摘要:

GENERAL DISCUSSION Prof. J.-J. Point (Uniuersity of Mons) said: These remarks should be treated as an extension of the argument in my paper. During the last few months, I have re-examined the mathematical tractability and the predictive ability of the various models discussed in my paper. I give now a brief report on this work. When the formation of a surface layer on the edge of a lamella is formulated as proceeding through the successive deposition of full stems, (§1), the model is easily tractable. But the variation of free energy associated with the deposition of a full stem is much greater than kT. The use of the theory of absolute reaction rates is not, a priori, justified and sometimes the expressions for the rate constants cannot be sup- ported even by intuitive arguments.When short segments ($3.3) are the crystallizable units, the model is analytically tractable, either if the postulate of persistence length is conserved,l or if the rate constants for attachment or detachment of a small segment do not depend on the environment of the attachment site (DiMarzio, personal com- munication). Without such simplifying assumptions, Monte Carlo calculations seem unavoidable. The lack of predictive ability of the current models concerns (i) the calculation of the degree of crystallinity (ii) the computation of the constant C of the Lauritzen- Hoffman formula ( I = C + B/AT). In fact the major part of C results from an hypothetical thermal dependence of the free energy of a fold. The observation of a plateau in the Z against T curve is general and this conclusion is thus deceiving.(iii) By use of the simplified version’ of the model of $3.3, the predicted degree of crystal- linity is again 1. Therefore, Monte Carlo calculations are made on the model of $3.3 and ref. (1). If aAZ, bAZ, . . ., iAZ, jAZ are the lengths of the n stems of a two-dimensional nucleus, this nucleus is denoted by the n-tuple of integers (a, b, . . . i, j ) . The transition prob- abilities p , q, r, s, . . . between the various states are defined as follow: (11) The observed Lauritzen and Hoffman (LH) law does not prove that the process of crystallization is secondary nucleation controlled. This law can be found for other processes, principally by the two-stage process, (precipitation of small parts of the chain, and then annealing) which I have described in ref.(7) and which Prof. Point calls the “ solidification model ”. In this model, in solution grown crystals or in the melt, the central idea is that the border of the crystal is a bad crystal in which the chains can reorganize by annealing, but at the same time, defects, kinks, vacancies are ejected from.the crystals, and therefore the mobility of the chain in the crystal decreases, and the annealing effect of the chain stops. The modified LH law is: where the term o! is the LH term, 2, the limiting fold period, B is inversely pro- portional to the activation energy for stem jump inside the crystal; in other words B is proportional, to the mobility of the chain in the crystal state.This law explains therefore the difference in behaviour of PE chain (highest mobility), PS (bulky groups, medium mobility) and nylons (very low mobility because of the hydrogen bonding between consecutive chains). This law also will explain the analogy between the dependences of I in melt crystal- lized polymers with the annealing temperature and with the temperature of crystalliza- tion. Skoulios has noted this analogy by studying the crystallization of POE chains with bulky ends groups or long un-crystallized end groups.8 The modified L.H. law seems to apply to melt crystallized polymers. But, because of the high temperature of crystallization, the process of thickening can be different from those described in solution grown crystals : entanglements are pre~ent.~ Did Prof.Point apply his theory to melt crystallized PEO chains of molecular weight M > lo4 and with different end groups to see the variations of the adjustable para- meters (oe, 0, AZ) with the nature and the importance of the non-crystallizable end group ? (111) Does Prof. Point think that from his theory or from the classical kinetic theory it is possible to predict the thickness of the amorphous layers in melt crystal- lized materials and its variation with temperature and molecular weight (variation of the crystallinity) ? Prof. J.-J. Point (University of Mons) said: (I) The contribution of Dr. Rault is to provide, without conceptual explanation, an estimation of the initial thickness of crys- talline lamellae, i.e." the length of the smallest part of the liquid chain which has a gaussian character ". The range of application of this relation may be not so large as implicitly assumed. At low supercooling when a decrease in the crystallization temperature induces a step on the surface of solution grown crystals,' the measured thickness is usually regarded as the initial thickness and does not obey the proposed relation. At high supercool- ing, I wonder of the proposition to use a single parameter in the study of cold crystal- lization2 or of an erstarrrungs pro~ess.~ Concerning my approach, if limitation of fold length is discussed in a way parallel to that used when the size and shape of a flexible macromolecule in the liquid state are studied, this does not imply that the crystal thickness may be related to a single para- meter of the liquid chain.In a wide range of crystallization rates, as shown by many contributions to this Discussion, the molecule reorganizes during its deposition. In studying such a process, the length of a crystallizable segment, the free energy of a fold, the afinity of crystallization, the excess free energy of an imperfectly crystallized segment on the growth face of the lamella, are all parameters of interest and cannot be reduced to a single one. The questionable equality of the values of lc for PE and PS does not imply the equality of all these individual parameters. (11) The first step of the two-stage model considered in $4 of my paper is not a solidzjkation process but on the contrary implies a transient reorganization of the whole oligomer molecule as a rectangular nucleus with adjacent stems and the lowest possible free energy.Thus, I do not see the analogy of this model with the model described by Rault4 (this last model is closely similar to a model previously given by Skoulios5 and is related to the various models in which the initial shape of the mole- cule in the crystal reflects the conformation of the molecule in the liquid state). As a further comment, since eqn (2) describes a process in the solid state, ATis the difference between the melting temperature of the crystal and the crystallization temperature. For solution grown crystals, similar equations are obeyed but in which AT [see for instance ref.(6)] denotes the difference between the dissolution and crystal- lization temperatures. That is quite a different result! Experimental data on ethoxy and hydroxy terminated PEO are closely similar (at least for the investigated fractions) and no major variations of the adjustable para- meters are deduced from the analysis of these data. Data from high molecular weight PEO are poorer than those obtained from low molecular weight fractions. Finally, for the progress of theoretical work, new data on systems much simpler than uu alkoxypoly(ethy1eneoxide) * are needed. (111) When persistence of stem length is assumed, and if the length 1 which appears in the expression of the rate constants [see for instance eqn (4.3) and (4.4) of the paper by Hoffman et al.] is the lamellar thickness, application of the principle of detailed balance leads to the conclusion that the degree of crystallinity is 1.However, in their paper, Hoffman, Guttman and DiMarzio suggest that loops and dangling ends of the molecules make a contribution to the amorphous component. Physical adsorp- tion of macromolecules is also considered by Breedong and Hoffman (this Discus- sion). But under these last assumptions, a clear distinction is to be made between 1 and the total thickness of the lamella. This may introduce a factor (for instance of 2) between the calculated10 and experimental'' values of the thickness of PS lamella of low crystallinity(2) The similar varia- poly- tions of L with the supercooling AT in MCP and SCP.(3) The analogy between the variation of L with the temperature of crystallization and with the temperature of annealing. (4) The following rule: the temperature range where lamella thickness is dependent on the temperature of crystallization is the same order of magnitude as that where thickening by annealing process appears in MCP. (5) The smaller variation of L(T,) of chains which have bulky end groups or long un-crystallizable end groups. (6) The very slight variation of L(TJ of chains which have hydrogen bonding in the crystal state [nylons, amylose, poly(ester amide), polypeptides]. (7) The steplike increase of L(T,) of small chains like PEO of molecular weight < lo4, and continuous increase for larger chains.(8) The non-observation of L(T,) variations in block copolymers (SCP and MCP) for long chains. (9) The dependence of L, in copolymers MCP swollen or not with the concentration of solvent, and with the ratio NJN, of the lengths of the two unlike parts of the chains (L, being the thickness of the crystalline layers). (10) The variation of L, in MCP with the temperature Ti of the melt follow- ing the law: L(T) = LC(T0" + P V i - 7-31 p being the temperature coefficient fi = d log r,"/aTi. (1 1) The variation of L, in statistical or alternating copolymers, xf being the concentration of defects in the chain or comonomer unit; L, follows this general law : where y is proportional (or equal) to the defect coefficient y = a log (r;)/ax.In other words, the variations of L, is similar to the variation of the characteristic ratio with the number of defects in the chain. I think that these features are explained by the two stage process of crystallization proposed in ref. (l), and by the fact that the folding in the solid state is the image of the folding state or, in other words, that the crystalline lamella thickness is propor- tional to the rigidity (the persistence length of the chain just before it crystallizes). I wonder how the kinetic theories would explain these different features. J. Rault, J. Phys. Lettres, 1978, 39, L411. GENERAL DISCUSSION 371 Dr. J. D. Hoffman (National Bureau of Standards, Washington, 0 , C . ) said: Prof. Point's statement that the shifts of log G for extended chain crystals of PEO of DP 43, 63, and 84 as a function of reduced undercooling 0 = P2[T'(00) - T2]/T2 are inconsistent with the tenets of the Lauritzen-Hoffman (LH) theory is in my view a result of a misunderstanding concerning the range of applicability of the LH theory (see his fig.2).Prof. Point suggests that classical nucleation theory breaks down at v = 1 for extended-chain systems because it results in a lateral surface free energy that is chain length dependent. Although it is difficult to follow Point's argument because of the paucity of detail, we suppose that he has used correctly for this case S = N,A,(A - B)/ (A - B + B,) where the A's and B's now refer to rates for adding whole molecules, which happen to be coincident with stems.It is to be emphasized that although this looks like eqn (l), the A and B of eqn (1) are for stems of a whole molecule which is composed of v stems on the crystal face, while the A and B in the latter case are for the extended chain molecules themselves. We should like to suggest that the large anomalous stem-length dependence for S obtained by Prof. Point arises from the fact that the nucleus length is not equal to the stem length, but in fact has some smaller value. This would result in a smaller variation of S with chain length, in agreement with the experimental trend. We believe that a proper theory for extended-chain crystallization can be obtained with this concept, provided extended-chain crystalliza- tion is nucleation controlled.Classical nucleation theory is not deficient, but one must be cautious in its application. Turnbull and Spaepen have analysed homogeneous nucleation data of various authors on the n-paraffins n = 5-32 using the expression, in their notation, where zl = ratio of interfacial tension/CH, group in the crystal boundary plane and GENERAL DISCUSSION 372 the heat of fusion/CH, group, V,, = volume per molecule, and Ahnf = enthalpy of melting per molecule. We are not in any general way opposed to Prof. Point’s discussion of alternative paths of nucleation: there must indeed be many. However, DiMarzio has shown elsewhere in the Discussion remarks that Point’s treatment and the simpler LH theory converge at low and moderate undercoolings where we have usually applied it in our work.It may be added that Prof. Point has found an interesting way of undoing the “ 61 catastrophe ” (“ blow-up ”) that appears for high yo values at high ATin the LH theory. We have already eliminated it1 by using low values of ly,, and it is believed that this approach is physically valid. The general argument for assuming a low yo value is given in the appendix of the paper by Hoffman et al. in the Discussion. seem to use Tg(co), i.e., the equilibrium We remark that Point and Kovacs et melting point of the chain of infinite chain length, as the temperature from which to measure the undercooling, for an oligomer of finite chain length. (See for example the definition of t9 in Point’s paper.) It is readily shown that ATshould be measured for a polymer of n chain units as AT = Tm(n) - T, where T,(n) is the melting point of the extended chain crystal of large lateral dimensions and thickness corresponding to n, and T, = T2 the crystallization temperature.The suggestion3 that we have introduced Tm(n) into the LH formulation in an ad hoc manner is incorrect; eqn (2.1) of the paper by Hoffman et al. in this Discussion, where Af= (Ah,)[Ti(n) - T,]fT~(n), can be derived in a simple and formal manner.6 For Tg(n), we used a simple variant of the familiar Flory-Vrij equation’ in the case of polyethylene. We are in full agreement with one major thrust of Prof. Point’s paper, and that is that the analysis of the impressive and superbly detailed rate of crystallization data of Kovacs and co-workers on PEO fractions deserves the attention of theoreticians.From this analysis one can expect to learn much more about the onset of chain folding as the molecular weight is increased. The rate of melting data presents a similar challenge. Meanwhile, we have the impression that the presence of -OH end groups in PEO complicates the situation and sets this material aside from polymers such as polyethylene, where strong attractive forces (hydrogen bonds) do not exist between the end groups. GENERAL DISCUSSION 373 Prof. J.-J. Point (University of Mons) said: No misunderstanding concerning the range of application of the LH theory is possible. For 20 years, the theory has been applied to low molecular-weight fractions ‘v2 as well as to high molecular-weight mate- rials.For instance, Hoffman et al. apply the theory to a PE fraction for which the ratio (denoted v in Dr. Hoffman’s comment) of the length of a molecule to the length of a stem is assumed2 to be 1.5. Thus, I do not understand why a lower bound (3 or 4) is now proposed without explanation. When v is low, as evident from fig. 13 of ref. (2), several molecules may be involved in the building of a single nucleus. A clear distinction is to be made between v and the number, let us say n, (which theoretically goes to infinity) of stages of the sequential process considered by Frank and No reasons are given by Dr. Hoffman for limiting the discussion of PEO data to extended chain crystallization, As explicitly stated in my $2.1, the LH theory does not apply either to extended or to forded chain crystallization.More extensive discus- sion may be found el~ewhere.~ The experimental data are interpreted in my $3.1, by assuming that the length of the nucleus depends neither on the temperature nor on the length of the stems of the mature crystal, in formal contradiction to the basic assump- tions of the LH theory. I greatly appreciate that Dr. Hoffman acknowledges that the nucleus length may differ significantly from the stem length. In a discussion4 of the PEO data reported in my $2.1, Prof, Kovacs and myself assume on the contrary that the current kinetic theories of polymer crystal growth apply to the PEO data.The obtained apparent variation of 0 is not taken as real but as a proof of the inapplicability of the theory. Thus, we never conclude that CJ may depend on the length of the molecule. Prof. A. J. Kovacs (Strasbourg) said: I would like to correct a statement made by Dr. Hoffman concerning our previous work,' and to answer his comment on the appro- priate choice of the melting temperature in analysing polymer crystal growth in the framework of the Lauritzen-Hoffman (LH) theory. (1) In our former analysis' of the growth rate, G(n,p), of PEO crystals (where n is the number of folds and p the number of monomer units per chain molecule, the latter being denoted by n in Dr. Hoffman's comments), we used amongst the various melting temperatures Tm(n,p) that which corresponds to extended chain crystals, i.e., T,(O,p), in conformity with his previous and present recommendation, rather than T,,,(O,co) = T:(co), as quoted in his comment.Interestingly, the use of T,(O,p) results in some partial agreement between the LH theory and the data obtained at relatively high supercooling, though still involving quite low values of n (e.g., n 21 1 for the fraction of molecular weight 2000). For fast growth, therefore, the agreement does not appear to be limited to large n values, as claimed by Dr. Hoffman. Nevertheless, when n is an integer or zero, T,(O,p) does not account for the data, even qua1itatively.l (2) Clearly, the appropriate melting temperature cannot be chosen arbitrarily, since its value is uniquely determined by the particular theoretical model used in defining the free-energy balance of the growth nucleus which, in turn, determines the various rate parameters, [A,, A etc.in eqn (1) of Dr. Hoffman's comments], control- ling the rate of nucleation and subsequent growth. It should be pointed out further, that the values of Tm(n,p) and TA(c0) are also uniquely related by the chosen rnodel,ln3 rather than being independent. It turns out that, for short chains, the simplest expression for the relevant rate parameters is obtained when the various surface free energies of the growth nu- cleus, (i.e., that of the lateral surface of the first stem, 0, that involved by each dangling chain end, oe, and that of the folds, of), are unambiguously separated from the bulk free energy, AA (which may include a Flory-Vrij4 term), of the successive depositing stems.In that case, and for low and moderate undercooling, Afis proportional to the undercooling AT(co) = T,O(co) - T,, which refers to the melting point of a large crystal containing neither chain folds nor chain ends. In fact, all the surface effects GENERAL DISCUSSION by Dr. Hoffman in ref. (6) of his comments. Prof. J.-J. Point (Uniuersity of Mons) said: I agree that the observation of a finite growth rate implies that the affinity of crystallization is strictly positive; but its lower bound is zero. Kovacs’ data show that PEO fractions crystallize even when this affinity is very low. In my paper, no critical discussion of the experimental data was made.There must be a mistake here, however; I do not see the dilemma. By suitable choice of the value of the parameters, any curve of L against T(of the general shape given by experi- ment) may be predicted. More extensive data are needed for a critical assesment of the predictive ability of the theories. Prof. B. Wunderlich (Rensselaer Polytechnic Institute, Troy) said : The importance of the possibility of a kinetic theory of crystal growth which may be independent of a side surface free energy is underscored by the following: The true van der Waals envelope of (1 10) or (200) growth faces of polyethylene are not as represented by the simplified schematic of fig. 1 of Point’s paper. They resemble more closely an assembly of grooves of saw-tooth-like cross-sections.Adding a fitting chain of proper rectangular cross-section to such a surface creates little new side surface and should thus lead to the “ 61 catastrophy ” even at low supercooling. Experimentally, the insensitivity of surface nucleation can be deduced, for example, from electron micrographs such as fig. 2 of our paper at this Discussion: see also ref. (1). A thin layer of polyethylene melt was grown in this experiment on substrates of extended chain crystals. The newly grown lamellae are seen side-on. They are aligned by epitaxy with their c-axis parallel to that of the substrate, but ignore completely the available surface ridges for nucleation which could have provided a surface free- energy advantage.Prof. J.-J. Point (Uniuersity of Mons) said: I greatly appreciate the approach of Prof. Wunderlich, which illustrates quantitatively the difficulties underlined in my $2.2. I remark, however that, at the present time, I need an excess free-energy term in the expressions of some rate constants [see eqn (1) of my verbal presentation of the Paper]- Dr. E. A. DiMarzio (National Bureau of Standards, Washington, D.C.) said: We agree that the formalism of Prof. Point described at the end of this paper and more completely in a recent publication’ does indeed avoid the blow-up problem at high supercoolings. We also wish to observe that the lamellar thickness and growth rates for his model are the same as those for the previous “ classical models ” of Hoffman, Lauritzen, Frank and Tosi, Sanchez and DiMarzio, etc., for low to moderate super- coolings.It is clear from the foregoing discussion that, from the standpoint of nucleation theory, the degree of perfection of chain-folded crystals and the probability of adjacent re-entry is a function of undercooling and molecular weight. Determinations of the structure for quenched samples, which are commonly used for SANS, obviously canriot be utilized to decide the entire issue. Consider now the evidence presently at hand for the case of single crystals of poly- ethylene as studied by neutron scattering. The discussion below is not exhaustive, tremendous undercoolings were generally used to form the PEH + PED single crystals but illustrates the issues that have been raised.The first point to understand is that used in neutron scattering and related studies. The AT involved is typically -45 "C (Ti in xylene -1 14-1 18 "C, T, - 70 "C). The large undercoolings were required to prevent isotopic segregation, It must be clearly recognized that some departure from adjacent re-entry might well be anticipated for crystals formed under such rough conditions. The final result is not yet completely clear. Krimm calls for considerable adjacent re-entry with superfolding according to his infrared technique. Meanwhile Yoon and Flory require the stems to be somewhat separated on the growth front (re- entry every second or third stem position; see their fig. 4 in this Discussion).We note parenthetically that even this seems to us to be a considerable departure from the random re-entry '' switchboard " model originally proposed; we have long held the view that the stems of a crystallizing molecule in single crystals from solution were mostly distributed along the growth front, and that any imperfections such as " loops " caused by non-adjacent re-entry were more or less parallel to that growth front [see fig. 7 and 25 of ref. (l)]. Yoon and Flory's result, if correct, is not inconsistent with deep Regime I1 or even Regime III crystallization. Meanwhile, Keller and Sadler call for adjacent re-entry with superfolding. N.m.r. results suggest rather random re-entry at high molecular weights, but adjacent re-entry at moderate molecular weights;2 if correct, this agrees with prediction (2) above.Perhaps all this can be settled, but it would clearly be useful to consider work on a polymer where single crystals could be formed at low undercoolings without separation of the protonated and deuterated species, Polystyrene represents such a possibility ; crystals formed from solution at the lowest possible undercooling should show considerable adjacent re-entry. The kinetic theory of nucleation with chain folds has not yet been developed to the extent that it can deal directly with " mistakes '' of the type that lead to interlamellar tie molecules, or nucleation of a molecule on two distant sites on the same growth face that forms a long loop. It is these effects that cause much of the increase of the radius of gyration in melt crystallized material above that calculated for regular folding.It is apparent from the treatment in my paper, and more especially that of Guttman et al., that relatively few such " mistakes " are needed to give the radius of gyration a value similar to that of the melt, even though a considerable fraction of the stems in the crystal exhibit adjacent re-entry. The observation of a liquid-li ke radius of gyration in a semicrystalline polymer does not necessarily imply that adjacent re-entry is mostly or entirely absent for the stems that are in the crystal (see for instance the depic- tions of the " double stem " and " central core " models). Accordingly, because of the considerable fraction of adjacent stems that are present in the crystal lamellae, we are not surprised that the kinetic theory for G(T) and I,* ( T ) with the approximation of adjacent re-entry works as well as it does, especially at low and moderate undercool- ings for polymer of ordinary molecular weight.Meanwhile, the energetics of the fold surface, as embodied in the quantity oe e q/2aobo that occurs in both the kinetic equa- tions and the fold period l:, seem to correspond rather well to theoretical and other estimates of the work of chain folding q estimated for a reasonably tight fold. We are unaware of any theoretical estimates of the surface energetics for models where the emergent chains always or almost always re-enter the crystal in a rather distant and non-adjacent position, such as Yoon and Flory's y = 1 or pes = 0.3 models. Attempts to find the original type of folded structure in melt-crystallized material at low undercoolings, i.e., high crystallization temperatures, may be defeated by the effects of lamellar thickening, which will tend to erase the chain conformation laid down in the primary nucleation and substrate completion processes.Because of the generally lower temperatures involved, thickening can usually be avoided in crystals formed from dilute solution. In conclusion, nucleation theory provides a rational basis for suggesting that fold surface perfection will be greatest for polymers of low or moderate molecular weight crystallized at low undercoolings, and conversely, that the perfection will be minimal for polymer of high molecular-weight crystallized at high undercoolings.Evidence was presented indicating that this view may have substantial validity. The conforma- tion of molecules in the melt is in my view not the only factor that should be con- sidered when the questions of the nature of local re-entry, crystallization kinetics and lamellar thickness are addressed : nucleation theory has a contribution to make here. Questions related to the amount of the amorphous fraction (especially that part resulting from tie molecules and multiple nucleation of a molecule at distant points on the same lamella) and the radius of gyration in a semi-crystalline polymer seem to me to be in principle treatable by a combination of liquid-state conformation theory and niche theory.GENERAL DISCUSSION R. Voelkel and H. Sillescu, Macromolecules, 1979, 12, 162. Dr. E. A. DiMarzio (National Bureau of Standards, Washington, D.C.) said: It appears that a correct theory of polymer transport in a crystallization process should include both diffusion and thermodynamic forces, just as for example the theory of spinodal decomposition involves both diffusion and chemical potential gradients. My reason for believing this comes from a comparision of the distance reptated (dif- fused) along a worm hole to the distance that the molecule drifts under an applied force during a time characteristic of the process. For a reeling-in time of low3 s the whole molecule is transported a distance of 9100 8, (M.W.= lo5) but the distance diffused in the worm hole is only 1000 A. The force used in the above calculation corresponds to a supercooling of about 20-25 K. For supercoolings significantly less than this the treatment of Klein is completely adequate. ( j l ) 2 - C,Nb2 + MI2 (& - Cn) (1) Klein has argued persuasively that the idea of slack or stored length which is in- herent to the reptation concept provides an essential ingredient to the process of attach- ment of stems to the crystal. A process is suggested which allows for overall chain dimensions in the crystal that are the same as for the melt. At high supercoolings one can have many niches per molecule which incorporate into the growing crystal face. Slack would allow clusters of stems to form at each niche.Because of reptation there would not be a viscosity barrier to their formation. To conclude: (a) suction may be an efficient crystallization process even for melts of high molecular weight; (b) if the opposite " cold crystallization " or " solidifica- tion " models can win in certain regimes, this must mean that the chain portions in- volved here are smaller than the length n* = l/(coq). I do not know any detailed discussion of that point; (c) suction leads to large reductions in entanglement num- bers. However, the suction process per se does not necessarily impose adjacent re- entry, but only re-entry within re; ( d ) finally, it may be useful to note that suction, like all reptation processes, is very strongly quenched by branching.2 Whenever the branches are long (compared with the classical distance between entanglements n,), with a branch point fraction larger than l/n*, we should find completely different kinetics.Dr. J, Klein ( Weizmann Institute, Rehovot) and Mr. R. C. Ball (Cavendish Labora- tory, Cambridge) said : There appears to be some misunderstanding as to the limiting nature of the " perfect defect sink " conditions which we have used in our calculations. To clarify this we must first consider the relationship between our " sink " and thermo- dynamic driving forces arising from the crystallization process ; except where stated, notation is the same as in our discussion paper. Consider the case of a weak crystallizing force acting on the given molecule within its tube at time t after deposition has begun.Putting Ftube as the effective force acting on the " tube ", and L, the length of " tube " down which tension has been induced at time t , we have the " tube deposition '' rate where kT/Dc is the friction coefficient of the whole tube (assuming the Kubo fluctua- tion dissipation theorem to hold for the weak force case), and this is scaled down by a factor L,/L to account for the fact that only a length L,[ z (At)*, see also fig. 5(b) of our main discussion paper] of tube is in tension at time t . For a slack density C , the molecular deposition rate S is given by and replacing Ftube = (1 + C)F where F is the crystallization force in the coordinates of the molecule, we have, in the weak force case, (1) (2) We had in our paper used Do z 5 x where n = number of -CH; cm2 units.s-l, which was estimated from a graph given by Klein and Briscoe,l since no numerical value was given. Henceforth we shall use eqn (2) in the calculations. Klein also gives the activation energy QD measured for centre-of-mass diffusion (which is inde- pendent of n) as (3) In our Discussion paper we had used the " universal " activation energy function exp [- U*/R(T - T,)] to represent the activation process in the melt that retards crystallization. Henceforth we shall use exp (- QD/RT)] in the calculations, since QD is a directly measured value rather close to the temperature range of interest. The use of exp (- QD/RT) does not mean that we would abandon the form exp [- U*/R(T - T,)] in the more general case, especially if correct results at low temperatures were desired.(4) of the text for all 11 specimens using plots of logloG + 7000/2.303RT against l/T(AT) We now proceed by analysing the growth rate data of the type illustrated in fig. 3 (5) Go(II) = 6.30 x 105/n3 cm s-l. K z 2.16. Since IC is now known, the experimental value of g can be estimated by the analogue of eqn (2.15) of the text g = (dn)ao (kT/hkP(- q/kT)exP( - QDIRT) whence it is determined that the " experimental " substrate completion rate at 400 K is gexpt. z 0.70/n cm s-l and thus the reptation rate derived from growth kinetics is rexDt. G 30.7/n cm s-l. (6) (14) GENERAL DISCUSSION 389 where aobo is the cross-sectional area of this chain in cm2 and Afis the free energy dif- ference between the subcooled liquid and crystal in erg ~ m - ~ , which is given by Af = Ah,(AT)/TA where ATis the undercooling in "C.This force comes to 2.5 x erg cm-l for polyethylene at AT = 20 "C. The reptation velocity calculated using eqn (14) above is quite large, and was introduced mainly to afford a comparison of the velocity associated with the smaller force that obtained when a thin chain folded lamellar crystal was considered as a sink. The effective force of crystallization is considerably reduced for a thin lamellar crystal with folds. The calculations given in the main text show that such a crystal has a maximum mean growth rate when its thickness is (1 5) to 1: = 2a,/(Af) + 61 where 61 is to a first approximation given by kT/boa.A crystal whose thickness has the " classical " value 2ae/(Af), i.e. 81 = 0, would melt at its own crystallization tem- perature and not grow at all, while one much thicker than 1; would grow much slower than one whose thickness was 1;. It is readily shown4 that a platelike crystal of thickness 1; melts at a temperature that is just above the crystallization temperature that is given by where T, is the crystallization temperature. The mean crystallization force exerted on a molecule by such a thin chain-folded lamellar crystal is reduced from the infinite crystal value by the factor 61/19 and comes which is 5.7 x erg cm-l for polyethylene at AT= 20 "C.The derivation of eqn (17) has been outlined in the paper by DiMarzio et al. DiMarzio in a subsequent comment discusses the subject of the crystallization force further, especially in regard to an objection to the effect that the free energy associated with this force was much smaller than kT, which then supposedly robs the force of its ability to bias the motion ot the reptating molecule toward the substrate. The free energy E associated with the directional forcef5, is in fact smaller than kT, but this does not prevent this force from strongly biasing the motion of the molecule in the " reeling in " process. J. Klein and B. J. Briscoe, Proc. Roy. SOC. A , 1979, 365, 53. A principal point at issue concerns the rate at which a molecule involved in crystal- lization can be extricated from the labyrinthian entanglements prevalent in the amorphous state, and thus meet the requirements for deposition in regularly folded array with self adjacency. Hoffman and co-workers,1*2 and also Klein? invoke a " reeling-in " scheme in an effort to confer plausibility on the regular folding hypo- thesis.The molecule undergoing crystallization is supposed to thread its way through a " tube ", within which it is confined by neighbouring chains, under the in- fluence of a " reeling-in force " generated by the decrease in free energy accompanying crystallization (which is very small; cf. seq.). The chain is delivered to the surface through a " hole " at the end of the tube. Both tube and hole are considered to be fixed during deposition of the molecule; the displacement of the deposition site and relaxation of the surrounding chains that define the tube are ignored.The model and assumptions are questionable, as we point out later. First, however, we call attention to errors committed by these authors 1-3 in treating their models. These errors greatly increase their calculated rates of " reeling-in ". DiMarzio, Guttman and HoffmanlJ and Klein3 make use of the reptation model developed by Edwards and de Gennes for treating diffusion and viscosity. The alter- native " sea snake " model offered by DiMarzio et aL2 may be dismissed, for it incor- rectly takes the frictional force to be proportional to the net mean displacement of a diffusing segment instead of to the displacement along the path of motion.Turning first to the analysis of the reptation model presented by DiMarzio et aZ.,2 we call attention to two principal errors in their calculations. In estimating the fric- tion constant c, per CH2 group they employ the translational diffusion constant D = 2.9 x cm2 s-l for a polyethylene chain of M = lo5 at 176 "C to treat crystallization at 126°C. Correction to the latter temperature according to results of Klein and B r i ~ c o e ~ * ~ gives D = 1.0 x 10-l' cm2 s-l at the lower temperature. Se- condly, the contour length L of the chain appearing in their eqn (4.5) should be replaced by the length Ltubc of the tube within which the chain is supposed to be confined.According to Klein's3 treatment, Ltube 2: 0.42L. Making these two cor- rections, we obtain (1) c r = (kT/3ND) <r2)/L2tube- Taking M = lo5, N = 7.1 x lo3 units per chain, the mean-squared end-to-end length <r2> = 1.16 x lo-" cm2, and Ltube = 3.8 x cm, we obtain C, = 2.1 x lo-' dyn s cm-'. This is greater by a factor of 18 than the value presented by DiMarzio et aZ.2 A somewhat larger value, 2.8 x lo9 dyn s crn'l, is obtained upon applying the Rouse expression for viscosity to melt viscosity of linear polyethylene below its critical molecular eight.'