GENERAL DISCUSSION 7 Prof. M. K16man (Universite' Paris-Sud, Orsay, France) said: I would like to mention that other kinds of walls than those presented by Prof. Meyer have long been observed in the Frederiks transition in small-molecule liquid-crystal nematics.' They arise, not from a dynamical instability as is the case in the work presented today, but from the fact that the molecules can tilt towards two different but equivalent directions in the magnetic field: hence the existence of domains separated by walls. In fact, such domains, which have a typical elliptical shape, can also be observed (and their dynamical behaviour followed) in polymer nematics. In the K3 geometry the ratio of the ellipse axes provides an estimation of the ratio K , / K Z . We have obtained K 1 / K 2 =r 10 in a polyester synthesized by Strzelecki and Van Luyen.' This ratio seems to be in agreement with separate measurements of K, and K2.3 We have also observed the walls discussed by Prof.Meyer. * F. Brochard, J. Phys. (Paris), 1972, 33, 607; L. LCger, Solid State Commun., 1972, 11, 1499. ' L. Strzelecki and D. Van Luyen, Eur. Polym. J., 1980, 16, 299. Dr H. J. Coles (University of Manchester) said: I address Prof. Meyer. In your paper you mention the determination of ratios of elastic constants and viscosities using quasi-elastic depolarised light scattering for planar samples. If you used homeotropic alignment, would it not be possible to measure the splay and twist elastic constants independently on the application of electric fields in the light- scattering experiment? Could a similar technique using either electric or magnetic fields not be applied in your existing experimental arrangement, with the added advantage that this would allow several of the individual viscotic constants to be determined? Sun Zheng Min and M.KlCman, Mof. Cryst. Liq. Cryst., 1984, 111, 321. Prof. R. B. Meyer (Brandeis University, U.S.A.) replied: In principle, an external field can be used to suppress fluctuations and thereby determine absolute values of elastic constants, assuming one knows the coefficient for the coupling to the field. In the case of PBG nematics there are very serious electrohydrodynamic effects up to frequencies of over 100 kHz, above which the dielectric anisotropy is negative. Using parallel boundary conditions with the sample contained between electrically conducting glass slides, and splay/twist geometry (1) described, the field would suppress the twist fluctuations. The only technical difficulty in carrying out this experiment might be the higher optical reflectivity of the electrically conductive glass, which makes the clean observation of the scattered light signal more difficult.With a negative dielectric anisotropy, the use of a homeotropic sample between parallel-plate electrodes would result in a Frederiks transition, which would be inappropriate for these experiments. Prof. G. C. Berry ( Curnegie-Mellon University, U.S.A.) (communicated): Accord- ing to the Manguin, or adiabatic approximation, with the geometry used in your studies of the twist Frederiks transition, a light beam linearly polarized parallel to the director at the entrance side emerges from a slab with polarization parallel to the director at the exit side. Apparently this approximation does not apply with Prof.Meyer's system - could he explain why? t Plates 1-10 face p. 190. 175176 GENERAL DISCUSSION Prof. R. B. Meyer (Brandeis University, U.S.A.) replied: The twist structures which I discussed are visible because the sample is not very birefringent. The adiabatic limit for optical propagation depends on both the wavelength of the twist and the birefringence being large; although the wavelength is large in the case studied, the low birefringence more than makes up for this. Even for more birefrin- gent samples, by using highly convergent illumination or even oblique illumination one can still see twist structures.Dr L. S. Singer (Union Carbide, U.S.A.) said: I thought it might be of interest to mention our results of a similar determination of the elastic constant for bend ( K 3 ) for our flat-molecule liquid-crystalline pitches. From plate 3 in our paper later in this Discussion, it is apparent that the magnetic coherence length 6 in the mesophase spheres is ca. 7 pm. Using the formula by de Gennes, (( H) = (5) 1'2 H with H = lo4 G and xa determined by Delhaes et aL,' we determined K3 to be 3 x lop5 dyn (at 300 "C). The corresponding values for PAA (at 120 "C) and MBBA (at 22 "C) are as follows. PAA: xa = 0.12 x dyn; MBBA: xa = 0.12 X dyn. It is of interest that these K , values for rod-like molecule mesophases are more than an order of magnitude smaller than the value determined for our disc-like carbonaceous mesophase.emu, K3 = 1.7 x emu, K3 = 0.7 x ' P. Delhaes, J. C. Rouillon, G. Fug and L. S. Singer, Carbon, 1979, 17, 435. Prof. P. J. Flory (Stanford University, U.S.A.) said: Drastic distortion of bond angles in the ester groups of poly(p-phenylene terephthalate) by substituents on the phenylene members seems unlikely. Even in the case of a phenyl substituent attached to the terephthalate residue, steric repulsion may be largely relieved by rotation of the ester group about its axis and rotation of the phenyl substituent out of the plane of the phenylene to which it is attached, as occurs in biphenyl. Thermal destabiliz- ation of the polymer by substitution may take precedence over distortion of the structure of the ester group.If distortion of the chain backbone is deemed to be a significant consequence of substitution, this possibility should be explored through determination of persistence lengths from radii of gyration evaluated using appropri- ate measurements on dilute solutions. The nematic-isotropic transition depends significantly on the free volume."* The depression of the transition on this account becomes marked at elevated temperatures where the free volume is large.',2 Substitution should be expected to obstruct efficient packing of chains in both the nematic and the isotropic liquid states. The free volume may thereby be enhanced by substitution. This effect, rather than the postulated flexibilization of the chains, is the more likely cause of the lowering of the glass-transition temperature by substitution. The effects of substitu- tion on the free volume could readily be ascertained from determinations of thermal expansivities.Additionally to be noted is the action of substituents as 'diluents' in the lattice theory of the liquid-crystalline state.3 The increase in free volume caused by the presence of a substituent and the simultaneous dilution of the semi-rigid cores may plausibly account for the effects observed.GENERAL DISCUSSION 1-77 In offering the Kuhn model as a basis for treating semiflexible chains4 we were well aware of the effect of temperature on the Kuhn segment. Recognition of the necessity of taking account of this temperature coefficient is recurrent throughout studies of the statistics of chain configurations.In focussing immediate attention on the isotherms describing biphasic equilibria,4i5 we have certainly not been oblivious of the role of temperature, as Prof. Krigbaum implies. The strong tem- perature dependence of the transition in solutions of cellulose derivatives was explicitly attributed to the temperature dependence of the equivalent Kuhn segment in a recent re vie^.