GENERAL DISCUSSION t Prof. E. Chiellini (University of Pisa, Italy) said: My question is related to the very last part of Prof. Samulski’s presentation and is concerned with the change in the sense of helicity of the cholesteric array in poly( y-benzyl-L-glutamate) which accompanies a change in the nature of the solvent, i.e. in going from dioxane to dichloromethane. Is that change accompanied by a change in the local helicity of the individual macromolecules in dilute solution? In other words, is there any possibility of predicting a correlation between the helicity of single cholesterogenic macromolecules and the helicity of the cholesteric supermolecular array in both lyotropic and thermotropic systems? Prof. E. T. Samulski (University of Connecticut, U.S.A.) replied: Classical 0.r.d.and c.d. experiments with PBLG in dilute solutions using dioxane or dichloromethane (and their mixtures) indicate that the a-helix maintains a right- handed conformation; i.e. insofar as one can extrapolate such findings to concen- trated, lyotropic solutions, there does not appear to be a correlation between the sense of the PBLG backbone helix and the sense of the cholesteric twist. Moreover, it has been demonstrated that a single chiral doping agent will induce a cholesteric pitch sense that depends on the specific achiral thermotropic nematic being doped. Hence, it does not appear that there is a straightforward way of predicting the macroscopic twist sense given the microscopic chirality in either lyotropic or ther- motropic phases. Prof.G. C. Berry (Carnegie-MeZZon University, U.S.A.) said: Liquid crystals are often studied, processed or utilized as thin layers bounded by surfaces. Without special preparations, the surfaces may orient the director in the plane of the surface, but with an orientational coherence length in the plane comparable with the sample thickness, producing a complex three-dimensional director orientation throughout the sample. Can Prof. Samulski comment on whether such effects might be par- ticularly important with long-chain polymeric liquid crystals, and what the effect of such a director field might be in the presence of orientational fields such as a magnetic or electric field or a shear deformation? For example, in the latter case, I suspect such effects could introduce boundary layer effects, giving rise to the observed increase in the apparent viscosity with decreasing rate of deformation for slow flows.Prof. E. T. Samulski (University of Connecticut, U.S.A.) responded: In the early studies of polypeptide liquid crystals it was noted that the cholesteric axis aligns normal to planar surfaces and that the resulting aligned domain could traverse the thickness of the sample cell - a distance of some millimetres [see ref. (9) of my paper]. More recently cell thickness has been exploited to affect textures (cholesteric versus nematic) and alignment mode (homeotropic versus planar).’ Thus boundary surface effects are not negligible in polymeric liquid crystals and may, as Prof. Berry suggests, profoundly influence delicate threshold level perturbations of the director by external fields.As to the relative importance of such effects in monomeric and polymeric liquid crystals, I can only speculate that as a coarse approximation one might anticipate t Plates 1-9 follow p. 123. 8586 GENERAL DISCUSSION the coherence length to scale with molecular dimensions. Hence for a high- molecular-weight polymer the propagation of boundary effects could conceivably exceed by two to three orders of magnitude coherence lengths commonly encoun- tered in monomeric liquid crystals. Y. Uematsu and I. Uematsu, Pofyrn. Prepr., 1979, 20, 66. Dr L. L. Chapoy (Technical University of Denmark) addressed Prof. Samulski: You said that the theory of liquid crystalline polymers is progressing. What is your feeling about the ability to predict the effect of defect structures, e.g.groups containing kinks, flexible links and aromatic substituents, in converting aromatic polymers which are largely intractable into thermotropic, rigid-rod, liquid-crystalline polymers? Prof. E. T. Samulski ( University of Connecticut, U.S.A.) (communicated): Let me begin to answer your question by stating that theoretical modelling of monomeric liquid crystals is not yet at a stage that enables the inclusion of specific chemical idiosyncracies of mesogens; for the most part, researchers are limited to tabulating trends within a given class. of mesogens, rank ordering ‘defect structures’ according to their influence on transition temperatures. However, one should not infer from the status of such modelling that the role of defect structures in polymeric liquid crystals will be even more elusive.On the contrary, subtle changes affected by chemical modification of monomer liquid crystals are frequently exaggerated in polymers. Thus it may be quite possible to categorize defect structures in a semiem- pirical manner via studies of their influence in ‘ideal’ polymeric liquid crystals, and thereby construct prescriptions for the use of defect structures in the modification of potential (and often intractable) polymeric liquid crystals. Moreover, as the modelling of semiflexible polymers progresses, it may be possible to delineate the influence of specific defect structures to a degree of sophistication that is currently not possible in theories of monomeric liquid crystals.It is this kind of interplay between research on monomer and polymer liquid crystals that would constitute the synergism that I anticipate will characterize progress in our understanding of liquid crystals in the next decade. Prof. R. B. Meyer (Brandeis University, U.S.A.) said: In the past we have discussed the question of a convenient material on which physicists interested in polymer liquid crystals might perform experiments. In the case of polymer nematics, this might really be a small family of materials rather than one. For instance, one might be a low-melting-point semiflexible polymer. Another might be a rigid-rod polymer conveniently soluble at room temperature. Each of these should be chemi- cally stable and available in various molecular weights.The general knowledge and availability of such materials as a starting point for physicists would be very useful. Does Prof. Samulski have any suggestions along these lines? Prof. E. T. Samulski (University of Connecticut, U.S.A.) replied: The establish- ment of a class of polymeric liquid crystal standards would indeed expedite the advancement of our understanding of these materials just as the development of stable, room-temperature, monomeric liquid crystals fifteen years ago for electro- optic applications facilitated fundamental experimental investigations. In the case of thermotropic polymers there is, unfortunately, no comparable impetus from the applications sectors ; industry is interested in high-temperature materials whichGENERAL DISCUSSION 87 generally preclude careful characterization. Such materials will have to come from a conscientious synthetic laboratory. I think the synthetic polypeptides are capable of fulfilling the role of a rigid-rod standard for lyotropic polymeric materials.Again there is a real need to make well characterized (narrow molecular-weight distribution) samples available to researchers. However, as the polypeptides are commercially available, perhaps a group of interested experimentalists could approach the U.S. National Bureau of Standards and request that such standard samples be made available. Dr W. J. Jackson (Eastman Koduk, Tennessee, U.S.A.) said: Prof. Lenz’s idea of quantitatively determining the ‘degree of liquid crystallinity’ is a very intriguing concept, and it certainly would be a very useful measure to have. In his preprint he suggested determining the degree of liquid crystallinity by measuring the area of the d.s.c.endotherm which occurs at the transition from the liquid-crystalline to the isotropic state upon heating (and the area of the exotherm which occurs at the transition from the isotropic state back to the liquid-crystalline mesophase upon cooling). Thermotropic, liquid-crystalline polyester plastics and fibres which have the highest tensile strength and stiffness contain only a limited amount of a flexible component or kinking component ;l consequently, the temperature at which the transition to the isotropic state occurs is appreciably higher than 400°C, which is above the thermal stability limit of all polyesters.Even if the d1s.c. thermogram is obtained at a high scan rate to minimize thermal decomposition, to the extent that decomposition does occur, the quantitative aspect of the determination is lost. Broad-line n.m.r. spectra obtained on melts often provide a basis for determining the amount and type of material in each phase of two-phase isotropic/anisotropic melts, and this could be a better approach to the determination of the degree of liquid crystallinity. Prof. Lenz showed an example of this type of data which was obtained by Dr V. A. Nicely of the Eastman Chemicals Division from examination of PET/p-hydroxybenzoic acid copolyesters. When sufficient information is avail- able to show that the narrow line is due to an isotropic melt and that the broad line is due to an anisotropic melt, the broad-line n.m.r.spectrum provides a direct measure of the amount of liquid-crystalline phase or, in effect, of the degree of liquid crystallinity. (Dr Nicely plans to submit further data and interpretation to Macromolecules ; his earlier publication2 describes the determination of the broad- line n.m.r. spectra.) ’ W. J. Jackson Jr, Br. Polyrn. J., 1980, 12, 154. F. E. McFarlane, V. A. Nicely and T. G. Davis, in Contemporary Topics in Polymer Science, ed. E. M. Pierce and J. R. Schaefgen (Plenum, New York, 1977), p. 109. Prof. R. B. Blumstein (University of Lowell, U.S.A.) said: I also turn to Prof. Lenz. Concerning your discussion of copolymers of linear mesogenic with non-linear non-mesogenic repeating units, let me suggest that reference to ‘degree of liquid crystallinity’ might be misleading inasmuch as it implies a conceptual analogy with ‘degree of crystallinity’ as applied to semi-crystalline polymers.Discussion of the nematic-isotropic biphase in copolymers is complicated by simultaneous presence of chain length polydispersity and heterogeneity of composi- tion. In the specific instance of your P/ M copolymers (p. 3 l), irreversible rearrange- ment to block sequences upon thermal treatment during lengthy experiments such as broad-line n.m.r. (which you use to estimate the fraction of isotropic phase88 GENERAL DISCUSSION present) cannot be excluded and may further complicate matters. Thus it might be difficult to distinguish between an N+ I biphase due to selective partitioning of chain lengths between the isotropic and anisotropic components' and microphase separation due to blockiness.In our investigation of nematic homopolymers with flexible spacer groups we have observed a broad N I biphase in polydisperse samples of molecular weight up to ca. 5000-6000. As M, increases, the biphasic range shrinks to a width of ca. 7-8 O C 2 The width of the N + I biphase and fN, the fraction of nematic phase present, can be measured by broad-line n.m.r. experiments.192 Comparison of n.m.r., d.s.c. and microscopy data indicates that the width of the d.s.c. peak gives a reasonable first approximation of the N + I biphase width, which microscopy tends to underestimate, especially in situations where trailing of a relatively minor isotropic component is ~bserved.~ As for copolymers, they usually show very broad phase transitions compared with homopolymers of similar M,.This might explain the problems which you encounter in observing d.s.c. transitions of your P/M copolymers. The magnitude of the d.s.c. peak area should not be used to estimate the 'amount of nematic phase', as the enthalpy at the N/I transition is merely indicative of the degree of nematic order present in the system. This is illustrated by the well documented instances of odd-even oscillations of nematic order, with concomitant odd-even oscillations of AHNI. Copolymers display a degree of nematic order and a value of AHNI that are dependent on composition. My second question concerns your interesting observation of spontaneous homeotropic alignment in polymers I1 (n = 2-4) in table 1 of your paper.You do not report the molecular weight of these samples. Have you investigated the influence of molecular weight on occurrence of homeotropic alignment? In our experience with the nematic series and twin model compounds with central spacers (rigid-flexible-rigid sequence; n up to 18) we have observed spontaneous development of homeotropic regions in samples having M, values up to ca. 5000-6000. For higher values of a,, textures with dense disclination lines develop, and homeotropic alignment is no longer observed. ' F. Volino, J. M. Alloneau, A. M. Giroud-Godquin, R. B. Blumstein, E. M. Stickles and A. Blumstein, Mol. Cryst. Liq. Cryst. (Lett.), 1984, 102, 21. R. B. Blumstein, E. M.Stickles, M. M. Gauthier, A. Blumstein and F. Volino, Macromolecules, 1984, 17, 177. R. B. Blumstein, 0. Thomas, M. M. Gauthier, J. Asrar and A. Blumstein, in Polymeric Liquid Crystals, ed. A. Blumstein (Plenum Press, New York, 1985), p. 249. Prof. A. Blumstein (University of Lowell, U.S.A.) said: It is interesting that in the series of polymers 11, i.e. endowed with an oxyethylene spacer, the increase in n produces a change in the mesophase from smectic to nematic. This is the reverse of the usual trend in alkyl spacers, in which an increase in the number of methyleneGENERAL DISCUSSION 89 groups, n, produces a change from a nematic to a smectic mesophase. Can this unusual observation be explained? Could it be due to the fact that n is an average value and that the polymers are not fractionated? Dr R.Zentel (University of Mainz, West Germany) said: I turn to Prof. Lenz. In your talk you used the term ‘degree of liquid crystallinity’, and I would like to comment on this. As far as I know, there is nothing like this in liquid-crystalline side-chain polymers and in main-chain polymers with small molecular weight distributions and without chemical inhomogeneities due to different copolymer compositions, except for a small temperature region at the nematic-isotropic transi- tion. However, if one is working with liquid-crystalline main-chain copolymers one often finds biphasic regions over a very broad temperature range. In my opinion this is due to the broad molecular-weight distribution and the chemical inhomogeneity in these multicomponent systems, and has nothing to do with partially crystalline polymers, for which motions are frozen in and one cannot reach equili- brium.Therefore it would be better to use the expression ‘volume fraction of nematic phase’ or something like this to explain your results instead of ‘degree of liquid crystallinity’. Prof. E. T. Samulski (University of Connecticut, U.S.A.) said: I wish to make two points about the use of the term ‘degree of liquid crystallinity’ in the characteriz- ation of the apparent two-phase regime reported for many thermotropic polymeric liquid crystals. (1) Nematics only‘differ from isotropic fluids by the subtle, long- range, orientational order [ extending over many hundreds of thousands of molecules (monomers) in a homogeneous ‘domain’] imposed on the fluid mesogenic units.