^ An even larger value is estimated from the monomeric friction coefficients of ethylene copolymers obtained by Ferry6 from viscoelastic measurements. These values are listed in table 1 together with quantities calculated therefrom, i.e., the rate of growth g , in the surface layer in the direction normal to the crystalline sequences or stems, the corresponding " reeling-in " rate s of growth along the stem, and the time t for deposition of an entire, regularly folded molecule.GENERAL DISCUSSION TABLE 1 .-REPTATION CALCULATIONS FOR PE WITH M= 10’ AT 126°C corrected reptation, version of DiMarzio DiMarzio Ferry’s presented in the penultimate column are seriously in error due to his assumption of total depletion of “free length” at the crystal surface, a matter to which we return later. The calculated time t (column three) required for delivery of a molecule through the tube to the growth site under the reeling-in force is about one-fifth the reptation time z 2: 0.2 s for the free molecule [see eqn (4.2) of ref.(2)] in absence of a force. The estimated fivefold effect of the force attributable to crystallization scarcely exceeds limitations of the model. The relaxation time for the molecule in the quiescent state, although larger, is nevertheless relevant, contrary to statements by DiMarzio et aL2 Even their uncorrected calculations given in the second column fall short of sup- porting their contention that disentanglement times are as much as five orders of magnitude faster than our e~timate,~ ‘‘ on the order of 1 s.” Correction of their cal- culations (third column) eliminates all basis for this assertion. Our rough estimate of the time that would be required was based on the shear-dependence of the viscosity and also on the Rouse-Bueche equation relating the maximum relaxation time to the viscosity.DiMarzio et aE. have criticized use of the latter beyond the range of its validity. The error is relatively small and of no consequence, within limits of present estimates at any rate. It is characteristic of crystallization in polymers that crystalline material formed at a temperature T, melts at a temperature T m only a few degrees above T,. For poly- ethylene, T, - T, = 5-10 “C, regardless of the degree of supercooling Tg - T,, which may be as great as 25 “C below the melting temperature TA = 420 K for in- definitely large perfect crystals. The free-energy difference AGm between the liquid and crystalline states per methylene group is therefore only x 10-20 cal mo1-I at T,.We note parenthetically that crystallization at the small degree of supercooling indicated must occur by diffusive processes typified by in which the reverse process occurs with a frequency nearly as great as that of the for- ward process. The ratio of the forward and reverse rates is 2: 1 + 2AGJRT. If the elementary process involves one CH2 group, this ratio is x 1.05 at 400 K. Con- ceivably, several methylenes may be deposited simultaneously. Likewise, several GENERAL DISCUSSION 392 CH2 groups may detach themselves from the surface. As a consequence of the various forward and reverse steps that may take place, deposition of any integral number of CH2 groups may occur.The actual kinetic pathways by which crystallization pro- ceeds are of no consequence to the argument that follows. Hence, the elementary step is appropriately represented as the deposition of a single CH2 group. In any event, characterization of the process as " zippering down ''2 is inapt. The marginal stability of crystalline material formed during isothermal crystalliza- tion at a temperature T, is taken into account by DiMarzio et aL2 through inclusion of a large interfacial free energy [see their eqn (2.1 l)]. Klein,3 however, adopts a boundary condition according to which the " length defects " of segments (according to his version of the reptation model) are zero at the deposition site. This is tanta- mount to the assumption that chain segments (estimated to consist of 50 to 100 CH2 groups) are free of length defects (i.e.? " perfect ") and hence fully extended at the site.As simple calculations show, the force associated with the free energy AGm of crystalli- zation can only extend the segment by x 15% ; full extension would require an elonga- tion of nearly 200%. In terms of Klein's model, this means that only a small fraction of the " length defects " can be suppressed by the crystallization force. Owing to artificialities of the model, it is difficult to quantify the error entailed in the adoption of this manifestly erroneous bondary condition. As a conjecture, we suggest that a value of AGm 21 kT, or x50 times the actual value, would be required to suppress length defects effectively in segments at the crystallization site.The diffusion gradients in Klein's treatment would then be exaggerated by a factor of about this magnitude. Correction of the results in the penultimate column of table 1 by such a factor yields the results shown in the last column of the table. These values are consistent with those in the third column. The two reptation carried out using equivalent molecular parameters as a base, are then in agreement. Of perhaps greater significance than the insufficiency of the estimated rate of de- livery of chain units to the crystallization site are patent deficiencies of the model as applied to transport of polymer chains engaged in crystallization. In the course of deposition of a molecule with M = lo5, the site of deposition, and hence the end of the tube as well, must shuttle back and forth some 40 times across the surface, a distance of 150-200 A, which is 5-10 times the tube diameter.Having fulfilled this feat, the hole will have had to undergo a translation aZong the surface a like distance (Le., 150- 200 A). A tube with dimensions and location fixed by neighbouring chains obviously cannot keep up with the action. The complications posed by these circumstances appear to have been ignored by advocates of the reptation scheme for unravelling a chain engaged at a growth site. They materially enhance the topological difficulties of pulling a highly entangled chain into a regularly folded array. As an alternative approach consider the portion of a crystallizing molecule extend- ing from the growth site to the region of the chain beyond which response to events at the growth site is negligible within the time interval required for deposition of several stems.Let n be the number of bonds in this sequence. The configuration free energy of the sequence is, in Gaussian approximation, Early in their written comments, Flory and Yoon say that the statement of Di- Marzio et al.’ to the effect that “polymer chains fractionate (and, therefore, dis- entangle during crystallization) ” is unfounded. Now it should be made clear that this remark of DiMarzio et al. was made with the object of supporting the concept that molecules could sometimes be separated (presumably by reptation) from one another from the entangled random coil melt during crystallization.Therefore, we take their objection to be part of their attack on the concept of reptation, at least as it is active in our view in the crystallization process. Basically, they still wish to assert that the difficulty of disentangling a molecule from the melt is an obstacle to any signi- ficant degree of adjacent re-entry, i.e., some degree of “ regular ” folding (more on this later). In commenting on their remarks, we shall deal with both molecular weight frac- tionation and the separation of isotopic species (PEH and PED). Whether poly- ethylene fractionates according to molecular weight, or segregates according to iso- topic species during crystallization, depends upon the degree of undercooling and rate of crystallization for the samples under investigation and, therefore, no sweeping generalities should be made.In their comments Flory and Yoon choose to look solely at the data of Jackson and Mandelkern* who saw no separate melting peaks in d.s.c. analyses of mixture of molecular weights 3.7 x lo5 and 9 x lo3 after crystallization GENERAL DISCUSSION 39 5 at 130.2 "C. However, other investigators using different techniques and different samples report evidence for fractionation by molecular weight during crystallization from the For example, Dlugosz et aL5 subjected melt-crystallized poly- ethylene to extraction in p-xylene and found from g.p.c. analysis that the extracted material was of lower molecular weight (Mw/Mn = 18 000/5 000) than the solid residue (Mw/Mn = 59 000/18 000).The same precautions about considering all relevant data must be taken when dis- cussing segregation of deuteropolyethylene from the protonated polyethylene matrix. Small-angle neutron scattering results do prove that a deuterated polyethylene mole- cule can be kept isolated from other molecules of the same kind during crystallization as Flory and Yoon state. However, in exactly the same reference that Flory and Yoon cite to show proof for non-separation of the deuterated species, Schelten et aL6 can be quoted as concluding: " This suggests that there is a natural tendency of PEH and PED molecules to segregate, and that a statistical distribution can only be achieved by restricting the mobility and crystallization time so that separation of the molecules is avoided ".The " clustering ", " para-clustering ", or " separation " of these isotopic species is a real and fascinating phenomenon that unfortunately pre- cludes examination of the question of chain folding in polyethylene except in care- fully chosen rapidly quenched specimens. This phenomenon is worthy of further investigation. In any case, we feel that DiMarzio's citing of the fractionation by molecular weight and the segregation by isotopic species during melt crystallization as evidence for the ability of polymer molecules to disentangle from the randomly coiled melt is in fact founded on experimental observations. Next, we choose to deal more directly with the subject of reptation and its relation- ship to chain folding.This will in effect deal with items (1) and (5) in Flory and Yoon's written remarks. Basically, Flory and Yoon take issue with our contention that the estimated reptation rate in polyethylene is sufficient to allow a considerable degree of adjacent re-entry (whether for other reasons it does or does not occur) and they further take issue with our estimates and those of Klein that disentanglement times (reptation rates) are orders of magnitude faster than they stated in their earlier disco~rse.~ In their article, Flory and Yoon stated that z z 1 s for a polyethylene with a molecular weight of lo5. We recognize this part of their critique as an effort to discredit the concept of reptation for the purpose of demolishing the idea that a chain-folded lamellar structure with considerable adjacent re-entry can be constructed from a random-coil liquid with copiously interspersed chains.' In the place of such a crystal, they would substitute one in which neighbouring stems belonging to the same molecule are the exception rather than the rule.7 In a comment8 communicated to the Faraday Division subsequent to the submis- sion of the paper for presentation at the meeting,g one of us (J.D. H.) gave corrected values of the " experimental " substrate completion rate gcxpt., and the reptation rate rexpt. derived from it. The new value of gexpt. (a factor of 4 times smaller than that presented in the meeting paper) arises from a reanalysis of the original crystallization rate data lo using the recently available activation energy for diffusive transport of polyethylene''( QD = 7.0 kcal mol-') rather than a " universal relation " found to be applicable for several other polymers.12 The theoretical calculation of the reptation velocity, u,,~, requires knowledge of the diffusion coefficient, D,, for the centre of mass of polyethylene of the appropriate molecular weight at the crystallization temperature.Again, subsequent to our initial submission of the paper for this meeting which used a value of D, extracted from the graph in the paper of Klein and Briscoe,13 a numerical value corrected for different polydispersity was reported-ll Revised estimates of 396 and g,,,,.taking these facts into account were included in our previous communi- cation. Using these better values of g,,,,. and D, previously communicated, the other parameters of interest were calculated and are presented in table 2. to be reeled in In table 2, z is the estimated time for a molecule of n-CH,-units from the melt. Since the velocity increases as the length of molecule remaining in the melt decreases, z is calculated with : 4.3 x 10-3 9.8 x 10-5 GENERAL DISCUSSION TABLE 2.-REPTATION RATES, SUBSTRATE COMPLETION RATES, AND RELAXATION TIMES " experimental " values inferred from polyethylene crystallization datato " theoretical " estimates from reptation theory 9 fir, q = fc/5n general expression value at n = 7140 general expression value at y1 = 7140 rexpt./cm s-I = 30.7/n 4.5 x 10-3" g,,,/cm S-' = 0.74/n 1.05 x g,,,,./cm s-l = 0.70/n Z,xpt./~ = 2.06 x 10-"n2 u,,,/cm s-' = 32.4/n zr,q/S = 1.96 x 10-10n2 ~ ~ 1.04 x 10-4 1.0 x lop2 ~~ a value of 1.3 x ' In the analysis which estimated an upper bound on the reptation velocity, a value of 3.8 x cm s-l was reported by DiMarzio.' When the diffusion coefficient estimated for the temperature of crystallization (126 "C) is used rather than the temperature of the diffusion measurements (176 "C), cm s-' is obtained for an upper bound on [dL/dt in the notation of ref.(l)]. where 9 is the initial contour length of the molecule. Theoretical values of the tionf, and estimates of the molecular friction coefficient for reptation in the melt, c, : reptation velocity have been calculated from the force on the chain due to crystalliza- Recall that we have in effect calculated Cr from the following expression: = nCo.C r = - = kT kT (R2> =- kTn2 - ( R 2 ) = - nkT D, 3 D C ( Y 2 ) 3DO(LZ2) 0.30500 Symbols are as defined in our original contrib~tion.~ The agreement between the " experimental " and theoretical values in table 2 is now even closer than given in the paper by Hoffman et a1.' We emphasize that the substrate completion rateg,,,,. (as well as rexpt.) was calculated on the basis of sub- stantially " regular " folding, i.e., assuming adjacent re-entry. Clearly the inde- pendently estimated values of ur,q, gr,q, and z, which depends fundamentally on Klein's experimental formula, D = 0.26 mol dm-3 cm2 s-l (subsequently adjusted for temperature), are very close to the values obtained from measured crystallization rates.Flory and Yoon have criticized the order of magnitude theoretical estimate of reptation rate of DiMarzio et aZ.l on two grounds. First, the diffusion coefficient was not adjusted for the change in temperature from 176 "C to the crystallization tem- perature of 126 "C which will reduce the reptation rate by a factor of 2.9. Second, they state that the contour length of the chain, 9, should be replaced by the length of the tube in which the chain is considered to be confined. They claim that according to Klein'sll treatment, this is 0 . 4 2 2 which, when squared, would reduce the reptation rate by a factor of 5.7.We accept the first criticism which is acknowledged in the footnote to table 2, but this occurred only in DiMarzio's first rough estimate and not in that given by Hoffman (3) GENERAL DISCUSSION 397 et aL9 However, with regard to the second criticism, it is inappropriate to mix the Klein theory with ours and to do so indicates a misunderstanding. A theory which includes both the external crystallization force and the slack concept will not have such a factor. Intuitively, we feel that slack will make the reeling-in process even easier when incorporated into the theory of DiMarzio, Guttman and Hoffman and that the crystallization force when incorporated into Klein’s theory will make the reeling-in process described by Klein easier. In neither case will the reptation rate be reduced.Flory and Yoon have stated that “ the alternative ‘ sea-snake ’ model may be dis- missed for it incorrectly takes the frictional force to be proportional to the net mean displacement of a diffusing segment instead of to the displacement along the path of motion”. We claim to have made no error in this regard. Both the Langevin equation and the Einstein-Smoluchowski equation show the frictional force to be proportional to the net mean displacement of a diffusing segment (in a time interval At). It is not proportional to the displacement along the path of motion for a microscopic segment undergoing Brownian motion. Flory and Yoon’s statement is true for a macroscopic particle but false for a microscopic particle.The correct friction coefficient to use with the “ sea-snake ” model is that of Rouse-Zimm- Bueche theory. As stated in ref. (l), “ one might expect the sea-snake model to be useful for dilute solutions and the reptation model to be useful for bulk polymers ”. We do not think it appropriate to use the friction coefficients tabulated by Ferry for the reptation model of de Gennes. These numbers depend on Rouse-Zimm- Thus we do not accept as meaningful the values of c,, g,, k and t listed under the Bueche models of polymer motion rather than reptation models of polymer motion. column “ Ferry6 ” in table 1 of Flory and Yoon’s response. for tlmol. s-l, in the first column of Flory and Finally, the number 2.4 x Yoon’s table 1 should be replaced by 1.2 x low3 as given in our paper.In order for the molecular transport process to be compatible with chain folding during crystallization it is only necessary that u,,~ (or dL/dt) be comparable to or faster than the rexpt. derived from the observed growth rates. Both the upper bound esti- mate of DiMarzio et a2.l and the revised values summarized in table 2 are close enough to the observed rates to justify our contention that “ our overall conclusion is that reptation is sufficiently rapid in polyethylene of low and moderate molecular weight to allow reeling in of a molecule onto the substrate 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 substantial 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 under- coolings in polyethylene.”’ We remain unrepentant protagonists of this view. Cer- tainly the relaxation time is not orders of magnitude too long to allow a substantial amount of folding as claimed by Flory and Yoon. (Recall that they estimate z N” 1 s for M = 105.)’J4 Some further points concerning reptation deserve attention. First, Flory and Yoon imply that we have somehow neglected the fact that the crystals melt at a T,, which is only a few degrees above the crystallization temperature T, = T,, which re- duces the free energy difference between the liquid and crystalline states.The kinetic theory of crystallization expressly predicts T, to be just a little above T, [see eqn (1 5) .f’c is corrected for the effect of the finite thickness of the crystals 2: = 2a,/(Af) + 61 and (16) of the comment by J. D. H. concerning 6E]. The mean force of crystallization by the factor dZ/Z,* in eqn (2) of this comment. For an indefinitely large crystal the GENERAL DISCUSSION 398 force is aobo(Af), and for a crystal of thickness Zg* the mean forceL is (dZ/Zt)aobo(Af). As we understand their further criticism regarding the force, Flory and Yoon appear to believe that we have somehow forgotten to consider the question of the forward and backward reactions that occur during substrate completion.A perusal of the Appen- dix in the paper by Hoffman et aL9 should dispel this notion. While one may dis- approve of the simplicity with which we have approached the problem, it is clear from the way 61 is calculated from a consideration of the forward and backward reactions that we have not in principle neglected this issue. Having disposed of the contention that there exists an insufficiency in the rate of delivery of chains to the crystallization site to sustain a reasonable degree of adjacent re-entry, we now remark on the objection related to the fact that adjacent re-entry requires the crystallizing molecule to shuttle back and forth across the surface during the period when adjacent re-entry is occurring (often several or more stems before an interruption).Flory and Yoon evidently surmise that the topological difficulties of doing this are alone sufficient to dismantle the concept of reptation as applied to crystallization. The problem can be clarified by pointing out that in our model the force of crystallization actually fluctuates. During the process which forms a stem, the force is at a maximum (which is well above the mean forcef,) and has the valuef, = aobo(Af). Then there is a considerable time delay during which there is no force on the pendant molecule during the formation of the fold. It is this time delay which allows readjustments to take place that allow adjacent re-entry of several or more stems.The process is then repeated and a new stem from the same molecule is put down until there is an interruption. The mean force for the overall process is L = (W3QObO(Af 1. de Gennes15 has pointed out that the deposition of a part of the molecule onto the growing crystal surface gives rise to a " shadow " effect. It is premature to speculate on exact details of how a molecule is deposited (such as the " shuttle ") but the resul- tant " shadow " mentioned by de Gennes may well facilitate to some extent the amount of adjacent re-entry. However, we immediately point out that the most probable prominent cause of adjacent re-entry in crystallization from the melt is a result of surface packing problems.It is simply not possible to have a large fraction of emer- gent cilia, each with a random-coil character, without incurring a serious density anomaly: to avoid this, the system elects to introduce folds with adjacent or near- adjacent re-entry at frequent intervals according to the kinetic schemes that we and others have p r o p o ~ e d . ~ ~ ' ~ In lieu of the deposition of molecular chains onto a crystal substrate with con- siderable adjacent re-entry as we have proposed, Flory and Yoon would describe crystallization in terms of changes in configurational free energy as outlined in eqn (2)-(5) inclusive in their comments. In their equations, they have omitted the major part of the free energy change due to crystallization, namely the enthalpy.A second point is that a change in Y in their eqn (4) can result in either a positive or nega- tive change in AG,. Eqn (4) should include a geometrical factor ar/ aZ' (ar/ al' = -cosO where 0 is the angle between I' and r ) . When I' r is positive, we get a result for AG, which is opposite in sign to that when I' r is negative. We expect the average value of I' r t o be zero so that AGr is much diminished from the estimate of Flory and Yoon. As the last part of our discussion, we comment on questions related to items (2) and (3) in the written remarks of Flory and Yoon, and related topics found in their work. Specifically, they take issue with the work of Guttman et aZ.I6 and Hoffman et aL9 suggesting that the probability of adjacent re-entry is z 0.65 in the PEH + PED specimen studied by Schelten et aZ.17 They also indicate that the serious density GENERAL DISCUSSION 399 defects exhibited by their “ p e s = 0.3 ” and “ y = 1 ” models do not invalidate them for the purpose intended, which was fitting neutron scattering curves. As regards Flory and Yoon’sp,, = 0.3 and y = 1 models, we agree that they can be caused to fit the scattering curves, and in the case ofp,, = 0.3 even the crystallinity and C, or the radius of gyration.But the density anomaly in both is so inadmissable as to surely tell us that the models are no guide to the physics of the situation. The methods they devised are to be admired for their thoroughness, and their favoured model with pes = 0.3 that gives a probability of adjacent re-entry of either 0.2 (our deduction) or zero (their input assumption) cannot be accepted as physically real.Their y = 1 model is subject to the same type of objection, but Yoon and Flory re- jected this model themselves. It has been pointed out repeatedly, first by Frank18 and later for example by US,^ that the assumption of too much fringed-micellar character is bound to lead to impossible situations at a plane surface. The probability of adjacent re-entry is undoubtedly much higher than zero or 0.2 in the sample con- sidered. In trying to get closer to the truth, we used the concept of maximizing the overall fit, including the fit of the neutron scattering curve, the characteristic ratio (or radius of gyration), and the crystallinity, under the condition that the liquid and crystal density be normal.Ironically, the latter requirement was taken seriously by us because of remarks made by Flory and Yoon in their now famous article in Nature.7 One way we found to meet these requirements simultaneously was to reduce the fringed-micellar character of the lamella by introducing adjacent folds. A considerable number of models was developed which have a reasonable overall fit, all of which yielded a probability of adjacent re-entry of 0.5 or higher. We did not then and do not now think the situation entirely satisfactory, or uniquely determined, but still considei it highly plausible to say that the most common event is in fact adjacent or near-adjacent re-entry .We are interested to see Flory and Yoon say in their remarks that “ one cannot . . . rule out the possibility of some limited degree of regular folding, perhaps involving successions of several stems ”. With only the smallest extension, this is what we found from our analysis of the same neutron scattering curves where they found vir- tually no adjacent re-entry, but incurred a density anomaly. The statement of Flory and Yoon that we have offered no explanation for the fact that the radius of gyration does not change on crystallization is without basis in fact. Even a glance at the pspers of Guttman et al.16 and Hoffman et aL9 show that we have accommodated a considerable degree of adjacent re-entry in our models, at the same time satisfying the measured radius of gyration.(Recall that the “ ACA ” model for melt-crystallized polystyrene advanced by Guenet et all9 in effect does the same thing.) Note also the results for the “ variable cluster ” model presented by Gutt- man on p. 433 of this Discussion. Much regular folding can and does take place locally, even though the overall conformation of a molecule of high molecular weight does not change much because of multiple nucleation. A liquid-like radius of gyration in a crystalline specimen does nut preclude the presence of a considerable degree of adjacent re-entry on a local basis. The reader should be aware that at lower molecular weights, the radius of gyration does change upon crystalli~ation.~~*~~ In our view, the picture of crystallization advocated by Flory and Yoon places too much emphasis on the role of liquid structures. This emphasis on liquid structure is evident, for instance, in the manner in which they analysed the neutron scattering data: 21 random or modified random flight trajectories in the liquid solely decided the site of re-entry. This approach leads to a substantially fringed-micellar model which accumulates too many segments in the boundary region and gives rise to density GENERAL DISCUSSION 400 anomalies that invalidate the models.While following their overall procedure (we always used proper liquid state configurations in similar efforts accounting for neutron scattering data), we also took surface packing problems into account and recognized the necessity of taking into account, however crudely, the energetics associated with niches.Liquid state configurations mitigate in favour of rather random re-entry and explain the long loops and interlamellar links but surface packing and the favourable energetics of crystallizing at a surface niche favour a considerable degree of adjacent or near adjacent re-entry on a local basis. For ourselves, we think that for polymer crystals, as in the case of many other crystals, that the structure of the liquid does not completely dictate crystal structure or morphology. The light of inquiry should to some extent be turned around and cast on the con- cepts of crystallization advocated by Flory and Y o o ~ . ~ In their approach, we see no explanation of the formation of lamellae.What in their view fixes its thickness as a function of under-cooling, and how does one quantitatively describe the kinetics of crystal formation ? Why does a lamella grow large lateral distances while maintaining the same thickness? How does one compute or estimate the surface free energy? The kinetic theory of nucleation with chain folding provides answers to these questions. The foregoing questions should be quantitatively answered by them in terms of their model if their views are to be accepted. We now reiterate that this shows that one of Flory and Yoon’s arguments against chain folding in crystallization from the melt, namely, that transport processes in the melt are orders of magnitude too slow to allow anything like chain folding with a substantial amount of adjacent re-entry, is incorrect for the range of n under considera- tion.The reptation process is clearly fast enough to provide the requisite molecular mobility for folding with some adjacent re-entry in crystallization from the melt at low and moderate molecular weights. Dr. E. A. DiMarzio (National Bureau of Standards, Washington, D.C.) said : Prof. Flory has made three points. First, he asserted that the crystallization force on a molecule is too small compared to thermal motion for the concept of reeling-in to be valid. Second, he suggested that the energy differences per CH2 unit are so small that there is much popping on and off the crystal of a CH, unit before it is finally incorpor- ated into the crystal even at large super-coolings. Third, he suggests that the process of crystallization is diffusion controlled. GENERAL DISCUSSION 402 Let us consider point 1.Our evaluation of the driving force via eqn (2.8) and (2.9) of the paper is, we believe, correct to within a factor of two or so. We also re- tain our estimates of the friction coefficients for both the reptation and the sea-snake models to within a factor of four or so. We cannot see how these quantities can be changed greatly by subsequent developments. Accordingly, we stand by our esti- mates of reeling-in times which are three orders of magnitude shorter than the 1 s disentanglement time estimate of Flory and Yoon. A small directional force always overwhelms diffusion.To see that this is so write (Xiif) = 2Dt so that the ratio of distance drifted under an applied force (Xd = v t ) to distance dif- fused ( d m is This ratio can be made large by making t large. How do these ideas relate to the reeling-in of one molecule? We have the full length of a molecule of M.W. = lo5 which is 9100 A reeling-in in s. During this same the molecule diffuses a dis- tance l/(xiif) = 2/2D,t- 10 in its worm hole while its centre of mass diffuses a distance 2 / ( ~ & , ) = 2/2D,t - 25 A. Thus if diffusion is important in describing the reptation to a surface then the reeling-in force is even more important and the applied force will dominate the feed rate. At this point we should reiterate the main point of the paper, which is that the rate of filling the niches, g , cannot in reality be larger than the g values estimated in the paper [eqn (2.10) and (2.1 l)].A kinetic theory of crystallization which predicts g values smaller or equal to the reptation and sea-snake model g values is a viable theory. Had Flory and Yoon been correct in their estimate of disentanglement imes, then the g values of the kinetic theories would have been too large and those heories would consequently have been disproved. Let us now consider point 2. If a is the rate of a CH2 unit popping on the crysta and that of popping off then Flory asserts that a-p< a,p. We agree. The kinetic theories of crystallization of Hoffman and Lauritzen, Sanchez and DiMarzio, Frank and Tosi, Point, and others easily handle the fact that cc and p are comparable.These heories have as their main objective the description of the crystal growth process in terms of these fundamental rate constants. On the whole these theories have been reasonably successful in their predictions. The fact that the stems pop on and off is an inherent and necessary part of rate theory, and is in no way antagonistic to the concept of reptation or of tube flow under an applied field. Let us now consider point 3. The fact that a-p< cc,B does not mean that crystal- lization is diffusion controlled. It means only that crystallization is a stochastic pro- cess. Indeed, as the supercooling decreases (AT+ 0) we have (a - p ) + 0 and in this limit there is less effect on the crystallization from melt viscosity.That is to say for (a - p) small, the viscosity has no sensible effect on the crystallization rate be- cause the crystallization rate is so small. Prof. P. J. Flory and Dr. D. Y. Yoon (Z.B.M., San Jose) said: The first two points raised by DiMarzio et al. are covered adequately in our contribution in response to GENERAL DISCUSSION 403 their paper. Their third point is groundless. We did not suggest that crystallization is diffusion controlled. Dr. J. Rault (Orsay) said: This comment is of relevance to three papers, those by DiMarzio, Wunderlich and Capaccio. In polyethylene quenched from the melt state the crystalline lamellae thickness L, is equal to -170 A. This is found by Raman spectroscopy' and by combined WAXS and SAXS measurements.L, does not depend on the molecular weight M , in polydisperse and monodisperse polyethylene. A chain length L, = 170 A corresponds to a molecular weight A4 = 1900. This is exactly the value of the average molecular weight Me between two entanglements given by viscoelasticity measurements on the melt.3 Assuming that similar correla- tions exist for other polymers, one concludes that the crystalline lamellae thickness in semi-crystalline polymers is prescribed by the average length L, of the chains linking two consecutive entanglements. This length is proportional to the persistence length. A dilatation of the space will change both the persistence length and the distance L,. This correlation between solid and liquid state suggests that, during the process of crystallization, the chain does not disentangle : but that the entanglements along the chains which crystallize are trapped and move towards the lamellae surface, according to the model of crystallization in two stages (freezing-annealing) described in ref.