^ ' P. A. Irvine and P. J. Flory, J. Chem. Soc., Faraday Trans. 1, 1984, 80, 1807; 1820. * M. Ballauff, P. J. Flory and E. M. Barrall 11, Ber. Bunsenges. Phys. Chem., 1984, 88, 524, 530. R. R. Matheson Jr and P. J. Flory, Macromolecules, 1981, 14, 954. P. J. Flory, Macromolecules, 1978, 11, 1141. P.J. Flory, Adv. Polym. Sci., 1984, 59, 1 . Prof. W. R. Krigbaum (Duke University, U.S.A.) replied: We agree that ring substitution is unlikely to cause drastic bond-angle distortion in the ester group. We propose, instead, that the high chain extension of poly(p-phenylene terephtha- late) is due to adoption of the planar trans conformation by a preponderance of the ester groups. So long as the carbonyl group is nearly coplanar with the ring, the partial double bond character (shown below in the structure on the left) can be stabilized by resonance with the aromatic T electrons. If substituent Y forces rotation of the carbonyl group out of the plane of the ring (illustrated on the right), the resonance stabilization and the partial double-bond character are eliminated, permitting rotation about the central C-0 bond and increasing chain flexibility.Such a substituent effect might be exhibited by aromatic polyamides or polyesters, but it could not occur in poly(p-phenylenes). This hypothesis will be tested by an experimental study of the persistence length and order parameter of the nematic phase of several substituted poly(p-phenylene terephthalates). We have explored the effect of temperature-dependent unperturbed molecular dimensions by a modification of Flory's treatment' of Kuhn chain polymers. Although substitution may lead to less efficient packing and a larger free volume, and free volume may play an important role in the thermotropic transition, it is not evident how this effect can be incorporated into that modified treatment.Ballauf et aZ.,2 in recognition of the artificiality of the lattice model for the treatment of free volume, confined their investigation to the effect on the orientational factor in the partition function. The magnitude of the orientation-dependent interactions will also be reduced. Flory's treatment of Kuhn chain polymers, in common with his earlier treatment of semi-flexible chain polymer^,^ does not derive an explicit relation for the orientation distribution. For this reason orientation-dependent interactions can not be incorporated in either of these treatments. Thus, precisely those factors which might be affected by free volume were omitted in treating the Kuhn chain model.178 GENERAL DISCUSSION Prof. Flory has, of course, been a leader in recognizing the effect of temperature on the unperturbed dimensions of coiling macromolecules.Nevertheless, so far as I am aware, this dependence has not been explicitly considered in any of his theoretical treatments of polymeric thermotropic or lyotropic mesophases. For example, his treatment of the Kuhn model is an isothermal one, and does not foresee the possibility of a thermotropic transition. By modifying that treatment through incorporation of a temperature-dependent Kuhn segment length, we predict a first-order thermotropic nematic-isotropic transition with a calculable enthalpy change. We have recently used d.s.c. data to measure these enthalpy changes for poly( n-hexylisocyanate) (PHIC) and hydroxytropylcellulose (HPC), as shown in the following table.AH,,/cal mol-' repeating unit polymer observed predicted4 PH IC 145 300 HPC 520 500 The experimental values are uncertain, owing to the possibility of degradation at the transition temperature. Despite this reservation, it appears that the predicted AHN, values are of the correct order of magnitude. P. J. Flory, Macromolecules, 1978, 11, 1141. M. Ballauf, P. J. Flory and E. M. Barrall 11, Ber. Bunsenges. Phys. Chem., 1984,88, 530. P. J. Flory, Proc. R. SOC. London, Ser. A, 1956,234,60. W. R. Krigbaum, H. Hakemi, A. Ciferri and G. Conio, Macromolecules, 1985, 18, 973. Dr K. F. Wissbrun (Celanese Corporation, N.1, U.S.A.) said: Prof. Krigbaum concludes from his studies of substituted poly(p-phenylene terephthalates) that substitution reduces not only the melting temperature but also the rigidity of the polymer chain.Would he speculate as to the effect upon chain rigidity of other methods of reducing the melting point, e.g. copolymerization with moieties such as naphthalene, to introduce a jog into the chain, or with biphenylene, to disrupt chain registration? Prof. W. R. Krigbaum (Duke University, U.S.A.) replied: We know from ther- modynamics that a terpolymer having a random sequence distribution must have a lower crystalline melting temperature than the homopolymer. However, we have had no experience with this type of polymer. I would speculate that extended-chain polymers, whether rod-like or having some jogs in the chain, would exhibit similar mechanical properties at low temperatures. At some higher temperature the latter polymers will begin to undergo crankshaft-type motions, and their modulus will decrease.There is anothLI difference which might be significant. The crystalline phase of the substituted poly(p-phenylene terephthalates) has three-dimensional order, despite the random placement of the ring substituents. The crystalline perfection of the random terpolymers appears to be of lower order. An interesting question is how these different degrees of crystalline order will affect the modulus, and its temperature dependence, for extended-chain polymers.GENERAL DISCUSSION 179 Dr G. R. Mitchell ( University of Reading) (communicated): There has been some discussion on the possible variation of the flexibility of various liquid-crystal-forming polymer molecules (in particular the length of the Kuhn link or its axial ratio) with temperature in polyester molecules.It has already been suggested in the discussion that available rotations of the phenyl rings within the polyesters will have no effect upon the chain trajectory because their rotation axes are collinear with the chain direction. A consequence of this is that substitution into the phenyl rings and the resulting change in the rotations possible, as described by Prof. Krigbaum, will have no effect upon the chain trajectory or the length of the Kuhn link size. Furthermore, there will be no variation in the Kuhn link size with