GENERAL DISCUSSION t Dr R. A. Chivers (ICI, Wilton) said: Prof. Thomas and Miss Wood have described the effect of tilt, lateral order and relative axial shift on the diffraction patterns of chain molecules. They have, however, only considered the molecules as lines of points, although the real molecular structure can have a major effect on the pattern. A real chain molecule, C(r, 4, z), can be described by the convolution of a point chain, A( z), and the electron density of one or more monomer ‘motifs’, p( r, 4 , ~ ) : ’ C(r, 4.4 = A ( z ) “A‘, 494. Ic(R, Q 7 2) = I-%c(r, 4, Z)l12 $[C(r, 4, z ) l = mwl * . R P ( r , 4, dl. I C W , @, z) = I.mwll’ - I%dr, 4, z)l12 (1) (2) (3) The diffracted intensity, Ic( R, @, Z), is given by where Therefore = I A Ip. (4) Cylindrical averaging may be performed2 to give a two-dimensional diffraction pattern.The diffraction from a nematic structure of periodic point chains is a series of continuous layer lines, except for the equator on which lie discrete maxima. In the case of aperiodic point chains, the layer lines are aperiodic and may be broadened in the chain dire~tion.~ This is only the I A term of eqn (4). When the atomic structure is also considered, I A is multiplied by the scattered intensity from this structure, Ip. The effect of this is that where Ip is very small or zero, then Ic will be likewise and the layer lines may no longer extend to infinity, possibly being just a short streak. The effect is of especial importance in nematic systems, as described above, in which I A has the form of continuous layer lines.The observed scattering, Ic, is then largely determined by Ip. In the case of a smectic system, however, I A will only consist of discrete maxima on the layer lines, and hence may be a more dominant factor on I , than Ip, which then serves to modulate the intensity of these maxima. Fig. 7 ( a ) and ( 6 ) of the paper by Blackwell et ai3 show the results of calculations of Ic for a random copolyester of p - hydroxybenzoic acid and 2-hydroxy-6-naphthoic acid for both the random and a rigid distribution of inter-residue torsion angles. In both cases, effects of the Ip modulation of I A (aperiodic layer-lines) can be seen, and in fig. 7 ( a ) this gives rise to clear differences in the lateral spread of the meridional maxima, as have been observed experimentally. This effect is of considerable importance if we wish to obtain information on intermolecular registration or ‘crystallite’ size from the lateral spread of meridional maxima.Stamatoff4 has observed discrepancies between equatorial peak widths and those of meridionals which he attributed to disorder caused by chain registration. He did not, however, consider Ip, which would indeed be extremely difficult to do with sufficient accuracy but which may serve to change the basis of some of his 1- Plates 1-8 follow p. 287. 273274 GENERAL DISCUSSION conclusions. Unless Ip is known, all crystallite size and registration information from meridional scattering in nematic systems must be treated with extreme caution. B. K. Vainshtein, Diffraction of X-Rays by Chain Molecules (Elsevier, Amsterdam, 1966), chap.IV. J. Blackwell, A. Biswas, G. A. Gutierrez and R. A. Chivers, Furaduy Discuss. Chem. Soc., 1985, J. B. Stamatoff, Mol. Cryst. Liq. Cryst., 1984, 110, 75. * R. A. Chivers and J. Blackwell, Polymer, in press. 79, 73. Prof. E. L. Thomas and Miss B. A. Wood (University of Massachusetts, U.S.A.) replied: The schematic diagram shown in our fig. 3 was to illustrate the specific effect of axial registry on the scattering patterns, permitting a distinction between nematic and smectic ordering and omitting the effect of the actual electron-density profile ,of the particular molecule on the scattering pattern. We certainly agree with Dr Chivers that this additional important factor should be taken into account for the detailed analysis of any actual polymer, since it is the product of the lattice factor (i.e. our fig.3) and the specific molecular transform which yields the observed scattered intensity distribution. Our point was that partial axial registration (a tendency toward fully smectic order) will be most apparent in the modulation of the scattered intensity on the lowerst-order layer lines. Prof. F. C. Frank (University of Bristol) said: The very interesting and