(4). Therefore, the concentration of entanglements in the amorphous phase would be about twice the concentration in the liquid phase (in quenched PE of molecular weight M z 10' the crystallinity is ~ 0 . 5 ) . The Raman spectrum of semi-crystallized PE cannot be interpreted as the super- position both of the spectrum of the melt and the entirely crystalline material.5 The difference between the amorphous spectra of the crystallized material and the melt spectra has been interpreted as coming from the difference in the conformation of the amorphous chain in these two materials.6 The change of the percentage of rota- tional isomers along the amorphous chains in the crystallized material can be due to the increase of entanglements concentration and/or to stress along these chains due to the presence of the crystallites.It should be interesting to perform accurate experiments for determining the characteristics (characteristic ratio, distance between two en- tanglements) of the amorphous chain in semi-crystalline materials crystallized in different ways. If the entanglement concentration is higher near the surface of the crystalline lamel- lae, the concept of the intermediate amorphous phase can be invoked. The two dif- ferent mobilities of the amorphous chains measured by the proton n.m.r.experi- ment have been explained by the presence of these two different amorphous layers. In any case, whether the intermediate amorphous layer exists or not, the amorphous chain cannot be considered in my opinion as an ideal chain. Hence, the topology of the fold cannot be described by the isomeric 3-state model of the ideal PE chain. In Nylon the crystalline lamella thickness is about 80 A. The ideal chain of Nylon 6 has a rigidity (characteristic ratio) similar to that of polyethylene, therefore we expect that the distance between 2 consecutive entanglements is also of the order of 170 A. The difference between crystallization of Nylon and PE from the melt could be ex- plained by the fact that the second stage (annealing process) is not operative in Nylon because of the hydrogen bonding which involves high activation energy for stem jumps4 in the crystal state.The crystalline thickness is not prescribed by the en- tanglements distance, but rather by the first stage of crystallization (freezing), which is similar in both solution and melt. These two opposite examples of high mobility chain PE and very low mobility 404 chain (Nylon) in the solid state tend to support the view that the process of crystal- lization is a two-stage pro~ess.~ GENERAL DISCUSSION G. Capaccio, I. M. Ward, M. A. Wilding and G. Longman, J. Macromol. Sci. Phys., 1978, B15, 381.E. Robelin and J. Rault, J. Phys. Lettres, submitted. J. D. Ferry, Viscoelasticity qf Polymers (John Wiley, 1969). J. Rault, J . Phys. Lettres, 1978, 39, L411. G. Strobl, W. Hagedorn, J . Polymer Phys. Ed., 1978, 16, 1329. L. Vinh, M. Abenoza and J. Rault, 1. Physique, 1979, 40, 597. Dr. F. Khoury (National Bureau of Standards, Washington, D.C.) said: Among the striking new features revealed by the thorough study reported by Bassett et al. is that the dominant lamellae in polyethylene spherulites (and sheaves) grown from the melt at relatively high undercoolings [see regions (iv)-(vii) in their fig. 61 exhibit S-like profiles when they are viewed along their b-axis which is oriented radially in the spherulites. The specific nature and origin of the factors which cause the S-lamellae to adopt an asymmetric transverse conformation (there is no mirror plane symmetry between the halves on opposite sides of the long axis) remain to be determined.We wish to point out in this connection, that in a study1 of the crystallization of poly- ethylene from dilute solutions in poor solvents at temperatures (105-1 15 "C) corres- ponding to high undercoolings in melt crystallization, we have grown lamellar crystals which exhibit high axial ratios (length along b-axisllength along a-axis) and which are also transversely asymmetric (see below). As an example we show in fig. 4(a) a dia- gram illustrating the lateral habit of the type of lamellar crystals which were formed, reproducibly, when a polyethylene fraction (fraction I, M, = 13 600, M , = 11 400) was crystallized at 115 "C from 0.01 % solutions of the polymer in dodecanol.These lamellae, whose axial ratio was 5.5-6, are bounded by { 1 lo} faces at both extremities W X FIG. 4.-(a) Profile of the lateral growth habit of polyethylene (fraction I) crystals grown from a 0.01% solution in dodecanol at 115°C. (6) Enlarged transverse cross-section of regions between K and N (e.g., ML) showing the tilt of the stems in a flattened (collapsed) lamella. See text. FIG. 5.-Dark-field scanning transmission electron micrograph of a portion of a crystal of the type illustrated in fig. 4. The crystal has been tilted by 34" about the vertical arrow. The opposite pairs of diffraction patterns were obtained from the pairs of circular regions ( z 0.4 pm diam.) situated on opposite sides of the central axis.These regions appear darker due to electron beam damage. One pair of (200), two pairs of (1 lo), and higher-index (hkO) spots were observed in all the patterns. The halos are due to shadowing material. [To face page 404 (c 1 FIG. 6.-Small-angle (H,) light scattering pattern. Sample crystallized at 130.6 "C for 30 days. (a) Fraction M, = 27 800; M, = 26 500; (b) 15% M = 19 700 added to (u); (c) 15% M = 46 200 added to (a). (Obtained by Dr. M. Glotin.) [To face page 405 GENERAL DISCUSSION 405 and their long sides are distinctly curved and apparently smooth. Metal shadowed crystals exhibited, in the electron microscope, a faintly discernible ridge corresponding to WX [fig.4(a)] suggesting that these crystals, in which WX is parallel to the b-axis, are not flat as grown. An examination (using scanning transmission electron micro- scopy, dark-field mode with annular detector) of the diffraction contrast characteris- tics (fig. 5) exhibited by the lamellae as they were variously tilted relative to the incident electron beam, coupled with selected micro-area (diameter w 0.4 pm) electron diffrac- tion (fig. 5), revealed an unexpected asymmetric feature. In all but one of the numerous crystals we have examined so far we have found that in the inner two-thirds to three-quarters of the width of the lamellae, at levels between K and N [fig. 4(a)], the chain stems (c-axis) are titled at close to 34" relative to the normal to the surface of the collapsed lamellae; i.e., the fold surface in these regions is (201) or close to (201).The surprising feature was that the sense of the tilt was the same on both sides of WX, as illustrated in fig. 4(b), and as evidenced by the diffraction patterns in fig. 5 (see caption). This feature clearly indicates that the conformation of the lamellae as grown is not tent-like. There are indications that the tilt of the stems is less pro- nounced? but in the same sense, closer to the periphery of the lamellae, as illustrated in fig. 4(b). Because most of the crystals we have grown so far from these solutions were multi-layered, the details of the stem tilts at and near the central region of the lamellae [level YZ fig.4(a)] have not yet been resolved. In the light of the observa- tions of Bassett et al. it is tempting to speculate that the solution-grown crystals described above may have shallow S-like transverse profiles. While this is mere speculation at this stage we feel that the further study of these " asymmetric lamellae '' as well as other types we have grown from solution in different solvents at tempera- tures in the range 105-1 15°C may well provide insights relevant to the elucidation of the origins of the asymmetric conformation of the less accessible S-lamellae formed in melt-crystallized polyethylene. An understanding of these origins may well shed some further light on the manifestation of banding (rotation of the molecular orientation along the radius) in polyethylene spherulites.F. Khoury and L. H. Bolz, Abstracts at 26th International Symposium on Macromolecules, IUPAC, 179, Mainz, Sept. 1979, vol. 111, p. 1302. Dr. I. Voigt-Martin (University of Mainz) said : In recent years we have performed experiments in Mainz along very similar lines to those employed by Bassett et al., using very narrow fractions prepared in Tallahassee by Prof. Mandelkern's group. We reported the results of our investigations at the IUPAC meeting in September, 1979.l The techniques employed were electron microscopy, X-ray small-angle scat- tering and Raman spectroscopy. The reasons for using these three techniques were to compare numerical data in those cases where all these methods lead to unambiguous results and to have at least one source of data in those cases where a unique interpreta- tion was difficult or impossible.The results of electron microscopy using both stained thin sections and replicas are in good agreement with the morphological map published by Maxfield and Man- delkern2 on the basis of their light scattering experiments, and differ in some respects from the one presented by Bassett et al. We have evidence which shows that even slight polydispersity has a considerable effect on morphology and consider this effect as the most probable source of disagreement. It was found in our work that the " rod-type scattering " reported in the earlier paper for isothermally crystallized samples arises from large lamellar sheets, occasionally having a " roof-shaped " structure with an apex angle of 144".The " random h-type scattering " arises from large curved lamellae having various random orientations (isothermal case, molecular GENERAL DISCUSSION I. G. Voigt-Martin, E. W. Fischer, W. Hagedorn, P. Hendra, L. Mandelkern and K. Mehler, 406 weight = 10 6, and small, crystalline units arranged randomly (quenched case, mole- cular weight = 10 ". The structures " a-type scattering, good spherulite '' and " b- type scattering, poor spherulite " were identified as spherulites consisting of long lamel- lae having only slight curvature and short lamellae having considerable curvature. Thus the trend with increasing molecular weight, (a) in the isothermally (130 "C) crystallized case, is large flat lamellar sheets -+ shorter flat or roof-shaped sheets -+ large random curved lamellae and (b) in the quenched case, is long, thin lamellae with little curvature -+ short thin lamellae with considerable curvature -+ small crystalline units.It has been shown in a previous investigation3 that if the electron microscopy on the stained thin sections is performed with extreme care, and the results plotted in the form of histograms depicting both crystal thickness distribution and long spacing distribution, then very good agreement can be obtained with X-ray small-angle scat- tering. Similarly it was found in this investigation that the values of L from the histograms were in good agreement with the X-ray small-angle spacings and the values of d from the histograms were in good agreement with the values of d obtained using the longtitudinal acoustic Raman mode, after allowing for tilt and applying corrections described el~ewhere.~ The value of E, = 2.9 x 10 l2 dyn cm-2 was taken from a calculation by Strobl and Eckel for paraffin^.^ In the case of high molecular weight material M = 6 x 10 the histograms indicate an extremely broad distribution in L and d, and the micrographs clearly show the presence of lamellae in random orientations, so that a continuous decrease is observed in the X-ray scattering curve.Similarly, the longitudinal acoustic Raman mode shows very little evidence of a peak. However the histogram clearly indicates the size dmax of the lamellae formed at T,, and the sizes of those which formed during subsequent cooling to room temperature.26th Int. Symp. Macromol. (IUPAC, Mainz, 1979). * J. Maxfield and L. Mandelkern, Macromolecules, 1977, 10, 1141. G. Strobl, M. Schneider and I. G . Voigt-Martin, J. Polymer Sci., submitted. R. Snyder, S. Krause and J. Scherer, J. Polymer Sci., 1978, 16, 1593. G. Strobl and R. Eckel, J. Polymer Sci., 1976, 14, 913. Prof. L. Manilelkern (Florida State Unitrersity), said : In morphological studies of the kind reported by Bassett et al., it is very important that one distinguish between molecular weight fractions and whole polymers, since the morphology is very sensi- tive to polydispersity. This phenomenon is not due to molecular fractionation; it has already been discussed in the literature1-3 and will be examined in further detail below.Therefore it would be very helpful in analysing present results if the molecular weight I distributions were reported in some convenient form, relative to the results presented in fig. 12. The information provided in the text and the figure captions is not adequate. Contrary to Dr. Bassett's statement, light scattering is not a superficial method. It is in fact a very general and theoretically powerful method which describes the type of anisotropy consistent with the crystalline morphology or supermolecular structure and which examines the complete sample. It then enables a systematic miscroscopic investigation to be made. It should be noted that the specifities of " folding " cannot be deduced from the observation of lamellae by means of electron microscopy.Dr. Voigt-Martin reported at the IUPAC meeting at Mainz4 that the molecular weight and crystallization conditions for the formation of the variety of morphological structures that were previously reported are confirmed by electron miscroscope studies. There is in fact a one-to-one correspondence of the two methods. Much of the work GENERAL DISCUSSION 407 reported here is confirmatory of this report. It is abundantly clear that spherulites are not a universal mode of polymer crystallization. The morphological map reported by Bassett et al., (fig. 6 ) is qualitatively similar to the one previously deduced from small-angle light scattering patterns3 and con- firmed by electron micros~opy.~ There are, however, a few exceptions, and the reasons for the differences are significant.Quenching is a subjective type of experi- ment. By adjusting cooling rates, or the temperature of the quenching bath, the non- isothermal, rapidly crystallizing region can be studied and the morphology is found to change in a very systematic manner.5 More specifically, regions (i) and (ii) in fig. 6, i.e., low molecular weight and high crystallization temperature, do not yield spherulites as Dr. Bassett indicates. The present results are probably due to sample polydispersity, as can be demonstrated by the following light scattering experiments. For the samples used by Bassett et al. in the present and previous work,' M,/M,, ranging from 1.3 to 1.7 for the (2-3) x lo4 molecular weight range are sufficiently polydisperse to yield the results found.Fol- lowing the original report,6 we have prepared a sample M , = 27 800; A4, = 26 500; M,/M,, = 1.1 and crystallized it at 130.6 "C for 20 days.' Its small-angle light scattering pattern shown in fig. 6(a) represents a rod-like ~tructure.~ Fig. 6(b) and (c) are the light-scattering patterns, after identical crystallization conditions, when 1 5 % by weight of fractions M, = 19 700 and 46 200 are homogeneously added, respectively. The two mixtures, which display only slight polydispersity, have started to develop an X-type pattern indicating some type of spherical symmetry and the initiation of spherulite formation.These samples simulate the lower molecular-weight samples used by Bassett et al. and explain the results reported here and previously6 for spheru- ite formation in this molecular-weight range. Dr. D. C . Bassett (University of Reading) (communicated): I think there are two main points to be made to these sets of related comments. The first concerns : what is a spherulite? According to Prof. Mandelkern it is an entity with spherical sym- metry (before impingement) and, by implication, large and mature enough for the common departures from spherical symmetry in the early stages of growth to be neg- lected. I consider this to be unnecessarily restrictive and regard a spherulite as a polycrystalline array of equivalent radiating branching units with a tendency to pro- duce a spherical envelope.This is in accord with observation and has the advantage of embracing immature forms of development within its scope. It thus seems to me that Prof. Mandelkern is calling a rod what I would term a particular type of imma- ture spherulite. When this is appreciated, the claimed differences seem to me more apparent than real. The second point is that our results, covering a very large number of fractioned polyethylenes with molecular average masses above !z 2 X 10 4, are remarkably insen- sitive to minor changes in molecular mass and polydispersity. We see only three types of lamellar profile viewed down b. In regime I1 growth there are dominant Ss and planar infilling sheets; in regime I ridged (201) sheets give way, in the neighbour- GENERAL DISCUSSION 408 hood of the change of regime, to planar and slightly curved intermediate forms.(Drastic quenching of thin films may give a further habit.) In our fig. 6 we have endeavoured, by incorporating minor differences of interlamellar organization, to compare our data with those of Prof. Mandelkern previously published in this format. It should surprise no-one that the two do not correspond exactly. Such features are affected by the sort of delicate changes Prof. Mandelkern has mentioned. For example, when the number of nuclei in a sample is reduced it grows larger and more developed spherulites. Doubtless this will alter the small-angle light scattering pat- tern but, in our experience, it does not change the type of lamellar profile.For this reason I consider the undoubted differences shown up by small-angle light scattering to reflect features such as the envelope which are secondary to spherulitic develop- ment. I intend no disparagement of a valuable method but simply wish to point out that its results are largely complementary to those of microscopy with a tendency to measure different, though related, quantities. Dr. W. F. X. Frank (University of U r n ) said: 1 would respectfully suggest that polyethylene is not the best substance for studying the process of crystallization from the melt. With this substance the crystallisation speed is so extremely high, that crystallization is controlled by heat conduction phenomena rather than by the effects discussed in these papers.In order to study the kinetics of melt crystallization a material like, for example, poly(ethy1ene terephthalate) seems to be more suitable. Dr. J. D. Hoffman (National Bureau of Standards, Washington, D.C.) said: At high undercoolings, the rate of crystallization from the melt in polyethylene can be extremely high. However, authors attending this Discussion are well aware of the variables which control crystallization rate, and purposely confined their investiga- tions to temperatures and sample sizes where the heat of crystallization was dissipated to the surroundings, In large samples of polyethylene ( z 3 g) in a thick-walled dila- tometer, the maximum temperature increase in the centre of the sample due to crystal- lization at 125.0 "C has been reported to be only 1.05 "C.I In the experiments on polyethylene fractions which revealed the transition from Regime I to Regime 11,2 heterogeneities leading to multiple nucleation were purposely reduced, and the samples were only 40 pm thick.The measured crystallization rates were independent of sample thickness (40-100 pm) and thermocouples imbedded in the molten film indicated no change in temperature as the crystallization front passed the thermo- couple for the range in temperatures reported. Furthermore, the results have been duplicated almost exactly in the thesis of Labaig3 in which even thinner samples were immersed in a stirred temperature bath where the heat of crystallization was dissipated even more efficiently than on a microscope stage.There is no indication whatsoever that heat conduction phenomena control the crystallization rate data for polyethylene in the temperature range (-124"-131 "C) reported in ref. (2). It is clear that the Regime transition effect is not a result of the onset of heat conduction effects. At undercoolings somewhat larger than AT = 21 "C (corresponding to T, = 124 "C) the crystallization rate in polyethylene becomes increasingly rapid, and some effect of the heat of crystallization can make itself felt even for fairly thin specimens. In such cases, the actual mean temperature of crystallization will be above the bath temperature. This may have occurred in preparing the PEH + PED specimens for the neutron scattering experiments.The actual mean temperature of crystallization in such cases can readily be determined by suitable mapping with fine thermocouples. We do agree with the implication in Dr. Frank's comment that it would be desir- GENERAL DISCUSSION 3. J. Weeks, J. Res. Nat. Bur. Stand., 1963, 67A, 441. 409 able to study crystallization rates over a much wider temperature range than is acces- sible to us in polyethylene. Such studies have in fact been made on a variety of poly- m e r ~ . ~ Polyethylene does have the advantage that there is available a wealth of independently derived physical constants (Ahf, T,", 0, a,) that zppear in the growth- rate equations which enable a meaningful comparison between theory and experiment to be made.Prof. B. Wunderlich (Rensselaer Polytechnic Institute, Troy) said : The proof that " niches " or surface steps seem to play a minor role in nucleation of new lamellae growing on an extended chain substrate as illustrated in fig. 2 of my paper rests with the observation that the lamellae start growing from random sites. Even the clearly visible surface steps which must have a molecular scale counterpart are avoided as initiation sites for crystallization. The detailed analysis of the nucleation and the subsequent growth of the surface growth is done in ref. (15) of my paper; cf. fig. 7 and fig. 11 of the reference. The explanation of Regime I -+ Regime I1 transition takes on a new interpretation, just as the surface or secondary nucleation takes on a new interpretation.The onset of Regime I1 is occasioned by multiple nucleation of a single molecule on the substrate or multiple molecules in close proximity, causing overlap of molecular growth do- mains. The surface or secondary nucleation governing crystal growth is equated by us with molecular nucleation. The difference from the prior concept is the repeated need for such nucleation for each molecule (to account for the nucleation governed segrega- tion). Our view of the detailed physical steps occurring just before and after attach- ment of the molecule to the surface must naturally be speculative. We assume that at low supercooling the adsorption step of a sufficiently large section of a molecule to undergo molecular nucleation is not rate dependent.Adsorption equilibrium exists. Nucleation of a sufficiently large portion of the molecule on the crystal surface is the GENERAL DISCUSSION 414 reversible step which causes segregation. At low supercooling it involves several folds. The folds are most likely irregular and constantly adjusting to lower free energy morphology. After nucleation, the continued growth is not separated from further rearrangement, but all later processes are again not rate determining and can only be discovered by thermal analysis [see ref. (15) of my paper, fig. 8 and 91. At high supercooling, starting perhaps close to the onset temperature of Regime I1 crystalliza- tion, shorter segments of the molecule satisfy the molecular nucleation requirement and increasing tie molecules between separate crystals are discovered [see ref.(1 8) of my paper]. Now the morphology changes from that of regular lamellae which are largely molecular weight segregated increasingly to that of cold crystallization or the Erstar- rungsmodell discussed by Stamm et al. at this Discussion. Prof. L. Mandelkern (Florida State Uniuersity) said : Prof. Wunderlich's paper raises some fundamental questions with regard to molecular segregation during crystal- lization as well as the value of the equilibrium melting temperature of linear poly- ethylene. This quantity is a fundamental parameter that is used in a variety of important calculations. In table 1 his " experimental critical molecular weight " increases three-fold with a two-degree increase in crystallization temperature.His " equilibrium critical molecular weight " increases imperceptibly under the same conditions. Serious questions as to the experimental method used immediately come to mind. We should also point out that a homogeneous mixture of two fractions, M,, = l o 3 and 3.7 x lo5, shows no evidence of fractionation over the complete composition range after crystallization at 130.2 "C for 30 days.l Although the frac- tionation of very low molecular weight species can be expected in bulk crystallization, the implications of table 1 are excessively high and inconsistent with other resu1ts.l Fractionation is an important but relatively restricted process. Perhaps more important is the incorrect use of 141.3 "C for the equilibrium melting temperature of linear polyethylene. This is the result obtained after high-tempera- ture-high-pressure crystallization of polymethylene and relatively rapid heating and is a unique result for this mode of crystallization.The claim of 10 pm for crystallite thickness is not substantiated by any other investigators, and the melting-temperature determination of this sample is obscured by melting kinetics. The melting tempera- ture is thermodynamically inconsistent with crystallization conducted under atmo- spheric pressure.2 A theoretical effort to justify this result by modification of the Flory-Vrij analysis3 has been attem~ted.~ I t should be recalled that the Flory-Vrij method yields an equilibrium melting temperature of 145.5 & 1 "C.Although super- ficially in apparent agreement, serious error exists between this m e t h ~ d , ~ the princi- ples of the Flory-Vrij method and the actual experimental result^.^ The claim that the temperature coefficient of the enthalpy of fusion is taken into account, while Flory-Vrij do not take it into account, is incorrect. In fact the Flory-Vrij paper gives very good agreement with this quantity where actual experimental data exist. The most serious error4 is the use of the melting point of chains of non-uniform length to substantiate the calculations, even though the length was calculated by etching away the non-crystalline region. This procedure is self-deluding, since the theory3 is absolutely rigid in the requirement of uniformity of chain length.A more detailed re-analysis of this problem will be reported ~hortly,~ pointing out the principles involved and the errors in analysis that were ~ommitted.~ Experimentally, a melting temperature of 146.0 & 0.5 "C has been reported for linear polyethylene crystals precipitated by high-speed stirring from solution.6 Since such samples are oriented, resulting stresses were removed by annealing at 142 and 145 "C for periods up to 30 days. This procedure leads to a reliable melting temperature as well as to a corresponding dissolution temperature. These results support the basic tenets of the original Flory-Vrij analysis, with an equilibrium melting tempera- ture in the range 145-146 "C rather than the lower value cited in the present paper.This difference is significant for many theoretical calculations. Dr. D. T. Grubb (Cornell Uuiuersity) said : Fractionation during crystallization is a very important phenomenon, and I would like to make some remarks about mole- cular nucleation. The first of these is that I hope Prof. Wunderlich will correct me if I misrepresent his analysis, as I am not completely confident that I follow it correctly. The minimum stable secondary nucleus is said to have the equilibrium shape, width av = al/6, and so to form a nucleus the molecule must have a lengthProf. J. H. Magill (University of Pittsburgh) said : In regard to his model for mole- cular nucleation and segregation I wish to inquire if Prof.Wunderlich has considered the complex " molecular traffic " pattern which is likely to exist at the crystal interface during solidification. Prof. B. Wunderlich (Rensselaer Polytechnic Institute, Troy) said : The disagree- ment of Dr. Mandelkern with our measured value of 414.6 K as the polyethylene melt- ing temperature is of long standing. Our measurements were published in 1967.l They were made on highly crystalline polyethylene which contained no fractions of molecular weight below 100 000 and was entirely in the extended chain macroconfor- mation. The biggest crystals of the sample, observed by electron microscopy, were 10 pm in the molecular chain direction and had many times this size in the other directions, i.e., the crystals were macroscopic in size.In the meantime these experi- ments have been repeated and extended in at least eight laboratories. All experi- ments produced extended chain crystals above 1 pm in the chain direction. X-ray diffraction data have shown close to 100% crystallinity and virtual perfect crystals in these samples. It is unreasonable to still call for further substantiation of these facts. The assumption of Dr. Mandelkern that the melting experiments on the extended chain crystals in ref. (1) are made by rapid heating are in error. In ref. (1) it is stated that 24 h were allowed to elapse between successive points in the melting region. The inconsistency with crystallization at atmospheric pressure first suggested by Dr. Mandelkern2 was fully shown to rest with the erroneous high melting temperature used by Dr.Mandelkern for his data analysis. These facts were fully documented in our rebuttal to the original remarks of Dr. Mandelkern.3 The major theoretical ob- jection to the " low " melting temperature was an extrapolation of Flory and Vrij4 of 33 paraffin melting points which led to 418.5 K for the melting temperature of infinite molecular weight. In the meantime, we could show that the unique temperature dependence of the heat of fusion of polyethylene neglected by Flory and Vrij is at the root of this erroneous melting temperature e~trapolation.~ The cryptic statements of Dr. Mandelkern about superficial, apparent agreement and serious error in our analysis will have to await the publication of the paper by Mandelkern and Stack in preparation. Anyone interested can check, however, that Flory and Vrij4 were not in possession of the proper data for the heat of fusion tem- perature dependence of paraffin and polyethylene.Taking the proper (experimental) paraffin heat of fusion temperature dependence into account, the same paraffin melting temperatures as used before and the same extrapolation formulae lead to an equili- brium melting temperature for polyethylene of 414.8 K,6 in good agreement with experiment. The experimental melting temperature of 419 K quoted by Dr. Mandelkern was determined on metastable crystals, produced from solution under conditions of exten- sive flow. Under such conditions the amorphous and crystalline areas are not inde- pendent, and the crystallinity model breaks down.Annealing at 415 K (above the melting temperature) will not separate crystalline and amorphous areas, only true melting will. It was shown later by Rijke et aL8 that etching the interfaces could sepa- rate the crystalline and amorphous areas with a drop in melting temperature to 409 K, a clear proof of metastability. Pressure-crystallized, extended-chain crystals of poly- ethylene are barely affected by such et~hing.~ These non-equilibrium melting tem- peratures of samples crystallized from stirred solutions are thus not an acceptable approximation to the equilibrium melting temperature. In the meantime, non- equilibrium melting temperatures as high as 463 K have been observed for crystals from solution, grown under conditions of extensive flow.GENERAL DISCUSSION 41 8 The specific criticism of Dr. Mandelkern of lacking end-group matching on the melting temperatures on etched extended chain crystals of 515, 912 and 6000 CH2 groups to substantiate our equilibrium melting temperature is well recognized, but was not the major support for the 414.6 K equilibrium melting temperature and does not change the conclusions. For the highest molecular weight of these samples, end pair- ing cannot cause an effect of more than 0.5 K as can easily be calculated. Similar effects, but of uncertain direction, are caused by the probable carboxyl terminal groups introduced by etching. The experimental melting temperature of 413.6 K is thus a good indication that 414.6 K is a much more likely equilibrium melting temperature for infinite molecular weight than 419 K.It is also of interest that the longest par- affin to date which has no difficulties of uniformity or end groups (C140H282) fits much closer to the Flory and Vrij equation including terms for the change of heat of fusion with temperature (-0.8 K) than any of the extrapolations leading to about 419 K (-3.0 K).l0 The equilibrium melting temperature of polyethylene, which is of key importance for the evaluation of the thermodynamic driving force for segregation, is thus derivable through the extrapolation of paraffin melting temperatures as suggested by Flory and Vrij if the experimental temperature dependencies are used. Three key melting experiments, the one of extended chain high molecular weight polyethylene, which still contains up to 10 folds per molecule,1 the one of fully extended end-unpaired polyethylene of 6000 CH2 units with -COOH end groups5 and the one of C140H232" fit the extrapolation derived from the lower paraffin data well.The only experiments which indicate a higher melting temperature are made on non-equilibrium ~arnples.