temperature. I would like to draw attention to the particular geometry of the ester units. Structural investigations of model compounds of esters [ e.g.ref. (1)-(3)] show that the valence angle about the oxygen atom differs from that about the carbon atom in the ester unit by 6-8”. If we consider a chain in which the esters (more strictly the carbon-oxygen double bond) are normal to the planes of the phenyl rings (thus minimizing non-bonded steric interaction), the trajectory of the chain will be circular, the radius of the possible circle being related to the differences in the valence angles within the ester units. A similar curved chain configuration is exhibited by poly( methylmetha~rylate)~ and by poly( dimethyl~iloxane),~ and it occurs for the same reason, namely unequal skeletal valence angles. The reason why the co- polyester chains are straight and comprise potential liquid-crystal material is that the phenyl units are rotated away from that ‘all-trans’ position to enhance the conjuga- tion effects.This rotation of ca. 30°, which is limited by steric interactions, will occur randomly in opposite senses and will lead to an overall ‘straight’ molecular trajectory. Substitution into the phenyl units will naturally effect the preferred level of twisting and hence the nature of the chain trajectory. However, this effect would be limited, with the possible variation in Kuhn-link aspect ratio being directly related to the difference in valence angles within the ester unit. J. M. Adams and S. E. Morsi, Acta Crystallogr., Sect. B, 1976, 32, 1345. J. Kaiser, R. Richter, H. Lemke and L. Golic, Acta Crystallogr, Sect. B, 1980, 36, 193. W. L. Bencze, B. Kiss, R.T. hckett and N. Finch, Tetrahedron, 1970, 26, 5407. R. Lovell, G. R. Mitchell and A. H. Windle, Faraduy Discuss. Chem. SOC., 1979,68,46. G. R. Mitchell and A. Odajima, Polym. J., 1984, 16, 351. Prof. W. R. Krigbaum (Duke University, U.S.A.) (communicated): I agree that the mechanism which Dr Mitchell suggests would offer only a limited variation in the unperturbed dimensions of the substituted poly(p-phenylene terephthalates) with temperature. Our conjecture concerning the temperature dependence has been offered in my reply to Prof. Flory’s comments, and I have nothing further to add at this point. In my view it will be more fruitful to pursue this discussion after we have accumulated data on the persistence lengths of some of these substituted polyesters. Dr K.F. Wissbrun (Celanese Corporation, N.J., U.S.A.) said: I address my comments to Prof. Berry. I would like to comment on your discussion concerning the low-shear-rate upswing of the viscosity with decreasing shear rate of the nematic solution. You suggested that this behaviour could be explained by an increase of the order parameter S with increasing shear rates because the viscosity calculated from the Doi molecular theorv decreases with S.180 GENERAL DISCUSSION Your arguments are based on the linearized version of the Doi theory applicable in the limit of zero shear rate. Prilutski and Metzner have recently obtained numerical solutions of the Doi equations without linearization. They do in fact find that the order-parameter tensor increases with shear rate and that the viscosity decreases, in qualitative agreement with your argument.However, in the limit of low shear rates the viscosity is constant. When the shear rate (normalized to the rotary-diffusion coefficient) increases above unity, the viscosity decreases with a concave downward shape on a doubly logarithmic plot. Their results suggest that your hypothesis may account for the high shear rate shear-thinning at reduced shear rates above unity on your fig. 2, but not for the concave-upward shear-thinning that you see at low shear rates. It is worth noting that the equations solved by Priiutski and Metzner were derived using the decoupling approximation originally employed by Doi and subsequently by Marrucci. As you point out, Kuzuu and Doi later found that not making this approximation results in the prediction of unsteady shear flow.Is it possible that such unsteady flow is a cause of the domain texture observed in the low-shear-rate (Region I) flow? Prof. G. C . Berry (Curnegie-Mellon University, U.S.A.) replied: I agree with you that the rheological behaviour observed with nematic polymer solutions at low shear rate in which the steady-state viscosity qK increases with decreasing shear rate K is yet to be definitively explained. Continuing studies in our laboratory on the flow birefringence of such solutions, mentioned briefly in our contribution to this meeting, have given results that indicate that a layer of strongly anchored polymer chains exists at the surfaces of the platens used in the rheometer. We postulate that the rod-like chain axes of such chains are in the plane of the platen, and that the chains tend to be parallel locally.However, there is no global, preferred orientation of the chains over the entire platen surface, with departures from linearity occurring either gradually ( i e . on a scale long compared with the chain length L ) or as disclinations near to or bound on the surface. This texture would propagate for some distance into the quiescent fluid, perhaps from one platen to the other, producing local twists in the director orientation. In a shearing deformation, the flow birefringence data are interpreted in terms of well oriented chains in the fluid interior far from the platens, but with an essentially stagnant boundary layer near each platen, produced by the anchored chains.The thickness I of these layers decreases with increasing K, so that qK calculated from the observed torque and deformation velocity decreases with increasing K until K is large enough to make 2 negligibly small. This range corresponds to K for which qK = qp. Similar behaviour has been reported for capillary flow of small-molecule liquid crystals [J. Fisher and A. G. Frederickson, MoZ. Cryst. Liq. Cryst., 1969, 8, 2671. With the polymeric fluids studied here, the presence of any disclinations bound to the surface may enhance the effect observed. Thus, we suggest that with the PBT nematic polymer solutions the decrease of qK with increasing K is caused by neglect of a boundary layer of variable thickness in the estimation of these parameters from observed torques and angular velocities, with the boundary being stabilized by rod-like chains strongly anchored to the platens.Work to assess this postulate is in progress in our laboratory. It does not appear that the decrease of qK with increasing K is accompanied by an inherently unsteady flow, in that the shear stress becomes independent of time after a sufficiently long time.GENERAL DISCUSSION 181 Dr G. R. Mitchell (University ofReading) said: I would now like to address my comments to the paper of Alderman and Mackley, and in