(2) At a fixed pressure and temperature, Gibbs tells us that a single-component material may exhibit only one phase. The first point suggests that defects in the primary structure of the polymer backbone (‘non-mesogenic segments’) could not be excluded from the liquid crystal (as they might be excluded from a single crystal) because of the rather mild orientational constraints of a nematic environment compared with that of a single crystal and because of the dimensional scale of a nematic domain (i.e. a single chain with defects would not span typical macroscopic domain dimensions). Therefore, the second point implies that thermotropic polymers exhibiting multiple phases must be composed of ‘sufficiently different’ species, i.e.high polydispersity and/or primary structures of distinctly different chemical compositions. In short, the so- called degree of liquid crystallinity is merely a coarse indicator of sample purity. One might obviate this problem by centrifuging a sample in the two-phase regime and examining the behaviour of the separate components, exploiting the mesophase’s natural tendency to fractionate chains according to molecular weight. In a sufficiently pure fraction, a first-order phase transition at a well defined temperature should be exhibited on heating and cooling thermotropic polymeric liquid crystals, as is found in their monomeric precursors. Prof. W. R. Krigbaum (Duke University, U.S.A.) said: Prof. Samulski has indi- cated that the Gibbs phase rule does not permit coexistence of the nematic and isotropic phases over a range of temperatures.This statement assumes that a polymer can be treated as a single component, despite its molecular-weight heterogeneity. This would be true if the properties of interest were independent of molecular weight. However, the melting and clearing temperatures of nematogenic polymers are observed to increase rapidly for low molecular weights and eventually to reach90 GENERAL DISCUSSION plateau values at higher molecular weights. Hence a polymer can be treated as a single component only if its molecular weight distribution is quite narrow or its average molecular weight is sufficiently high such that species of low molecular weight are present in negligible amounts.The average molecular weight plays another important role in nematogenic polymers. One frequently finds the homeotropic texture in samples of low molecular weight, while higher-molecular-weight samples of the same polymer exhibit a planar texture. Since formation of the homeotropic texture involves anchoring of the chain ends to the glass surface, this difference probably arises from the higher number density of chain ends in polymers of low molecular weight. Prof. P. J. Flory (Stanford University, U.S.A.) said: The nematic domains in a liquid-crystalline polymer should not be regarded as equivalent to the crystalline regions in a semicrystalline polymer or copolymer. In the first place, nematic domains are liquid rather than solid, and the molecules therein partake of the mobility characteristic of a liquid, apart from their axial orientation. Moreover, the stringent requirements of exact registry between a molecule and its neighbours in the crystalline state are inoperative in a nematic. For these reasons, the sizes of liquid-crystalline domains are typically very large in all directions, unlike submicro- scopic crystallites, whose extensions in space are severely restricteb by kinetic factors that control crystal growth. The distinction is most striking in the case of a copolymer, the co-unit of which is rejected by the crystalline phase comprising the rigid, or crystallizable, units.In the liquid-crystalline state, on the other hand, the co-units are not rejected and hence may be interspersed with the rigid member units of the polymeric molecules.Such intermixing is implicit in the liquid nature of the nematic and cholesteric states. On another matter, the coexistence of nematic and isotropic phases over a finite range of temperature is unambiguously indicative of a plurality of components, as follows from the phase rule. The comparatively broad biphasic ranges for the copolymers reported in this paper may reflect polydispersity in molecular weight or in composition. If the length of the chain is very great, a purely statistical variation in composition should be quite small and, hence, insufficient to promote the frac- tional partitioning of molecules between the coexisting phases that would be required to account for the biphasic gap. Dr H. J. Coles ( University of Manchester) said: In his paper Prof.Lenz mentions the concept of 'degree of liquid crystallinity' which seems to be related to the occurrence of two-phase regions above the melting point, T,, of the polymers. Is this a new concept particular to these main-chain polymer liquid crystals or is this a manifestation of distribution in size of the polymers he is studying? In the latter case, low-molecular-weight components would be expected to undergo a transition to the isotropic phase at much lower temperatures than the high-molecular-weight components, and this could explain the existence of the biphasic regions reported. Dr A. H. Windle (University of Cambridge) said: Prof. Lenz has presented data which he has interpreted as showing that there are two phases in a 60/40 random copolymer of PHB/PET, one of which is isotropic and is present in gradually increasing proportions over the approximate temperature range 125-400 "C.We have looked at copolyesters of this composition (Tennessee Eastman X7G) using hot- stage microscopy and are not able to confirm his proposal.' Fig. 1 shows a summary of the phases observed as a function of temperature. The mesophase and isotropic91 4 20 3 50 340 9 \ h 190 GENERAL DISCUSSION sanple optically isotropic development of optically isotropic phase nucleation of isotropic phase continuous Schlieren texture interrupted Schlieren texture onset of mobility ? 20 T Fig. 1. Diagram of phase stability regions of 60/40 PHB/PET determined by hot-stage microscopy and d.s.c.' phase do indeed coexist, but only within the temperature range 350-400°C.The endotherm corresponding to the transition is also confined within this temperature range. At lower temperatures, in samples which have been held in the liquid state for sufficient time to produce a coarser texture, two phases can be observed, but they are both optically anisotropic. Plate 1 shows such a microstructure at 150 "C. The phase within circular boundaries (the 'ring' structures of Mackley et aL2) is the first to become isotropic, but not until 350°C. ' C. Viney and A. H. Windle, J. Muter. Sci., 1982, 17, 2661. ' M. R. Mackley, F. Pinaud and G. Siekmann, Polymer, 1981, 22, 437. Dr G. R. Mitchell (University of Reading) said: I would like to comment upon the evidence presented by Prof. Lenz, and in particular the n.m.r.results, to support his notion of a two-phase structure in the rigid-chain thermotropic copolyester of hydroxybenzoic acid and poly( ethylene terephthalate). This copolymer exhibits a number of transitions as revealed by thermal analysis.' At ca. 190 "C the optical textures become mobile, while below that temperature the material is solid and immobile on a 1 pm scale, although dielectric measurements292 GENERAL DISCUSSION indicate significant segmental motion. The long-axis orientation parameters have been measured using wide-angle X-ray scattering techniques described el~ewhere.~ Up to temperatures of 230°C there is no significant reduction in the long-axis orientation parameters, the orientation parameter (P2) is ca. 0.6. Above 250 "C the global long-axis orientation is rapidly lost, although of course locally the material is aligned as seen in the birefringent textures.The detailed optical microscopy on the HBA/PET copolyester described by Viney et al.' shows that optically an isotropic component is not observed until temperatures above 350°C. On cooling, this component transforms back to a liquid-crystal phase. In fact Viney et al. were only able to retain an isotropic component at room temperature by extremely rapid cooling of very thin samples, and even then the isotropic component existed only at the edges of the slice. We have also performed broad-line n.m.r. spectroscopy on the melt-extruded pellets and the detailed results of this are recorded el~ewhere.~ We have measured the second moment of the absorption curve both as a function of temperature in the range -150 to 200 "C and as a function of y, the angle between the extrusion direction and the magnetic field vector of the spectrometer. The use of aligned samples is particularly useful for discriminating between the different possible motions in the material.5 Fig.2 shows some of the results of these experiments taken from ref. (4) and some more recent unpublished work.6 As the temperature increases from -150 "C, there is a general drop in the values of the second moments for all three y values shown. There is a more rapid drop for y = 45 and 90 " in the region of 50"C, which we may associate with the glass-like transition observed in the thermal-analysis curves. This 'motional' narrowing of the n.m.r.absorption peak arises from two sources. The first is the interchain proton interactions, which are anisotropic in n a t ~ r e . ~ The second, which is the more substantial contribution, arises from intrachain proton interactions. There are two types of protons in the HBA/PET chain which are, however, sufficiently widely separated in terms of distance to allow them to be considered as non-interacting independent units in relationship to the broad-line n.m.r. spectrum. Thus the protons may be separated into those of the phenyl group, and those of the -CH2-CH2- linkage. The interproton vectors within the phenyl units which make a significant contribution to the absorption spectra are parallel to the chain direction. If rotation of the chain, or of a particular phenyl group, occurs, since its rotation axis is parallel to the proton-proton vector, these rotations will not lead to any substantial motional narrowing.On the other hand, rotation of the chain or the -CH2--CH2- linkage will have a considerable effect upon the proton-proton vector, magnetic field vector angle, which will result in motional narrowing. Thus the reductions in the second moments with temperature are greatest for y = 45 and 90 ", and results from the loss of interchain interactions, and from the mobility of the ethylene linkage. This is not to say the motion of the aromatic rings does not take place, but simply it does not seriously affect the width of the absorption peak. In fact, model calculations4 show that at 200"C, the second moments approach the values which relate to the phenyl contribution alone, indicating considerable mobility of the ethylene com- ponent.That match also confirms that there is no significant motion of the chain about an axis not parallel to the chain direction. This is expected in view of the X-ray orientation measurements described above. In fact, if we cool the n.m.r. sample from 200 "C back down to - 150 "C, we recover the same second moments measured previously. This indicates that there has been no change in the orientation of the molecular chains, and that the reduction in second moments arose purely from rotations of segments or chains about the chain axes.GENERAL DISCUSSION 93 08 O oQoo 0 - 0.20 - 0.15 rn f - 0.10 .. - 0.05 0 B 0 I I I I , GI -100 0 100 200 T / "C Fig.2. Temperature dependence of the observed second moments (AH2) of the broad-line n.m.r. absorption peak for melt-extruded pellets of the random copolyester HBA/ PET (60/40) measured at y = 0" (0), y = 45 O (0) and y = 90 O (0). y is the angle between the extrusion axis and the magnetic field vector of the spectrometer. The right-hand axis corresponds to the measured mobile fraction f (D), which was independent of y. The measured molecular orientation parameter (from wide-angle X-ray scattering measurements3), { P2), is ca. 0.65. There is a further observation from the n.m.r. results which Prof. Lenz drew attention to, and which is displayed in fig. 2. I refer to the resolution-limited narrow component which appears in the absorption spectra above 130 "C. This is plotted as solid squares in fig.2, and these points refer to the right-hand axis of the plot, where f is the fraction of the absorption curve which relates to this narrow com- ponent. Prof. Lenz interpreted this narrow component as arising from an isotropic component, and hence f in his terms is equated to the fraction of the copolyester in the isotropic phase. I would like to propose an alternative interpretation which is more consistent with the optical microscopy, X-ray scattering analysis and dielectric measurements. Let us assume that the narrow component of the n.m.r. signal does relate to an isotropic component. Since, if we reduce the temperature, the narrow component is lost, it is clear within the above assumption that the isotropic phase transforms to a liquid-crystalline form.This re-formed liquid-crystal material would then have a range of preferred molecular orientations, since it will have lost the memory of the original melt-extruded direction. Under those circumstances we would expect a substantial change in the measured molecular orientation since we would have at least 20% of the material (fig. 2) randomly disposed throughout the sample. No such changes are observed either using quantitative X-ray analysis of the molecular orientation at the elevated temperatures or from n.m.r. or X-ray measurements made at room temperature or below. We suggest that the narrow component does not arise from an isotropic com- ponent. Instead, it is suggested that the narrow component corresponds to the increasing liquid-like motion of the ethylene linkage at temperatures above 130 "C, prompted by the relative freedom of motion of the -0-CH2-CH2-O- linkage.Note that for the 60/40 composition of the HBA/PET compolymer some 28% of the relevant protons reside in this linkage. It would seem that the strong interactions94 GENERAL DISCUSSION between the aromatic components maintain the long-axis orientation while the ethylene linkage has almost liquid-like freedom. This mobility facilitates changes in the rotational configurations of the chains (with respect to rotational correlations), and it is these rotation motions which are related to the mobility of the optical textures observed at ca. 190 0C.1,5 