~ The comments by Dr. Grubb and Dr. Mandelkern concerned with the steep in- crease in critical molecular weight above 400 K on crystallization from the melt as shown in table 1 (360 K from solution inp-xylene) deal with experimental observations and should be treated as such. Assuming a simple two-dimensional molecular nucleus11 we calculated a critical molecular weight of 13 300, which is lower than the last entry in table 1 but higher than the value estimated by Dr.Grubb. As is shown by the contribution of Dr. Point, there are, however, serious shortcomings in our pre- sent crystal growth rate theories. We are actively working on improvements to the theory of molecular nucleations. The more limited segregation mentioned by Dr. Mandelkern must be viewed in the light of his experimental conditions. A compari- son shows that Dr. Mandelkern never attempted a separation of the molecular weights and concluded " non-segregation " wholly on the appearance of the melting curves of metastable crystals.12 To the specific questions of Dr. Grubb I would like to reply that very little is known about the detailed path of a molecule crossing the nucleation barrier (fig.1 of Dr. Grubb). We hope that the contradiction: absence of surface nucleation and need of stabilization of molecules only slightly longer than critical nucleus size, will be resolved with a better model. Note that length and width changes of a molecular nucleus are of different nature. The first is a solid state rearrangement (fold length extension), while the second involves sequential addition of repeating units (which should be treated as a cooperative process and not as a fixed, length-independent rate). In our experiments we noted the remarkable similarity of rejected molecular size with critical nucleus size." The size of a stable nucleus cannot be derived without further assumptions (see fig.10 of Dr. Grubb). One of these assumptions is the one of Hoff- man (1964), mentioned by Dr. Grubb, that cilia alone may cause segregation. Since side surface free energies are rather small and fold free energies are at given fold length proportional to the length of the molecule, the molecular weight for rejection is in this case also A T 2 dependent. Under such conditions molecular nucleation without 419 use of side surface contact to neighbouring molecules would be less likely. We sug- gested, since experiments show that ledges in the surface are no source of preferred crystallization (see fig. 2 of our contribution), that this may not be the nucleation path taken.To the final question of Dr. Grubb, I can only add that the observed fold length is indeed the result of crystal growth and thickening due to solid state rearrange- ment [fig. 111.13 of ref (1) of the original contribution]. How far these two processes need to be considered separately in molecular nucleation is not known at present. Additional experimentation in this area of small supercooling may be of help to sort out the processes of importance to crystal growth of macromolecules. Finally, with regard to the question of Dr. Magill concerning the interface struc- ture, a detailed answer is at present not possible. It must be remembered that in order to achieve such a sharp segregation, forward and reverse processes of molecular nucleation must have closely similar rate constants and the processes must occur many times for each molecule.Such reversibility would exclude grossly irregular nucleus shapes. Dr. D. Vesely (Brunel University) said: I would like to point out that the preferred orientation of lamelae in PE spherulites as observed by the dark field STEM technique is consistent with the results presented by Krimm and Cheam. Specimens prepared from melt or solution at high undercoolings have (I 10) preferred orientation of lamel- lae. For low undercoolings only melt crystallization can be used and the lamellae have (020) preferred orientation. The analysis of microdiffractions indicates that the preferred orientation of the spherulite lamellae means a higher degree of order along some crystallographic planes.The folding with re-entry along these planes would result in a good periodicity and allow a higher disorder in the other planes. Dr. D. M . Sadler (University of Bristol) said: To our knowledge we are the only group to measure i.r. and SANS on the same samp1es.l Our basic i.r. observations are similar to Prof. Krimm’s, with the use of a range of“ guest ” molecular weights as in his work presented here, but with the difference that we also go to smaller mass con- centrations of guest (down to 1%). We concur that there are major differences in guest peak profile between solution grown polyethylene crystals, melt grown, and paraffins. However, we would like to add a significant qualification: our observa- tions indicate a large concentration dependence of the detail of the profile.For example to achieve a resolution of a doublet for single crystals (for this we require a minimum in the centre of the peak) a guest concentration of 5% is required and then only when M , is in the range above 234 000. At 1 % we have not seen a doublet resolution with dispersive spectrometers, even with the use of liquid nitrogen tem- peratures. Fig. 12 shows some representative peak profiles. We conclude that details in 420 peak profile are not easily related to conformational effects, since concentration de- pendence clearly indicates contributions from inter-chain interactions. SANS has shown the existence of a finite degree of fractionation even at high supercoolings.2 For example, an overall concentration of 1 % may result in local concentrations in the range 055%.In most cases of high supercoolings we can separate the scattering caused by this fractionation from the proper form factor corresponding to the indivi- dual guest molecules.2 The former is highly concentration-dependent while the latter is not (in other words derived R, values are independent of concentration). It is probably this fractionation which increases the concentration dependence of the i.r. measurements., which, from a priori considerations, ought to be small in the range 1-5%. Correlations of fractionation (from SANS) and i.r.I is very relevant to one of the conclusions of Prof. Krimm. He claims to derive a model very similar to super- folding from the molecular weight dependence.We have found, contrary to simple ideas but consistent with detailed measurements of crystallization kinetic^,^ the dif- ferences in local concentration became larger with higher molecular weights in the range above 50000. Hence the molecular weight dependence of the i.r. observa- tions, which we also observe, may be due to interchain effects rather than to con- formational differences. It should be remembered that at molecular weights as high as 280 000 (table 2) the molecule will contain in the region of 5-10 constituent sheets (this is derived from radius of gyration values, the higher number relating to diluted rows of stems). If these sheets were adjacent or close to each other, and if there was dilution along each sheet, in the middle of the molecule the chain interactions would be the same as for a random mixture with high concentration.With as many constituent sheets as this, the analysis by Prof. Krimm would presumably predict a value of splitting very near that for the pure polymer if there were no stem dilution and if the constuent sheets were adjacent. In this light, the models that we show and the one that Prof. Krimm claims to derive from his data, are not so very different, since ours involves more intra-chain contact at right angles to the sheets, whereas his has more contact along the sheets. The main difference is that SANS is compatible with the former model (it was derived using this technique) but not the latter. Prof.A. Keller (University of Bristol) said: 1 note that the situation has become considerably more involved then it was in the early days of this subject. As I recall at first it was a question of whether the appropriate bands were singlets or doublets, and in the case of doublets the magnitude of the doublet separation. Now I note that often the doublets are not apparent as such, the doublet nature becoming revealed only by curve deconvolution procedures. In this latter case, in addition one has to take into account the existence of a third band in between the doublet components and also one needs assignments for the band shapes. On the whole there appears to be a significant departure from the simple situation of " look, see and measure " and the final conclusions, apparently so vital for the whole central issue of stem adjacency, seem to depend critically on the treatments to which the experimental data need to be subjected. Is this a fair assessment of the situation? Prof.S. Krimm (Uniuersity of Michigan) said: Yes and no. The qualitative dif- ference that we observed' between a singlet CD, bending mode (for melt-crystallized mixed crystals) and a doublet (for dilute solution mixed crystals) is apparent without further analysis, and shows that chain organization in these two systems cannot be the same.l While the doublet nature in the latter case can be readily observed in the infrared spectrum, particularly if (as in our present work) the sample is at low tem- perature, the exact value of the splitting can only be obtained by analysis of the band contour.The reason is that allowance must be made for the possible presence of a crystalline singlet that can arise from isolated deuterated chain stems. When such a band resolution is done, the exact value of the splitting will depend somewhat on the band contour used, viz., whether it is a gaussian function, as in the work reported here, or a gaussian-plus-lorentzian function, as in our more recent work.2 While the details are altered slightly by this difference, the conclusions are essentially the same as we have reported here. GENERAL DISCUSSION Prof. L. Mandelkern (Florida State University) (communicated) : In his paper, Prof. Krimm states that 50-60% of the intensity in question is associated with a non- crystalline component.If I understood the oral presentation on this matter correctly, this component can be associated with ~ 2 0 % disordered material. In view of his own work, as well as other evidence and experiments, would Prof. Krimm care to comment on the molecular nature of these disordered chain units? In previous work,l Prof. Krimm interpreted and argued strongly that the band splitting in melt-crystallized polymer co-crystals resulted from adjacent re-entry in the (200) plane. However, in his oral presentation today he stated that previous work showed that melt-crystallized samples did not demonstrate any adjacent re-entry. Are these apparently contradictory statements due to new infrared experiments, a re-examination of the old data, or recognition of the neutron scattering results as well as other properties? Prof. Krimm made the point, orally, that from a theoretical point of view segrega- tion or aggregation would not affect the interpretation of his results.This con- clusion is que~tionable.~.~ However, after making the statement that segregation is not important to the matter at hand, he went into great detail trying to demonstrate that it does not occur. The major points of his argument are not correct. The segre- gation is governed by the equilibrium phase diagrams and the difference in crystalliza- tion kinetics between the two species.2 Both these factors depend on the equilibrium melting temperatures and not on the ones directly measured.This fact is very well known, as is the fact that the directly observed melting temperature willdepend on many many factors not pertinent to the present problem. For comparable molecular weights the six-degree difference in equilibrium melting temperare is maintained over the complete molecular weight range, irrespective of the directly determined ones. The crystallization procedure that Prof. Krimm describes practically ensures segregation and a non-uniform composition distribution. Crystallization from dilute solution beginning at z 85 "C represents isothermal crystallization for the H species and virtually none for D, which will separate out at a much lower temperature.2 Hence segregation and non-uniform composition is inevitable when crystallization starts at 85 "C, and comparison with n-paraffins of the same nominal (original) composition is impossible.Prof. S. Krimm (University of Michigan) (communicated) : I stated that, based on a gaussian-plus-lorentzian band shape, z 40-50z of the integrated intensity is associated with the crystalline doublet. The remainder is due in part to a crystalline singlet and in part to a non-crystalline singlet. The latter, which we estimate to be 2520% of the total, is associated with non-trans-planar-zigzag conformations, which could arise, for example, from folds, chain ends and adsorbed molecules. In our earlier work1 we found that melt-crystallized mixed crystals give rise to singlet CD2 bending modes, in contrast to the doublets observed for dilute solution crystals.We noted that such singlets can arise from random re-entry as well as from folding with adjacent re-entry along (200) planes. The former, in the sense of a statis- tical arrangement of deuterated and protonated chain stems, was clearly excluded on the basis that the CH2 rocking mode splittings were larger than in n-paraffin mixed crystals of the same composition. We therefore concIuded that (200) folding was present in melt-crystallized samples. As in the case of the present work on solution- crystallized samples, isolated chain stems cannot be excluded, and the important GENERAL DISCUSSION 423 question becomes the extent to which they are present. We will deal with this in a subsequent publication.2 I never said that ".. . from a theoretical point of view segregation or aggregation would not affect the interpretation of (our) results ". Obviously it would, which is why, as Prof. Mandelkern points out, we went into " great detail " to show that it does not occur! What I did say is that the meaning of " segregation " in neutron diffrac- tion studies is different from that in mixed-crystal infrared spectroscopy. In the neutron case, any departure from statistical mixing of deuterated molecules (which has been referred to as " segregation ") manifests itself in the scattering pattern. In the infrared case, such departures have no efect whatsoever on the CD2 spectrum unless deuterated molecules are contiguous to each other on adjacent lattice sites.This is how we have used the term " segregation ",3 and clearly such structures are only the extreme example of the neutron scattering problem. Similarly, heterogeneity in composition, while presenting difficulties in interpreting neutron scattering results, has no efiect on the conclusions from infrared spectroscopy, so long as it does not result in deuterated molecules coming within the domain of first nearest neighbour positions of chain stems of other deuterated molecules. Experimental evidence that composi- tional heterogeneity does not result in such contiguity is amply provided by the results on low concentration n-paraffin mixed crystals.' The absence of such con- tiguity from our polymer systems has already been ~ h o w n , ~ and is further supported by the present studies.In view of the above, it is clearly illogical to equate, for spectroscopic purposes, " segregation and a non-uniform composition distribution ". Our specimens were not crystallized at 85 "C, but, as stated in our paper, at 55 "C. This resulted in a large undercooling on crystallization, which, together with the low PED/PEH ratios used, minimized the probability of contiguity of different molecules. In any case, our experimental results sustain the conclusion that we are seeing the spectroscopic effects of isolated PED molecules. Of course, if this assumption canot be made for the neutron scattering calculations (which we believe it can), then the present computa- tions on isolated chain stem arrangements are totally irrelevant for comparison with experimental observation.Prof. E. T. Samulski (University of Connecticut) said: I want to draw attention to an alternative experimental technique which yields local structural details of the molecular morphology in polyethylene crystals : the moment analysis of proton n.m.r. lineshapes in isotopically diluted cocrystals of PEH and PED.I The intermolecular contribution to the proton n.m.r. second moment Ml is a function of internuclear distances between neighbouring stems with an inverse sixth-power dependence (only nearest-neighbour interactions are probed). Since internuclear distances vary for interactions along the (100) and (1 10) (170) planes and as a consequence of the in- herent sensitivity to relative distances, it is expected that the predominance of ad- jacent re-entry along one such plane would be manifested in the measured Mi.Preliminary measurements on etched cocrystals of PEH and PED were best ac- counted for by random re-entry molecular morphologies.' Subsequent criticisms relating to the details of the procedure employed to carry out the n.m.r. measurements2 and the use of etched samples3 have been raised. The former are partially mitigated by the fact that relative measurements were ~tilized.~ The latter (diffusion within the cocrystals during etching yielding a random array of stems) would also appear to be GENERAL DISCUSSION applicable to the more classical chromatographic analyses of etched samples and should be considered further.It is clear, however, that this powerful probe of local morphology should be added to the arsenal of experimental techniques currently utilized in order to expedite the painfully slow convergence of agreement about the molecular morphology in polyethylene. K. M. Natarajan, E. T. Samulski and R. I . Cukier, Nature, 1978, 275, 527. ' R. Voelkel and H. Sillescu, Macromolecules, 1979, 12, 162. Prof. S. Krimm (University of Michigan) said: In the n.m.r. work referred to by Prof. Samulski,l solution-grown crystals were subjected to etching with fuming nitric acid at 80 "C. I t was assumed that the distribution of deuterated stems after etching was the same as that before, thus permitting inferences about the chain organization in the original sample.Recent infrared studies on etched mixed crystals2 indicate that this assumption is unwarranted. We have examined the effect of etching at 60 and 80 "C on the CD, bending region of lOH/lD and 40H/lD mixed crystals. Comparison of these spectra with those of non-etched crystals suggest that deuterated chains tend to disperse as a result of the etching treatment. This effect is clearly de- monstrated by the results of subsequent annealing as compared to similar treatment of unetched crystals. It cannot, therefore, be assumed that deuterated chain stem organ- ization in mixed crystals remains unaltered by etching with fuming nitric acid. Prof. A. Keller (University of Bristol) said: Referring to the paper by Guenet et al., it would be interesting to know (i) How was the degree of crystallinity altered? (ii) In particular, was it ensured that the samples having different crystallinities have been fully crystallized in the morphological sense? (iii) I mean, did they consist fully of spherulitic material as opposed to containing extended regions of a still uncrystallized amorphous matrix? Prof.B. Wunderlich (Rensselaer Polytechnic Institute, Troy) said : The Erstarrungs- modell for a quickly cooled melt which requires no " long range diffusion or significant reorganization in the chain conformation " fits very well into the framework of '' cold crystallization " proposed by Dole' and analysed by us in detail2 which is the short time crystallization limit " which allows only nearest neighbours in the amorphous state to crystallize ".It represents the " non-equilibrium limit of random crystalliza- tion of linear high polymers ". M. Dole, Kolloid-Z., 1959, 165, 40. * B. Wunderlich, J. Chem. Phys., 1958, 29, 1395. Dr. P. D. Calvert (University of Sussex) said : During rapid crystallization from the melt there will be an abundance of growth sites (niches) on the crystal surface such that individual chains will attach to several widely separated points on the surfaces of the growing crysta1.s. This will prevent long-range reorganization of chain and lead to a structure similar to that described by the solidification model of Stamm et al. Poly- mer crystallinities can be calculated on this basis, values in the range of 30-50% being obtained.However, in many polymers isothermal annealing may follow crystallization lead- GENERAL DISCUSSION 425 ing to higher crystallinities and extensive rearrangement of the chains. Thus the final chain conformation is not a product of crystallization only but of both crystalliza- tion and annealing.’ P. Calvert, J. Polymer Sci., Polymer Phys. Ed., 1979, 17, 1341. Dr. C. M. Guttman (National Bureau of Standards, Washington, D.C.) said : I have four questions for Prof. Fischer and Dr. Stamm. (1) In your solidification model you disregard the scattering from the chains in the amorphous zone. What is your justification for this? (2) We have shown the Yoon and Flory pes = 0.3 irregular re-entry model has a serious density anomaly.(See paper in these Discussions by Guttman et al.) Your solidification model seems to have a stem distribution similar to the Yoon and Flory irregular re-entry model. Have you shown whether your stem distribution yields a density defect in the amorphous phase? ( 3 ) You quote long spacings, I, for quenched PED + PEH mixtures as I = 244 A for 0% PED, 1 = 196 A for 50% PED and I = 168 A for 100% PED. For molecules supposedly identccal are you not surprised that the long spacings vary so much? How do you explain these differences ? With such broad long spacing variations do you feel the PED is represen- tative of the PEH material ? (4) You have shown thaf for mixtures of deuterated and hydrogenated paraffins the single-stem scattering function, as expressed in the first then assume that this first term is enough to explain the scattering in PED + PEH term of eqn (2) in your paper, is sufficient to explain the experimental scattering.You mixed systems. Have you shown that the diffuse wide-angle scattering on the semi- crystalline polymer mixtures obeys the concentration dependence [x( 1 - x)] expected from the first term in eqn (2) of your paper? Prof. E. W. Fischer (University of Maim) said: With regard to Dr. Guttman’s question about the density of the amorphous phase in the solidification model we can only offer a qualitative discussion, since no special assumptions about the statistics of the non-crystalline sequences were introduced in our analysis of the SANS curves. From a qualitative point of view we believe that the random closest packing structure (RCP) introduced by Bernal1+* is a good model of the packing of amorphous poly- ethylene.RCP has a packing density of q = 0.637, compared with q = 0.630 of amorphous PE, and the volume change by the transition from the crystalline closest packing (CP) is =15%, which is again comparable with PE. If we draw threads through the spheres of the RCP structure in a complete random fashion and cut a plane through the “amorphous region”, then the average flux of threads through this plane will be Dr. M . Stamm (K.F.A., Jiilich) said: With regard to Dr. Guttman’s first question I may refer to the remarks of Prof. Fischer saying that there should be at least an interfacial zone, where there is a large amount of orientation present in the amorphous phase.The scattering from this region should not differ very much from the crystal- line scattering. In the pure amorphous region on the other hand one may assume a gaussian scattering behaviour similar to melt scattering resulting in a plateau level in the Kratky plot at smaller scattering angles. To a first approximation one thus only gets an upward shift in the scattering curve, and since the crystallinity of the samples amounts to 70-80%, the error should not be too serious, if one neglects the scattering of the amorphous regions. The second question has already been answered by Prof. Fischer in detail. Con- cerning the concentration dependence of the long spacing of the melt-crystallized samples, mentioned in the third question, I would like to refer to our paper, where we noted a difference in the branching ratio of the PED and PEH materials, which we believe to be responsible for this effect.Since we do not observe a concentration- dependent change of the form of the scattering curve, however, we believe that this effect does not significantly affect the conformation and spatial arrangement of the chains. Ballard et aZ.l investigated on isotactic polypropylene the influence of a change of the long period on the chain conformation and did not observe a significant effect of the variation of the long period in this case, too. To answer the fourth question I would like to refer to fig. 15, where the scattered intensities of melt-quenched samples at a given k-value are plotted as a function of the PED concentration, xD.The expected concentration dependence of the intensity according to eqn (2) ZccxD(1 - x,) is well reproduced by the experiments. Eqn (2) is in general used for alloys composed of two components, but we actually could show by theoretical considerations that it may well be applied to polymers under the assump- tion that no specific interaction between molecules of one sort exists (segregation).2 The density fluctuation term also present in the complete formula has been neglected in the form given in eqn (2) of our paper, since it may be considered as background scattering in the analysis given here. ’ M. G. Brereton et al., to be published.D. G . H. Ballard, P. Cheshire, G. W. Longman and J. Schelten, Polymer, 1978, 19, 379. Prof. P . H . Geil (Uniuersity of Illinois) said: It is important that we remind our- selves of the type of sample being used for all of the polyethylene solution-grown crystal studies by neutron diffraction that are being interpreted in terms of stacked- sheet models. Although no micrographs have been published, to my knowledge, 428 1 0.5 0 GENERAL DISCUSSION xo FIG. 15.-Dependence of the diffuse scattering intensity of melt-quenched polyethylene samples on the concentration of tagged molecules xD. The experimental points are taken at a fixed k-value, and the solid line is computed according to an expected dependence IccxD(1 - xD). crystallization from xylene at 60 "C, as described in this paper, will result in highly dendntic crystals.In 1961 Reneker and I described the morphology of such crystals,l attributing the development of the re-entrant faces to, among various factors, back folding. Back folding is also inherent in Regime I1 crystallization, that involving multiple secondary nucleation on a growth face.2 It is thus expected that in highly quenched, solution-grown crystals one will find stacked sheets or superfolding, but this does not detract from the possibility of single-sheet, adjacent re-entry folding in dia- mond shaped crystals grown more slowly. Dr. M. Stamm (K.F.A., Jiilich) said: We are pleased of course that Prof. Geil agrees with our proposed model for the rapidly solution-crystallized samples.Un- fortunately we only obtained micrographs of the melt-crystallized samples showing a normal spherulitic morphology. In the TEM mode single crystalline lamellae can be observed.* On the other hand we also tried to grow single mixed crystals of PED and PEH at higher crystallization temperatures (up to 92 "C), but did not obtain unsegregated samples. The interpretation of absolute intensities is therefore impossible, but if one tries to interpret the form of the scattering curves, one clearly observes a certain ten- dency to a folding in a single plane at increasing crystallization temperatures in accor- dance with your suggestions. Unfortunately polyethylene is not a suitable material for this sort of experiment, however, and I agree with you that further investigations in this field maybe on other polymers would be very interesting and necessary.* The EM investigations have kindly been performed by Dr. I. Voigt-Martin at Mainz University. GENERAL DISCUSSION D. G. H. Ballard, P. Cheshire, G. W. Longman and J. Schelten, Polymer, 1978, 19, 379. 429 Dr. R. Ullman (Ford Motor Co., Dearborn, Mich.) said: SANS experiments on polyethylene are generally restricted to cases in which crystallization is sufficiently rapid to prevent large scale separation of protonated and deuterated species. This may mean that the molecular arrangements which are observed are quite different from those which would be seen if crystallization was conducted much more slowly. It would seem that the molecular conformations to be found upon slow crystal- lization are those which are close to free energy minima in a constrained state characterized by a given lamella thickness.The molecular conformations, and especially the nature of chain folding near these states of metastable equilibrium, are of primary interest in characterizing the structure of crystalline polymers. To what extent have neutron-scattering studies shed light on this question? Dr. M. Stamm (K.F.A., Jiilich) said: To my knowledge the effect of crystalli- zation conditions on the chain conformation has mainly been studied by Ballard et al. for melt crystallized polypropylene. By means of neutron small-angle scattering they investigated the change of the chain conformation in dependence of the long spacing, which has been varied by annealing and different crystallization conditions.They do not observe a significant influence of the crystallization conditions on the chain con- formation, however. For solution-crystallized samples I refer to my previous re- mark on the question of Prof. Geil. For a detailed understanding of the scattering curves and the crystallization mechanism it may be, however, still interesting to per- form experiments on well defined samples at high concentration of tagged molecules and in an extended angular range. The method of neutron scattering should be well suited to shed more light on the question of crystallization under equilibrium condi- tions, too. Dr. D. M. Sadler (Uniuersity 9f'Bristol) said: Data of the kind presented by Stamm et al.were published in ref. ( 1 ) to a 9 value of 0.4 A-' on melt grown (and solu- tion grown) crystals. I wish to describe briefly the conclusions of new analyses car- ried out by myself and R. Harris of McGill University, MontreaL2 Fig. 16 shows Kratky-type plots for melt grown crystals, the abscissa (1q2)c being corrected so that independent scattering from stems of polyethylene chain give a straight line (shown by broken lines). This presentation eliminates the effects of the finite radius of the chain. As concluded previously' the asymptotic behaviour is independent stem scattering for all molecular weights. A significant test of the data is provided by low molecular-weight samples where the chain is only long enough to make one stem .. . as predicted single stem scattering is observed for the whole of the q range [fig. 16(a)]. Our calculations refer to the departures from single stem scattering which arise from systematic (non random) mutual arrangements of stems from longer molecules, the departures being due to inter-stem interference terms. Scattering for three models is shown in fig. 17 (solid lines). Fig. 17(a) illustrates how adjacent re-entry (in this case with short rows of stems) gives too much inter-stem interference. 17(b) refers to a " freezing-in '' model for which, apart from the actual formation of stems, the chain elements are required to move the least possible distances during crystallization.This seems a natural model given that the radius of gyration does not change. The calculation is done by specifying a two-dimensional stem distribution which is the projection of the original melt three-dimensional gaussian distribution. Fig. 17(b) shows that the inter-stem interference is predicted to be much too small compared with experiment. Our conclusion is that locally there is substantial chain movement during crystal- lization, and we surmise that this is likely if only because of the need not to overfill 430 FIG. 16.--Kratky-type plots for melt grown crystals of between 1 and 1.7 polyethylene (cooling rate 10 K min-'j, the ordinate (I-*) being corrected by a quantity near unity so that a polyethylene chain gives a straight line through the origin. This calculation is based on standard bond lengths and angles.[Re-plotted from ref. (l).] The broken lines are inferred from the data, and correspond to the single stem scattering if approximately 70% of the labelled chains are in the form of straight stems. The molecular weights are (a) 5200, (b) 10 200, (c) 31 000, ( d ) 97 000, (e) 271 000. q is 4n sin 8/2 where 28 is the scattering angle. I is in the same units as in ref. (1). space at the crystal surfaces. Fig. 17(c) shows calculations on the resulting model based on the idea of " subunits ". Within each subunit of z2-10 stems the separa- tions between successive stems have values in the range 4-12 A (one third adjacent re- entry, see also my earlier contribution after the paper given by Dr.DiMarzio and printed near the beginning of the first Discussion Section). We retain the idea of least movement during crystallization, but only on a larger scale. This " freezing- in " will then specify the relative position of different subunits. It may be that the subunit and the " solidification " models are not too dissimilar, but in our case we emphasize the significant degree of local rearrangement, giving approximately one third adjacent re-entry, with most of the other folds being 12 A or less. Fig. 18 shows the two-dimensional arrangement within a lamella. The need for such a model GENERAL DISCUSSION FIG. l8.-Two dimensional description of the subunit model. The features that are most significant are (1) Predominance of stem separations of % 4, 8 and 12 A.(2) Approximately straight subunits with a range of sizes. (3) Random arrangement of one subunit with respect to the others, subject to an overall Gaussian probability defined by the chain prior to crystallization. subunit are required both because of the magnitude and q dependence of the inter-stem scattering, and because of the need to avoid surface overcrowding. The larger separations between different subunits are required to explain the radius of gyration. D. M. Sadler and R. Harris, to be published. D. M. Sadler and A. Keller, Macromolecules, 1977, 10, 1128. Dr. M. Stamm (K.F.A., Jiilich) said: Since Dr. Sadler mentions his paper on melt and solution grown crystals' I would like to point out the main differences from our work. First we used mixtures of high concentrations of tagged molecules, which enabled us to extend the angular range up to approximately k <1 A-1.This results in important additional information on the chain conformation as may be seen e.g., from fig. 7(b), 11 or 14 of our paper. Secondly the interpretation of the scattering curves Dr. Sadler gives in his paper differs at least in the case of the solution crystal- lized materials. I further believe that it is not possible to use the small-angle formulae at k-values >0.2 A-'. For example the difference between eqn (3) of ref. (1) and a calculation taking the molecular structure of polyethylene into account may be as large as 30% at k = 0.4 A-'. GENERAL DISCUSSION 433 Concerning the recent conformation model illustrated in fig.18 I also believe that our concepts are indeed fairly similar. Within his subunits Sadler assumes a switch- board-like conformation of the chains. The corresponding correlations of the chains will be seen in the intermediate scattering range. Since on the other hand his sub- units are placed at distances typically 60 8, apart, the correlations between subunits would affect mainly the scattering in the k-range k 5 0.2 A-l. This small-angle scattering region has been more closely discussed in a previous publication presented at the D.P.G. meeting on high polymers.2 Here we considered a certain number of stems passing into the neighbouring lamellae. The presence of parts of the molecule in a second lamella may also be concluded from recent results of Ballard et aL3 show- ing that a large number of tight bonds is present in polymer crystals.The subunits may thus not be restricted to one lamella only as it is imposed from fig. 18 of the question. Concerning the remarks on the frozen-in structure, a comparison of fig. 17(b) of the question and of fig. 5 of our paper clearly shows some differences in the calculations. Unfortunately Dr. Sadler does not give details of his model, but in general I would believe that a computer simulation of the crystallization process would be very diffi- cult to do since problems of crystallization kinetics as e.g., the movement of entangle- ments, the loop diffusion, the reptation etc. are involved.In our solidification model we merely assume certain similarities between the chain statistics of the melt and the crystal, but do not necessarily keep the parameters involved constant. D. M. Sadler, and E. Keller, Macromolecules, 1977, 10, 1128. * M. Dettenmaier, E. W. Fisoher and M. Stamm, Fruhjahrstagung der DPG, Physik der Hoch- polymeren, Munster, 12-14.3.1979, PH34; proceedings to be published in Progr. ColloidPolymer Sci. Dr. C . M. Guttman (National Bureau of Standards, Washington, D.C.) said: In our paper we have shown a number of models of PE which have folding and which fit the neutron-scattering data of Schelten et al. to intermediate angles. In these remarks we would like to show data from one of these models which yield a dependence of molecular weight, M,, on radius of gyration, ( S 2 ) similar to that shown by Ballard et al.in the present paper. The model called the variable cluster model is described in our paper on models for neutron scattering of polymers. Fig. 19 shows a sche- matic of a representation chain which obeys the rules of the model. The SANS and other data for this model are displayed in fig. 5 and table 3 of our paper. We cal- culated M, as a function of (S2)+ = R, for this model assuming a crystallinity near FIG. 19.