particular to add further experimental evidence relating to the problem of skin/core variation. The variation of orientation through the extrudate of a rigid-chain thermotropic copolyester may be considerable, and thus correlations drawn between mechanical properties and molecular orientation averaged over the complete sample volume will possibly be misleading.Plates 1 and 2 show wide-angle X-ray scattering patterns for extrudates of a random copolyester which were prepared by Dr Mackley. Each figure contains three patterns: (A) relates to scattering from the complete extrudate, (B) is a pattern obtained from a thin slice taken from the skin or surface of the extrudate, while (C) relates to sample taken from the central core of the extrudate. The principal features of the scattering patterns are the peaks, which are most intense in the equatorial section (perpendicular to the extrusion direction) and arise from correla- tions between chain segments. The degree of arcing of these peaks is a measure of the molecular orientation.The scattering patterns of plate 1 are for an extrudate for which there was no post extrusion drawing. The difference between the high orientation in the skin and the low orientation in the core section is most pronounced. Plate 2 shows the results for an extrudate with draw-down. There is now very little difference between the orientation in the skin and core sections. The draw-down appears to have only a limited effect upon the level of molecular orientation reached in the extrudate. Its particular effect is to produce an extrudate of uniform orientation and therefore presumably uniform physical properties. The presence of uniformity of orientation may well limit the capacity for delamination. Prof.M. Kleman (Univeriste' Paris-Sud, Orsay, France) said: Alderman and Mackley claim that the 'dense disclination texture' they observe is thermally stable: the density of defects is reversible and depends only on temperature. This result, if it is confirmed, raises interesting questions. Thermal disclinations have been advocated recently in a number of situations with 'frustrated' molecular structures, in particular in disordered systems' (liquids, glasses and blue fog, which is a disordered blue phase); periodic disclination arrays can also relieve frustration in some cases (Frank and Kasper phases2 and blue phases3). In all these cases disclinations separate domains inside which the frustration is weak. Why an uniaxial nematic phase should present frustration is hard to imagine.I would like therefore to consider seriously the possibility that these copolyesters are biaxial, like those of Windle et uZ.,~ with which they have much in common. This possibility suggests some comments. (1) Disclinations in biaxial nematics do not obey the same rules of interaction as those which apply in uniaxial nematics; while in the latter case disclinations can easily cross without obstruction (this is expressed by the fact that, in the topological theory of defects, disclinations are classified by the elements of the commutative group with two elements Z2), it is predicted that there is obstruction to crossing in the former case.5 (In a biaxial nematic disclinations are classified by the quaternion non-commutative group Q.) Fig. 1 represents a typical crossing of two disclinations belonging to two non-commuting elements of Q: a third disclination segment appears between both and the total density of disclinations is increased.If such crossings occur when the temperature of the sample is changed, and are at the origin of the change in density with T, then the fact that this density is smaller when T is higher (as stated by Alderman and Mackley) implies that crossings with T going downwards are more effective than those with T going upwards. If this is the case, it means182 GENERAL DISCUSSION Fig. 1. Typical crossing of two disclinations (see text). probably that there is some activation energy against annealing which is in the temperature range considered. (2) Frustration should be a usual characteristic of biaxial nematics if biaxiality is due to some anisotropic coiling of the long molecules one around another.As discussed briefly in ref. (6) and in more detail in a forthcoming publication of this discussant, one would expect in such a case that domains made of coiled-together molecules would have a transverse characteristic size (a correlation length for coiling) and would be separated by disclinations or some sort of wall. A hierarchy of domains might also occur (supercoils). The analogy with the blue fog (if disclinations are at random) or the blue phase is evident. We expect that any reasonable theory of random disclinations relieving frustra- tion would predict a density of defects increasing with T. This is not the case here. Therefore both frustration (leading to a thermal distribution of defects) and obstruc- tion to crossing with activated annealing have to be considered. Of course, all our comments are of an heuristic nature, and should be taken into consideration only if the basic experimental facts have been correctly interpreted above.If this were the case, even more could be said! M. KlCman and J. F. Sadoc, J. Phys. (Paris) Lett., 1979, 40, L-569. F. C. Frank and J. S. Kasper, Acta Crystalfogr., 1958, 11, 1984; 1959, 12, 483. See for example S. Meiboom, M. Sammon and W. F. Brinkman, Phys. Reu. A, 1983, 27, 438. A. H. Windle, C. Viney, R. Golombok, A. M. McDonald and G. R. Mitchell, Faraday Discuss. Chem. Soc., 1985, 79, 55. G. Toulouse and M. KlCrnan, J. Phys. (Paris) Lett., 1976,37, L-149; G.Toulouse, J. Phys. (Paris) Lett., 1977, 38, L-67. M. KlCman, Faraday Discuss. Chem. Soc., 1985, 79, 215. Dr M. R. Mackley (University of Cambridge) said: Prof. KICman raises an important issue concerning the temperature dependence of the disclinations observed in our samples. Temperature cycling of samples presents two experimental difficul- ties. A temperature change can lead to a change in sample thickness and of perhaps greater importance to local flow within the sample. From our observations so far, it is not possible to say that the disclination density changes without any local flow occurring. We also note that the greatest change in the disclination density appears to occur in the temperature ranges where there are changes in the melting or cooling endotherms of the material’s d.s.c.traces. This itself suggests that the overall observed decrease in disclination density with increasing temperature is not related to thermal activation in a simple way. Dr. G. R. Mitchell (University of Reading) said: I would like to comment on the remarks of Prof. Kl6man relating to the level of local orientation in liquid-crystal polymers. We may describe the orientation of molecules, or perhaps more realisti- cally (for polymers) the orientation of chain