion.The work on crystallization has been supported in our laboratory by the National Science Foundation (Polymers Program) grant no. 78 15279. B. Wunderlich, Macromolecular Physics, vol. 1 , Crystal Structure, Morphology, Defects (Aca- demic Press, New York, 1973). B. Wunderlich, Macromolecular Physics, vol. 2, Crystal Nucleation, Growth Annealing (Aca- demic Press, New York, 1976). M. Dole, Kolloid-Z., 1959, 165, 40. B. Wunderlich, J. Chem. Phys., 1958, 29, 1395. W. M. Ewers, H. G. Zachmann and A. Peterlin, Kolloid-Z., 1972, 250, 1187. Faraday SOC., 1955, 51, 848. H. G. Zachmann, Kolloid-Z., 1967, 216-217, 180; 1969, 231, 504. A. J. Kovacs, B. Lotz and A. Keller, J. Macromol. Sci., 1969, 133, 385. ’ K. Herrmann, 0. Gerngross and W. Abitz, 2. phys. Chem. 1930, 10, 371. ’ P. J. Flory, Principles qfPoIymer Chemistry (Cornell Univ. Press, Ithaca, N.Y., 1953); Trans. lo B. Wunderlich, MacromolecuZar Physics, vol. 3, Melting (Academic Press, New York, 1980). l1 H.-C. Shu and B. Wunderlich, J . Crystal Growth and J . Appl. Phys., in press. l2 R. G . Crystal, J. Polymer Sci., Part A-2, 1970, 8, 2153. l3 G. Czornyj and B. Wunderlich, J . Polymer Sci., Polymer Phys. Ed., 1977, 15, 1905. l4 J. D. Hoffman, L. J. Frolen, G . S. Ross and J. I. Lauritzen, Jr, J . Res. Nat. Bur. Stand., 1975, l5 B. Wunderlich, L. Melillo, C . M. Cormier, T. Davidson, and G. Snyder, J . Macromol. Sci., l6 B. Wunderlich and A. Mehta, J. Polymer Sci., PoZymer Ph-vs. Ed., 1974, 12, 255. l7 A. Mehta and B. Wunderlich, Colloid Polymer Sci., 1975, 253, 193. l8 A. Mehta and B. Wunderlich, Makromol. Chem., 1974, 175, 977. l9 F. C . Stehling, E. Ergos and L. Mandelkern, Macromolecules, 1971, 4, 672. ’* P. Sullivan, Thesis (Rensselaer Polytechnic Inst., Troy, N.Y., 1965). ” U. Johnsen, G. Nachtrab and H. G. Zachmann, Kolloid-Z., 1970,240,756. 23 P. J. Flory and D. Y. Yoon, Nature, 1978, 272, 226. 79A, 671. 1967, B1, 485. G . Nachtrab and H. G. Zachmann, Ber. Bunsenges. phys. Chem., 1970, 74, 837.

ISSN:0301-7249    

DOI:10.1039/DC9796800239

出版商:RSC    

年代:1979

数据来源: RSC