The high mobility of the ethylene linkages occurs within the framework of a liquid-crystal phase and simply reflects the configurational freedom of those subchains, despite a measure of constraint from their connection to the relatively static aromatic components.Thus it is not necessary to invoke an isotropic phase to account for the n.m.r. results reported here and el~ewhere,~ and this interpretation has the utility of being consistent with the other wide-ranging experimental data available. However, it is also appropriate to present a caution concerning the consistency of the material. The results reported here are all for material from one batch of the copolyester supplied by Eastman Kodak. There are obvious possibilities that the molar mass distribution, the distribution of monomer units within the chain (which for materials used in this study were shown to be r a n d ~ m ) ~ and the levels of impurities or side-products, may vary from batch to batch, and thus could account for variations in experimental results.' C. Viney and A. H. Windle, J. Muter. Sci., 1982, 17, 2661. Y. Takase, G. R. Mitchell and A. H. Windle, Polym. Commun., in press. G. R. Mitchell and A. H. Windle, Pol-vmer, 1983, 24, 1513. G. R. Mitchell and F. Ishii, Polym. Commun., 1985, 26, 34. V. J. McBrierty, Polymer, 1974, 15, 503. F. Ishii and G. R. Mitchell, unpublished work. ' G. R. Mitchell and A. H. Windle, Polymer, 1982, 23, 1269. Prof. R. W. Lenz ( University of Massachusetts) (communicated): I am grateful to questioners for their interest in my paper and respond to them as follows. ( 1 ) First Dr Jackson: I agree that the quantitative interpretation of the d.s.c.endotherm can only be applied to a copolymer which has its isotropization temperature well below its degradation temperature. Therefore, this approach would not apply to the 60/40 copolymer of p-hydroxybenzoic acid and ethylene terephthalate units which is referred to as X7G by the Eastman Kodak Company and which has a value of T well above 350 "C. However, we have other copolyesters containing both mesogenic and non-mesogenic groups which have Ti transitions well below their thermal decomposition temperatures. (2) Secondly Professors R. B. and A. Blumstein: In your application of n.m.r. spectroscopy and d.s.c. to the determination of the nematic phase within the N + I biphase region, could you not be observing two effects, the decrease in order within the nematic phase and the formation of the separate isotropic phase? The d.s.c.endotherm should contain information on both of these contributions. Similarly, for our copolymers, we believe that the visual observations of a non-birefringent phase with a polarizing microscope correlates with the smaller d.s.c. endotherm of the T, transition, and both indicate that we also have biphasic behaviour over the entire temperature range between T, and T for such copolymers. The anisotropic phase may also be of lower order in our copolymer systems, as you suggest, and that could also contribute to the smaller endotherms for copolymers containing increasing amounts of non-mesogenic units. With regard to your second point, I must say, no, we have only observed this effect on one sample of the polymer, which most likely had a molecular weight wellGENERAL DISCUSSION 95 below 10000.We intend to study the homeotropic orientation of these polymers much more carefully in the future. Finally in this section I confirm to Professor R. B. Blumstein that the polymers in this series in which n had values of 1 , 2 , 3 and 4 were prepared from pure glycols of those compositions, not from oligomeric glycols. You will note that we used the same aromatic ester triad for the mesogenic groups in this series as we did for the series with the polymethylene spacers. In the latter case we did not observe a simple change from nematic to smectic phase formation with increasing number of methyl- ene units.Instead, we observed an odd-even effect in which the polymers with n = 4 and 6 formed nematic phases, while those with n = 3, 5 , 7 and higher formed smectic phases. (3) Thirdly Dr Zentel: The degree of crystallinity of copolymers is determined by their chemical heterogeneity, which is apparently also responsible for the formation of two phases in our copolymers, which contain both mesogenic units and non-mesogenic units. That is, we suggest that the isotropic phase contains copolymer chains which have either larger amounts or longer sequences of non-mesogenic units. On this basis, your term ‘volume fraction of nematic phase’ and our term ‘degree of liquid crystallinity’ are not different in concept. (4) My response to Professor Samulski is the same as those above to Professor Blumstein and Dr Zentel.We are very much interested in doing exactly what you suggested, i.e. separating the isotropic and anisotropic phases for analysis. As Dr Jackson has pointed out, and as I mentioned in my presentation, in a sense that is what Dr Nicely has done by broad-line n.m.r. spectroscopy, which enables him to analyse the two phases independently. (5) Dr Griffin’s informal observation of the range of compositions in X7G is in agreement with Dr Nicely’s results, which I described and refer to above. The compositions of the isotropic and anisotropic phases, which he estimated by fast Fourier transform broad-line n.m.r. spectroscopy, differed considerably in oxyben- zoate content. The isotropic phase contained cu. 35 mol% oxybenzoate units, while the anisotropic phase contained ca.80molOh of such units. Dr Nicely intends to publish these results in the near future. (6) I turn now to Professor Flory’s remarks: I agree that crystallization is kinetically controlled, although by proper methods and data interpretation it is possible to estimate an equilibrium melting point if not an equilibrium degree of crystallinity. I also agree that the isotropization of a liquid-crystalline phase, and its re-formation from the isotropic phase, should be essentially equilibrium processes, and the lack of undercooling in deisotropization indicates that is so. However, as discussed above, we believe that the chemical heterogeneity of mesogen-non-mesogen copolymers can lead to the formation of a two-phase melt in which the anisotropic and isotropic phases can exist in equilibrium.(7) In response to Dr Coles: I would merely comment that I suggested the term ‘degree of liquid crystallinity’ in broad analogy to ‘degree of crystallinity’ to describe, in at least a semi-quantitative manner, a liquid-crystalline melt in which an isotropic phase can exist in equilibrium with a nematic phase, as discussed above for the reasons mentioned. I believe that the isotropic phase differs in composition from the nematic phase and not just in molecular weight, although the latter could contribute also. There is no doubt from96 GENERAL DISCUSSION our studies that such a biphasic behaviour can exist for certain types of copolymers, as indicated by a variety of experimental characterization methods, including polar- ized-light microscopy, d.s.c., broad-line n.m.r. spectroscopy, density, melt viscosity and small-angle light scattering.(8) I am grateful to Dr Windle for showing us his new results. We have also observed the presence of a second, apparently denser texture, region in samples of X7G by polarized-light microscopy. However, we could not see non-birefringent regions in the melt of this copolymer below 350 "C as we can with other copolymers containing non-mesogenic units. (9) Finally I turn to Dr Mitchell: I must emphasize that the broad-line n.m.r. results on X7G were not from our work but were given to me for review by Dr Vincent Nicely of the Research Division of the Eastman Kodak Company in Kingsport, Tennessee. However, in contrast to your conclusions, Dr Nicely was able to measure directly the composition of the narrow-line component, and he found that it contained substantial amounts of oxybenzoate units, as I discussed in my previous responses.Dr K. F. Wissbrun ( Celanese Corprution, N.J., U.S.A.) addressed Prof. Blum- stein: You report the interesting observation of the odd-even effect on both the order parameter and on the X-ray diffraction evidence for the occurrence of 'cybotac- tic domains'. I wonder whether this effect may not also extend to the rheology of your polymers. Looking at your fig. 2 (as well as at similar data that I have seen from your laboratory on higher-molecular-weight samples), it appears that the shape of the flow curve of DDA-9 shows a greater tendency to resemble the three-region behaviour proposed by Onogi and Asada than does that of the AZA-9 polymer. Also, the decrease in viscosity upon going from the isotropic phase to the mesophase is much greater for MA-9, which does not have cybotactic structure, than for DDA-9, which does.The question is then whether you think it likely that the same structural factors that lead to a high order parameter and to cybotactic domain structure may also be responsible for these apparent differences in rheology? I might add that we have observed in our laboratory some systematic differences in shapes of flow curves with variation of chemical structure of aromatic copolyesters, but have no explana- tion for these observations at this time. Prof. A. Blumstein (University of Lowell, U.S.A.) replied: Your question is very interesting.It is difficult to answer it from the data provided in our fig. 2 because the comparison here is made between unfractionated samples of DDA-9 and frac- tionated samples of AZA-9 of similar Mn. Very recent measurements of q*(o) over the range'l0 d O / O S lo2 were performed on fractionated samples of DDA-9.' The results'indicate that the high degree of shear sensitivity of DDA-9 shown in fig. 2 of our paper is due mainly to the polydispersity of DDA-9, albeit that a larger, shear dependence for DDA-9 is still present for fractionated samples. The viscosity difference between the isotropic and the nematic states is larger for DDA-9 than for MA-9 of similar molecular mass, and not vice versa. The shapes of the q * ( o ) curves for DDA-9 and AZA-9 appear very similar for 1 0 lo2.The conclusions from our very limited study of sharp fractions of AZA-9 and DDA-9 is that, taken as a first approximation, both polyesters behave in a similarGENERAL DISCUSSION 97 way. Small differences such as a increased shear sensitivity of DDA-9 and a lower viscosity increase at the N/ I transition are apparent. Whether these differences are significant enough to be due to the structural differences between DDA-9 and MA-9 can only be answered with many more measurements performed on well fractionated and well characterized samples. ' A. Blumstein, 0. Thomas and S. Kumar, J. Polym. Sci., Polym. Phys. Ed., in press. Dr H. J. Coles (University of Munchester) said: In table 1 of Prof.Blumstein's paper the biphasic range is given as a function of the length, n, of the flexible spacer. An interesting feature of these data is the odd-even alternation of both the width of the biphasic region and the order parameter, S,. A wide biphasic region is synonymous with a high order parameter, and this is an extremely important obsermtion for polymer liquid crystals. Does he have any further experimental evidence to link the width of the biphasic region in these materials to their distribution in size with changing n? Prof. A. Blumstein (University of Lowell, U.S.A.) replied: We do have some limited additional experimental evidence (p.m.r.) that even sharp fractions of DDA-9 ( n = 10) when compared with sharp fractions MA-9 ( n = 7 ) display a larger width of the biphasic region.A thorough exploration of this question is important and is under way in our laboratory. Prof. E. L. Thomas (University of Massachusetts, U.S.A.) said: It is interesting to note the appearance of both smectic and nematic order in the various flexible- spacer thermotropic liquid-crystalline polymers materials such as those synthesized by Profs. Blumstein and Lenz. Various researchers have now reported the dependence of liquid-crystal type on such variables as spacer length and temperature. As is indicated in the published work of Dr Noel,' the identification of the type of liquid-crystal phase of a polymer is a difficult task. Moreover, the papers at this Discussion by Windle et al. and by Blackwell et al. underscore the need for carefully addressing the degree of axial shift ciisorder in liquid-crystalline polymers.There- fore, I would like to emphasize a point here that is made in our later contribution, namely a continuous spectrum of liquid-crystal states of increasing axial registration are possible between the axially disordered nematic and axially ordered smectic states. Fig. 3 of our contribution presents idealized scattering from a nematic, a smectic and a hybrid liquid-crystalline structure with partial axial registration over finite lateral regions. One may view a general smectic polymer structure as one in which the direct correlation2 between chains is given by two terms: (i) a liquid-like correlation in the lateral direction and (ii) a finite (non-zero) correlation in the chain axis direction.I.e. the structure could be treated as two-dimensional liquid in the lateral direction and a one-dimensional crystal in the axial direction. If the correlations in the lateral and axial directions are independent, then the direct correlation function C(r, z) may be given by a product of the lateral and axial correlations in which the lateral correlation is, for example, the hard-disc correlation function CHD(r), and the chain axis correlation is a gaussian distribution of finite width A, analogous to the type I1 disorder in crystals.3 Thus98 GENERAL DISCUSSION Fig. 3. Schematic intensity distribution in normal-beam photograph of cybotactic nematic (after de Vries). The magnitude of A determines the nature of the phase, with A = O the ideal smectic and A = a0 the ideal nematic as limits to the continuous distribution. ‘ C.Noel et al., Polymer, 1984, 25, 1281. * As defined by L. S. Ornstein and F. Zernike, Roc. Akad. Sci. (Amsterdam), 1914, 17, 793. Y. Cohen, R. Saraf and E. L. Thomas, Mol. Cryst. Liq. Cryst., in press. Prof. A. Keller ( University of Bristol) commented: Prof. Thomas has just presen- ted a classification of the different states of mesomorphic order to rationalize some of our present definitions. I am puzzled as to where the ‘nematic cybotactic’ fits in. Or rather, why is it necessary to invoke a category under this name? I would have thought that by Prof. Thomas’ criteria the ‘nematic cybotactic’ would fall in the appropriate subgroup of the smectic family. Prof. E. L. Thomas ( University of Massachusetts, U.S.A.) responded: The charac- teristic feature of the so-called cybotactic nematic structure is the set of four low-angle reflections tilted with respect to the molecular axis in the X-ray scattering pattern from a uniaxially aligned sample (see fig.3). deVries’ recorded