segments, with respect to some external axes, or relate the orientation of the chain segments to each neighbouring chain segment. The former mode, which describes the distribution of individual chainGENERAL DISCUSSION 183 segments, I will term global orientation. The alternative mode of description specifies the interactions or correlations between chain segments.Since it is the correlations which occur in the immediate environs of each chain segment which are of interest, I shall term this specification local. The difference between these terms is principally one of scale, and a knowledge of both is a prerequisite for any satisfactory model of liquid crystals. The wide-angle X-ray scattering observed for an aligned liquid-crystal polymer, of which fig. 2 of our paper is an example, contains both scattering which arises from correlations from individual chain sequences and scattering which may be related to the correlations between chain segments. Thus it should be possible in principle to extract both a measure of the global orientation and the level of local orientation correlation.The scattering which occurs at scattering vectors > 2 A-' results almost entirely from correlations within separate chain segments. The scatter- ing observed at one such scattering vector is then simply the convolution of the scattering for a perfectly aligned chain segment I,,( a) and the orientation distribution function D(a). If we express these functions in terms of a series of Legendre polynomials we may express the observed anisotropy ( P 2 n ( ~ ~ ~ as (PZn(C0S 4 ) I = (P2n(COS 4)lu(P2n(COS 4 ) D (1) where the subscripts D and I,, relate to the distribution function and the scattering from a perfectly aligned unit. For the rigid-chain copolyesters under consideration (see our paper at this Discussion) we may calculate ( P2n (cos a ) ) I , from a knowledge of the chemical configuration and thus obtain a measure of the global orientation (Pzn(cos a)), as a series of quotients.In fact it is possible to determine the correctness of the conformation of the molecule used in the analysis by exploiting the spherical-harmonic analysis as described elsewhere.273 Values of ( P2( cos a)) obtained in this way for typical melt-extruded copolyester pellets are ca. 0.5-0.6. The scattering which occurs at s = 1.5 A-' results from spatial correlations between chain segments, and as such its anisotropy results from the orientation of those correlations. If it were a crystal reflection, and hence if it were assumed that for a perfectly aligned system the intensity of the reflection would be limited to the equatorial plane, we would be able to extract the molecular orientation functions using eqn (1) with ( P 2 n ( ~ ~ ~ a ) ) I , set to values given elsewhere.' Such a method involves obvious approximations (although it is in widespread use), for it ignores for a liquid-crystal system the effects of intrachain scattering and the finite correlation length of the molecules.An ap roach will now be described which utilizes the interchain scattering at s = 1.5 I-' to provide values for the local orientation function. If we ascribe some local orientation (P2n(c0s a)), to a small volume of the material, and also describe the orientation of those volumes using (Pzn(cos a))", we may write the global orientation as (&"(COS 4 ) D = (P2n(COS 4>L(PZn(COS a h .(2) For a liquid-crystal sample in which the local orientation is relatively high the arcing of the peak at s = 1.5 A-' is related to the anisotropy of those local volumes. In other words, (Pzn(cos a))v is equivalent to ( P 2 n ( ~ ~ ~ a!))* for s = 1.5 A-'. Since we can obtain, independently, values of (P2n(c0s a)), the values of ( P 2 n ( ~ ~ ~ a))L are available as a series of quotients (P2n(COS a))DI(Pzn(COS a >>v where the divisor is obtained from the anisotropy of the peak at s = 1 . 5 A - ' .184 GENERAL DISCUSS I 0 N However, before performing these manipulations it is necessary to correct the ( P2n (cos term for the effects of finite-length segments and the inclusion of some intrachain scattering. Those corrections reduce the anisotropy of ( P2,, (cos to 86-92% of their recorded value^.^ Values were recorded for the copolymer of hydroxybenzoic and hydroxynaph- thoic acids (70/30) of (P2(cos a))D = 0.53 and (P2(c0s = 0.55, which give a local orientation parameter ( P2(c0s of 0.95.Thus the local correlations between chain segments are considerably enhanced above the general level of global orienta- tion. The extent of this enhanced orientation is currently unknown. It is only possible from the X-ray analysis to suggest a correlation volume with a radius of at least 30A. ' R. Love11 and G. R. Mitchell, Acta Crystallogr., Sect. A , 1981, 37, 135. G. R. Mitchell and A. H. Windle, Colloid Polym. Sci., 1982, 260, 754. G. R. Mitchell and A. H. Windle, Polymer, 1983, 24, 1513. G. R.Mitchell, in preparation. Dr D. J. Blundell (ICI, Wilton) said: I wish to remind the meeting of the evidence of the flow regime in main-chain thermotropics under high stress that is revealed by looking at the microstructure of injection mouldings. This was well exemplified by the excellent microscopy shown in the poster from Brunel University by H. Thapar, P. Allan and M. J. Bevis. After sectioning longitudinally along injection-moulded bars, one can often see with the naked eye a series of light and dark bands closely related to the flow history during mould filling. By making thin sections and observing by light microscopy my colleague A. D. Curson has shown that there is a substructure which usually appears as elongated layered structures typically 0.25 p m thick and elongated by several p m in the flow direction. The Brunel SEM pictures reveal a similar picture.Taking a simple view of what is seen, it is difficult to avoid the conclusion that these entities are related to the units that have sheared or flowed passed each other during the mould filling process. Are these entities perhaps related to the cells modelled by Dr Wissbrun? There is a close resemblance to the phenomena presented by Prof. Meyer. As Prof. Meyer has suggested earlier, these flow entities may be the products of a mechanical instability under the influence of a high melt stress. This would suggest that it is the regions between them where flow occurs and where disclinations may presumably play a role. In our studies we have examined longitudinal sections with a 100 p m microbeam X-ray camera.This gave an assessment of the molecular chain orientation in the flow entities within the region probed by the beam. We found the net degree of orientation varied from region to region. The orientation tended to correlate both with the size and disposition of the flow entities and with the flow regime in the mouldings. Similar conclusions were drawn by the Brunel poster. We also believe that