instructive electron micrographs shown by Prof. Thomas and Miss Wood give a clear impression of domains, delimited by characteristic boundaries, which I called ‘caterpillars’ when they were first shown to me, but for which a more professional-sounding and informative name is ‘confluence lines’.I do not like the authors’ name ‘axial lines’ for them, because I do not see a precise significance for the word ‘axial’ in that name. In fact, these domains are an illusion and the confluence lines a mathematical artefact, which we do not immediately recognize as such because we are unaccus- tomed to seeing director fields portrayed by their orthogonal trajectories, as Thomas and Wood demonstrate is the case here. The confluence lines indicate no physical singularity in the underlying director field: in particular, they do not indicate disclinations of strength S = f 1, as suggested, or any other disclinations: but they do frequently terminate on disclinations of S = f $. Example 1 : Consider a sinusoidally wrinkled director field F, represented by Y F = a cos k x + p where p is a parameter distinguishing different members of the family of director trajectories.Differentiating, we obtain dy,/dx = -ak sin kx. Then, for the orthogonal field G: dy,/dx = -l/(dyF/dx) = (l/ak) cosec (kx). This integratesIa to give the orthogonal trajectories as: The integration generates logarithmic singularities wherever dyF/ dx is zero, and these produce the confluence lines. See fig. 1.275 GENERAL DISCUSSION Fig. 1. Example 1: (a) a sinusoidal director field and ( b ) an orthogonal field to that of ( a ) .276 GENERAL DISCUSSION Example 2: the confluence lines:lb Adding a linear term produces alternatively wide and narrow bands between Y ~ = a c o s ( k x ) + b x + p -- dyF - -ak sin (kx) + b dx - l/[ak sin (kx) - b] -- dyG dx tan (x/2) - ak/ b + ( a2k2/b2 - 1)1/2 yG = ( a2k2 - b2)-1/2 In tan (x/2) - ak/ b - ( a2k2/ b2 - 1) v2) + 4.This has confluence lines at kx = arc sin (b/ ak). See fig. 2. Example 3 : A single smoothly curved kink-band may be represented by" yF=barctan(x/a)-ex+p a2+x2 a6 - c( a 2 + x') _ - -- dyG dx X a6 2 + 4. a b l e - a ) YG =-- If c < b/a, this has two confluence lines at x = *(ab/c - a2)lj2. Example 4 : A field of hyperbolae, with asymptotic slopes 6 for x > 0, - b for x < 0 is given byId yF= b(a2/b2+x2)1/2+p (positive root) -- dyF- b(a2/b2+x2)-1/2/x dx -- dyG - -( a2/ b2 + ~ ~ ) ' / ~ / e x dx yG= -(a2+x2/b2)'I2+ (;) 7 In ( a / l ~ + ( a ~ / b ~ + x ~ ) ' / ~ X ) +4. This has a single confluence line on the y axis. See fig. 3. These are all examples of translationally parallel fields, the trajectories of which are families of congruent curves such that the vector p joining points of the same slope on any two members of the family is a constant.Confluence lines in theGENERAL DISCUSSION 277 I i i / 8 i /' c .. Fig. 2. Example 2: ( a ) a sinusoidal field modified by a linear term and ( b ) an orthogonal field to that of ( a ) .278 GENERAL DISCUSSION Fig. 3. Example 4: (a) a hyperbolic director field and ( b ) an orthogonal field to that of fig. 1( a ) (alternatively, a confluent director field).GENERAL DISCUSSION 279 orthogonal trajectories of such a field are produced where p is orthogonal to the tangent vectors t of the field, i.e. where p t = 0. There are no confluence lines for the orthogonal trajectories of either equidistantly parallel fields (in which the distance between any two curves is a constant) or in harmonic fields. The latter correspond to curves of constant value of either the real or the imaginary part of an analytic function of (x + iy ) and describe two-dimensional equilibrium configurations for isotropic curvature elasticity, in which K , = K 3 .Neither of these cases yields con- fluence lines because the condition p - t = 0 is satisfied everywhere. Although translational parallelism is not obeyed over large distances, the ideal- ized examples (1) to (4) so closely simulate textures observed locally by Thomas and Wood that one must infer that translational parallelism is a rather strong approximate rule governing the textures in these specimens.The reason for this is not obvious. A strong splay constant, K1, will go some of the way towards explaining it, but since the textures have been formed in flow it is likely that anisotropic viscosities as well as