such patterns from small-molecule liquid crystals and proposed that the molecules are organized into groups which have all the ends of the molecules lying in planes at a large angle to the molecular axis. Azaroff2 criticized de\-’ries’ model and proposed instead a structure consisting of parallel sheets of tilted layers of molecules. I believe Prof. Blumstein’s cybotactic nematic structure is a version of the deVries model adapted for rigid/ flexible thermotropic liquid-crystal polymer molecules.All these proposed models could be classified in the family of smectic liquid-crystal structures. ’ A deVries, Mol. Cryst. Liq. Cryst., 1970, 10, 219. L. V. Azaroff, Roc. Natl. Acad. Sci. USA, 1980, 77, 1252. Prof. A. Blumstein (University of Lowell, U.S.A.) said: I also would like to respond to Prof. Keller because he posed a good question bearing on the discrepancy between the mesophase assignment based on crystallographic models and miscibility experiments accepted as criteria for mesophase assignment. There is definitely a difficulty to overcome in reconciling the model of a nematic cybotactic suggested by the SAX diffraction pattern’ and the miscibility criterion put forward by Arnold and Sackmann.2 Cybotactic nematic has been so named because of its complete miscibility with other nematic systems and only partial miscibility with smectic A or smectic C systems.The polymer DDA-9 is totally miscible with AZA-9 and PAA, which are classical nematics. ’ A. deVries, Mol. Cryst. Liq. Cryst., 1970, 10, 219. * H. Arnold and H. Sackmann, 2. Phys. Chem., 1960, 213, 137.GENERAL DISCUSSION 99 Prof. F. C. Frank (University of Bristol) said: The lateral correlation length in a smectic is in any case in principle non-infinite. A non-infinite length may be long or short, but that affords no sharp distinction. The cybotactic nematic structure, as described, falls within the class smectic C, and is not a sub-class of nematic structure. Perhaps it is useful to have some way of saying it is nearly nematic, but for purposes of phase classification I think ‘cybotactic nematic’ is a term which can be dispensed with.Prof. E. T. Samulski (University of Connecticutt, U.S.A.) said: Dr Yoon’s paper marks a significant step toward an understanding of the conformational constraints imposed on semiflexible polymers in liquid-crystal phases. However, I do have some reservations about the ability of n.m.r. data to confirm unambiguously that the spacer conformers of odd-parity alkyl chains are limited to those that place every second bond exclusively in the trans state. While the authors give thermody- namic arguments consonant with these conclusions, I am uncomfortable with the highly constrained spacer proposed for this fluid state. Could Dr Yoon alleviate some of my discomfort by commenting on the following: The ‘linewidths’ (ca.7 kHz) of the polymer deuterium n.m.r. spectra (fig. 7 of the paper) are significantly broader than those encountered in monomer and dimer liquid crystals and there would appear to be evidence for unresolved quadrupolar splittings on the inner edges of the spectra. Note that spectra of the structurally related dimer and the same polymer mixed with a monomer liquid crystal show resolved splittings which would be masked by the reported linewidth (see fig. 4 of my Introductory Lecture). Such splittings, if present, would imply that the averaging of the C-H bond vectors relative to the nematic director is not the same at each methylene in the spacer, and thereby imply the existence of less severe conformational constraints, i.e. a gradient of spacer conformational freedom along its length. Prof. R. B. Blurnstein (University of Lowell, U.S.A.) said: It is apparent from fig. 7 and 10 in Dr Yoon’s paper that all the n.m.r. spectra were traced in the nematic-isotropic biphasic region. P.m.r. measurements carried out in the N + I biphase of polymer IV’-2 show that the temperature dependence of the mesogen order parameter is more pronounced in the biphasic region than it is in the homogeneous nematic phase. In contrast, Dr Yoon reports a nearly constant orientational order parameter of ca. 0.8 in the biphasic region, and I wonder whether he would comment on the seeming discrepancy between his data and our data on mesogen order in the N + I biphase. Also, both d.m.r. and p.m.r.data on alkyl chain flexibility in the homologous series described in ref. (3) indicate that in the homogeneous nematic phase the spacer disorders more rapidly than the mesogen. R. B. Blumstein, E. M. Stickles, M. M. Gauthier, A. Blumstein and F. Volino, Macromolecules, 1984, 17, 177. * F. Volino, J. M. Alloneau, A. M. Giroud-Godquin, R. B. Blumstein, E. M. Stickles and A. Blumstein, Mol. Cryst. Liq. Cryst., (Lett), 1984, 102, 21. A. Blumstein, M. M. Gauthier, 0. Thomas and R. B. Blumstein, Faraday Discuss. Chem SOC., 1985, 79, 33, and references therein. Dr D. Y. Yoon (IBM, U.S.A.) (communicated): The observation of Prof. Samulski concerning the asymmetric profile of our peaks in fig. 7 is correct. As he suggests, this implies the presence of less extended conformers.However, the extent of deviation to produce this asymmetric profile is small and thus does not affect the main conclusion of our paper. Concerning the seeming discrepancy between our100 GENERAL DISCUSSION results of the order parameter and those of Prof. R. Blumstein’s group, it is likely that both the temperature dependence of the order parameter near the istotropic - nematic transition and the magnitude of the order parameter are highly dependent on the molecular weights of the polymer. In this regard, I note that the average molecular weights of the samples used by Prof. Blumstein’s group (for p.m.r. measurements) are rather low. Dr R. Zentel (University of Mainz, West Germany) said: Dr Windle and his colleagues have found evidence for the existence of a biaxial orientation in the partially crystalline material, which is not surprising, because a lot of crystals are optically biaxial.However, they give no direct evidence for a biaxial orientation in the nematic phase, except for the conservation of the texture and of the orientation of the sample as I can see it. In my opinion this may be a simple paramorphism, whilst a biaxial nematic phase means that the rotations around the long axis of the liquid-crystalline polymers are still strongly restricted. This has nothing to do with a conservation of the orientation of the long axes. I would thus like to ask whether they have more evidence for a biaxial nematic phase. Dr G. R. Mitchell ( University of Reading) (communicated): Dr Zentel has raised doubts concerning the interpretation of the optical microscopy/ X-ray diffraction observations on rigid-chain thermotropic copolyesters presented in our paper and in particular, the relationship of the observations made at room temperature and their extension to the liquid-crystal phase.I would like to draw attention to the following points. The X-ray scattering patterns of these copolyesters recorded at room temperature (fig. 2 of our paper) show no evidence of crystallinity. Some results have been interpreted by others [ e.g. ref. (l)] as indicating a low level of crystallinity (ca. 10% ), although that figure and its derivation may also be open to question. However, even if that were the case, it does not offer a satisfactory and consistent explanation of the results presented in our paper and elsewhere.273 The optical textures observed are the same in their appearance throughout the sample; there are no features which may be interpreted as crystallites.The optical textures observed for the copolyesters upon heating through the softening point remain the same, other than it becomes m ~ b i l e . ~ If the optical textures and their biaxial properties arise from some crystal- linity as supposed by Zentel, then we would expect some particular change in the optical properties when these ‘crystallites’ melt out. No such change is ob~erved.~ Thus, even if there is at room temperature a small fraction of crystallites, they have no significant effect upon the optical observations and their interpretation. In that case, the biaxial optical properties of the copolyester samples at room temperature arise from an optically biaxial non-crystalline structure.The correspon- dence between optical textures and other physical properties above and below the softening point provide considerable evidence that the room-temperature structure is essentially a static version (frozen in) of the mobile liquid-crystal phase. It has been shown that for very thin samples it is even possible to quench in the isotropic phase observed at 420 “C for one of the copolye~ters.~ D. J. Blundell, Polymer, 1982, 23, 359. * C . Viney, G. R. Mitchell and A. H. Windle, Polym. Commun., 1983, 24, 145. C. Viney, G. R. Mitchell and A. H. Windle, Mol. Crysf. Liq. Cryst., in press. C. Viney and A. H. Windle, J. !dater. Sci., 1982, 17, 2661.Dr A. H. Windle ( University ofcambridge) said: What is the evidence for biaxial properties actually in the melt phase? Although many of our photographs have been taken at room temperature (one cannot use the highest-resolution objectivesGENERAL DISCUSSION 101 on the hot stage), there is an underlying observation that there is no change in microstructure at the solid-liquid transition. The lack of correlation between chain orientation and optical orientation, which is an important aspect of the case for biaxiallity, can still be seen above the solid-liquid transition, although in the case of polymer I (B-N) of our paper, the X-ray orientation relaxes over a minute or so. However, polymer 11, (B-ET), when held above its melting point of 190°C but below 250°C, retains X-ray orientation for several hours.In this case the fine Schlieren texture is mobile on a timescale of a few seconds even though the pre- ferred orientation of the chains has decayed little. This is shown in plate 2. We see these observations as yet further evidence for the lack of correlation between the optical extinction directions and the chain axes, and thus for biaxiallity. Another striking piece of evidence relevant to the same issue has recently been obtained by T. J. Lemmon using the microscope hot stage. Plate 3 is a series of micrographs of one of the phases of polymer I1 (B-ET). The included phase shows a fine Schlieren texture which is stable up to ca. 240"C, above which it begins to transform into a much simpler radial texture.The significant aspect is that the transition is reversible and, on cooling, the simple radial texture changes back into the fine Schlieren network. We were not successful in quenching-in the high-temperature form. We have here a reversible transition between two birefringent liquids. We believe the higher-temperature phase to be uniaxial nematic, which transforms to biaxial nematic on cooling, the development of the fine texture being a direct consequence of the reduction of symmetry. It is reminiscent of 'transformation' or 'multiple' twinning seen in crystalline materials at transitions such as cubic to tetragonal. In his oral question Dr Zentel also asked how we can make deductions on the hgstrom scale from observations made in the light microscope. Given that there is a priori evidence for molecules, then aspects of their behaviour can be inferred from macroscopic observation of physical properties.For example, birefringence can tell us about the first harmonic of the orientation probability function about a symmetry axis, ( P2), and discontinuities in optical properties can indicate rapid changes in orientation on a molecular scale. Furthermore, any observation of macroscopic symmetry will bear important information regarding the local correla- tions of molecular orientation. C . Viney, G. R. Mitchell and A. H. Windle, Mol. Cryst. Liq. Cryst., 1985, 129, 75. Dr K . F. Wissbrun (Celanese Corporation, N.J., U.S.A.) (communicated): Dr Windle's observations of the effect of temperature upon the timescales for microstruc- tural mobility and for loss of global orientation for the B-ET polymer are consistent with the effect of temperature upon the melt rheology of this polymer.' Above the ca.240°C d.s.c. endotherm the melt appears to be typically viscoelastic in nature, albeit with an unusually large relaxation time. However, below this endotherm the melt becomes progressively more solid-like, and eventually exhibits a yield stress. In agreement with Dr Windle's interpretation, we also believe that the 240-250 "C transition is the melting of small crystallites. X-ray diffraction data of fibres spun, annealed and measured at various temperatures support this interpretation and suggest that the crystalline phase is that of the hydroxybenzoate species. The presence of residual crystallites in the melt also explains qualitatively the change in rheology and activation energy of melt viscosity with temperature, and the pronounced effect of thermal history upon the shape of the flow curve and the magnitude of the viscosity.As to the B-N polymer, I would merely note that between ca. 280 and 310 "C there is also a pronounced discontinuity in the activation energy of the melt viscosity. Thermal-history dependence of the melt rheology suggests that the cause of this102 GENERAL DISCUSSION transition is, as in the B-ET polymer, melting of residual crystallinity. However, in this case we have no direct structural observations to support the conclusion. K. F. Wissbrun, Br. Polym. J., 1980 12, 163. Dr A. H. Windle (University of Cambridge) (contributed): Our data relating to timescales appear as plate 2 of this Discussion in our response to Dr Zentel's question. Certainly, d.s.c.traces on B-ET polymers of different compositions show that the small 250 "C endotherm appears and intensifies with increasing HBA content, and I agree it is tempting to associate it with minute reinforcing crystallites of this component. Regarding B-N, we find that the melting transition gives a broad endotherm at ca. 280°C for the 70/30 material, so we are not very sure that one should expect the material to be completely molten below 310 "C. There may well be a few residual crystallites of greater than average perfection still present at 3 10 "C. Prof. F. C. Frank (University of Bristol) said: I .am willing to agree that Dr Windle and his colleagues present evidence making it plausible and even persuasive (although not conclusive) that they have here examples of biaxial nematics: the strongest evidence, perhaps, being that if that is the case it helps one to understand the remarkable lack of observable correlation between chain orientation and optical orientation.On the other hand, I see no force in the quantitative interpretation and analysis of the optical properties put forward by these authors. Their analysis is dependent on two assumptions, one explicit and the other implicit. The implicit assumption is that orientation is uniform through the thickness