the gross dark/light banded appearance seen in the mouldings is the result of differences in the light scattering between different bands, resulting from the differen- ces in the size and orientation of the component birefringent units making up the microstructure. Dr M. R. Mackley (University of Cambridge) replied: Dr Blundell raises a point concerning instabilities within thermotropic liquid-crystal polymer injection mould- ings.In my view this could be an important factor and deserves both theoretical and experimental attention. The results presented in our own paper suggest that the stability of the director trajectory is dependent on whether the fluid is beingGENERAL DISCUSSION 185 axially accelerated or decelerated. The injection moulding process is complex and will contain flow regimes of these types although their occurrence will be a function of both time and position. Our results also illustrate the extreme shear sensitivity of these materials. Thus flow instabilities within injection-moulded articles should certainly be expected. Dr B. Griffin (ICI, Welwyn ) said: Tennessee Eastman's 60% p-oxybenzoate-40% PET copolyester, known as X7G, was the first freely available thermotrope and as such has now received detailed attention at a number of centres.Because of its historical significance I feel it is important to draw attention to its untypical character. In particular, the synthesis by melt acidolysis with p-acetoxybenzoic acid of preformed PET polymer, followed by melt and solid-state repolymerization, gives rise to chemical inhomogeneity. This is in addition to the normal molecular-weight distribution found in most thermotropes prepared by conventional condensation of AB or AA plus BB type monomers. Work in the ICI laboratory during the late 1970s for example has shown, using graded solvent extraction, that X7G samples contain a continuous range of copoly- mer compositions varying from ~ 2 0 % to 280% p-oxybenzoate units.Under the polarizing microscope the PET-rich fractions furnish only isotropic melts at all temperatures. Intermediate fractions give mesomorphic melts similar in appearance to unfractionated X7G but with a narrower biphasic temperature interval near TI. Fractions with ca. 80% p-oxybenzoate show no TI below the decomposition point (350-400°C). Thus it is important to realise that the isotropic character revealed by n.m.r. studies below TI and the more obvious biphasic separation observable at TI owe their origin to both the flexible PET-rich fractions as well as normal TN-,I transitions observable for each molecular weight (axis-ratio) species present in conventional, chemically homogeneous, completely rod-like thermotropic melts and lyotropic solutions. The fact that rapid demixing of the phases between T, and TI has not been reported is believed to be a reflection that the low-shear-rate viscosity of the extremes of composition present are in fact closer together than they are to that of the mean composition.Certainly at ca. T, + 40 "C slow separation of isotropic material was evident in the ICI work. Prof. Lenz's proposal to form an IUPAC study group for liquid-crystal polymers would now seem most timely. Apart from X7G there are a number of development materials available which would now repay more careful characterization. Dr K. F. Wissbrun (Celanese Corporation, N.J., U.S.A.) said: I have two brief comments to make on this very interesting work.One is to correct a possible misimpression, namely that the effect of shear upon domain size was proposed independently by Marrucci and by myself. Speaking for myself, and I believe also correctly for Prof. Marrucci, the concept was based on the pioneering observations of Graziano and Mackley, and the quantitative relation of domain size to stress was formulated by Marrucci. Secondly, the idea that the velocity rearrangement of a power-law fluid upon exiting from an extrusion die was the cause of a skin-core morphology has also been presented by Ide and Ophir.' I do not believe that they considered the effect of subsequent draw-down as Dr Mackley did to explain the increasing growth of the skin fraction with increasing stretching. * Y.Ide and 2. Ophir, Polym. Eng. Sci., 1983, 23, 261.186 GENERAL DISCUSSION Dr A. H. Windle ( University of Cambridge) said: I have a comment and a question. ( 1 ) Dr Mackley has shown us the dynamic response of the microstructure of a thin sample under shear. We have been concerned whether the proximity of static glass slides might also influence the microstructure of a thin section, and have compared the textures of thin samples (ca 2-3 pm) prepared as a melt between glass slides with samples of much the same thickness microtomed from the bulk. The textures observed, whether fine Schlieren or coarsened by annealing, were closely comparable. On the other hand, the annealing on rock salt of samples only ca. 0.1 p m thick (i.e. of the order of the molecular length), produced domain textures of a type not observed in 2-3 p m samples.The domains in such thin specimens also appeared exceptionally rapidly, and were well formed after a second or two. (2) Do the disclinations observed by Dr Mackley play any significant role in the mechanism of shear deformation, or should we regard them simply as markers going along for the ride? Prof. A. Keller (University of Bristol) said: I would like to clear my own mind as to what is meant by ‘domains’. I note that such ‘domains’ are being referred to in several papers and discussion remarks and this in different contexts. In some instances I get the impression that they are supposed to be separate entities similar to grains in a polycrystalline material, while in others they refer merely to compara- tively defect-free regions with directors all parallel which, while delineated by disinclinations, do not possess materially distinct boundaries.Neither do references to the role of these ‘domains’ in flow and/or deformation help me to appreciate what they are supposed to stand for. Further, are these ‘domains’ meant to be equilibrium structures under the prevailing constraints imposed on the system or are they, in analogy to polycrystalline grains, the results of a nucleated growth process? I would be most anxious to have some clarification on this matter. Dr A. H. Windle (University of Cambridge) replied: In taking up Prof. Keller’s challenge to define a ‘domain’ we at once find Marrucci’s particular description restrictive, although Dr Wissbrun has shown it may be a useful structural model when discussing deformation.In keeping with previous usage of the term ‘domain’ or ‘grain’ in metal crystals to describe regions in which a particular type of order is preserved (such as crystal orientation, solid solution ordering or magnetic orienta- tion), we see a domain, when it exists in the liquid-crystalline polymer