-Schematic of variable cluster model. Notice that for this model loops of < 20 segments are made into folds. 434 65% and a long spacing of 250 A as described by Schelten, et al. Fig 20 shows the plot of Mw3 against R, for this model along with the data of Ballard et al.(see their paper in this Discussion). The agreement of model and experiment is apparent. We do not, of course feel this model is unique in that it can fit this data. A variety of other models would be expected to do so. FIG. 20.-Radius of gyration R,, plotted against the square root of molecular weight, M,$, for two variable cluster models of polyethylene. pstem is the a priori probability of forming a fold in the Monte Carlo program. All calculated chains have a crystallinity near 65 % and par > 0.5. Squares are data of Ballard et al. (paper at this Discussion) on polyethylene. 0, pstem = 0.5; x ,pstem = 0.4. Dr. D. C . Bassett (University of Reading) said : I should like to point out that what are described as pressure-crystallized polyethylenes are, in fact, pressure-annealed. Although they have been temporarily converted into the disordered hexagonal phase, they have never been molten at high pressure.Had they been, their lamellar thick- nesses would have been higher by a factor of 2-3 than the ~2200 nm reported which is typical of pressure-annealed samples. Dr. D. G. H. Ballard (I.C.I., Runcorn) said: Dr. Bassett's comments are correct. The samples were annealed below the melting point and not crystallized from the melt. Dr. R. Ullman (Ford Motor Co., Dearborn, Mich.) said: In their experiments on pressure crystallized polyethylene, Ballard et al. report radii of gyration of M 580 A. From their earlier paper', I find that the range of KR, used for this determination satis- fies the inequality 1.4< KR*< 3.0.Normally, one has little confidence in experimental values of A, unless experiments are carried out at lower K , particularly if the system is polydisperse. Have you anything to add on this question? D. G. H. Ballard et al., Polymer, 1977,18, 259. Dr. D. G. H. Ballard (I.C.I. Runcorn) said: Guinier plots were used to derive a value of R,. These were linear in the range 0.002< K/A-'< 0.005 for which we have experimental points. If there was any change in the stem length measured this would be equivalent to a change of between 3000 and 1700 A; it is evident from fig. 2(d) of our paper that R, is independent of molecular weight and equivalent to a stem length GENERAL DISCUSSION 43 5 of 2000 A.The intensity values at these low K values were obtained at the maximum sample-detector distance of the Julich instrument of 17.6 m. Finally corrections for polydispersity have no significance since R, is independent hii(c*) 21 AJ(l) of M,. Dr. F. Rys (University of the Saar) said: The following remark concerns the poly- mer crystallization from dilute solutions which was discussed in the paper by Yoon and Flory. The behaviour of a long polymer chain in a solution of shorter polymers with a concentration c due to excluded-volume forces can be studied by using the mathematical analogy of the polymer problem with the n-vector model in the limit n = 0. The above-mentioned problem is equivalently described by the spin-aniso- tropic model in an external magnetic field having a longitudinal (hi[) as well as a traverse (hl) component.If the longitudinal direction refers to the single ion chain, then the suitably taken limit hi, -+ 0 describes the infinitely diluted chain; the deviation from the critical temperature T - T, is inversely proportional to its length, L-'. On the other hand, the transverse field component hL represents the chemical potential of the smaller chains; a finite concentration c is expressed by a suitably chosen value of hL.This result is of a certain importance in the crystallization process from dilute solu- tions. The (long) polymer assumes a swollen shape in the dilute bulk solution. On approaching the growth front it has to pass the amorphous region formed by a large amount of relatively short chain pieces (with fixed ends). Whenever the concentra- tion c exceeds c* the long polymer will be compressed to its random-walk size thus decreasing the relative distances between the segments of the chain in solution.We would speculate that this effect could increase the probability of chain folding and therefore of adjacent re-entry. Dr. D. M. Sadler (Uniuersity ofBristoZ) said: I would like to comment firstly on how our own past and present data analysis correlates with the Monte Carlo method of Dr. Yoon, and secondly mention new results (some in press) which show directly GENERAL DISCUSSION MEASUREMENTS TO q VALUES OF 0.7 A-' 436 the existence of " stem dilution " along the folded rows.This yields some further qualifications to the model as described by Dr. Yoon. In order to interpret the new results from neutron scattering the questions to be tackled were put in an order of priority. These may be seen in the presentation of ref. (1) : firstly on an empirical basis do solution and melt grown crystals have similar fold arrangements, secondly how far can simple sheet and rod models rationalize the two types of scattering curve, and lastly to what extent does one need to elaborate on the simple models of purely adjacent and purely random re-entry. On the first two issues there is now a degree of consensus, and most of the discussion centres on the third. I have already described in relation to Dr. Stamm's paper how in melt grown crystals the idea of purely random re-entry must be qualified, there being a large number of " nearby " folds.For solution-grown crystals the analysis has progressed further, and the basic sheet-like conformation has already acquired detailed qualifica- tion [see ref. (2) and the paper under discussion]. We would suggest (a) the analysis in terms of sheet scattering has a simplicity which enables alternative models to be assessed readily and (b) before adopting a new concept it is desirable to invoke addi- tional evidence. The second point is evidenced by the matching by Dr. Yoon of basically similar data by two different models [see ref. (3) and his present paper]. In support of (a), even in our preliminary publication4 the idea of superfolding was implicit in terms of interference between sheets, and fold dilution was discussed as a possibility. These two issues are immediately obvious if measures of sheet thickness (D) and density (nA) (coming from the slope and intercept of a h e , respectively) are compared with predictions.If D is too large in relation to a single straight row of stems, we can invoke superfolding (or " staggering '' of the stems in a row). The separate measurement of R, values made the former concept much more appealing2 If superfolding is adopted, all the nA values for various molecular weights become too low, hence the need for fold dilution. Below I describe briefly other results support- ing this conclusion. As regards the desirability or otherwise of Monte Carlo calcula- tions as opposed to analysis in terms of sheet scattering involving stems only (p.368) it is clearly not a crucial matter otherwise the conclusions from the two methods would not coincide to the degree they do. However, I would like to point out that the Monte Carlo method has in fact been incomplete although in a different way to the stem-only calculations. It supposes an unrealistic idealized two-phase structure and does not yet allow for all-trans sequences going into the surface disordered region. In other words, the choice of the method of analysis at the moment lies between specifying a rather arbitrary surface structure, or saying that much of the surface will be in the form of stems anyway, and to neglect the rest of the disordered chains.These have been made by myself and Dr. Spells. If there were no stem dilution, the Kratky-type plots would extend beyond those published in a continuous fashion. If there were a strong preference for stem separation of two sites, a broad peak would be seen at the corresponding inverse spacing of z q = 0.7 A-'. Fig. 21 shows a type of Kratky plot (chosen so that the effects of stem radius are removed, by plotting (1q2)c, see my contribution after the paper by Dr. Stamm). It can be seen that a minimum followed by a maximum as expected for a strong preference for double folds has not been observed. Fig. 21 also shows the results of preliminary calcula- tions where the experimental intensities have been scaled to achieve an approximate agreement (see caption).While at this stage in the analysis no definite agreement has been achieved with any one model, it seems likely that a random dilution along 437 GENERAL DISCUSSION FIG. 2 1 .-Kratky-type plot for solution-grown crystals, where (Zq2)c (arbitrary scale) is corrected so that the scattering from independent straight stems of polyethylene is a straight line going through the origin. The circles are data, the solid line is a “ stem only ” calculation for a superfold structure (50 % probability of adjacent and 50 % of next to adjacent re-entry) with the sheets being (randomly) either adjacent or spaced by one lattice spacing, and the broken line corresponds to a preference for next but one re-entry. The comparisons with preliminary calculations are made primarily on the q dependence of (Zq2)c (q = 4n sin O/A where 28 is the scattering angle).the folded ribbon (solid line) is more likely than a systematic preference for next but one re-entry (broken line). INFRARED MEASUREMENTS I give a more extended description of the relevant work5 after the paper by Prof. Krimm. In summary, we observe a much broader guest peak for solution-grown crystals than for either melt-grown crystals or paraffins, and we conclude that this is indeed a genuine conformational effect. However, the details or the peak profile, in particular whether the peaks are resolved into doublets, are dependent on guest con- centration, and in this case intermolecular interactions must be important.By empirical comparisons with isotopic mixtures of paraffins we derive an effective local concentration of the deutero polymer of w 50%. A superfolded structure with stem dilution, as deduced from neutron scattering, would predict a local guest concentration of ~ 5 0 % . If adjacency were avoided as Dr. Yoon suggests, the chain interactions would be less than those predicted by the local concentration alone. Dr. D. Y. Yoon (I.B.M., Sun Jose) said: Dr. Sadler asserts that the local concentra- tion of deutero polymer is ~ 5 0 % according to his mixed-crystal infrared results on solution-crystallized PE crystals. Our model, as shown in the lower portion of fig. 4 GENERAL DISCUSSION 438 of our paper yields a local deuterated stem concentration of ~ 5 0 % and, hence, is completely consistent with the i.r.measurements. A local concentration of deutero polymer of 50% implies that the re-entry sites are two lattice spacings (Z 10 A) apart on the average. Hence, adjacent re-entry is not predominant. As for the details of the distribution of re-entry distances, we wish to point out that the type of distribution proposed by Sadler et al. is incompatible with their neutron scattering results of lower M, samples, e.g., PE with M, = 5200 (see our fig. 5). Our conclusions that adjacent sites are disfavoured have been drawn from analyses of these data. Dr. E. A. DiMarzio (National Bureau of Standards, Washington, D.C.) said: The following comments apply only to the discussion of Yoon and Flory on crystallization from dilute solutions.First, it is apparently not recognized that the superfolding concept which has been used to explain neutron scattering results also provides an explanation of the fact that the growth rates of polyethylene crystals vary with a fractional power of the concentra- tion. I. C. Sanchez and E. A. DiMarziol postulate a self-nucleating mechanism in which a cilium formed in an underlying growth strip nucleates a new growth strip [see fig. 3 of ref. (l)]. The concentration dependence is predicted correctly both as a func- tion of molecular weight and temperature. The intuitive appeal of the superfolding concept, and its correct explanation of crystal growth rate and neutron scattering results all argue for the validity of the concept.The point to be made here is that one does not need more than one molecule in the nucleation event to explain the fractional concentration dependence. Consequently, there need not be (though there may be) a stem dilution effect as required by Yoon and Flory to explain the neutron scatter- ing data. The stem dilution effect, if it occurs, would be more prolific at higher con- centrations and supercoolings. Interesting experiments as a function of these variables immediately suggest themselves. Second, the " diluted superfolding model " of Yoon and Flory is far removed from the random switchboard model originally proposed by Flory. It is much closer to the regular adjacent re-entry folding models of Hoffman and Lauritzen and of Frank and Tosi and is literally a slightly diluted form of the model of Sanchez and DiMarzio.' Third, in developing the statistics of an isolated polymer chain it is known that the conformations of the rest of the chain affect the conformations and statistics of a given loop.One can describe the statistics of an isolated loop only by the use of a grand canonical ensemble or equivalently by use of generating function techniques. When this is done a factor appears which is exponential in the number of segments of the loop. The effect of this factor is to weight smaller loops more heavily than larger loops. Yoon and Flory do not include this factor and consequently their estimate of loop size is too large. There is a large literature on this subject.Three relevant papers are collected as ref. (2) below. Fourth, for chains of moderate molecular weight long cilia are created at the ex- pense of both the number and the size of loops. This is a general phenomenon that occurs for helix-random coil transitions in biological macromolecules, adsorption to a surface, and in the model for crystallization discussed by Roe [see ref. (2)]. One can understand the physics of the phenomenon and at the same time make an estimate of loop size and extent of adjacency for crystals by reference to fig. 22. In this model the last stem is imagined to slap on and off so that equilibrium obtains between the loop of length ZI and the cilia of length Z2. The partition function for the combination is GENERAL DISCUSSION FIG.22.-Model for crystallization. E. A. DiMarzio and M. Bishop, Biupolymers, 1974, 13, 2331. where the factors ql, qc for the loop and cilia are given in a paper by DiMarzio and B i ~ h o p . ~ One finds that the results are sensitive to whether the loop and cilia are near a surface or not. If one uses the statistics appropriate to loops and cilia near an infi- nite plane surface, then one finds that the size of the loop is small ( NN 3 units) and the expected value of x is 1. That is to say cilia are so favoured relative to loops that the loops draw tight and the cilia lengthen. These estimates were made assuming the modified gaussian distribution of the DiMarzio-Bishop reference and without allow- ance of energy effects (which also favour small x).They provide a rationale for tight loops and large amounts of adjacent re-entry in crystallization from dilute solution. One cannot on the basis of these calculations decide on next-nearest rather than nearest neighbour adjacency, the statistics break down for small Zl, 12, but one can say that the loops are so tight that they are determined more by details of energetics than by entropic considerations. Dr. D. Y. Yoon and Prof. P. J. Flory (I.B.M., San Jose) said: Neutron-scattering results from solution-crystallized polyethylene single crystals require a stem dilution as shown by our calculations,' as well as by those of Stamm et aL2 and Sadler et aL3 This experimental fact contradicts the statement of DiMarzio and the self-nucleated adjacent re-entry model postulated by Sanchez and DiMarzio.The fundamental premise raised by the " switchboard " models of Flory4 and Fis- cher et aL5 has been the untenability of the regular folding model with adjacent re- entry. Our results confirm that premise of " switchboard " models and contradict the regular adjacent re-entry folding models of various forms. The comments and conclusions of the third and fourth paragraphs result from the use of unrealistic chain models to represent real chains of short lengths. The defi- ciency of random-walk models or gaussian distributions in representing relativeIy short chains has now been demonstrated in numerous examplese6 Statistics of chain folding drawn from such unrealistic models are hence misleading, as we have D.Y. Yoon and P. J. Flory, Faraday Disc. Chem. Soc., 1979, 68, 288. M. Stamm, E. W. Fisher, M. Dettenmaier and P. Convert, Faraday Disc. Chem. Soc., 1979,68, 263. GENERAL DISCUSSION Prof. S. Krimm (University of Michigan) said: I wish to comment on what seems to be a contradiction between the Yoon-Flory model for polyethylene single crystals and our infrared results. The model in the lower part of fig. 4 of their paper corres- ponds to the arrangement of stems of a single PED molecule that gives best agreement with the neutron scattering data, the influence of other PED molecules being con- sidered negligible. Our results support the assumption that (at PED concentrations of z 3 % or lower) individual PED molecules are, at least from the spectroscopic view- point, isolated from one another.However, the proposed model of Yoon and Flory is inconsistent with the significant doublet, with splitting > 6.5 cm-’, that we observe for fractions with ~ 4 0 stems: a higher degree of site adjacency would be required than is depicted in their arrangement. Dr. D. Y. Yoon (I.B.M., San Jose) said: We only wish to point out that the analysis of mixed-crystal i.r. results is by no means a settled issue among workers in this fie1d.l Even the presence of a significant fraction of adjacent stems (yielding a doublet) versus isolated stems (yielding a singlet, whose presence is undeniable) seems open to ques- tion, not to mention the determination of the actual magnitude of splitting.Prof. P. H. Geil (University of Illinois) said: As Prof. Keller pointed out in his Introduction to this section on Crystalline Polymers, two distinct, but related, funda- mental questions about the morphology of polymers crystallized from the melt have recently been raised. The first of these, promulgated primarily by Yoon and Flory in this and earlier papers, is whether there is sufficient molecular mobility to permit the development of significant numbers of adjacent re-entry folds during crystalliza- tion of polymers from the melt. The second, instigated primarily by neutron diffrac- tion studies during the past several years (see papers by Guenet et al., Stamm et al. and Ballard et al., this Discussion) and also raised in this paper, is whether adjacent re-entry folding does occur in melt crystallized polymers.Here I am interested in what might be called normal or practically interesting polymers and crystallization conditions ; e.g., for linear polyethylene molecules with molecular weights between 10 000 and several hundred thousand and supercoolings of 10-30 K, with related con- ditions for other polymers. At the March meeting of the American Physical Society this year I considered the evidence obtained from morphological observations over the last 20 years or so for molecular motion during crystallization from the melt. This includes such observa- tions as: (1) growth of single crystals with fractionation and sectorization near the melting point (Tm); (2) growth of isolated hedrites or axialites from originally uniform thickness films ; (3) easy interlamellar splitting in slow-cooled samples indicating few or no tie molecules; (4) segregation and fractionation during spherulite growth for a wide range of supercoolings and growth rates ; ( 5 ) extended chain crystallization under pressure, again for a wide range of crystallization rates including pressure quenching; and (6) phase separation of deuterated and hydrogenated polyethylene during prepara- FIG.23.-Linear polyethylene crystallized from the glass at 200 K. A microbeam (f 1200 8, diameter) electron diffraction pattern from a similar area is inset [see ref. ( 5 ) ] . [To face page 440 FIG. 24.-Single crystals of polycarbonate crystallized from a uniform thickness glassy film at 145°C.The upper structure has lamellae both parallel and perpendicular to the substrate [see ref. (6)]. [To face page 441 GENERAL DISCUSSION 441 tion of samples for the neutron scattering experiments which have led to the raising of the second question. In that paper I also pointed out, contrary to the statement of Yoon and Flory,' that knowledgeable persons in the area of polymer morphology have recognized from the beginning of the research on lamellar crystallization from the melt the presence, origin and significance of such features as tie molecules, irregular and/or non-adjacent folds, cilia, non-crystallizable molecules, etc. [see e.g., ref. (4)]. In view of time (and space) limitations and other papers in the Discussion which consider similar effects, we will not include the evidence here. Clearly, however, conclusions of little or no molecular motion occurring during crystallization near T' are inconsistent with a wide range of experimental evidence and, on that basis alone, should be discarded.In fact, as I also discussed in March, the conclusion of little molecular motion does not seem to apply to any temperature of crystallization. Substantial molecular motion can occur even during crystallization near the glass-transi tion temperature (Tg), as shown by our results with linear polyethylene and polycarbonate.6 Starting with uniform thickness, thin (<lo00 A) films one can grow isolated, lamellar single crystals, as shown by electron diffraction, just above TJL) (as defined by Boyer7).The crystals of polyethylene (fig. 23) grew in several hours, those of polycarbonate (fig, 24) in several days, each time being much less than the molecular relaxation time calculated using the equations used by Yoon and Flory.2 The holes in these films and the resulting lamellar structure (most obvious in the polycarbonate sample) indi- cate that the molecules must have moved and moved substantially. On the other hand, clearly no evidence was obtained and no statement can be made as to the regu- larity of folding in these crystals. Rather than deal further with the question of molecular motion (the error in the approach of Yoon and Flory was proposed to be the equating of the types of motion, and molecular stresses, involved in viscosity and those involved in crystallization) we consider rather the question of the actual degree of adjacent re-entry folding.As Prof. E. Clark pointed out at the March 1979 American Physical Society meeting, a survey of the literature suggests that any polymer that has a direction to its backbone crystallizes from the melt and from solution in a unit cell in which the chains are anti- parallel. This result, which he has formulated as Clark's rule, is easy to interpret in terms of adjacent re-entry folding, but much more difficult to explain on any non- adjacent re-entry model. For instance if the crystalline segments more or less solidify from a random-coil melt conformation onto the crystal growth face, as proposed by Fischer in his second paper at this Discussion, then a rearrangement of the stems would be required to produce an antiparallel arrangement.Only a few out-of-place stems would result in a measurable decrease in crystal perfection. I now wish to consider our recent results with one of the polymers used by Clark in formulating his rule, poly(pivalolactone).9 This polymer crystallizes as readily from the melt and to a higher degree than linear polyethylene (T, M 250 "C). Large, lamellar (as shown by electron microscopy) spherulites grow in molten films on glass slides cooled slowly (fig. 25). In the resulting crystal form, labelled a, the chains are antiparallel." When drawn, as also suggested in general by Clark: a /3 form is pro- duced, one in which there is statistical disorder in the segment directions.s*ll Thus a random chain direction packing is physically reason?-ble.Now I ask what crystal form should one expect if a sample is rapidly quenched from the melt ? If a solidifica- tion-type model with little molecular, as contrasted to segmental, motion would be appropriate I believe one would expect a disordered chain direction type of packing. On the other hand, if there is sufficient molecular mobility to permit extensive confor- mational rearrangements, then an antiparallel chain packing with predominantly GENERAL DISCUSSION 442 adjacent re-entry might still develop. With increasing quenching, a decrease in crystal size and/or perfection would obviously be expected.The results of quenching a thin film on a glass slide to room temperature from above the melting point are shown in fig. 26. Clearly a different type of spherulite is formed. Fig. 27 shows electron micrographs and corresponding electron diffraction patterns (from different areas) of polymer crystallized in the two forms. The t( form is monoclinic, while the quenched, y, form is orthorhombic. Its unit cell has been defined recentlyI2 and has been shown to also involve antiparallel chains; i.e., it is distinct from and much more perfect than the p form. The electron diffraction pat- terns, themselves, indicate that the crystals are of substantial lateral size ( > 1000 A) and a reasonable degree of perfection. Thus, in summary, the question should not be whether or not regular, adjacent re-entry chain folding can occur and is an appropriate model for normal crystalliza- tion from the melt, clearly it does and is, but rather the degree to which defects are introduced into it as a function of processing history and the effect of these defects on properties.On the other hand, this is not to say that some fringed micelle, pos- sibly fringed lamella (or switchboard) model, is not appropriate under some condi- tions also; it seems to be an appropriate model for, e.g., poly(viny1 chloride) gels13 and linear polyethylene crystallized rapidly from the glass.I4 For example the neu- tron diffraction results suggest the solidification model is appropriate for highly quenched linear polyethylene (papers by Stamm et al.and by Yoon and Flory, this Discussion) although the data can be fitted, perhaps even better, by a model with substantial (x 70%) adjacent re-entry folding (paper by Guttman et al. this Discus- sion), whereas for isotactic polystyrene of molecular weight < lo6 crystallized from the melt an adjacent re-entry model is used to fit the data. Clearly both models are and will be of use. We suggest, however, that further progress in the physics of normally (practically) crystallized polymers, with degrees of crystallinity above x 50%, will be based on an adjacent re-entry, chain folded lamellar model as the ideal system rather than a lamellar fringed micelle model; the original fringed micelle model resulted in a period of more than 30 years of near stagnation in the physics of crystalline polymers and it is to be hoped that such a period will not be repeated.Prof. D. R. Uhlmann (Massachusetts Institute of Technology) said: I wish to com- ment on a small part of Prof. Geil’s critique of the paper by Yoon and Flory. The crystallization of polymers almost certainly involves reconstructive molecular re- arrangements at the crystal-liquid interface. Lacking any physical basis for suggest- ing that this is not the case, one is led to linking in models between the crystal growth rate and transport in the liquid phase. Before giving up such linking, for which there FIG. 25.-Poly(pivalolactone) crystallized from the melt by slow cooling. FIG. 26.-Poly(pivalolactone) crystallized rapidly from the melt.[To face page 442 FIG. 27.-Electron micrographs and corresponding electron diffraction patterns of poly(piva1olactone) crystallized in the (a) a and (b) y forms. [To face page 443 GENERAL DISCUSSION 443 is abundant support from data on a wide variety of materials, from simple organics to oxides to polymers, it seems important to scrutinize carefully the evidence offered by Prof. Geil for crystallization at reasonable rates at temperatures below the glass transition. The method used by Prof. Geil to prepare his glassy polyethylene involves casting thin films from solution, melting the films and rapidly quenching them to temperatures below the glass transition. Use of the solution casting process involves the possibility of retained solvent in the films; and such solvent (or other adventitious impurities) could have a substantial effect on crystallization behaviour. As an example, glassy Ge02 has Tg E 550 "C.Yet the material will develop notable crystallinity when left over a weekend at ambient temperature in a laboratory atmosphere. The same glass, heat-treated for the same time at 400 "C in a dry nitrogen atmosphere, did not develop such crystallinity. The marked difference in crystallization behaviour was associated with solution-recrystallization of GeO, involving water adsorbed from the atmosphere. In light of such observations, and in light of the connection between molecular mobility and crystal growth rate in all theoretical models of growth, it seems impera- tive to establish that observations of crystallization below Tg which are apparently at variance with this connection have not been affected by impurities such as retained solvent. Mr. D. Rigby and Dr. R. F. T. Stepto (UMIST) said: Yoon and Flory have argued against the occurrence of adjacent re-entry of the folded chain, using, in part, an analysis of the statistics of chain folding based on unperturbed polymethylene (PM) chains of up to 15 C-C bonds. However, the use of such statistics in arguments for or against adjacent re-entry should be viewed with caution. First, with respect to crystallisation from the melt, it is a priori not at all certain that unperturbed configurations will be adopted in the interfacial region between bulk, amorphous polymer (with unperturbed configurations) and the growing surface of the crystal (an array of extended configurations), particularly by a molecule or molecules in the process of adding to the crystal. The symmetry, present in the melt, of the interaction forces experienced by segments will be perturbed by the presence of the crystal. Second, with respect to crystallisation from dilute solution, an analogous situation will exist, with the additional possibility of perturbed configurations already present in the solution. Also, there are indications that the chain lengths in the loops between re-entry points are sensitive to the solvent used.l Further, the intrinsic vis- cosity of polyethylene in solvents, which are good solvents at higher temperatures, exhibits anomalous behaviour in the region between the dissolution temperature, Td, and the crystallization temperature, T,, indicative of molecular association.' Third, assuming net, attractive non-local interactions between chain segments during crystal- lization, such interactions can have marked effects on the configurational statistics of polymethylene chains of greater than about 15 skeletal bonds, the longest chain con- sidered by Yoon and Flory. This result comes from recent calculation^,^^^ and its manifestations and possible relevance to chain-folding form the remainder of this contribution. The calculations were carried out using the Abe-Jernigan-Flory (A.J.F.) rota- tional isomeric state (R.I.S.) model for the local interactions, over 4-bond sequences, coupled with Sutherland or Lennard-Jones (L-J) potential functions for non-local CH,-CH, interactions, that is, interactions between CH2 groups separated by more than 4 skeletal bonds. The R.I.S. model, alone relevant to unperturbed chains, was the same as that used by Yoon and Flory. Examples of the effects of non-local inter- 444 actions, using in this case a L-J function, are given in fig. 28, in terms of the chain- length dependence of the characteristic ratio (r)’/n, where (r’) is the mean-square end- to-end distance and n is the number of skeletal bonds. At sufficiently low tempera- tures, chain contraction occurs. The behaviour is not specific to the potential func- tion used, although the ranges of temperature and the values of n for which (r2)/n exhibits a well-defined maximum are sensitive to potential function. However, for DISCUSSION Discussion in terms of (r2)/(s2) gives only average behaviour, but a closer investi- gation of the populations of configurations shows that (r2)/(s2) starts decreasing as a function of n when significant fractions of a population are constituted of configura- tions having small end-to-end distances, r, and configurational energies less than that of the all-trans chain. This can be seen by considering first the average configura- tional energies relative to those of the all-trans chains, as in fig. 31 for chains at 100 K. Consideration of the behaviour of chains at 100 K, as opposed to that at higher tem- peratures, enables attention to be focused more on the configurations of lower energies, which fig. 29 and 30 indicate are composed of folded configurations. The 500 FIG. 29.-( r 2 )/( s2 ) plotted against n for chains with the non-local interactions from fig. 28, at 500,298.2 and 100 K. We concur with the first point made by Rigby and Stepto, namely, that chain configurations are perturbed in close proximity to the crystal interface. Indeed, one of us was amongst the first to make this observation. This circumstance does not undermine our argument, which concerns the relative incidence of loops of various lengths. Their second point pertains to perturbation of configurations in solution by any of several factors : (a) solvent interaction, (b) excluded volume effects and (c)molecular association. An abundance of evidence demonstrates the absence of a specific solvent effect (a) of discernible magnitude. Effects (6) do not perturb short sequences appre- ciably. This is shown by cyclization equilibria and other characteristics. Molecular association (c) is unsupported. The results of Nakajima and Hamadal refer to lamel- lar thickness, not to loop lengths as stated by Rigby and Stepto. The remainder of the contribution by Rigby and Stepto concerns calculations in which an arbitrary non-local attraction is introduced between any pair of CH2 groups belonging to the given chain and within range of the postulated interactions. In liquids and solutions the effects that such interactions might otherwise have on the configuration are neutralized by the interchange of a neighbouring group from another molecule for the one from the same molecule. Since the two groups have (nearly) equivalent fields of force, the effect is nil. This assertion is supported un- equivocally by investigations on n-alkanes, polyethylenes, and other polymers in solutions and in .,melts. The hypothecated interactions have no significant effect whatever on polymer liquids and solutions. That they should be operative in polymer crystallization is unlikely. The calculations would, in any event, have to be altered so that the force field is " turned on " only when an approaching CH2 group senses the field of the crystal surface, other proximate pairs being unaffec- ted. Even if the prospective CH, group were able to anticipate the interactions to which it would ultimately be subjected in the crystal, it is not evident that the group at the end of a short loop would be affected to a greater (or lesser) degree than one belonging to a longer loop. Moreover, as the calculations presented by Rigby and Stepto show, the inter- actions they imagine to be operative affect only sequences of the order of 15 bonds. Cyclic configurations for shorter sequences are statistically disfavoured, as we have shown, and hence their terminal groups seldom would be subject to the artificial interactions arbitrarily postulated by Rigby and Stepto. Longer loops are not rele- vant. etc. etc.