of the specimen: in view of the small scale on which the optical pattern varies laterally, that is not very likely. The explicit assumption is that the chain orientation coincides with a principal axis of the optical indicatrix.I see no good reason for making that assumption, save when the indicatrix is uniaxial: both in B-N and in B-ET the lack of symmetry axes along the chain in any of the chain constituents makes that improbable (although pairing to produce an effective diad axis is not impossible). Consequently I place no reliance at all on the deduction of the angle between optic axes. Dr A. H. Windle (University of Cambridge) said: Sir Charles Frank points to two assumptions in our study of optical microstructures. The first concerns through-thickness variations in structure where the scale of the texture is of the same order as the thickness of the sample. Our optical analysis aims to relate the extinction orientations (crossed polars), observed at any position, to the principal axes of the in-plane section of the indicatrix representing the local optical properties.For this approach to be meaningful we need to assume that the optical orientation of any resolvable portion of the microstructure can be described by a single indicatrix. In terms of the samples which might be examined, there are obviously two extreme cases. In one, the presence of 'macro domains', within which the indicatrix orientation is constant, and having lateral extent much greater than the specimen thickness, would enable the assumption to be made without qfiestion. In the other extreme one can imagine the indicatrix orientation changing on a scale very much smaller than the specimen thickness.Light traversing the specimen will therefore sample a number o'f different indicatrix orientations, and it will be imposs- ible to relate its subsequent polarization state to any particular orientation within the microstructure. The issue seems to boil down to this: are we entitled to relate a fine-scale Schlieren texture such as that of plate 4 (thickness 2 pm) to particular variations in the optical orientation across the sample? We believe that the specimens are sufficiently thin for them to approximate satisfactorily to two-dimensional sections for the purposesGENERAL DISCUSSION 103 of our arguments. The criteria by which we assess that a section is sufficiently thin are as follows. ( a ) Every portion of the sample under examination shows full extinction at some rotation angle between the crossed polars, and this extinction is repeated with an angular period of ~ / 2 .Overlaid layers of different optical orientation will in general preclude full extinction at any rotation angle. (This aspect of the optical behaviour is discussed in greater detail by Dr Viney in a written communication below). ( b ) The dark regions of the microstructure form a resolvable pattern, which in the case of Schlieren textures, consists of dark bands which locally scan the specimen as the sample is rotated. Accord with both these conditions is lost when the sample thickness is increased in relation to the scale of the microstructure. Plate 5 shows a sample, melted on a glass slide, which changes abruptly in thickness from 2 to 8 pm.Similarly, plate 6 is a series of cut sections of increasing thickness prepared by Dr Viney. The loss of both ‘connectivity’ of texture and of contrast as the thickness is increased is apparent between crossed polars. Furthermore, the thicker samples begin to show contrast without the polars being present. This is presumably the result of selective loss of optical information at the back focal plane of the microscope, leading to phase contrast, this being more apparent in the thicker samples since they allow for a greater variation in phase from position to position. The second assumption concerns our estimate of the angle between optic axes. Our calculations of the relative proportions of dark areas visible in circularly polarized light, as a function of section angle [plate 3 ( c ) of our paper] for the biaxial cases ( i e .p # 0) are for the special geometry in which one principal axis of the indicatrix is parallel to the chain axis. We have not yet treated the general case, which for a biaxial indicatrix would require a further term (P,) in the product in the equation for P (page 62 of our paper). The term would be the magnitude of the harmonic function at x, which is the angle between the largest principal axis of the biaxial indicatrix and the local chain axis. We accept Sir Charles’ caveat on this point. Dr C . Viney (University of Cambridge) (communicated): Sir Charles Frank has drawn attention to the problems involved in interpreting textures in specimens whose thickness may be greater than the lateral distance over which molecular orientation changes significantly.In other words: can one be certain that the specimen is thinner than a ‘domain’ size, so that molecular orientation is roughly constant through the specimen thickness at any point? If, during microscopic examination of the specimen, light does follow paths along which the optical orientation changes, individual regions in the specimen will not show extinction between crossed polars. Either one can treat such paths as consisting of a series of layers having discrete optical orientations, or one may have to regard the optical orientation as varying continuously and sufficiently gradually for optical guiding to occur. In the former case, whatever the direction of polarisation of the wave incident on the bottom of the specimen, the light will always have been resolved into two vibration directions by the time that it reaches the top.Thus, the light emerging from the top surface of the specimen cannot be extinguished by an analyser, whether crossed relative to the polariser or not. The overall contrast in the observed texture will therefore be diminished, with individual areas showing four intensity minima and four intensity maxima per 360” rotation of the crossed polars.’ (One could of course obtain extinction in monochromatic light if the path difference of the two emergent waves corresponded to a whole number of wavelengths in the specimen. However, all our microscopy was performed in white light.)104 GENERAL DISCUSSION If, on the other hand, optical guiding is occurring, the vibration directions of the light change continuously as it travels upwards through the specimen.In this case, extinction can always be achieved by uncrossing the polars, provided that the incident light is polarised parallel to a vibration direction at the bottom of the specimen. However, extinction between crossed polars can only be observed in the particular instances when the optical orientation of the top of the specimen differs from that of the bottom by a multiple of 180". If sufficiently thin sections (G2 pm) of our specimens are viewed between crossed polars, it is observed that individual areas show 4 extinctions per 360" rotation of the crossed polars, so one can be confident that there is no significant change in optical orientation through the specimen thickness in this case.A question related to that asked by Sir Charles Frank is whether light, in passing through our thin specimens, encounters optical discontinuities (refractive-index changes) which are severe enough to deviate light from travelling parallel to the thin direction of the specimens. If this were the case, some areas of the specimen might appear dark simply because there is no light emerging there. However, the light which was refracted away from the specimen normal must be expected to emerge somewhere else. After being deviated from its original path, it will have encountered sections of optical indicatrix which are not representative of the specimen plane. Such light has in effect followed a path along which changes in optical orientation have occurred.Therefore, the area where it emerges will not show extiiiction, in accordance with the arguments given earlier. Our thin specimens (e.g. plates 1 and 2 in our paper) do not contain any areas which never show extinction. The textures should therefore be a direct and reliable indication of the optical orientation in these specimens. ' C. Viney, G. R. Mitchell and A. H. Windle, Mol. Cryst. Liq. Cryst., 1985, 129, 75. Prof. F. C. Frank (University of Bristol) (communicated): To Dr Viney: Resolution of a wave into two conjugately polarized waves (e.g. two plane-polarized waves with crossed planes of polarization, or two oppositely cir- cularly polarized waves, or waves in any other two states of polarization represented by diametrically opposite points on the Poincark sphere) is not a physical phenomenon, but a mathematical operation performed by the physicist to help him understand the physics.To Drs Viney and Windle: All possible states of plane polarization for the input light are represented on the Poincari sphere by points on the equator, and if the polarizer is turned at uniform angular velocity the representative point travels round the equator at twice that angular velocity, making an excursion of 360" while the polarizer rotates through 180". The effect on the light of a plane-parallel slab of birefringent material, of thickness h, and strength of effective birefringence Anl, is to rotate all representative points on the Poincark sphere by an angle w1 (proportional to hlAn,) about an axis represented by the unit vector I , .I , lies on the equatorial plane: +Il corresponds to the major and -Il to the minor principal axes of effective birefringence. The resulting states of polarization are represented by a great circle inclined by w1 to the equator, and intersecting the equator at two points, representing plane polariz- ation: one at + I , corresponding to the input polarization and the other at - l , , crossed with respect to the input polarization. For uniform rotation of the polarizer the representative point travels uniformly round the inclined great circle, with twice the angular velocity as before.GENERAL DISCUSSION 105 A second birefringent layer effects a second rotation w2 about a second axis 1,.The orbit of representative points becomes another inclined great circle, around which the representative point travels uniformly for uniform rotation of the polarizer. However, if 1, differs from ll the orbit no longer crosses the equator at either of the points lI or 12. With any further increase in the number of birefringent layers, each effects successive rotations which transform the great circles into great circles and preserve the uniformity of orbital motion around them. The orbit therefore always crosses the equator at two points (unless it totally coincides with the equator). The crossing points are 180" apart on the equator, and also on the orbit. There are thus in any 180" rotation of the polarizer two settings producing plane- polarized light, and therefore capable of being extinguished with an analyser.These polarizer settings are 90" apart, and so are the corresponding analyser settings for extinction; however, the polarizer and analyser settings are in general not 90" apart, in distinction from the case of the single homogeneous birefringent layer. The theory applied here is not exact, making no allowance for back-reflected waves, but the italicized results are topologically robust, and are insensitive to small errors: they disagree with the second sentence of point ( a ) in Dr Windle's response. Let the rotations (1, w ) be represented by their Rodrigues vectors R = 1 tan ( w / 2 ) . Suppose that in a particular case both they and their cumulative resultant rotations are small (note that this does not preclude the angle between different axes li and l j being large).Then since the rule of combination of Rodrigues vectors representing successive rotations is the correction terms for non-commutativity remain of the second order of smallness. Since all the vectors Ri lie in the equatorial plane, then within second-order errors so does their resultant. The orbit becomes moderately inclined to the equator, a first-order effect, but there is negligible displacement of points around the orbit. This behaviour is indistinguishable from that of a single birefringent layer, giving extinction at the appropriate two settings in a 180" rotation between crossed polarizer and analyser. Here we have an important class of examples of inhomogeneous structures which would pass the test which Windle and Viney regard as a test for homogeneity.The theory employed above is a single-beam theory. If beams traversing different paths in the specimen are observed together they will not in general reach extinction conditions simultaneously, and may not have the necessary coherence to produce a joint extinction. When the observation is made microscopically beams in several directions are necessarily employed. If the inhomogeneity is not in the form of parallel layers as assumed above we shall have refractions with ordinary and extraordinary rays following deviant paths; scattering can give rise to more widely deviant independent paths by which light reaches a particular point in the image. Minima of intensity rather than perfect extinctions are therefore always to be expected: generally speaking, the more so the thicker the specimens.Dr C: Viney and Dr A. H. Windle ( University of Cambridge) (contributed). First, is the presence of two waves having crossed planes of polarisation a mathematical convenience or a physical reality, when light travels through a linearly birefringent medium? The only simple plane-polarised harmonic waves which can describe an optical disturbance within an anisotropic medium are those for which the wavevector106 GENERAL DISCUSSION k, the electric field vector E, and the electric displacement vector D are eoplanar. ( D is normal to k.) These conditions are met for two orthogonal orientations of D which are parallel to the semi-axes of the appropriate section of the optical indicatrix.We are persuaded that these two waves are physically distinct by the phenomenon of double refraction seen so clearly in calcite cleavage rhombs. Although the k vectors of the two waves are identical, their E vectors are in general not. In one case (the ‘ordinary’ ray), E is collinear with D ; in the other (the ‘extraordinary’ ray), it is not. Because the ray propagation direction is normal to E (it is in fact along E X & the direction of Poynting’s vector), the two simple harmonic waves are each identified with an experimentally distinguishable ray. They can each be extinguished separately with an analyser. Through the elegant application of the Poincark sphere representation, Sir Charles Frank has demonstrated that, for specimens consisting of a succession of birefringent layers, there are two distinguishable settings of the polariser, 90” apart, for which light after transmission is capable of being extinguished by the analyser; the analyser settings necessary for extinction are