context, as a region within which an orientation parameter varies no more than slowly with position, compared with its rapid variation at the delineating boundaries. For a number of reasons, including some observations of the structure of the boundaries themselves, we are drawn to the analogy with ferromagnetic domains as being the most useful. For example, the orientation of the extinction directions in a fine Schlieren texture (plate 3) varies comparatively rapidly with position, and yet, as far as can be seen, the variation is continuous.We do not call any part of this microstructure a ‘domain’, even though it might be possible for some local areas to satisfy Marrucci’s description. On the other hand, polymers such as ClQT-QG (polymer 111 of our paper), in which the microstructure of the mesophase coarsens very rapidly with time, show regions of fairly uniform orientation with clear-cut boundaries. We call these regions ‘domains’ (plate 4). Domains also form very rapid1 during the one of Dr Donald’s dark-field electron micrographs. It shows a fairly uniform annealing of samples thin enough to be observed in TEM (ca. 1000 x ). Plate 5 isGENERAL DISCUSSION 187 orientation within the domains and comparatively localized boundaries, which on analysis show features similar to either Bloch or NCel walls in ferromagnetic materials.''2 Prof.Keller also enquires as to the mechanism of domain formation. Starting with a fine Schlieren texture in a 60/40 HBA/ET, we have followed the coarsening sequence on annealing at 290 "C. The fine Schlieren textures themselves are formed when the liquid-crystalline polymer is either: (i) cooled from the isotropic phase, (ii) subjected to complex flow situations in the mesophase, e.g. extruded, or (iii) cooled across the transition from uniaxial to biaxial. The initial stages of coarsening occur with the appearance of circular zones with a comparatively coarse radial texture.Three such coarsening centres can be seen in plate 6 . The contrast between crossed polars is sometimes a four-fold brush and is very similar to the Maltese cross characteristic of spherulites in crystalline systems. During the anneal the circular regions increase in number and size (plate 7), until the remaining fine-scale Schlieren texture appears as isolated 'knots' in the otherwise coarsened microstructure. The general appearance is then as in plate 8, while the fully coarsened texture is shown in plate 9. It has not yet been possible to follow the complete sequence in thicker specimens, where the fine microstructures are superimposed leading to a confused texture. ' A. M. Donald, C . Viney and A. H. Windle, Philos. Mag., Part A, in press. ' A. M. Donald and A.H. Windle, Polymer, 1984, 25, 1235. Dr M. R. Mackley (University of Cambridge) said: I am grateful to Prof. Keller and Dr Windle for their remarks. Our own optical observations are concerned with both birefringence and scatter- ing, from which we believe that the scattering originates from line defects within the material. For the samples we have examined we do not have any experimental evidence to support the view that sharp domain walls are present. Plausibly it could be envisaged that the disclinations represent boundaries in the fluid; however, this does not mean that there are well defined surfaces separating different domains. Concerning flow, we envisage the roll of disclinations in liquid-crystal polymers to have similarities with that of disclinations previously studied in small-molecule liquid crystals.' In the latter case, material that started defect-free in the director vertical state was initially oriented by low shear rates with the director horizontal along the direction of shear.At higher shear rates, disclination loops were nucleated and they could subsequently both multiply and relax. During flow, the presence of the disclinations will only locally modify the conditions around the line defect. On cessation of flow, the relaxing disclination loops influence the director trajectory over extended distances within the fluid. In terms of liquid-crystal polymers, similar events occur. Flow causes both matrix orientation and disclination multiplication. Unlike the role of dislocations in the plastic deformation of metals, disclinations in thermotropics do not appear to be essential for the material to have fluidity.However, the presence of disclinations does depend on the past shear history of the material, and the line defects act as boundary constraints that will effect the director trajectory within the material, particularly during relaxation after shear. In concluding the discussion on my paper I would like to emphasize that it is important to appreciate the factors that thermotropic main-chain liquid-crystal polymers have in common with both conventional flexible thermoplastics and small-molecule liquid crystals. In relation to thermotropics, common factors are ( 1)188 GENERAL DISCUSSION Fig. 2. Schematic diagram of isotropic phase (top) and nematic phase with orientation domains (bottom) [taken from ref.(2)]. a molecular weight distribution and (2) melt-processible, high-viscosity viscoelastic behaviour with an associated broad range of relaxation time constants. In relation to small-molecule liquid crystals common factors are (1) anisotropic elastic and viscous behaviour (2) line defects that occur as disclinations which can multiply as a consequence of shear. Thermotropic liquid-crystal polymers do not appear to have as simple solid/liquid boundary conditions as small-molecule liquid crystals can have. The elastic properties of thermotropic liquid-crystal polymers also appear to have greater complexity than the splay, twist and bend distortions present in nematic small- molecule liquid crystals. Fluid and solid properties of thermotropic polymers can be expected to depend on both the anisotropic behaviour of the material, together with the defect structure within the fluid or solid.D. Graziano and M. R. Mackley, Mol. Crysr. Liq. Cryst., 1984, 106, 103. W. G. Miller, C . C . Wu, E. L. Wee, G. L. Santee, J. H. Rai and K. G. Goebel, Pure Appl. Chem., 1979, 38, 37. Prof. E. L. Thomas (University of Massachusetts, U.S.A.) said: I would like to raise the question of domains as a key microstructural feature in liquid-crystalline polymers since Dr Wissbrun indicated an important role for such structures in determining rheological behaviour. Fig. 2 is often cited in the literature as a schematic illustration for what is meant by an orientation domain structure in the liquid-crystalline state. The domains are bounded by surfaces where the molecular director changes discontinuously from one domain to the next.As we will show in our contribution, the presence of disclinations and bands give rise to various textures in the field of lamellar trajectories, but we have found no