ISSN:0301-7249    

DOI:10.1039/DC9796800365

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

GENERAL DISCUSSION 49 1 ADDITIONAL REMARKS Dr. D. M. Sadler (University of Bristol) (communicated): Dr. Stamm has referred in his comments to differences between our respective methods of data analysis. This should not obscure the essential agreement in our models for the conformation in solution grown crystals. (For melt-grown crystals there is at least an implied difference: we would maintain that his model must involve a more significant re- arrangement of chains during crystallization than suggested by the term " solidifica- tion ".) Dr. Stamm mentioned in particular the use in our 1977 paperi of eqn (4) for testing the scattering for solution-grown crystals against that expected for rows of stems (sheets), implying that a large error was involved. This is most misleading, since the error we committed was the entry of 1.6 A for the D parameter predicted for single sheets in table IV which should have been 0.95 A.A difference of only 0.6 8, when considering data to this resolution can hardly be considered very significant. The physical conclusions drawn in the paper are in no way invalidated, especially since for typical molecular weights we found D values of ca. 3 A, significantly larger than 0.95 A (or 1.6 A). My comments in the main text of the discussion explain how such large D values were attributed to interference between sheets as expected for " superfolding ". The use of " low-angle " equations is not limited by the absolute value of q, rather its value relative to the relevant special distances. My own calcula- tions based on atomic coordinates show that the scattering expected at q = 0.4 A-1 for a row of stems along (110) is 0.91 times that expected for an equivalent infinitely thin sheet.The result using the approximation as given in eqn (4) of ref. (1) is 0.87, which is in reasonable agreement. This does not bear out the statement of Dr. Stamm concerning large discrepancies because of the equations that we used. D. M. Sadler and A. Keller, Mucromoleczdes, 1977, 10, 1128. Mr. D. Rigby and Dr. R. F. T. Stepto (UMIST) (communicated): We wish to take this opportunity to clarify our position uis-6-vis Dr. Yoon and Prof. Flory. Whilst the statistics of unperturbed R-I-S chains have direct relevance to the melt and to chain configuration in 0-solvents there is no particular reason to believe that they are the correct statistics to use for chains undergoing crystallisation. Given that net, attractive forces ultimately exist between the majority of chain segments involved in crystallisation, we have reported on the effects of net, attractive inter- segmental forces on the statistics of isolated chains.Our thesis is merely that if the configurational statistics of such chains are to be used to obtain information on chain folding then chain models showing a net (albeit weak) intersegmental attraction should be investigated, and not only those models based on unperturbed chains. We are well aware that our calculations, as well as those of Yoon and Flory, strictly apply only to isolated chains, and we agree that calculations using such chains can offer no more than possible explanations of the configurational behaviour of folded sections of longer chains.Any argument based on the equilibrium statistics of isolated chains and ignoring the perturbing influences of the crystal surface and the crystallisation process which is occurring could be labelled specious. However, subject to these limitations our results show that, for chains of >ca. 15 bonds, closer end-to-end separations are significantly more probable for chains with relatively weak attractive forces between segments than for unperturbed chains. We do not infer that regular folding results from this behaviour - we consider that prediction of the form of folding is too large an extrapolation to make solely from the con- figurational statistics of isolated chains, whatever the model ! We would argue that492 GENERAL DISCUSSION there are numerous possible distributions of re-entry distances between those studied by Yoon and Flory, for unperturbed chains of various lengths, and those consistent with adjacent re-entry.What may be inferred from our results is that ifthe statistics of isolated chains, only slightly longer than those studied by Yoon and Flory, are to be applied to configurations in loops then CH2 interactions can become an important factor. In this context, it should be remembered that Yoon and Flory’s model cannot be used to simulate effects of solvent on configurations in loops. Finally, we apologize for the loose quotation of the work of Nakajima and Hamada [ref. (l), previously].It was written as a review paper and was referenced in that sense. The work of Nakajima et aZ.l quoted therein in fact deals with varia- tions in the lengths of amorphous loops with solvent used, and lengths in excess of 15 bonds have been deduced. A. Nakajima, F. Hamada, S. Hayashi and T. Sumida, KoIIoid-Z., 1968, 222, 10. Dr. D. G. H. Ballard (I.C.I. Runcorn) (communicated): I wish to make a con- sidered response to comments by Dr. Stejny, which only came to my notice in April 1980. Our studies of the etching of crystalline polyolefins has been extensive and we have taken particular care to define the limitations of the technique. We have had no difficulty in obtaining reproducible data. Without having any preconceived views about the conformation of the molecules we observed the facts recorded in table 2 of our paper.The oxidation of isotropic systems, derived from polyethylene and polypropylene, the g.p.c. measurements showed an initial rapid drop in molecular weight. In the case of annealed polyethylenes this corresponded to the removal of about 15% of the polymer. The system then equilibrated and did not change further. The g.p.c. showed two peaks corresponding to molecular weights given in table 2. It was only after a period of days, using our oxidation conditions, that the large molecular-weight fraction could be induced to oxidise further to give material with only one g.p.c. peak. The technique is high yielding and we have used the process to make 10 g quantities of difunctional hydrocarbons for block copolymer synthesis.It should also be noted that the etched plaques have been studied using SANS.l These data are reported in table 1 and eqn (2) and show that although the stems are disconnected by the oxidation process they retain their original position about the centre of mass of the molecule that they had in the polymer matrix. A direct com- parison can now be made for the stem length (In) measured in this syscem with that obtained by dissolving in a solvent and measuring the molecular weight of the com- ponents. The oxidation has some features which have not been commented on previously. Crystalline polyolefins are characterised by having a large number of voids. These are probably located at the interface between folds of the molecule and this explains why the oxidation medium finds ready access to this part of the molecule.Further- more the severing of the folds leads to an increase in the mobility of the chain and allows it to crystallise, thereby protecting it from further attack by the oxidation medium. The nett effect of this is to increase the density of the system and in the case of annealed polyethylene very little weight loss occurs. What seems to have been overlooked by Dr. Stejny is that of the several systems we have studied there are some which give only one stem. These are pressure crystal- lised polyethylene and drawn polypropylene. In the latter case we have looked at biaxially drawn and cold and hot drawn polypropylene. In each case oxidation only produces one molecular-weight fraction corresponding approximately in length to theGENERAL DISCUSSION 493 d-spacing.The pressure crystallised polyethylene is a particularly important ob- servation since this is an isotropic system in which the lamellae thickness and the neutron stem length In [fig. 2(4] are identical suggesting that the chain is folded into one lamellae in this particular instance, as represented by fig. 3(b). The fact that etching of this system gives only one stem length close to the value of In shows, in our view that the etching technique gives similar information to that being obtained by combining the information of SAXS and SANS. Dr. Stejny’s point of view is that “ we know ” the structure of polymer crystals, therefore etching of this system will give definitive information on the technique.The implication here is that polymer crystals have the perfection generally associ- ated with crystals of small molecules. That this is not so is well established. More recently Sadler and Keller have studied the conformation of PED in a PEH matrix of polymer crystals obtained from solution.* They obtained a curve similar to that shown in fig. 2(c). However, unlike pressure-crystallised PE the value of I,, was at least twice the lamellae thickness. Their explanation for this was similar to ours for isotropic PP, namely that the molecule inhabits several lamellae. The solution- produced lamellae are, in fact, aggregates of several crystals; “ tie fragments of molecules ” exist between lamellae. This would explain why mixtures of stem lengths are obtained on etching of polymer crystals. We would advocate that the organisation of the macromolecule in polymer crystals is less clearly defined than in pressure-crystallised polyethylene. It is with the latter system, in which the crystal- linity can approach nearly 100% that SANS, electron microscopy and etching give consistent information. Finally, I would like to emphasise that the most important result to be obtained from SANS studies was to establish the existence of molecular fragments which traverse lamellae. The intense discussion which has taken place at this meeting concentrated on the conformational arrangement within one lamella and made no comment at all on how they are connected together. That this is essential is obvious if one considers how the stresses are to be distributed over the molecule as a whole when a tensile force is applied to the material. D. G. H. Ballard, 3. Schelten, G. W. Longman, T. L. Crowley and A. Cunningham, Polymer, 1979, 20, 399. D. M. Sadler and A. Keller, Science, 1979, 203, 263.