in general not crossed relative to the polariser.It follows that extinction will, in general, not be obtained in multi-layer specimens observed between crossed polars at any setting of the crossed polars relative to the specimen. This is exactly what was said in our previous comment (A. H. Windle replying to F. C . Frank) in setting down the first criterion ( a ) for testing through-thickness uniformity of our specimens. There is another point we should make here. Our observations have been made in white light, and our extinction criterion is for that condition.Sir Charles’ result is for monochromatic light. Since the retardation introduced by individual birefrin- gent layers depends on the wavelength of light passing through it, the final orbit of representative points will cross the equator of the Poincark sphere at opposite points of a diameter whose azimuth depends on the wavelength of light used. In white light, for a multi-layer specimen, the colour components will extinguish at different settings of polariser and analyser. If a specimen were to have the particular characteristics of a series of infinitesimally thin birefringent layers, which both separately and cumulatively are represented as small rotations of the Poincari sphere, the polariser and analyser settings required to produce extinction will be practically the same for each wavelength.The specimen will then indeed behave as a single birefringent layer,’ as Sir Charles points out. However, we have observed birefringence of up to 0.1 in the B-ET and B-N copolyesters; such a value is especially high for a polymer. We would not expect a model based on small rotations to be appropriate in this case. Finally, we appreciate the concern that ordinary and extraordinary rays (or, in the general case of an optically biaxial region, the separate extraordinary rays) may follow significantly deviating paths. For light incident at a given angle on a birefrin- gent layer, the angle between the two transmitted rays can be calculated from the geometrical properties of the indicatrix, if the principal refractive indices are known.Given a maximum birefringence of 0.1, one can make a rough estimate of the relevant principal refractive indices in a B-ET domain by interpolation from data2 for PET fibres. We estimate that the maximum angular deviation between the two transmitted rays is of the order of 3”. Thus we do not expect them to experience significantly different refractions. Also, after travelling through 2pm of sample, their spatial separation resolution is only of the order of 0.1 pm, which is below the resolution limit of the microscope. F. Pockels, Lehrbuch der Krisralloptik (Teubner, Leipzig, 1906). D. W. van Krevelen, Properties of Polymers (Elsevier, Amsterdam, 1976), p. 320.GENERAL DISCUSSION 107 Prof. A. J. Leadbetter ( Rutherford - Appleton Laboratory, Chilton) said: A biaxial nematic must have an intrinsically anisotropic diffraction pattern in the equatorial plane. Has Dr Windle observed this? The observation of a diffuse scattering peak at slightly higher scattering vectors than the first (hkO) Bragg peak from the average hexagonal packing of long molecules is commonly observed in diffraction patterns of smectic B phases of thermotropic liquid crystals.In this case it arises from a local herringbone type of packing with lower symmetry than hexagonal. Could this be the explanation of similar observa- tions in the experiments reported by Dr Windle and Prof. Blackwell? Dr A. H. Windle (University of Cambridge) said: Prof. Leadbetter suggests that a diffraction pattern obtained with the beam parallel to the chain axis would be useful in confirming biaxiallity. We agree that it is an important experiment, but the difficulty lies in the making of a large enough monodomain sample of suitable orientation.Also, if such an experiment showed no clear evidence of non-axial packing, one would still have to be very careful in ruling out biaxiallity. Long-range rotational correlation about the chain axes may well contribute to biaxial optical properties, without necessarily disturbing the chain packing significantly from a two-dimensional liquid-like correlation. The pattern would be intrinsically anisotropic, but the anisotropy may not be very apparent. Dr G. R. Mitchell (University of Reading) said: I would first like to address my comments to the remarks of Prof.Leadbetter, relating to the desirability of generating a monodomain in the biaxial nematic phase of the copolyesters described in our paper. Naturally the availability of a monodomain sample, or indeed a sample with domains larger than ca. 1 p m observed at present, would be particularly useful for conoscopic imaging. The viscosity of these rigid-chain systems would appear to preclude the effective use of electric and magnetic fields, although attempts have been and will continue to be made. The use of a mechanical field was also used to attempt some realignment of the ‘domains’. The material used was the Eastman Kodak X7G copolymer of hydroxybenzoic acid and poly( ethylene terephthalate), and was in the form of a melt-extruded rod. X-ray scattering analysis showed the sample had a high global orientation (P2) value of ca.0.7,’ while X-ray scattering patterns taken with the X-ray beam along the extrusion axis contained a uniform distribution of intensity along a ring, indicating no preferential alignment transverse to the chain direction.’ A sample of that extrudate was compressed normal to the extrusion direction. Plate 7 shows the X-ray scattering pattern obtained when the X-ray beam is parallel to the original extrusion axis. The compression axis is horizontal. The scattering observed arises from spatial correlations between chain segments (ca. 5 A). The scattering pattern clearly exhibits some anisotropy, which might as a minimum be interpreted as indicating some structural unit which is anisotropic transverse to the chain direction, and thus responds to the mechanical field.However, the interpretation of this result is not so straightforward on two accounts. The first relates to the effect of some misorientation of the long axis of the chains in the starting sample. The effect of the lateral compression will also affect those chains, which will also result in an anisotropic scattering pattern similar to plate 7. However, even if it were possible to obtain a large monodomain, it is not clear that the scattering pattern obtained would exhibit an orthorhombic or other ‘biaxial’ packing arrangement. The rotational correlations in a biaxial nematic phase result from the presence of some transverse anisotropy, which may be repulsive or shape-related, or due to attractive interactions. These attractive correlations108 GENERAL DISCUSSION might, for example, arise from dipole-dipole interactions of the ester units.The X-ray scattering observed at s == 1.5 A-1 arises principally from correlations between aromatic rings (the greater proportion of the sample). The correla- tions between esters may be maintained in the absence of significant rotational correlations between aromatic rings. Thus rotational correlations could exist without the need for some ‘biaxial’ packing arrangement of the chains as a whole. ’ G. R. Mitchell and A. H. Windle, Polymer, 1983, 24, 1513. Prof. J. Blackwell (Case Western Reserve University, U.S.A.) said: I would like to comment on the paper by Dr Windle on a topic that is not discussed in our paper, but in which we have considerable interest.The X-ray patterns of the melt-spun fibres show evidence for ordering of the copolymer chains. Bragg maxima on the equator point to hexagonal packing, and the presence of an off-equatorial at d = 3.1 A shows that there is three-dimensional order, i.e. some of the chain sequences are in register rather than randomly staggered as in a nematic structure. Dr Windle has suggested that this three-dimensional order is due to registration of short, identical sequences. In the example that he gives, he discusses the probability of the formation of crystallites ca. 3 0 8, in width by association of pentamer sequen- ces, and concludes that this is a conceivable mechanism for the development of order. The problem with this explanation of the ordering is that it underestimates the size of the ordered regions.Our measurements of ‘crystallite size’ by application of the Scherrer equation to the equatorial peak widths lead to lateral dimensions of ca. 90 A for the as-spun copoly(HBA/HNA) fibres, and this dimension increases on thermal annealing. These observations point to the existence of domains consist- ing of ordered arrays of at least 300 chains. Blundell’ has reported a ‘degree of crystallinity’ of ca. 21 ‘/o for copoly(HBA/HNA; 40/60). Whatever the exact mean- ing of this measurement for this type of copolymer, it is clear that a significant fraction of the chains is involved in formation of ordered regions. Given the large number of identical sequences that would need to be brought into register, it is unlikely that this can explain the development of order.Our view is that the order is developed by lateral aggregation of random sequences. The homopolymers poly( HBA) and poly( HNA) probably pack in a similar manner, and these structures may be able to tolerate a significant number of the other monomer as defects while still retaining the basic homopolymer packing. The distortion necessary to accommodate different monomers will be appreciable, but not all that great in view of the similarity of the HBA and HNA structures. The fact that the residue lengths are in the approximate ratio of 3 : 4 may in itself lead to significant register between totally random sequences. It is possible that there is some degree of segregation such that the ordered regions consist of HBA-rich or HNA-rich sequences, but at present there is no physical evidence for this.D. L. Blundell, Polymer, 1982, 23, 359. Dr D. J. Blundell (ICI, Wilton) said: I would like to make some comments relevant to papers by Dr Windle and Prof. Blackwell concerning the nature of the three dimensional ordered regions in thermotropic copolyesters of the form:GENERAL DISCUSSION 109 35 30 25 20 15 10 2 e p Fig. 4. WAXS diffractograms for polymer with x = 0.4 (see text). ( a ) 20, ( b ) 230 and (c) 300 "C. These comments are based on data that were used as a basis for a previous publication.' Fibres which are melt-drawn from this family of polymers show broadly similar X-ray patterns. As shown in Prof. Blackwell's paper the main variation with composition x is in the meridional reflections. The insert in fig.4 shows a tracing of an X-ray photo of a high orientation fibre from a polymer with x=O.73. There is also diffuse background diffraction on the equator which is not shown on the tracing. For samples with lower orientation the sharp diffraction spots spread into arcs. The WAXS diffractograms shown in the main part of fig. 4 were obtained from a near randomly oriented sample of polymer with x=O.4. The sample was prepared by loading small pieces of polymer into a 2 mm diameter thin-walled glass tube which was then mounted in a transmission hot stage. The WAXS scan at room temperature shows two sharp diffraction peaks superimposed on an amorphous background. The peak at 28 = 20" corresponds to the main equatorial reflection in the fibre pattern, while the shallow reflection at 28 = 26" corresponds to the off-axis spots.The presence of this reflection shows that three-dimensional ordered regions are present in this sample. The weak outer equatorial spots in the fibre pattern are out of the range of the diffractometer hot cell. When the temperature of the cell was increased the intensity of the two sharp reflections reduced in a way that correlated with the broad d.s.c. melting endotherm. The peaks completely disappeared at 300 "C, which is above the final d.s.c. melting process, leaving only the amorphous background. The peaks reformed on sub- sequent cooling. The area under the sharp peaks relative to the area under the amorphous background, indicates that ca.20% of the polymer is associated with the three- dimensional ordered regions that form on cooling. The d.s.c. melting endotherm indicates a heat of fusion of 20 kJ kg-' of 'crystalline' material. The half-width of the diffraction peaks imply that the lateral size of the ordered regions are CQ. 100 8, across. This is significantly larger than the 30A suggested by Dr Windle and is closer to the estimate made by Prof. Blackwell in his paper.110 GENERAL DISCUSSION - Fig. 5. Tracings of X-ray photographs of polymer with x = 0.73. The first point I would therefore like to make to Dr Windle is that if he is to succeed with explaining the three-dimensional ordered regions in terms of his new and interesting concept of a non-periodic layer crystal, then his model must be able to accommodate 20% of the material and involve lateral sizes of ca.lOOA in individual crystals. The second point I would like to make involves the degree of order of the 'crystalline' regions. Our observations indicate a significantly higher order than suggested by Dr Windle and are closer to those shown in Prof. Blackwell's paper. In our experience, most forms of extrusions, mouldings and fibres show evidence of the 26" off-axis reflection ( i e . indicative of three-dimensional order) as well as the stronger 20" equatorial reflection. On annealing, significantly higher degrees of order can be attained. This is exemplified in fig. 5 , which shows tracings of X-ray photographs of polymer with x = 0.73 which ( a ) has been freshly melt-drawn into a fibre and (6) has been subsequently annealed at progressively higher temperatures near the melting point.The annealed pattern shows a greater number of diffraction spots arranged in a pattern of higher symmetry. After projection onto the (hkO) plane, the spots in pattern ( a ) can be shown to be consistent with a hexagonal packing of chains. In view of the biaxial nematic state deduced in Dr Windle's paper, is it not surprising that the most ordered regions in the system appear to choose to pack with a hexagonal symmetry rather than a 'biaxial' one? It appears that it is only after prolonged annealing that the more ordered regions move from a hexagonal packing to one possessing a degree of biaxiality as in pattern (b). ' D. J. Blundell, Polymer, 1982, 23, 359.Dr A. H. Windle ( University of Cambridge) (partly communicated): Dr Blundell disagrees with our statement about the lateral size of the ordered material as estimated from the half-width of the equatorial reflection.GENERAL DISCUSSION 111 h U .- 2 U .- ......... .... .... * . . . . . . . . a . 