evidence for orientation domain boundaries as such. The concept espoused by Marruccil and presently further developed by Wissburn of defining an ‘effective domain’ as a stable array of disclinations such that the ‘domain’ has no net overall orientation is appealing, but it is not clear to me whether the grouping of the disclinations provides any unique domain morphology appropriate to rheology. Furthermore, how such domains (really disclinations) interact and change their number, size and shape during flow is still an open question.Dr Mackley’s flow-visualization experimentsGENERAL DISCUSSION 189 seek to answer this question, but it appears that the size scale is beyond the resolution of his optical technique. Finally, as a note on the value of preprinting and circulating the Faraday contributions, I would like to remark that Dr Wissbrun previewed our paper and used a slide in his oral presentation today to illustrate the concept: ‘domain = stable array of disclinations’. We saw Dr Wissbrun’s paper, re-examined our images, and found a frequently occurring disclination array (plate 10). The molecular director field suggested by the lamellae closely resembles Dr Wissbrun’s schematic representation of a single domain; nevertheless we are unable to reconcile images of larger areas with the stipulation that assemblies of the ‘domains’ must be space-filling.’ G. Marrucci, paper presented at Int. Congr. Rheology, Acapulco, 1984. W. Miller et al., J. Polym. Sci., Polym:Symp., 1978, 65, 91. Prof. A. Keller (University of Bristol) asked Prof. Thomas: Are disclinations equilibrium defect structures? Prof. E. L. Thomas (University of Massachusetts, U.S.A.) responded: I think the analogy between dislocations in crystalline materials and disclinations in liquid- crystalline materials is relevant here. In crystalline materials the dislocation density is lowered by annealing. This is because the increase in internal energy of the crystal by the presence of the dislocation more than offsets its entropic contribution.Such is not the case for vacancies, which are equilibrium point defects. I expect the trade-off between internal energy and entropy for disclinations will be similar to dislocations, i. e. disclinations are not equilibrium defects. This has been verified in our experiments in which the disclination density of a film was observed to decrease with long-time annealing. Dr R. Zentel (University of Mainz, West Germany) said: I am rather astonished about the different approaches which people interested in low-molar-mass liquid crystals and in polymer liquid crystals seem to use. For low-molar-mass liquid crystals one starts with the definition of five different viscosity coefficients and three elastic constants,* which can be determined indepen- dently for well oriented samples without disclination lines.Starting from this one hopes to understand more complex behaviour also. In polymeric liquid crystals it is recognized that this must be the case,2 but people normally start with unoriented samples and use only one viscosity coefficient. This may be the right way if one is only interested in processing properties, where one also works with unoriented material. However, if one tries to gain a better understanding of the behaviour, would it not be better to start with five coefficients? See for example: P. G. de Gennes, The Physics of Liquid Crystals (Clarendon Press, Oxford, 1975). * See for example: P. G. de Gennes, S. Chandrasekhar or W. R. Krigbaum, in Polymer Liquid Crystals, ed. A. Cifem, W.R. Krigbaum and R. B. Meyer (Academic Press, New York, 1982). Dr K. F. Wissbrun (CeEanese Corporation, N.J., U.S.A.) responded: It would be very desirable in principle to measure the three elastic constants and the five Leslie coefficients, as Dr Zentel suggests. In practice this is very difficult for the main-chain thermotropic polymers, especially the all-aromatic polymers that I have been prin- cipally concerned with. The difficulties arise from the strongly persistent domain texture of these polymers and their high melting temperatures. A beginning has been made at studies of the sort Dr Zentel suggests with lyotropic main-chain polymers. Prof. Meyer’s work presented at this conference is the most advanced that I am aware of; DuPre has also measured elastic constants of poly(benzy1190 GENERAL DISCUSS ION glutamate). Some measurements of anisotropic viscosity of poly(p-benzamide) solutions have been reported by Kulichikhin et al.' I do agree with Dr Zentel that eventually it will be necessary to make such measurements in order to understand the flow behaviour of polymer liquid crystals. It may be necessary to devise new measurement techniques for special requirements of polymeric liquid crystals. This is one of the problems that I proposed at a workshop on orienting polymers.2 Dr Zentel then continued: This is right for liquid-crystalline main-chain polymers, but liquid-crystalline side-group polymers can be well oriented by surface effects and in electric and magnetic fields3 V. G. Kulichikhin et al., Vysokomol. Soyed., 1979, 21, 1407. ' K. F. Wissbrun, in Orienting Polymers (Lecture Notes in Mathematics), ed. A. Dold and B. Eckman (Springer, Berlin, 1984). See for example: H. Finkelmann and G. Rehage or V. P. Shibaev and N. A. Plate, in Adv. Polym. Sci. (Springer, Berlin, 1984), vol. 60/61.Plate 1. Plate 2. Plate 1. Wide-angle scattering patterns for different sections of a melt-extruded sample of a rigid-chain thermotropic copolyester. The extrusion direction is vertical, and the principal feature of the patterns corresponds to a real-space correlation of CQ. 5 A. (A) Complete extrudate, (B) thin section taken from skin of extrudate and (C) thin section taken from the central core of the sample. Plate 2. Wide-angle scattering patterns for different sections of the same copolyester as plate 1 but extruded with a post extrusion pull-off. Key as plate 1. [facing p g e 190Plate 3. Fine Schlieren texture in B-ET cooled rapidly from 340 "C. Plate 4. Domains in a specimen of ClQT-QG viewed between crossed polars; sheared and subsequently coarsened at 350 "C.'Plate 5. A thin film of polymer B-N sheared and annealed for 20 s at 320 "C on rock salt. TEM dark-field image. Plate 6. Fine Schlieren texture in B-ET showing coarsening centres. Samples rapidly cooled from 340 "C and annealed at 290 "C (T. J. Lemmon).Plate 7. Growth of coarsening centres. B-ET annealed at 290 "C (T. J. Lemmon).Plate 8. Predominantly coarsened texture with isolated 'knots' of remaining fine Schlieren texture (T. J. Lemmon). Plate 9. Fully coarsened texture after annealing at 300 "C for several hours, showing domains (C. Viney).Plate 10. ( a ) Stable array of disclinations defining an ‘effective domain’ (Wissbrun). ( b ) Image of array of pairs of S = +$ and S = -4 disclinations (Thomas and Wood).