ISSN:0301-7249    

DOI:10.1039/DC9796800491

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

Introductory Lecture : Solid-state Polymerization BY GERHARD WEGNER Institut fur Makromolekulare Chemie der Universitat Freiburg, Hermann- Staudinger-Haus, Stefan-Meier-Strasse 3 1, D-7800 Freiburg, Federal Republic of Germany Received 3rd December, 1979 Two different approaches to the problem of how to synthesize macroscopic and nearly defect-free single crystals of polymers are reviewed with the aim of clarifying the underlying physico-chemical principles and of defining the scope of such methods for the further development of the solid-state physics of polymers. The two methods are (i) the topochemical polymerization of diacetylenes and (ii) the simultaneous polymerization and crystallization of trioxane close to the ceiling-equilibrium. Polymers with a backbone of conjugated multiple carbon bonds are formed in the first case via a reaction which proceeds without nucleation phenomena such that the single-crystal nature of a polymerizing crystal is always retained up to quantitative conversion.Single crystals of poly(oxymethy1ene) grow in the second case following a BCF-type of crystal growth, the growth features being controlled by the nature and the concentration of the catalyst employed. Most polymers do not crystallize completely but rather form semi-crystalline solids when crystallization is attempted from either the melt or from solution. In such semi- crystalline solids a single macromolecule may traverse many crystalline and amor- phous regions; the size of the crystallites is generally very small compared with the dimensions of the extended polymer chain.For some time it was even believed that perfect polymer single crystals do not exist at all because there seemed to be no way to control the crystallization process so as to prevent the formation of a semicrystal- line morphology. It was therefore a challenge to devise methods which allow the synthesis of large, nearly defect-free polymer single crystals with the aim of studying the physical be- haviour of such materials. Once such materials were successfully prepared it soon turned out that the methods as well as the materials constituted a new branch of poly- mer science in their own right. All methods which allow the synthesis of macroscopic polymer single crystals in- volve organic solid-state chemistry, if this term is understood in its broadest sense, including such phenomena as reactions occurring at the gas/solid or liquid/solid inter- face.The polymer crystal, therefore, is always obtained as a consequence of a chemical reaction and not just as a consequence of the change in the physical state of the matter as in normal crystallization procedures. In the following, two different approaches to the problem of the direct synthesis of polymer single crystals will be reviewed with the aim of clarifying the underlying physical chemical principles and of defining the scope of such methods for the further development of polymer physics. The first method is based on a polymerization which proceeds in the crystalline state and converts monomers with conjugated triple bonds as the reactive element into the corresponding polyconjugated macromolecular structures [" poly-(diacety1ene)s "I.The second comprises a simultaneous poly- merization and crystallization where many of the details of the crystal growth process have been elucidated, and by which even single crystals of random copolymers can readily be obtained. The method is confined so far to the cationic polymerization of trioxane, but there is no reason why there should not be other systems available whereG . WEGNER 495 similar growth features could be exploited for the production of macroscopic polymer crystals. 1. TOPOCHEMICAL POLYMERIZATION OF DIACETYLENES BASIC PRINCIPLES OF THE REACTION MODE The production of macroscopic polymer single crystals by the solid-state poly- merization of various substituted diacetylenes was first described in 1969.l The under- lying reaction is termed '' topochemical polymerization of monomers with conjugated triple bonds " and can be formulated as follows: R may be any possible substituent which does not disturb the packing necessary to bring about solid-state reactivity.l" The true nature of the reaction is better ex- plained by fig.1 and 2. The polymerization is understood as a diffusionless solid- state transformation of a single crystal of a monomer into the corresponding single crystal of a polymer such that all reactivity comes about by very specific rotations of the monomer units on their lattice sites, the reactivity being completely controlled by the packing interactions. Thus the consequence is a unique direction of chain growth which, in turn, results in the formation of extended chain crystals at complete conver- sion.The reaction proceeds via carbenes as the active intermediates of chain growth as depicted in fig. 1 ; many details of the nature of these carbenes and their electronic structure have been elucidated in recent years by e.s.r. and U.V. spectroscopy 7*10-15 in combination with X-ray structure data of the monomers and their corresponding polymers. The topochemical polymerization of diacetylenes has a rather wide scope, considering the variability in the structure of R, the substituents to the con- jugated triple bonds. At present well over 200 different monomers have been found to undergo the reaction, and quantitative data on crystal structures and details of the reaction mechanism are available for approximately 20 different corn pound^.^^^^*'^ The majority of experimental studies have dealt with the bis(p-toluene sulphonate) of 2,4-hexadiyne- 1.6-dio1, hereafter abreviated as PTS (1) 1 The polymerization of this compound was first described by Wegner.17 The poly- merization process as well as the physical behaviour of the monomer, the polymer and the intermediate stages have been subsequently studied by a variety of physical tech- niques and by a number of different groups.The experimental techniques involved in the polymerization itself are extremely simple. The monomer is grown into single crystals from concentrated solutions and the monomer crystals are then annealed for some hours at elevated temperatures, but well below the melting point, during which time the polymerization proceeds and finally, quantitative conversion is reached.In the case of PTS an S-shaped time- conversion curve is observed which has attracted much attention among those in-496 SOLID-STATE POLYMERIZATION terested in the details of the reaction me~hanism.l'-~l Typically, quantitative con- version is reached after ~9 h of annealing a PTS single crystal at a temperature of 70 "C. Alternativeiy, the monomer crystals may be exposed to U.V. or high-energy radiation to bring about polymerization. The same polymer is formed regardless of the method applied but polymer crystals of the highest quality are generally obtained R-C \ C R-C 1450 FIG. 1 .-Model of the solid-state polymerization mechanism of diacetylenes via carbenes as the active chain-end intermediates according to ref.(7). The data refer to the specific case of PTS. y and z are the principal axes of the fine-structure tensor. (a) and (b) are mesomeric forms of the chain end. by thermal polymerization only. Single crystals of the polymer weighing several g each have thus been easily prepared. They compare very well with the most carefully grown single crystals of other organic compounds such as anthracene or naphthalene with regard to chemical purity and crystal perfection. A homogeneous mode of chain growth was recognized as the origin of this rather unusual result of a solid-state reaction in 1972,22 and has since been proven by many different experiments and by different groups applying such techniques as, for ex- ample, light m i c r o s c ~ p y , ~ ~ * ~ ~ U.V.spectroscopy and X-ray Brillouin scattering,26 Raman spectroscopy 27 and n.m.r. relaxation studies2* All these studiesG . WEGNER 497 came to the conclusion that the chain growth starts at points distributed at random throughout the lattice: it is not cooperative. Thus, intermediate stages of the poly- merization of a single crystal are best described as a solid solution of individual ex- tended chains of varying length all stretched out along a unique crystallographic direction inside the matrix of the as yet unreacted monomer as depicted in fig. 3(b). All available evidence supports the view that extremely high molecular weights are 5.11 A I 0 e ,. c 7 &..FIG. 2 .-Projections and polymer PTS (1 of the CI eft) and 4.91 A I 7 14 2.-crystal structure onto the plane of the polymer backbone for monomer PTS (left) 0, C; 0, 0; @, S . ystal projection of a monomer onto a corresponding polymer repeat unit (~-ight);~*~ obtained at quantitative conversions, and that the chains stretch out over macroscopic dimensions in the polymer single ~ r y ~ t a l ~ . ~ ~ ~ ~ ~ ~ ~ * ~ ~ - ~ ~ In other words, polymerization proceeds without any signs of phase separation, as is normally observed in organic solid-state reactions including polymerizations where the matrix strains associated with the process of nucleation and phase growth result in a fragmentation of the parent ~ r y s t a l ~ ~ ~ such as to produce a multitude of small crystallites as depicted in fig.3 (a). Various aspects of such considerations and their impact on the question under what circumstances can oriented, fibre-like product phases be obtained, have been reviewed recently. 32*33 These considerations are important in order to understand the morpho- logies obtained in the solid-state synthesis of (SN), or POM, just to mention two of the best known materials which can be obtained by solid-state processes. The perfection of polymerizing single crystals can easily be judged if the reaction is followed by a polarizing microscope, making use of the strong optical dichroism associated with the polymer ~tructure.l*~~ Fig. 4 shows the effect observed in such studies. It should be mentioned that the crystal optics and related properties of this material have been carefully studied by the Queen Mary College group.24*30s31498 SOLID-STATE POLYMERIZATION I c SOME PROPERTIES OF PTS The fact that the reaction proceeds without phase separation in PTS single crystals does not imply, however, that there are no elastic strains during the reaction. On the contrary it seems that the sigmoidal time-conversion curve observed in PTS poly- merization can be explained by assuming that polymer chain initiation and pro- pagation are controlled by the elastic interaction of the monomer lattice and the homogeneously distributed polymer chains according to a Voigt mode1.9925~34 The agreement between the calculated and observed reaction kinetics for PTS is good, al- though it is not clear how the chain-ends are mechanically coupled to the surrounding monomer lattice.Because of the mascroscopic size and the generally high degree of perfection of the crystals, a variety of techniques well known in solid-state physics but not much in use in the realm of polymer physics can be readily applied to assist the elucidation of the details of the chemical reactions as well as to provide basic data of more general interest. One such example is the measurement of the tensor components of the elastic modulus of the PTS crystal as a function of conversion into polymer, using the techniques of Brillouin spectroscopy.26 Fig. 5 shows the scattering geometry employed in order to measure the most interesting component c22 which is essentially equal toFIG. 4.-Dichroism observed in polymerizing single crystals of PTS.The plane of polarization (indicated by the arrow) coincides with the chain direction of one crystal and is perpendicular to the other. [To face page 498FIG. 11 .-Single crystals of POM grown by simultaneous polymerization and crystallization under crystal ripening condition^.^^ [To face page 499G. WEGNER 499 the macroscopic Young’s modulus observed in a stress-strain experiment with stress applied in chain direction. Fig. 6 shows a typical Brillouin spectrum obtained at x 1 % conversion, and fig. 7 gives the result in terms of a plot of c22 against the degree of conversion to polymer. The solid line marked V describes the theoretical expectations for a simple model FIG. 5.-Scattering geometry employed in the determination of cz2 of PTS single crystals by Brillouin k , and k, designate the wave vector of the incoming and outgoing wave, k, is the wave vector of the phonon propagating in the crystallographic b-direction (chain direction).which assumes the intermediate stages to consist of extended rigid rods with the dimension of the macromolecule and the modulus of the final polymer to be embedded in the soft matrix of the modulus of the monomer (Voigt model). The experimental points fall reasonably close to the ,V-line and are far from the line marked R which would describe a Reuss model of a composite material as depicted in the insert of fig. 7. The small deviations from the Voigt model at low conversion have been treated as a chain-length effe~t,~ but this is questionable as long as the stress distribution around the chain ends is not known in more detail.The value of c22 at a quantitative conversion of 4.4 x lo4 N mm-2 compares very well with theoretical expectations for a perfect crystal of extended chains.26 The other moduli are similar to those observed in low molecular-weight organic crystals. Moreover, the non-linear mechanical properties have been investigated and in parti-500 70 60 50 ul 40 I c '0 30 20 10 0 SOLID-STATE POLYMERIZATION 25 0 25 v 1 GHz FIG. 6.-Example of a Brillouin spectrum obtained from a partially polymerized PTS-crystal at 1 % conversion. 5 .O 4 .O 3.c I E E Z 2 .c % \ N b 1.c I I I l r l I I I T 0 10 20 30 40 50 60 70 80 90 100 conversion ( o / ~ ) FIG. 7.-cz2 as a function of conversion to polymer.The solid line (V) is calculated according to a Voigt model, the line (R) according to a Reuss model of a composite materiaLg cular it has been possible to study for the first time the defects and deformations of large polymer single crystals .23 9 28 *35 A series of other experiments, as well as a number of theoretical studies, has been devoted to the investigation of the electronic structure of the material which, because of the extreme optical and mechanical anisotropy, has been considered as a model for a one-dimensional material l6 (a topic of increasing interest, especially in the light ofG . WEGNER 50 1 recent developments in the area of highly conductive polymer materials based on poly- conjugated macrom~lecules).~~ ELECTRONIC AND OPTICAL PROPERTIES Polydiacetylene single crystals such as PTS consist of parallel chains of macro- molecules with a backbone of conjugated single double and triple bonds which deter- mines both the optical 37938 and the charge-transport properties.3942 Band-structure calculations 43-45 indicate a strong dispersion of the free electron states along the poly- mer chain comparable with that of the electron bands in inorganic semiconductors. 20 - 0 10 c C CI C 0 V z o -2 -10 Y V aJ # .- 30 20 N 0 10 0 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 photon energy I eV FIG.8.-Electronic spectra of PTS single crystals in terms of the real and imaginary part of the dielectric constant.4s (-) T = 9 K, (- - - -) T = 295 K. These calculations have been supported by results of ESCA s t ~ d i e s .~ ~ , ~ ' On the other hand there is overwhelming evidence that the lowest optical transition, which dominates the absorption spectrum in the visible (cf. fig. S), is an exciton rather than a band-to-band t r a n ~ i t i o n , ~ ~ s ~ ~ @ the exciton being of the Frenkel type with some charge- transfer c~ntribution.~~ The results of photoconductivity studies 41342 as well as of electroreflectance and electroab~orption~~ are in excellent agreement with this descrip- tion and the band gap is found to be near 2.44 eV at 2 K from electroreflectance measurements of PTS, and near 2.1 eV at room temperature by photoconductivity experiments, i.e. at only slightly higher energies than the main exciton peak at 2.0 eV. Similar values are found for other polydiacetylene crystals differing from PTS in the chemical nature and packing interactions of the side groups to the polyconjugated ba~kbone,~'.~~ and it thus seems that the polydiacetylenes provide excellent models for the study of the physics of polyconjugated macromolecules in general.502 SOLID-STATE POLYMERIZATION RECENT DEVELOPMENTS Although most of the studies in the area of polydiacetylenes have been con- centrated on PTS because of the ease with which extremely pure and perfect single crystals can be prepared, a number o f other materials have become available in recent years.These have attracted more and more interest. Details will be found in a recent review.16 Among others DCH (2) deserves to be mentioned: it may be considered as the single-crystal polydiacetylene analogue of poly(vinyl~arbazole).~'-~~ 8- c-CEEC-c CH2-N \ CH2, I f 2 The relation between the crystal structure of the monomer and the polymer is shown in fig.9. The monomer and polymer crystals have been studied for their electronic properties, and a number of results obtained by various groups have already been published, confirming in general the picture developed in the study of PTS.41p54p55 tb 4.91 A 1 A B FIG. 9.-Projections of the monomer and polymer crystal structure of DCH onto the plane of the polymer Mixed crystals of the solid-solution type of the monomer DCH with 1-(9'-anthra- cenyl)-6-(N-carbazolyl)-2,4-hexadi-in (3) or 1,6-bis(9-anthraceny1)2, 4-hexadi-in (4) have been prepared and p~lymerized.~~ Similarly, PTS forms a series of mixed crystals with the bis-p-chlorosulphonate ester of hexadi-indiol which can be polymerized in theG .WEGNER 503 same manner as pure PTS.” Thus a series of materials has become available which allow the impact of well defined defect sites on the electronic properties of polymer crystals to be studied. 4 C H z - C E C -C C-CH, A CH,-C= C - C E C -CH, - N 3 Another interesting development is the preparation of regular multilayer aggre- gates of polydiacetylenes starting from the corresponding monomer multilayers.44~s*~s9 The preparation takes advantage of the property of soap-like monomer molecules containing the reactive triple-bond sequence to form extended monomolecular films at the air-water interphase of a Langmuir trough. The monolayers thus formed are transferred onto solid substrates by the Langmuir-Blodgett technique.The number of dippings defines exactly how many layers are piled up on top of each other. Con- sequently, multilayers with exact thickness and molecularly smooth surface are obtained which are readily polymerized by exposure to a U.V. light source without destruction of the order. Depending on the molecular geometry and the number of dippings, layers with thicknesses between 30 and several thousand A can be prepared. They can be used as well defined models for mernbranes6O and for the investigation of all kinds of transport processes.42 Fig. 10 shows a typical example of a multilayer-forming structure before and after polymerization. The remarkable point is that such multilayers, once they have been polymerized, are of extreme stability, in contrast to the usual LB-multilayers of low molecular-weight materials which tend to decompose into regular crystallites after some time by temperature-assisted annealing processes.61 2.SINGLE CRYSTALS OF POLY(0XYMETHYLENE) BY CRYSTALLIZATION SIMULTANEOUS POLYMERIZATION AND GENERAL DESCRIPTION OF THE PROCESS True single crystals of macromolecules may be grown by simultaneous poly- merization and crystallization as was first pointed out by Wunderlich,62 provided one succeeds in controlling the nucleation step sufficiently so as to prevent irregular over- growth features or the build-up of semicrystalline morphologies. Although such reactions are of considerable importance in the technical production of some polymers,504 SOLID-STATE POLYMERIZATION 1st layer 1 st layer 2nd Layer FIG.10.-Example of a multilayer-forming structure of a monomer and polymer diacetylene mono- carbonic acid.s8 the nucleation processes are not well understood so that rather irregular materials are obtained in most cases. One of the better investigated examples of a simultaneous polymerization and crystallization is the cationic polymerization of trioxane from the melt or from ~ o l u t i o n . ~ ~ ~ The reaction described by is of particular interest for the subject of polymer crystallization, since it constitutes a case where polymer crystals grow near the equilibrium conditions of their forma- tion. If a catalyst, typically BF,*Et,O, HC104 or similar cationically active com- pounds, are added to the melt or solution of the monomer, crystals of the polymer start to separate after a well defined nucleation p e r i ~ d .~ ~ ? ~ ~ Further growth occurs by reactions of the monomer at the crystal surface so that each elementary step of the crystal growth is an elementary step of chain growth at the same time. The reaction proceeds until chemical equilibrium between the solid crystalline polymer and the residual monomer is reached, the equilibrium conversion depending on temperature and pressure in the system. Moreover, if the crystals are annealed in such a closed system with the catalyst necessary to establish the equilibrium still active, a typical Ostwald-ripening of the crystals is observed. Smaller crystals dissolve again in favour of the further growth of already larger specimens because of the contribution of sur- face free energy to the stability of the crystalline phase.67 Thus fairly large crystals are obtained up to several 10 pm in diameter which extend up to 1 pm in the chain direction.They show all the properties expected for the pure crystalline phase of macromolecules, e.g., a sharp melting point, theoretical density, etc.68979 Crystal growth also proceeds in the presence of comono- mers such as dioxolane, 1,3-dioxane, etc7* The comonomer units are incorporated Fig. 11 shows an example of such crystals.G . WEGNER 505 into the POM chain and therefore also into the lattice in a random fashion and thus give rise to the formation of a solid-solution type crystal. These crystals have been used as models to describe the reference state of a crystalline c ~ p o l y m e r .~ ~ - ~ ~ The maximum mole fraction of comonomer units xB which can be incorporated without disturbing the build-up of large single crystals depends on the molecular structure of the comonomer and is generally xB < 0.1. SOME DETAILS OF THE CRYSTAL GROWTH PROCESS The growth features observed during the early stages of the polymerization process are of some interest because they not only give insight into the mechanism of that particular polymerization, but also reveal the general laws of crystal growth controlled by the presence of a catalyst rather then by the supersaturation of the solute. If perchloric acid is used as the catalyst and CH2C12 as the reaction medium the ob- served morphology becomes particularly simple.Fig. 12 shows examples of crystals isolated at conversions < 1 % at different concentrations of catalyst. The chain direction is always perpendicular to the hexagonal base lamella; thickening of these lamellae occurs via a single growth spiral emanating from a screw dislocation at the centre of the crystal. In contrast to the growth of folded chain lamellae from dilute solutions of macromolecules, a massive crystal is here built up via a typical BCF Addition of the monomer to cationically active chain ends or chain growth via a catalyst-assisted insertion reaction of the monomer into chain folds (transacetalization) occurs at low-energy kink sites of the growth spirals. A possible description of the chemical reactions and the topology involved is sketched in fig.13. inactive s i t e s FIG. 13.-Chain growth at a kink site of a growth spiral uia catalyst assisted transacetalization at the surface of a POM crystal. The catalyst is thought to be adsorbed onto the surface but will be inactive for an inser- tion reaction except near a kink site of a growth spiral. The mechanism sketched in fig. 13 is only one out of a manifold which may be, and have been, discussed in the context of the chemical details of the growing chains and their interaction with the catalytically active ~ p e c i e s . ~ ~ ’ ~ ~ ’ 72 It is shown here to illustrate how the morphology may be linked to the chemical details of the chain growth and the reader is referred to the literature7’ for a more specific discussion. A comparison of the crystals shown in fig.12 shows that the step width of the growth506 SOLID-STATE POLYMERIZATION spirals varies with the catalyst concentration, all other variables being the same during the growth process. Experimentally a reciprocal relationship is observed between catalyst concentration and step width. If one takes into account the fact that the catalyst concentration in these experiments is rather small, being of the order of mol dm-3 and that the surface area of the crystalline phase is rather large (actually of the order of some 10 m2g-I) it is reasonable to assume that part of the catalyst is reversibly adsorbed to the most developed surface of the crystals, which is the (001) surface of the hexagonal crystals. Now, following the Burton-Cabrera-Frank treatment of crystal growth we des- cribe the growth spiral in first approximation as an Archimedean spiral where the step width d is connected to the critical radius Y, of the spiral by d = Kr,.(2.2) Since rC varies with the catalyst concentration at constant monomer feed and, since we want to assume that the catalyst effective for crystal growth is the one adsorbed onto to the surface, we postulate [HC1O4Ieff. is the concentration of the catalyst reversibly adsorbed to the surface and is related to the overall concentration [HC10410 by r c = k/[HC104l,ff. (2.3) assuming that the adsorption can be described by a Langmuir isotherm with kl and k2 being constants. This gives the final expression which relates the growth features with the catalyst concentration by with k' being the product of the constants kl, K and k according to k' = kl/Kk.(2.6) A plot of the experimentally observed values as a function of the catalyst concentra- tion according to eqn (2.5) is shown in fig. 14. The agreement is very good and, more- over, the finite value of d at large values of the catalyst concentration indicates where LOO. 300. Ec \ -u 200. 5 i o [HCIO,],' / lo4 dm3mol-' FIG. 14.-Relation between step width of the growth spirals and the catalyst concentration according to eqn (2.5).FIG. 12.-POM crystals isolated at small conversions with HC104 as the catalyst; (a) [HC104] = 1 x mol dm-3, (b) [HC104] = 5 x lop5 mol dmP3. [To face page 506FIG. 15.-Grystal of POM grown under the same conditions as the ones shown in fig.12 except for the catalyst concentration which was raised to lop3 mol dmp3. [To face page 507G . WEGNER 507 the inherent limitations for this crystal growth process are to be found. Extrapola- tion to infinitely large catalyst concentration gives the limiting value of d = 33 5 nm. An actual catalyst concentration of [HC104],, > is already reasonably close to that limiting value and it was therefore interesting to investigate what would happen to the crystal growth if such high catalyst concentrations were employed. Fig. 15 gives the result of such experiments. Not unexpectedly, the simple BCF mechanism breaks down because of excessive overgrowth uia spontaneous surface nucleation. Crystal growth not only proceeds by insertion into the (001) surface in this system but also by lateral growth via addition of oligomers to the lateral surfaces.A de- tailed analysis of the whole process has been published el~ewhere.~~ It sould also be mentioned that different morphologies of POM have been described, namely sheaf- like crystals consisting of extended chains which were obtained under very special growth condition^.^^'^^ It seems that it is the nucleation process and the morphology of the nuclei which in turn depend on the solvent system and other conditions of the system which define the final shape of the crystal. Nevertheless, it seems that the system described above for the first time allows one to obtain some insight into the details of a simultaneous polymerization and crystallization and therefore into the formation of polymer crystals as such.G. Wegner, Z . Naturforsch., 1969, 24b, 824. G. Wegner, Makromol. Chem., 1972, 154, 35. R. H. Baughman and K. C . Yee, J. Polymer Sci., Polymer Chem Ed., 1974, 12, 2467. R, H, Baughman, J. Polymer Sci., Polymer Chem. Ed., 1974, 12, 1 5 1 1 . G. Wegner, Pure Appl. Chem., 1977, 49, 433. G. Wegner in Molecular Metals, ed. W. E. Hatfield (Plenum Press, New York, 1979), p. 209 ff. V. Enkelmann and G. Wegner, Angew. Chem., 1977, 89,432. V. Enkelmann, R. J. Leyrer and G. Wegner, Makromol. Chem., 1979, 180, 1787. lo G. Bubeck, H. Sixl and H. C. Wolf, Chem. Phys., 1978, 32, 231. R. Huber, M. Schwoerer, C. Bubeck and H. Sixl, Chem. Phys. Letters, 1978, 53, 35. l2 H. Sixl, W. Hersel and H. C . Wolf, Chem. Phys. Letters, 1978, 53, 39.l3 C. Bubeck, Ph.D. Thesis (University of Stuttgart, 1979). l4 Y. Hori and L. D. Kispert, J . Amer. Chem. Soc., 1979, 101, 3173. The radicals seen by these l5 H. Gross, H. Sixl, C. Krohnke, V. Enkelmann, Chem. Phys., 1980, in press. l6 G. Wegner in Chemistry and Physics of One-Dimensional Metals, ed. H. J. Keller (Plenum l7 G. Wegner, Makromol. Chem., 1971, 145, 85. l9 A. R. McGhie, P. S. Kalyanaraman and A. F. Garito, J. Polymer Sci. Polymer Ed., 1978, 16, 2o G. N. Patel, R. R. Chance, E. A. Turi and Y . P. Khanna, J. Amer. Chem. Soc., 1978,100,6644. 21 C. Krohnke, Ph.D. Thesis (University of Freiburg, W. Germany, 1979). 22 J. Kaiser, G. Wegner and E. W. Fischer, Israel J. Chem., 1972, 10, 157. 23 W. Schermann, G. Wegner, J. 0. Williams and J. M. Thomas, J. Polymer Sci., Polymer Phys. 24 D.Bloor, L. Koski and G. C. Stevens, J. Mater. Sci., 1975, 10, 1689. *'D. Bloor, L. Koski, G. C. Stevens, F. H. Preston and D. J. Ando, J . Mater. Sci., 1975, 10, 26 R. J. Leyrer, W. Wettling and G. Wegner, Ber. Bunsenges. phys. Chem., 1978, 82, 697. 27 D. Bloor, R. J. Kennedy and D. N. Batchelder, J. Polymer Sci., Polymer Phys. Ed., 1979, 17, 28 J. U. v. Schutz and W. Hopfner, J . Polymer Sci., Polymer Phys. Ed., in press. 29 R. H. Baughman, H. Gleiter and N. Sendfeld, J. Polymer Sci., Polymer Phys. Ed., 1975, 13, 30 D. Bloor and F. H. Preston, Phys. Stat. Sol. (a), 1976, 37, 427; 1977, 39, 607. ' H. Eichele, M. Schwoerer, R. Huber and D. Bloor, Chem. Phys. Letters, 1976, 42, 342. authors are probably artefacts arising from extensive radiation damage of the sample. Press, New York, 1977), p.297 ff. R. R. Chance and G. N. Patel, J. Polymer Sci., Polymer Phys. Ed., 1978, 16, 859. 335. Ed., 1975, 93, 753. 1678. 1355. 1871.508 SOLID-STATE POLYMERIZATION 31 D. Bloor, D. N. Batchelder and F. H. Preston, Phys. Stat. Sol. (a), 1977, 40, 279. 32 G. Wegner, E. W. Fischer and A. Mtinoz-Escalona, Makromol. Chem. Suppl., 1975, 1, 521. 33 R. H. Baughman in Contemporary Topics in Polymer Science, ed. E. M. Pearce and I. R. 34 R. H. Baughman, J. Chem. Phys., 1978,68, 3110. 35 R. J. Young, D. Bloor, D. N. Batschelder and C. L. Hubble, J. Muter. Sci., 1978, 13,62. 36 A. G. MacDiarmid and A. J. Heeger in Molecular Materials, ed. W. E. Hatfield (Plenum Press, 37 R. H. Baughman, J. D. Witt and K. C. Yee, J.Chem. Phys., 1974,60,4755. 38 D. Bloor, D. J. Ando, F. H. Preston and G. C. Stevens, Chem. Phys. Letters, 1974, 24, 407. 39 R. R. Chance and R. H. Baughman, J. Chem. Phys., 1976,64, 3889. 40 B. Reimer and H. Bassler, Phys. Stat. Sol. (b), 1978, 85, 145. 41 W. Spannring and H. Bassler, Ber. Bunsenges. phys. Chem., 1979, 83,433. 42 K. Lochner, H. Bassler, B. Tieke and G. Wegner, Phys. Stat. Sol. (b), 1978, 85, 653. 43 E. G. Wilson, J. Phys. C, 1975,8, 727. 44 D. E. Parry, Chem. Phys. Letters, 1977, 46, 605. 45 M. Kertesz, J. Koller and A. Azman, Chem. Phys., 1978, 27, 273. 46 G. C. Stevens, D. Bloor and P. M. Williams, Chem. Phys., 1978, 28, 399. 47 J. Knecht and H. Bassler, Chem. Phys., 1978, 33, 179. 48 B, Reimer and H. Bassler, Phys. Stat. Sol. (a), 1975, 32, 435.49 M, R. Philpott, Chem. Phys. Letters, 1977, 50, 18. 50 L. Sebastian and G. Weiser, Chem. Phys. Letters. 1979, 64, 396. 51 V. Enkelmann, R. J. Leyrer, F. G. Schleier and G. Wegner, J. Muter. Sci., 1980, 15, 168. 52 V. Enkelmann, G. Schleier, G. Wegner, H. Eichele and M. Schwoerer, Chem. Phys. Letters, 53 K. C. Yee and R. R. Chance, J. Polymer Sci., Polymer Phys. Ed., 1978, 16,431. 54 R. J. Hood, H. Muller, C. J. Eckhardt, R. R. Chance and K. C. Yee, Chem. Phys. Letters, 55 H. Eichele, M. Schwoerer and J. U. v. Schiitz, Chem. Phys. Letters, 1978, 56, 208. 56 G. Schleier and V. Enkelmann, personal communication. 57 V. Enkelmann, Makromol. Chem., 1978, 179,2811. 58 B. Tieke, G. Wegner, D. Naegele and H. Ringsdorf, Angew. Chem. (Znt. Edn), 1976, 15,764. 5 9 B. Tieke, G. Lieser. and G. Wegner, J. Polymer Sci., Polymer Chem. Ed., 1979, 17, 1631. 6 o D. Day and H. Ringsdorf, J. Polymer Sci., Polymer Letters Ed., 1978, 16, 205. 61 B. Tieke and G . Wegner in Topics in Surface Chemistry, ed. E. Ke (Plenum Press, New York, 62 B. Wunderlich, Angew Chem., 1968,80, 1009; Adv. Polymer Sci., 1969,5, 568. 63 K. Weissermel, E. Fischer, K. Gutweiler, H. D. Hermann and H. Cherdron, Angew. Chem., 64 V. Jaacks, Adv. Chem. Ser., 1969, 91, 371. 65 H. Cherdron, J. Macromol. Sci. Chem. A, 1972, 6, 1077. 66 L. Leese and M. W. Baumber, Polymer, 1965, 6,269. 67 R. Mateva, G. Wegner and G. Lieser, J. Polymer Sci., Polymer Letters Ed., 1973, 11, 369. 68 M. Droscher, G. Lieser, H. Reimann and G. Wegner, Polymer, 1975, 16, 497. 69 M. Droscher, K. Hertwig, M. Rodriguez, B. and G . Wegner, Makromol. Chem., 1967, 177, 70 M. Droscher, K. Hertwig, H. Reimann and G. Wegner, Makromol. Chem., 1976,177, 1695. 71 W. K. Burton, N. Cabrera and F. C. Frank, Phil. Trans. A, 1951, 243, 299. 72 G. Wegner, M. Rodriguez, B. A. Lucke and G. Lieser, Makromol. Chem., 1980, 181, in press. 73 M. Rodriguez B., Thesis (University of Freiburg, W. Germany, 1978). 74 A. Lucke, Thesis (University of Freiburg, W. Germany, 1979). 75 M. Iguchi, I. Murase and K. Watanabe, Brit. Polymer J . , 1974, 6, 61. 76 A, MQnoz-Escalona and S. J. Guerrero, Makromol. Chem., 1976, 177, 2169. Schaefgen (Plenum Press, New York, 1977), vol. 2, p. 205 ff. 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ISSN:0301-7249    