10 20 30 2 e p Fig. 6. Reflection diffractometer scan of a sample of polymer B-N (75/25 HBA: HNA) without macroscopic orientation. The radiation used was filtered CuKa, and the data points were obtained by step scanning at 0.05” (28) intervals. The background is an estimate by eye (see text). In our paper we describe our estimate as a lower limit and add the rider that the ‘actual dimension will almost certainly be larger’. Dr Blundell obtains a dimension of ‘ca. 100A’ and makes an issue of this value.His first figure (room- temperature plot) makes assumptions about a two-phase structure and he draws in a background in that light. We do not disagree with his choice of background, except that it leaves the peak tails rather lopsided, nor with the fact that it leads to a smaller value of peak half-width. However, choosing to draw a background at all raises an additional issue which would detract from the generality of our argument. Incidentally our measurement of Dr Blundell’s half-width on his figure using his background gives an apparent crystallite size of 76 A. We have now carried out a room-temperature reflection diff ractometer scan on a nominally unoriented sample on a composition which compares more closely with Dr Blundell’s fibre diagrams and also the previous data in our paper.The result is shown below, together with our own estimate of an amorphous-type background (fig. 6 ) . The half-width of the main equatorial peak gives an apparent size of 63 A. Bearing in mind the different sample compositions, the fact that the thermal histories were not necessarily the same (our sample was cooled from the mesophase at ca. 1 K s-’), and the inevitable differences in diffractometer geometries, it is difficult to see the contention. If one draws in a halo-shaped background, the minimum size is in the region of 60-80A, if one does not then the absolute minimum will be around 30A. Also, I must re-emphasize that the actual size will be considerably greater than these values if there is a substantial type-I1 disorder contribution to the peak half-width.Before leaving the matter of size we should also like to draw attention to a feature of Dr Blundell’s scan at 230°C. The ‘crystal’ peak is noticeably sharper than at room temperature. This indicates that some of the smaller ordered entities112 GENERAL DISCUSSION have 'melted out' at 230 "C even though the solid-liquid transition does not occur until ca. 290 "C. We see this effect as supporting evidence for the d.s.c.-based argument in our paper that the entities melt out over a very wide temperature range. The concept of non-periodic layer (n.p.1.) crystallites accounts for the parallel observations that the positions of the meridional peaks is consistent with the non-periodicity of the random copolymer molecules,132 and yet on annealing the intensity of the lowest-order peak concentrates onto the meridian without any other sampling of that 'layer line'.Thus we have comparatively extensive lateral order associated with an intrinsically aperiodic molecule. A crystallinity of 20% and a lateral size of 100 A, as suggested by Dr Blundell, could be satisfactorily accommo- dated by the model. Finally, Dr Blundell discusses the particular arrangement of equatorid maxima seen in his photographs. His statement that the 26" off-axis reflection is 'indicative of three-dimensional order' needs qualification. This maximum, which is also a feature of our quantitative contour plots (see for example our response to Prof. Blackwell's question), is particularly significant in that its displacement in the meridional direction is not sufficient to place it on even the first 'layer line' at ca.1 kl. The full implications of the off-equatorial component are uncertain, but we see it as representing an association between the units of adjacent chains which gives long-range near-lateral order despite the aperiodicity along the chain axis. Dr Blundell's contention that the arrangement of equatorial and near-equatorial maxima, when projected onto (hkO), indicates hexagonal packing, is difficult to substantiate. Hexagonal packing implies that the first two equatorial maxima have scattering vectors with amplitudes in the ratio of 1 : 1.732. The observed ratio, as projected and stated elsewhere in his question, is of the order of 1 : 1.3 (20": 26").The extra order shown by the appearance of additional peaks in the equatorial cluster in samples heated for substantial periods near to their melting points has also been observed by ourselves. It must represent a change in local molecular organization, but before attempting to draw any conclusion one has to be very careful to ensure that the molecules have not themselves become more periodic as a consequence of a process such as transesterification. G. A. Guitierrez, R. A. Chivers, J. Blackwell, J. B. Stamatoff and H. Yoon, Polymer, 1983'24,937. G. R. Mitchell and A. H. Windle, Colloid Polyrn. Sci., 1985, 263, 230. Dr G. R. Mitchell (University of Reading) (communicated): I also would like to address some of the issues raised by Dr Blundell. It is clear from the thermograms presented by Dr Blundell,' from those of our paper at this Discussion and elsewhere, that some first-order transition occurs at ca.300 "C. The first question to answer is whether this transition corresponds to a weak transition of the complete sample volume, or if it arises from the transition of a small component of that sample volume. If it is the latter, then the interaction of this small component must be such that it locks the remaining bulk of the sample, since the optical structure exhibits no mobility below the softening point.* If we accept the evidence presented in our paper that the hydroxybenzoic acid/ hydroxynapthoic acid copolymers (HBA/ HNA) exist in a biaxial nematic phase above the softening point, in other words if we exclude the possibility of the softening point being a biaxial/uniaxial nematic transition, the softening point must correspond to the melting out of crystallites or some other enhanced order.Dr Blundell uses particular interpretations of the experimental X-ray scattering patterns to support the notion of a significant level of crystallinity. Those interpreta-GENERAL DISCUSSION 113 tions, while highly plausible, are not unique, and I would like to draw attention to the following points. Fig. 12 of our paper shows the equivalent X-ray scattering patterns of HBA/HNA at room temperature and at a temperature above the softening point, as displayed by Dr Blundell. There is clearly a marked reduction in the positional order upon passing through the softening point.The two peaks in the 20-30”26 region are related to interactions between chains and both these peaks, albeit considerably broadened, are still present in the ‘melt’. The peak at ca. 45” 26 arises from correla- tions within single-chain molecules, and its breadth is related in part to the correlation length of the copolyester molecule^.^ It is clear that the correlation length of the molecules is also reduced above the softening point. If we compare the two curves of fig. 12 in our paper, there appears to be no reason to assume that the room- temperature curve consists of two components (crystalline and ‘amorphous’) as argued by Blundell. It has the appearance of simply a ‘sharper’ version of the high-temperature curve. This reasoning would support the idea that the softening transition is a homogeneous event.This has additional support from the results of optical microscopy and from electron microscopy, which confirm the absence of a two-phase structure unless the samples are annealed and particularly if the samples are first highly oriented. Small-angle X-ray scattering curves show no evidence for any significant density variations2 The interpretation followed by Dr Blundell of the X-ray scattering data also utilizes the presence of off-equatorial diffraction maxima to support the concept of crystallinity. The first point relating to this line of reasoning is that those reflections do not lie on a layer line corresponding to the first meridional peak, nor do they lie on a layer line appropriate to the napthoic repeat unit (however unlikely that might be).A model which satisfactorily accounts for the presence of these off- equatorial maxima and also accounts for their position off a layer line is displayed in fig. 7. It is suggested that those off-equatorial maxima result from the loose correlation of aromatic units which are inclined to the general chain direction. The experimentally recorded azimuthal angle and the scattering vector of the off - equatorial peaks are in accord with such a model. In addition, the off-equatorial maxima are sharper (in terms of scattering vector) than the main equatorial maxima at s = 1.5 A-’. The association of these off-equatorial maxima with a specific correlation within the structure is again in agreement with such an observation. There is strong evidence to suggest that, even in non-crystalline polymers, specific interactions will occur between phenyl groups when present.4i5 The longitudinal correlation shown schematically in fig.7 is observed in cylindrical distribution functions derived from the X-ray scattering patterns of aligned copolyester ~arnples.~.’ These functions show that the axial register is limited to a scale of the order of aromatic units rather than a point-to-point atom correlation. It is also reasonable to expect that this limited axial register will develop after and additional to the biaxial ordering of the molecules. If we relate these off-equatorial peaks to the correlations outlined above, then the assignment of a ‘hexagonal’ lateral packing scheme is void. The fact that a weak peak is seen at the same scattering vector (s = 1.9 A-’) in the scattering curve for the globally isotropic sample at a temperature above the softening point [fig. 12(b) of our paper] demonstrates the retention of some level of rotational correlation between chains as would be expected in a biaxial nematic structure. It would appear that this rotational correlation is consolidated and enhanced by some limited axial register in one direction (normal to the aromatic ring plane) upon cooling the sample to the solid state.These correlations clearly cannot be equated with three-dimensional crystallinity.114 I I I I 1 I I I I I GENERAL DISCUSSION Fig. 7. Schematic representation of the solid-state molecular organization in the HBA/ HNA random copolymers, to account for the occurrence of the off-equatorial maxima at s = 1.9 A-’.The ‘molecules’ are viewed edge-on to the aromatic rings. The development of a further additional level of order upon annealing, as demonstrated in our paper by thermal analysis and electron microscopy, requires careful thought. We can partition the possible crystalline models into those which ( a ) involve significant run lengths of one of the homopolymers, (6) involve some distorted structure, predominantly of one homopolymer type, but which allows the introduction of some defects in the form of the other monomer type, and ( c ) involve in any one crystal only one particular random sequence of monomers. The latter are the non-periodic layer crystals described in our paper. The first of these choices will certaintly not match the 20% suggested by Dr Blundell, since the molecular chains have been shown to have a random distribution of monomers [ref.(3) and papers by Windle et al. and Blackwell et al. at this Discussion]. ’ D. J. Blundell, Polymer, 1982, 23, 359. * C. Viney, G. R. Mitchell and A. H. Windle, Mol. Crysf. Liq. Cryst., in press. G. R. Mitchell and A. H. Windle, Colloid Polym. Sci., 1985, 263, 230. T. P. H. Jones, G. R. Mitchell and A. H. Windle, Colloid Polym. Sci., 1983, 261, 110. G. R. Mitchell and A. H. Windle, Colloid Polym. Sci., 1985, 263, 280. G. R. Mitchell and A. H. Windle, Polymer, 1982, 23, 1269. ’ G. R. Mitchell contribution to this Discussion (as a comment to Prof. Blackwell’s paper.)GENERAL DISCUSSION 115 Dr G.R. Mitchell (University of Reading) said: I would like now to direct attention to the paper of Blackwell et al. We also have performed analyses of the scattering patterns from aligned samples of the rigid-chain thermotropic copolyesters of hydroxybenzoic and hydroxynapthoic acids. These structural investigations have proceeded in two stages. The first objective was to obtain chemical and structural parameters relating to individual molecules, and in particular the nature of the distribution of the ‘monomers’ within each molecule. We utilized an approach for calculating the meridional intensities which was a development of that proposed initially by Zernicke and Prins’ for simple disordered systems. We extended the method to a two-component system which allows the meridional scattering for a random copolymer to be written in analytical form.2 The comparison of such calculated scattering patterns with those obtained experimentally confirmed the initial expectations of randomness.Scattering patterns calculated for ‘blocky’ sys- tems were at variance with the experimental data. The meridional scattering for the HBA/HNA copolymer exhibits an intense peak at s = 3 A-’, which is almost invariant in position with changing HBA and HNA proportions. It may be considered to be a combination of the fourth-order maxima from the HNA repeat (ca. 6.3 A) and the third-order maxima from the HBA repeat (ca. 6.3 A). The fact that there is not an exact match of those repeats leads to a broadening component, which is additional to any broadening due to restricted correlation along the chain resulting from bending or other defects.We have calculated from the model scattering2 the breadth of the peak at s = 3 A-’ as a function of the correlation length of the molecule, and the results are shown in fig. 8. The straight line represents the relationship between breadth and correlation length for a perfectly invariant peak. The curve away from that straight line results from the slight mismatch of the repeat units and must be taken into account when determining the Correlation length. In a particular melt-extruded pellet of HBA/HNA (70/30) examined the breadth of the peak at s 3 A-’ was measured at As = 0.1 A-’, which corresponds to a correlation length involving ca. 10 repeat units or ca. 69 A. It would be reasonable to expect that this correlation length would be dependent upon both the particular chemical composition and the mechanical and thermal treatment of the sample.The second stage of the analysis is concerned with the packing of these random copolymer molecules. We have obtained quantitative X-ray scattering data (fig. 2 of our paper) which have been transformed to a real-space cylindrical distribution function W( r, a) using procedures described in detail el~ewhere.~ Fig. 9( a ) and (6) show these cylindrical distribution functions for the Eastman Kodak X7G copolymer of hydroxybenzoic acid and poly( ethylene terephthalate) and for the HBA/HNA (70/30) copolymer. There are three distinctive features of these func- tions for both copolymers. The first is the peaks which are centred along the meridian or extrusion axis. Those peaks represent the correlations with each molecule.The second are the columns which extend up from the equator. These are the correlations between neighbouring chain segments. The lack of arcing of these columns indicates a high level of local segmental correlations, although the global-orientation ( P2) value is only ca. 0.6. Both the features outlined above are expected for liquid-crystal systems of highly oriented almost rigid rods. However, a third feature indicates an additional level of correlation. Both cylindrical distribution functions exhibit a maximum in those columns which is out of the equatorial plane. This indicates a preference for some level of longitudinal register between adjacent molecules.However, this register is limited and appears to be restricted to register between aromatic groups. In other words, it is not a point-for-point atom-position register.116 GENERAL DISCUSSION 0 10 20 30 LO 50 60 number of units, n Fig. 8. Plot of the reciprocal of the calculated half-width (As) of the peak in the region of s = 3 A-' against the number of units in the correlation length of the chain. The solid line is for an invariant peak ( i e . with exactly matching repeat units of 6 and 8 A). The points are for the equivalent peak but with the real repeat lengths of HBA of 6.3 8, and HNA of 8.3 A. In the case of the HNA/HNA cylindrical distribution function, the correlation appears at a distance commensurate with the napthoic unit repeat. We need to interpret these results with caution.However, they do indicate a preference for an axial shift in addition to lateral spatial correlations. This enhancement of the local order may only occur in a limited volume of the material, and perhaps represents the nearest to crystallization that a random copolymer can attain. ' F. Zernicke and J. A. Prins 2. Phys., 1927,41, 184. G. R. Mitchell and A. H. Windle, Colloid Polym. Sci., 1985, 263, 230. G. R. Mitchell and R. Lovell, Acta Crystallogr., Sect. A, 1981, 37, 189. Br R. A. Chivers (ICI, Wilton) said: Another aromatic copolyester which forms a liquid-crystalline melt is that known commonly as HNATH. This material is made from 2-hydroxy-6-naphthoic acid (HNA) and equimolar quantities of terephthalic acid (TPA) and hydroquinone (HQ).I have prepared fibres from the molten polymer, and the X-ray diffraction pattern of fibres of HNA/TPA/HQ 50/25/25 is shown in plate 8. This pattern is very similar to those of the HBA/HNA system' in that aperiodic meridional maxima (in this case five out to d = 2 .$) are seen, and also intense equatorials and off -equatorials on broad, more diffuse equatorial scatter. Calculations have been performed on the meridional diffraction of the HNATH system and will be reported fully elsewhere. In essence, the meridional diffraction can be explained as being derived from a random copolyester chain as has been shown by us for other systems.',2 However, there is one clear difference between the diffraction from HNATH and that from these other systems.This is the presence of further off-axial maxima, most clearly those continuing the ca. 4.2 8, 'layer line'. Maxima can also be resolved on the upper and lower extremes of the broad equatorialGENERAL DISCUSSION 117 r / A 1 ° 15 15 Fig. 9. Cylindrical distribution functions W( r, a) derived from the scattering data of fig. 2 of our paper using the procedures described in ref. (3). The extrusion axis is vertical. ( a ) For a melt-extruded pellet of a random copolymer of hydroxybenzoic and hydroxynaphthoic acids in the ratio 70/30. ( b ) For a melt-extruded pellet of a random copolymer of hydroxyben- zoic acid and poly(ethy1ene terephthalate) in the ratio 60/40. The dashed lines represent contours for negative values. scatter that are quite distinct from, and at lower d-spacings than, the usual off- equatorials.My calculations of the full three-dimensional transform of the atomic chain: similar to those reported here for HBA/HNA,' show considerable intensity out along the ca. 4.2. A layer line which may help to explain some of these maxima. It may be also that the lateral intermolecular packing is better in this system. HNATH is therefore a similar material to the others discussed, but it shows interesting differences in its diffraction which make it worthy of further study. The work described here was performed at Case Western Reserve University, Cleveland, Ohio, and I am grateful to Celanese Research Company, Summit, N.J. for provision of the polymer. J. Blackwell, A. Biswas, G. A. Gutierrez and R. A. Chivers, Faraday Discuss.Chem. SOC., 1985, 79, 73. * G. A. Gutierrez, J. Blackwell and R. A. Chivers, Polymer, 1985, 26, 348. Prof. J. Blackwell (Case Western Reserve University, U.S.A.) said: I agree with Dr Chivers in that these off-equatorials for HNATH [copolyesters of HNA, hydro- quinone and terephthalic acid (TPA)] occur further from the equator than those seen for copoly( HBA/HNA), which suggests that there is more extensive lateral register of the chains in the former copolymer. This observation contrasts with what we have previously reported for copolymers prepared from HBA, 2,6-dihydroxy- naphthylene (DHN) and terephthalic acid.' The latter copolymer has a similar chemical structure to that of HNATH except for a reversal in sense of some of the ester groups.The X-ray patterns of as-spun fibres of three HBA/DHN/TPA molar ratios (60/20/20, 50/25/25, 40/30/30) show an intense off-equatorial on a 'layer118 GENERAL DISCUSSION line' at ca. 12 A, as is seen for both copoly(HBA/HNA) and HNATH, but there are no strong off-meridional maxima as far from the equator as those seen for HNATH. This is a further example of the differences that can result from an apparently minor change in polarity of the ester groups, as was commented on earlier by Dr Yoon. It suggests that this polarity affects the lateral registration of the chains, although it should be noted that the HNATH preparations contain higher proportions of naphthylene units. * J. Blackwell and G. A. Gutierrez, Polymer, 1982, 23, 671. Dr A. M. Donald (University of Cambridge) said: Dr Chivers has shown that the ternary copolyester based on hydroxynaphthoic acid, hydroquinone and tereph- thalic acid (N-QT) may show a greater richness of structure, as revealed by X-ray diffraction, than the simple random copolyester discussed in detail by Prof.Black- well. My own electron-diffraction studies of members of the N-QT series, in which the ratio of the components was varied, supports this conclusion. When thin samples of the polymer are annealed for 10 min at 300 "C on, for convenience, a rocksalt substrate, dramatic changes in both the meridional and equatorial reflections may occur. Faint hints of off-meridional reflections, perhaps related to those observed by Dr Chivers, can occasionally be seen, but the most striking feature is the appearance of a set of aperiodic meridional lines which are much less arced than the main 3s line (which is still present), as shown in plate 9.Only a small percentage (estimated to be ca. 5%) of the specimen exhibits these additional reflections along the meridional, and hence it is probable that X-ray techniques will be hard-pressed to detect their presence, demonstrating the usefulness of electron microscopic tech- niques. Most intriguing of all, different regions may show a different set of the aperiodic lines, as can be seen by comparing plates 9 ( a ) and ( b ) , both taken for specimens with a ratio of 70: 15 : 15 for the naphthoic: hydroquinone: terephthalic residues, respectively. Interestingly, a comparison of the meridional lines shows that plate 9( a ) contains more lines, and they are sharper than in plate 9( b ) ; however, the converse statement is true for the equatorial reflections.Additional reflections are likewise seen for the other compositions examined, namely samples containing 60 and 50% of the naphthoic residue. As yet, the origin of these lines is not clear, but what is demonstrated by the diffraction patterns is that quite marked changes in packing are occurring locally during annealing, on a size scale which is hard for standard X-ray techniques to probe. Dr A. H. Windle (University of Cambridge) said: I should first like to comment on Prof. Blackwell's paper. He alludes to the less-than-satisfactory agreement between the best model predictions for the intensity of the first meridional peak and the experimental data.We should like to support his suggestion that this is due to 'preferred axial stagger'. We showed in our paper that this first meridional maximum, observed in electron diffraction patterns of thin (1000 A) samples, con- centrated on the meridian after the polymer had been annealed in the solid state. We have now performed a similar experiment, employing X-ray diffraction and using fibres of some Celanese 73/27 copoly (HBA/HNA) material (B-N). Fig. 10 shows recent data collected by Ruth Golombok. It compares the patterns of as-spun fibres with those annealed for 1 day at ca. 10 "C below the melting point. The anneal4 3 s/A-' 1 0 4 3 2 1 0 1 2 3 A Fig. 10. Wide-angle scattering intensity for two fibre samples of B-N. ( a ) Unannealed.( b ) Annealed at 280°C. The fibre axis is vertical.120 GENERAL DISCUSSION 0 1 . 0 s/A-' 0 s/A-' Fig. 11. Detail of fig. 10 showing the intensification of the s = 1 k' reflection onto the meridian in ( a ) the unannealed sample and (b) the annealed sample. has had comparatively little effect on the third (s == 3 &*) strong meridional maximum, some influence on the second peak and a strong effect on the first, which concentrated onto the meridian as shown in detail in fig. 11. In the annealed material the apparent lateral width of the 1s peak is 0.14 A-*, whereas that of the 3s peak is ca. 1.6 kl. Hence the longitudinal register between units 6-8 A long in the chain directions (the copolymer units) appears to extend laterally for at least 50 A.However, the register is not especially perfect and matching on the finer scale of 2 8, is difficult to recognize. As with the electron diffraction, the only sampling of the first 'layer line' is on the meridian, and this again requires interpretation in terms of non-periodic layer (n.p.1.) crystallites. In response to Prof. Blackwell's informally posed question it is possible, indeed likely, that there are specific mistakes in the matched sequences and that the lateral extent of the register significantly exceeds 50 A. We believe, however, that the n.p.1. crystallites represent the most useful starting point in considering the order in these systems. The annealing treatment decreases the arcing of the equatorial peaks and shar- pens equatorial maxima. The asymmetric nature of the equatorial maxima prompts my second comment, which is a rather more general one. Non-crystalline polymers which contain aromatic groups within their backbones have a special signature on their diffraction scans. The main interchain peak is asymmetric, with a distinct shoulder or even subsidiary maximum at s = 1.9 A-'. Data collected by Dr T. P. H. Jones for several such polymer glasses are reproduced in fig. 12. Furthermore, the scattering from liquid benzene also shows a shoulder in the same position (fig. 13) which has been interpreted by Narten in terms of special correlations between the rings. Short-range rotational correlation (or biaxial- lity!) thus seems to be a feature of aromatic backbones. The fact that the diffraction patterns of all the aromatic ester liquid-crystal polymers examined show a high-angle shoulder which resolves to a width corresponding to at least 100 A in the solid and less in the liquid implies that there is rotational correlation of the aromatic rings. Although such correlations may be associated with biaxial order, they are notGENERAL DISCUSSION 121 d 0 1 2 3 4 5 1 0 1 2 3 4 5 6 0 1 2 3 4 5 6 s/A-' Fig. 12. Interference functions from a number of glassy polymers containing aromatic groups in the backbone.' In each case a shoulder or small peak at s = 1.9 A-1 is apparent. ( a ) Poly( p-phenylene sulphide), ( b ) poly( dimethylphenylene oxide), (c) polycarbonate, ( d ) poly(ether sulphone), ( e ) poly(ether ether ketone) and (f) polysulphone (UDEL).122 GENERAL DISCUSSION u 0 4 slA-1 6 Fig. 13. Interference function of liquid benzene showing the shoulder at s = 1.9 A-’ on the ‘high-angle’ side of the main intermolecular interference peak.* PHBA PHNA Fig. 14. Sketch showing repeat units of PHBA and PHNA in an ‘extended’ conformation.GENERAL DISCUSSION 123 necessarily the cause of it, as the dipoles on the ester groups are likely to have a greater influence. The s = 1.9 A-' shoulder in copolyesters makes an angle of 13-14" with the equator. If the molecule is in an extended-chain conformation it is noteworthy that the projection of the vertical bond (through the aromatic ring) makes an angle of this order with the local chain axis (fig. 14). T. P. H. Jones, Ph.D. Thesis (University of Cambridge, 1983). ' A. H. Narten, J. Chem. Phys., 1977, 70, 299.Plate 1. The microstructure of 60/40 PHB/PET at 150 "C, showing the two phase structure. (T. J. Lemmon). [ f o o n g page 124Plate 2. A sequence of micrographs of the same area of a thin section of B-ET at 220°C between crossed polars: ( a ) 0, ( b ) 15 s, (c) 30 s and ( d ) 10 min. The texture is seen to be mobile on a timescale of seconds, but the X-ray orientation (determined at room temperature from the same thin section) has decayed little after 10 min.'Plate 3. A series of three micrographs of the same area of B-ET sample 8 pm thick. The microstructure, showing two phases, has been established by annealing at 290 "C for 1 h. On cooling below 250 "C the discontinuous phase has a fine Schlieren texture (a). This texture disappears at 245 "C on heating (b), to be replaced by a course radial texture ( c ) . The transition is reversible on cooling. The specimen was photographed at the temperatures indicated.Plate 4. Fine Schlieren texture in a 2 pm thick sample of B-ET between crossed polars (T. J. Lemmon).Plate 5. Sample of B-ET of thickness 1-2 pm in the centre of the field and 8 pm to the right. The uneven boundary on the left is the specimen edge (T. J. Lemmon).( a ) - 10 ptn (6)- 10 pm (d- 10 pm Plate 6. A series of micrographs of B-ET showing sections of increasing thickness: ( a ) 2, ( b ) 5 and ( c ) 10p.m. The top row shows textures between crossed polars, while the bottom row shows the corresponding contrast obtained when both polars are removed.Plate 7. X-Ray scattering pattern of a melt-extruded pellet of Eastman Kodak X7G cop- olyester which has been compressed at room temperature in a direction normal to the extrusion axis. The incident X-ray beam is parallel to the extrusion axis, and the compression direction is horizontal in the figure. The scattering maxima corresponds to interchain correlations, real space distance of ca. 5 A. Plate 8. X-Ray fibre diffraction from melt-spun HNA/TPA/HQ, 50/25/25.Plate 9. Selected area electron diffraction patterns of N-QT of composition 70: 15 : 15 follow- ing a 10min anneal at 300°C.