DOI:10.1039/DC9796800494

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

Structure and Morphology of Polydiacetylene Single Crystals BY ROBERT J. YOUNG AND ROBIN T. READ Department of Materials, Queen Mary College, Mile End Road, London El 4NS AND DAVID BLOOR AND DAVID ANDO Department of Physics, Queen Mary College, Mile End Road, London El 4NS Received 1st May, 1979 Single crystals of certain diacetylene monomers prepared by solid-state polymerization offer a unique opportunity to study the structure and properties of polymer crystals. Two distinct morpho- logical forms of one polydiacetylene (pTS) have been examined by transmission electron microscopy. In one case crystals have been prepared in the form of lamellae which are 100% crystalline. It has been shown by electron diffraction and cleavage experiments that in these crystals the polymer mole- cules are in a chain-extended conformation in contrast to the normal chain-folded lamellar single crystals obtained by solution crystallization of conventional polymers.A completely different form of pTS is obtained by crystallization of partly polymerized material from dilute solution. In this case thepTS is in the form of fibrous crystals up to 1000 A in diameter and several pm long. It has been found that the fibrous crystals have a crystal structure which is different from that of the solid- state polymerized crystals but the direction of chain orientation within the fibres is not yet known. Investigations into the structure and properties of crystalline polymers have in the past been frustrated by difficulties in dealing with only partly crystalline materials and having samples with complex morphologies.Significant advances in the understanding of the properties of polymer crystals have been made through the preparation of semi- crystalline polymers in the form of lamellar single crystals grown from dilute polymer so1ution.l Although it is known that such materials possess a high degree of molecular order they are not normally completely crystalline and are somewhat disordered ; both of these factors can to some extent limit the detailed information that can be obtained. An important step forward was made by Wegner2 through the discovery that certain substituted diacetylene monomers are capable of polymerizing in the solid state to produce polymer crystals which contain molecules which are in a completely chain-extended conformation and are 100% crystalline.This work has been extended by Wegner and co-workers in Germany, at Allied Chemicals in the U.S.A.3 and at Queen Mary College, L o n d ~ n . ~ ~ ~ Diacetylene polymer crystals have now been prepared in a variety of morphological forms which include macroscopic lozenge crystals4 and single crystal fibres6 depending upon the type of monomer and solvent used and the crystallization conditions. In this present work the structure and morphological forms of the polymer of 2,4-hexadiyne- 1,6-diol bis(p-toluene sulphon- ate), which will be referred to as pTS, have been investigated by transmission electron microscopy. In order to study the structure of this material in the electron micro-5 10 POLYDIACETYLENE CRYSTALS scope it is necessary to have samples < z 1000 A thick.The two different morpho- logical forms investigated in this present work both have thicknesses below this value. They are lamellar polymer single crystals obtained by thermally polymerizing lamellar monomer crystals grown from dilute solution and fibrous polymer crystals grown by recrystallizing partly-polymerized pTS polymer from dilute solution. It is possible to obtainpTS in at least two other different forms such as macroscopic single c r y s t a l ~ ~ * ~ or thin polymer single crystal film.7 These morphologies have also been investigated by transmission electron microscopy and their structures are discussed in a recent publication. EXPERIMENTAL PREPARATION OF LAMELLAR SINGLE CRYSTALS A dilute solution mol dm-3) of the TS monomer was prepared and several drops of the solution were deposited upon a 25 pm thick polyester film and allowed to dry.The TS monomer crystals which remained after evaporation of the xylene were annealed on the film in an air-oven at 60 "C for *70 h to complete the p~lymerization.~ The formation of the polymer crystals was manifest by the change in appearance of the initially colourless film. After annealing it became purple when viewed in transmitted light and had a gold metallic lustre in reflected light. The films containing the pTS crystals were lightly shadowed with gold-palladium and the polymer crystals were extracted using 25% aqueous polyacrylic acid s ~ l u t i o n . ~ They were then carbon-coated and the polyacrylic acid was dissolved in distilled water, leaving the shadowed polymer crystals adhering to a carbon film floating on the surface of the water.The film was collected on grids for examination in the transmission electron microscope, Some of the pTS crystals were examined after deformation by stretch- ing the polyester film to a tensile strain of x 15% before extracting the crystals. PREPARATION OF SOLUTION CRYSTALLIZED POLYMER Fully polymerized pTS cannot be dissolved in any known solvent. However, Wegner2 showed that partly polymerized material could be dissolved in some solvents, the principal one of which was nitrobenzene. Crystals of the TS monomer were heated for 3 h at 60 "C to give crystals containing x 1% of polymer. The polymer was then extracted by dissolving away the unreacted monomer in acetone and filtering.The red residue was relatively low molar mass polymer which is completely insoluble in acetone. However, it was found that it would dissolve with the application of heat in nitrobenzene or a mixture of nitrobenzene and xylene to give an orange-coloured solution. A number of solutions of the partly polymerizedpTS were made in both pure nitrobenzene and a series of nitrobenzene + xylene mixtures. The solubility of the pTS in pure nitrobenzene was determined at 22 "C by air- cooling several solutions of different concentrations and determining the concentration at which there was no observable precipitation on cooling to this temperature. The solubility in the mixed solvent at 22 "C was found by taking a series of solutions at concentrations just below those at which-precipitation would be expected and titrating a small quantity of xylene into the solution until precipitation took place.The precipitates were all seen to be red and fibrous in appearance; they were collected on carbon-coated e.m. grids for examination in the transmission electron microscope. ELECTRON MICROSCOPY The two morphologies of pTS were both examined in transmission electron microscopes; either a JEOL JEM-7 or a JEOL lOOCX, both operated at 100 kV. Both of the morphologies were beam sensitive and so they were observed at relatively low magnifications and low beam intensity. Using this technique it was found that significant beam damage, as monitoredFIG. 1 .-(a) Transmission electron micrograph of lamellar single crystals of pTS grown from dilute solution and thermally polymerized.(b) SADP from double-exposed area in (a). [To facepage 510FIG. 2.-Transmission electron micrograph of large pTS lamellae showing bend contours. FIG. 3.-Lamellar single crystal ofpTS deformed to a tensile strain of 15% in the direction indicated by the arrow. Note the cleavage cracks and twins. [To face page 511R . J . YOUNG, R . T. READ, D . BLOOR AND D. J . AND0 51 1 by the loss of diffraction patterns or the disappearance of bend contours in some bright field images, did not occur until at least 15-20 s had elapsed. RESULTS LAMELLAR SINGLE CRYSTALS Examination of the carbon film prepared as described in the experimental section showed that it was covered in lamellar single crystals ofpTS.Fig. l(a) shows a typical area and the doubly-exposed area is that taken for the selected area diffraction pattern (SADP) in fig. l(b). The crystals were found to be of the order of 5-25 pm in lateral dimensions and their thickness was determined as w 500 A by shadowing at a known angle. The orientation of the polymer chains in the lamellae and the Miller indices of the large flat face were determined from the SADP in fig. l(b). The crystal struc- ture ofpTS has been determined by Kobelt and PauIusg as monoclinic with a = 14.94 A, b = 14.49 A, c = 4.91 8, and y = 118.1" (taking the chain direction as c). This structure has been confirmed by Bloor et aL4 Using this crystallographic in- formation it was possible to show that the SADP in fig.l(b) corresponded to a beam direction of [120]. This means that the large flat face of the lamellae is (010) and the chain direction, c, lies in the plane of the lamellar single crystals. The lamellae do not lie exactly flat on the carbon film and tend to be somewhat corrugated. This gives rise to the bend confourslo that can be seen in the crystals in fig. 2. The bend contours enable the degree of crystal perfection to be determined.1° It can be seen that the bend contours are sometimes stepped. It is known that they can be displaced by certain types of dislocations or other defects within the crystals; in principle'* this interaction can be used to study the crystal defects. The chain direction and degree of chain extension in the crystals can be demon- strated by deforming the crystals before examination in the electron microscope. Fig.3 shows a large crystal that was deformed in a direction approximately perpendi- cular to its chain axis to a tensile strain of w 15%. The crystal cleaved parallel to the chain direction during deformation and the well-defined cracks show clearly the degree of chain extension in the lamellar crystals. During deformation the crystals are also seen to form twins. In the twins the molecules tend to kink across the boundary and this type of twinning has been referred to as chain axis rotation twinning and is discussed in detail for pTS elsewheie.11J2 Fig. 4 shows a schematic diagram of a lamellar crystal ofpTS and the corresponding [120] SADP. The striations in the crystal indicate the chain direction and the degree of chain extension that must exist.SOLUTION CRYSTALLIZED pTS The results of the quantitative precipitation of pTS from nitrobenzene solutions and the solvent mixtures are given in fig. 5. The area below the line corresponds to the region in which there is complete solubility at 22 "C. Above the line precipitation takes place and fig. 5 can be considered as a type of phase diagram. The dashed line is a rough extrapolation since the pTS is only slightly soluble when > 50 % xylene is present and it is extremely difficult to determine when precipitation occurs in this regime. Fig. 6(a) and (b) are two electron micrographs ofpTS crystals precipitated from a fairly concentrated solution in nitrobenzene by cooling a hot solution in air to 22 "C.ThepTS crystallizes in the form of fibrous crystals radiating out from a central512 POLYDIACETYLENE CRYSTALS 0 . 0 . 0 . . 211 001 2ii 0 . 0 . 0 . . - 210 000 210 . 0 -0- 0, 0- 0 0 211 001 211 a e o o 0 0 0 FIG. 4.Cchematic diagrams of a pTS lamellar single crystal and SADP for a beam direction of [ 1201. 0 0.25 0.50 0.75 1.0 volume fraction xylene FIG. 5.-Solubility at 22 "C ofpTS polymer extract (1% converted) in nitrobenzene + xylene solvent mixtures. In the area A there is complete solubility, in the area B precipitation occurs.FIG. 6.-(a) Electron micrograph of fibrous crystals of pTS grown by cooling a solution of pTS (1% converted) in nitrobenzene to 22 "C. (b) Higher magnification micrograph of (a) showing the variation in crystal diameter.[To face page 512FIG. 7.-SADP from a mat of fibrous crystals of pTS similar to those in fig. 6 grown from solution. [To face page 513R . J . YOUNG, R . T. READ, D . BLOOR AND D. J . A N D 0 513 nucleus. In fig. 6 the crystals are shown at two magnifications and it can be seen that they are up to 1000 A in diameter and several pm long. It has not been possible yet to determine the chain direction in the crystals since the diffraction from a single fibrous crystal is too weak. However, fig. 7 shows a SADP from a large mat of fibres using an aperture z 2 pm square. Within the mat the fibres were randomly oriented in the plane perpendicular to the electron beam and so the diffraction pattern consists of a series of rings. This clearly indicates that the recrystallized fibres are at least partially crystalline.TABLE 1 .--CALCULATED NI SPACINGS OBTAINED FROM ELECTRON DIFFRACTION PATTERN (FIG. 7) AND DEBYE-SCHERRER X-RAY DIFFRACTION PATTERN FOR THE~TS POLYMER (1% CONVERSION) CRYSTALLIZED FROM NITROBENZENE SOLUTION (APPROXIMATE ACCURACIES INDICATED) d-spacing/ A ~~ ~ spacing electron diffraction X-ray diffraction number rt 10% k5% 12.3 7.3 4.7 4.0 3.7 3.2 2.7 2.2 13.3 7.1 4.8 3.9 3.4 3.1 2.8 1.9 The crystalline nature of the fibrous crystals has also been demonstrated by ob- taining a Debye-Scherrer X-ray powder pattern from a small amount of the precipitate. A series of broad lines is obtained enabling a series of d-spacings to be determined for the crystals. The spacings are listed in table 1 along with similar measurements obtained from the rings in the diffraction pattern in fig.7. The Debye-Scherrer method is more accurate than the electron diffraction measurements but it can be seen that there is quite good agreement between the two techniques. The d-spacings cannot be related to those expected for the conventional crystal structure of pTS obtained by solid-state polymerization of the monomer and determined by Kobelt and P a u l ~ s . ~ It seems that the solution crystallized pTS has a different structure. However, the c repeat of 4.91 8, appears to be maintained (ring number 3). The diffraction informa- tion that has been obtained so far is not sufficiently accurate or precise to enable the new crystal structure to be determined. DISCUSSION The lamellar single crystals ofpTS are interesting in that although they have dimen- sions which are similar to those of solution grown single crystals of conventional polymers they are 100% crystalline and possess completely chain-extended molecules.They are really small versions of the macroscopic pTS single crystals which can be obtained with dimensions of the order of ~entimetres.~ It appears that the nucleation and growth kinetics of the TS monomer crystallizing on the polyester film by solvent evaporation from xylene are exactly what is required to form monomer lamellae. The polymer lamellae are formed directly with the same dimensions by solid-state polymerization. The SADP in fig. I@) shows clearly that the polymer chains are oriented in the514 POLYDIACETYLENE CRYSTALS planes of the lamellar crystals. This can also be demonstrated by the deformation of the crystals but the presence of sharp cleavage cracks has also been interpreted as an indication of regular folding in conventional polymers such as polyethylene.' It is also necessary to determine the chain direction by electron diffraction before chain extension can be proved unambiguously.It is possible to look in detail at the deformation of pTS from micrographs such as fig. 3. As well as obtaining cleavage cracks the polymer crystals are seen to undergo twinning. The twin boundaries all make an angle of 72" with the chain direction (defined by the cleavage cracks). This corresponds to a (101) trace and has been predicted theoretically for chain axis rotation twinning in pTS.11v12 In addition it is possible using electron micro-diffraction to determine the angle the molecules bend across the boundary.This will be the subject of a future p~b1ication.l~ This work on the deformation of pTS has furthered our understanding of the mechanical pro- perties of crystalline polymers and enabled a completely new twinning mechanism to be identified in polymer cry~ta1s.l~ The structure of the solution crystallized fibrous crystals of pTS may be contrasted with that of the lamellae obtained by monomer crystallization followed by solid-state polymerization. In the lamellae thepTS polymer is forced to adopt a crystal structure which is similar to that of the monomer, whereas when the pTS crystallizes from solu- tion it is not under such a constraint and it is therefore not surprising that the two crystal structures are different.The fibrous morphology is interesting in itself and is an unusual morphology for a polymer to adopt. It will be possible to shed more light upon the reason why the fibrous crystals are formed when the relative orienta- tions of the chain axes and fibre axes are known. However, it is possible at this stage to speculate as to why the fibrous morphology is obtained. The polydiacetylene molecule is conjugated and rather rigid. Any main-chain rotation will also be in- hibited by the presence of the large bulky side groups,' although a certain amount of co-operative rotation is required to form the twins.12 It seems likely that chain folding will be rather difficult and so the recrystallized polymer may also contain chain-extended molecules giving rise to fibrous crystals rather than conventional chain-folded lamellae. CONCLUSIONS It has been shown that the polydiacetylene pTS can be obtained in rather unusual morphological forms.By solid-state polymerization it is possible to obtain 100% crystalline chain-extended lamellar single crystals w 5-25 pm across and w 500 A thick with the polymer molecules lying in the plane of the crystals. The other form is obtained by crystallization of relatively low molar mass polymer from dilute solution whereby fibrous crystals up to 1000 A in diameter and several pm long are formed. The crystal structure in the two cases appears to be different. It has been demon- strated that pTS offers a unique opportunity to study the structure and properties of polymer crystals on a level which was hitherto impossible to attain and it is expected that significant progress will be made in future investigations. A. Keller, Rep. Progr. Phys., 1968, 31, 623. G. Wegner, Makromol. Chem., 1971,145, 85. R. H. Baughman and R. R. Chance, J. Appl. Phys., 1976,47,4295. D. Bloor, L. Koski, G. C. Stevens, F. H. Preston and D. J. Ando, J. Mater. Sci., 1975, 10, 1678. D. Bloor, L. Koski and G. C. Stevens, J. Mater. Sci., 1975,10,1689.R. J . YOUNG, R . T. READ, D. BLOOR A N D D. J . A N D 0 515 R. H. Baughman, H. Gleiter and N. Sendfeld, J. Polymer Sci., Polymer Phys. Ed., 1975, 13, 1871. ' R. T. Read and R. J. Young, J. Mater. Sci., 1979, in press. D. T. Grubb, J. Mater. Sci., 1974, 9, 1715. D. Kobelt and E. F. Paulus, Actu Cryst., 1974, B30,232. W. Jones and J. 0. Williams, J. Mater. Sci., 1975, 10, 379. R. J. Young, D. Bloor, D. N. Batchelder and C. L. Hubble, J. Muter. Sci., 1978, 13, 62. 1979, in press. l2 R. J. Young, R. Dulniak, D. Bloor, and D. N. Batchelder, J. Polymer Sci., Polymer Phys. Ed., l3 R. T. Read and R. J. Young, to be published. l4 R. J. Young, Developments in Polymer Fracture, ed. E. H. Andrews (Applied Science Publishers, London, 1979), chap. 7.

ISSN:0301-7249    

DOI:10.1039/DC9796800509

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

GENERAL DISCUSSION Prof. J. H. Magill (University of Pittsburgh) (communicated). Following the excellent overview of solid-state polymerization by Dr. Wegner, I wish to inquire if selective chemical etching techniques have been used to investigate the surface topology of his crystals. It is known that conformational and molecular packing requirements are the two major factors which dominate the chemistry for solid-state polymerization(s), but surface roughness must also play an important role in producing an equilibrium polymer crystal. Prof. G. Wegner (Freiburg im Breisgau) (communicated) : Surface topology does not play any role in the topochemical polymerization of diacetylenes where the reaction takes place in the bulk of the material. It is, however, of critical importance in the growth of crystals of poly(oxymethy1ene) in the course of the cationic polymerization of trioxane.Here, surface defects such as emergent dislocations or mechanically induced defects due to breakage of crystals under the action of a stirring device act as secondary nucleation sites and frequently cause irregular overgrowth features. This is especially true at high catalyst concentrations such as are usually employed in the BF3. Et,O induced polymerization. In general, all observations which have so far been made studying the kinetics and topology of crystal growth of poly(oxymethy1ene) under nascent conditions can very well be explained on the basis of the well accepted theories of crystal growth as they are used in the development of the BCF theory.Dr. G. Hohne (University of Urn) said: I would like to point out the importance of the twinning process. The observation of such chain-axis rotation twins or c-twins in pTS crystals is the first direct proof of their existence in polymers. This type of twinning has been predicted by Pietrallal by a re-examination of the experimental results on the deformation of polyethylene. He could explain very easily some features of the first deformation stage not well understood otherwise. And since this type of twinning seems to be a general deformation process in crystallizing polymers it must be observed in the pTS single crystals of course. As Dr. Pietralla told me, Attenburrow and Bassett have probably observed c-twinning in deformed extended chain polyethylene. It would be interesting to hear whether Dr. Bassett agrees with this statement. M. Pietralla, Dissertation (University of Ulm, 1974); Cotloid Polymer Sci., 1976, 254, 249. G. E. Attenburrow, D. C. Bassett, 4th Int. Conf. Deformation Yield and Fracture of Polymers, Cambridge, 2-5 April, 1979. Dr. R. J. Young (Queen Mary College) said: I would agree wholeheartedly with Dr. Hohne’s comments concerning the importance of the chain-axis rotation twins that can be seen in fig. 3 of my paper. The chain-extended pTS crystals allow this type of twinning to be examined for the first time in polymers. I agree with Dr. Hohne that they are probably present in deformed chain-extended polyethylene and could explain many of the deformation features observed in crystalline polymers.

ISSN:0301-7249    

DOI:10.1039/DC9796800516

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

INDEX O F NAMES* * The page numbers in heavy type indicate papers submitted for discussion. Ando, D., 509 Atkins, E. D. T., 116, 409 Ball, R. C., 198, 383 Ballard, D. G. H., 279, 434, 492 Barham, P. J., 484 Bassett, D. C., 218, 407, 434, 483 Benoit, H., 251 Bloor, D., 509. Blundell, D. J., 127 Booth, C., 411 Burgess, A. N., 279 Calvert, P. D., 424 Capaccio, G., 328 Champion, J. V., 122 Cheam, T. C., 244 Convert, P., 263 Crowley, T. L., 279 Cutler, D. J., 320 de Gennes, P. G., 96, 381 Dettenmaier, M., 26, 263 Dill, K. A., 104, 106, 452 DiMarzio, E. A., 108, 177, 210, 297, 376, 381, Dowell, F., 110 Everett, D. H., 112 Fischer, E. W., 26, 114, 119, 263, 425 Flory, P. J., 14, 109 288, 389, 402, 439, 447, 448, 449, 452,489 Frank, F. C., 7,105 Frank, W. F. X., 127,408 Geil, P.H., 141, 427, 440, 470, 473 Grossmann, H. P., 58 Grubb, D. T., 125,415, 487,489 Guenet, J. M., 251 Guttman, C. M., 108, 177, 210, 297, 393, 425, 433, 449,454,457 Hearle, J. W. S., 471 Hendra, P. J., 320, 477 Hodge, A. M., 218 Hoffman, J, D., 108,177,210,297,371, 378, Hohne, G., 516 Keller, A., 1 18, 128,145,421, 424, 460 Khoury, F., 404 Klein, J., 198, 383, 386, 400 Kovacs, A. J., 225, 374, 409, 477 Krimm, S., 244,421,422, 424, 440, 477 393, 401, 438, 454 385, 386, 393,401, 408, 409, 413,454,464,469 Longman, G. W., 279 Lovell, R., 46, 115 Magill, J. H., 417, 463, 481, 516 Mandelkern, L., 117, 310, 375, 406, 414, 422, 454, 465, 468, 469, 471,489 McBrierty, V. J., 78 Mitchell, G. R., 46, 115 Olley, R. H., 218 Pechhold, W. R., 58, 114 Pennings, A. J., 345, 486 Picot, C., 251 Point, J. J., 167, 365, 369, 373, 376, 377 Posthuma de Boer, A., 345, 488 Rault, J., 367, 370, 403, 475 Read, R. T., 509 Rigby, D., 113, 443,491 Rys, F., 435 Sadler, D. M., 106, 419, 429, 435, 482, 490,491 Sang, R. D., 320 Samulski, E. T., 11 1, 423 Schelten, J., 279 Stamm, M., 26, 129, 263,427,428, 429,432, Steidle, N., 26 Stein, R. S., 110 Stejny, J., 479 Stepto, R. F. T., 113, 443,491 Stevens, G. C., 138 Straupe, C., 225 Strobl, G. R., 26 Thomas, E. L., 122 Uhlmann, D. R., 87, 121, 129,412,442 Ullman, R., 429, 434,448 Van der Sande, J. B., 129 Vesely, D., 125, 419 Voigt-Martin, I., 405 Ward, I. M., 119,328, 478,481, 482, 484 Waring, R., 122. Wegner, G., 494,5 16 Wilding, M. A., 328 Windle, A. H., 46, 111, 114, 115, 117, 120, 122, 454 450.466 Wunderlich, B., 239, 376, 412, 413, 417, 424, 470,477 Yoon, D. Y., 109,288,389,402, 437, 439,440, 447,448,449,452 Young, R. J., 509, 516

ISSN:0301-7249    

DOI:10.1039/DC9796800517

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

GENERAL DISCUSSIONS OF THE FARADAY SOCIETY Date 1907 1907 1910 191 1 1912 1913 1913 1913 1914 1914 1915 1916 1916 1917 1917 1917 1918 1918 1918 1918 1919 1919 1920 1920 1920 1920 1921 1921 1921 1921 1922 1922 1923 1923 1923 1923 1923 1924 1924 1924 1924 1924 1925 1925 1926 1926 1927 1927 1927 Subject Osmotic Pressure Hydrates in Solution The Constitution of Water High Temperature Work Magnetic Properties of Alloys Colloids and their Viscosity The Corrosion of Iron and Steel The Passivity of Metals Optical Rotatory Power The Hardening of Metals The Transformation of Pure Iron Methods and Appliances for the Attainment of High Temperatures in a Laboratory Refractory Materials Training and Work of the Chemical Engineer Osmotic Pressure Pyrometers and Pyrometry The Setting of Cements and Plasters Electrical Furnaces Co-ordination of Scientific Publication The Occlusion of Gases by Metals The Present Position of the Theory of Ionization The Examination of Materials by X-Rays The Microscope : Its Design, Construction and Applications Basic Slags : Their Production and Utilization in Agriculture Physics and Chemistry of Colloids Electrodeposition and Electroplating Capillarity The Failure of Metals under Internal and Prolonged Stress Physico-Chemical Problems Relating to the Soil Catalysis with special reference to Newer Theories of Chemical Action Some Properties of Powders with special reference to Grading by Elutriation The Generation and Utilization of Cold Alloys Reistant to Corrosion The Physical Chemistry of the Photographic Process The Electronic Theory of Valency Electrode Reactions and Equilibria Atmospheric Corrosion.First Report Investigation on Oppau Ammonium Sulphate-Nitrate Fluxes and Slags in Metal Melting and Working Physical and Physico-Chemical Problems relating to Textile Fibres The Physical Chemistry of Igneous Rock Formation Base Exchange in Soils The Physical Chemistry of Steel-Making Processes Photochemical Reactions in Liquids and Gases Explosive Reactions in Gaseous Media Physical Phenomena at Interfaces, with special reference to Molecular Orientation Atmospheric Corrosion. Second Report The Theory of Strong Electrolytes Cohesion and Related Problems 192 8 Homogeneous Catalysis Volume Trans. 3 3 6 7 8 9 9 9 10 10 11 12 12 13 13 13 14 14 14 14 15 15 16 16 16 16 17 17 17 17 18 18 19 19 19 19 19 20 20 20 20 20 21 21 22 22 23 23 24 24GENERAL DISCUSSIONS OF THE FARADAY SOCIETY 519 Date Subject Volume 1929 Crystal Structure and Chemical Constitution 25 1929 Atmospheric Corrosion of Metals.Third Report 25 1929 Molecular Spectra and Molecular Structure 26 1930 Colloid Science Applied to Biology 26 193 1 Photochemical Processes 27 1932 The Adsorption of Gases by Solids 28 1932 The Colloid Aspect of Textile Materials 29 1933 Liquid Crystals and Anistropic Melts 29 1933 Free Radicals 30 1934 Dipole Moments 30 1934 Colloidal Electrolytes 31 1935 The Structure of Metallic Coatings, Films and Surfaces 31 1935 The Phenomena of Polymerization and Condensation 32 1936 Disperse Systems in Gases: Dust, Smoke and Fog 32 1936 33 1937 33 1937 Reaction Kinetics 34 1938 Chemical Reactions Involving Solids 34 1938 Luminescence 35 1939 Hydrocarbon Chemistry 35 Structure and Molecular Forces in (a) Pure Liquids, and (6) Solutions The Properties and Functions of Membranes, Natural and Artificial 1939 The Electrical Double Layer (owing to the outbreak of war the meeting was 35 1940 The Hydrogen Bond 36 1941 The Mechanism and Chemical Kinetics of Organic Reactions in Liquid Systems 37 1942 The Structure and Reactions of Rubber 38 1944 Molecular Weight and Molecular Weight Distribution in High Polymers. (Joint Meeting with the Plastics Group, Society of Chemical Industry) 40 1945 The Application of Infra-red Spectra to Chemical Problems 41 1945 Oxidation 42 1946 Dielectrics 42 A 1946 Swelling and Shrinking 42 B 1947 Electrode Processes Disc.1 1947 The Labile Molecule 2 1947 Surface Chemistry. (Jointly with the SociCte de Chimie Physique at Bordeaux.) 1947 Collodial Electrolytes and Solutions Trans. 43 1948 The Interaction of Water and Porous Materials Disc. 3 abandoned, but the papers were printed in the Transactions) 1941 The Oil-Water Interface 37 1943 Modes of Drug Action 39 Published by Butterworths Scientific Publications, Ltd. 1948 The Physical Chemistry of Process Metallurgy 4 1949 Crystal Growth 5 1949 Chromatographic Analysis 7 1949 Lipo-Proteins 6 1950 Heterogeneous Catalysis 8 1950 Physico-chemical Properties and Behaviour of Nuclear Acids Trans. 46 1950 Spectroscopy and Molecular Structure and Optical Methods of Investigating Cell Structure Disc 9 1950 Electrical Double Layer Trans. 47 195 1 Hydrocarbons Disc 10 1951 The Size and Shape Factor in Colloidal Systems 11 1952 Radiation Chemistry 12 1952 The Physical Chemistry of Proteins 13 1952 The Reactivity of Free Radicals 14 1953 The Equilibrium Properties of Solutions on Non-Electrolytes 15 1953 The Physical Chemistry of Dyeing and Tanning 16 1954 The Study of Fast Reactions 17 1954 Coagulation and Flocculation 18 1 955 Microwave and Radio-Frequency Spectroscopy 19520 GENERAL DISCUSSIONS OF THE FARADAY SOCIETY Date Subject Volume 1955 1956 1956 1957 1958 1957 1958 1959 1959 1960 1960 1961 1961 1962 1962 1963 1963 1964 1964 1965 1965 1966 1966 1967 1967 1968 1968 1969 1969 1970 1970 1971 1971 1972 1972 1973 1973 1974 1974 1975 1975 1976 1977 1977 1977 1978 1978 1979 1979 Physical Chemistry of Enzymes 20 Membrane Phenomena 21 Physical Chemistry of Processes at High Pressures 22 Molecular Mechanism of Rate Processes in Solids 23 Interactions in Ionic Solutions 24 Configurations and Interactions of Macromolecules and Liquid Crystals 25 Ions of the Transition Elements 26 Energy Transfer with special reference to Biological Systems 27 28 Oxidation-Reduction Reactions in Ionizing Solvents 29 The Physical Chemistry of Aerosols 30 Radiation Effects in Inorganic Solids 31 The Structure and Properties of Ionic Melts 32 Inelastic Collisions of Atoms and Simple Molecules 33 High Resolution Nuclear Magnetic Resonance 34 The Structure of Electronically-Excited Species in the Gas-Phase 35 Fundamental Processes in Radiation Chemistry 36 Chemical Reactions in the Atmosphere 37 Dislocations in Solids 38 The Kinetics of Proton Transfer Processes 39 Intermolecular Forces 40 The Role of the Adsorbed State in Heterogeneous Catalysis 41 Colloid Stability in Aqueous and Non-Aqueous Media 42 43 44 45 Molecular Dynamics of the Chemical Reactions of Gases Electrode Reactions of Organic Compounds Homogeneous Catalysis with Special Reference to Hydrogenation and Oxidation 46 Crystal Imperfections and the Chemical Reactivity of Solids The Structure and Properties of Liquids Bonding in Metallo-Organic Compounds 47 Motions in Molecular Crystals 48 Polymer SoIuZions 49 The Vitreous State 50 Electrical Conduction in Organic Solids 51 Surface Chemistry of Oxides 52 Reactions of Small Molecules in Excited States 53 The Photoelectron Spectroscopy of Molecules 54 Molecular Beam Scattering 55 Intermediates in Electrochemical Reactions 56 Gels and Gelling Processes 57 Photo-effects in Adsorbed Species 58 Physical Adsorption in Condensed Phases 59 Electron Spectroscopy of Solids and Surfaces 60 Precipitation 61 Potential Energy Surfaces 62 Radiation Effects in Liquids and Solids 63 Ion-Ion and Ion-Solvent Interactions 64 Colloid Stability 65 Structure and Motion in Molecular Liquids 66 Kinetics of State Selected Species 67 Organization of Macromolecules in the Condensed Phase 68 For current availability of Discussion volumes, see back cover.

ISSN:0301-7249    

DOI:10.1039/DC9796800518

出版商:RSC    

年代:1979

数据来源: RSC