curvature-elasticity constants exert significant control over the texture. The fields do not appear to be splay-free. In plate 4 of their paper Thomas and Wood have drawn an (unduly straightened) director trajectory across two kink bands. The confluence lines do not bisect the angles between director trajectories inside and outside the kinks: in terms of example 3 we have c > 6 / 2 a : neighbouring director trajectories are therefore closer together outside than inside the kinks: they are actually furthest apart on the confluence lines bounding a kink.Supposing that the director trajectories correspond to highly aligned polymer chains one infers that the material is more highly drawn at the kink boundaries: with corresponding splay in the neighbourhood of these boun- daries, which should be accommodated by an accumulation of chain ends or ‘hairpins’. In this class of material, with flexible links of n methylenes between the rigid segments, the energy cost of a hairpin should be fairly low if n exceeds 5 or 6 (and it is 10 in the material of Thomas and Wood) so that, except for the lowest molecular weight, hairpins should predominate over chain ends for splay accommo- dation in highly aligned material (a condition which has to be distinguished from full extension). These inferences as to splay and non-uniformity of drawing could be made firmly if the specimens were thick: actually they are very thin, and therefore a small variation in thickness can produce compensating splay in the third dimension, so that they may be invalid: nevertheless ‘serpentine’ bending has been reported in relatively thick specimens. The orthogonality relationship between fields F and G is recursive.If G is taken as a director field then F is its field of orthogonal trajectories. This applies particularly to example 4 above. Regarding the field G (with 6 replaced by 6’ = - 1/ 6) as well as the field F as a director field they represent, at least qualitatively, two possible configurations for a symmetrical tilt boundary between two uniformly aligned regions of different orientation: one in which directors bend hyperbolically across the boundary and the other in which they are confluent to it.Plate 7 of Thomas and Wood shows a boundary containing alternating stretches of these two alternative structures: they make disclinations of strength +; or -; at each transition from one structure to the other. (Of course, a stretch appearing hyperbolic in the orthogonal trajectories is confluent for the directors, and conversely). Thomas and Wood have other electron-micrographs showing longer boundaries of this alternating kind. A probable interpretation is that for a given change of orientation one or other of the two alternative configurations has the lower energy: if the flow process has generated the boundary in its higher-energy configuration it can, on annealing, be converted into the other by nucleating pairs of S = *$ disclinations which migrate apart to280 GENERAL DISCUSSION annihilate with their opposites arising from another pair-nucleation point: boun- daries of alternating structure have been caught in the process of conversion.It is intriguing to speculate on the details of molecular mechanism, presumably involving rearrangement of hairpins and chain-ends, and perhaps also involving truns- esterification. Finally, it is interesting to observe that the trajectories shown in the ‘schematic diagram’ of plate 2 in Dr Singer’s paper at this Discussion are qualitatively very similar to director trajectories in the specimens of Thomas and Wood. However, Singer’s trajectories, being those of major polarizability in an optically negative nematic, are orthogonal to the director field.In this case, then, it is the director-field which is relatively rich in confluences. One may associate this relationship between the two cases with the fact that in Singer’s material simple shearing flow is easiest on planes orthogonal to the director, whereas in the material of Thomas and Wood it is easiest on planes parallel to the director. I thank Prof. Thomas and Miss Wood for letting me see some of their electron- micrographs in advance, and Dr John Hannay for constructing fig. 1-3 for me. M. B. Dwight, Tables of Integrals (MacMillan, New York, 1947), ( a ) items 432.10 and 603.6; (6) item 436.00; (c) items 512.3, 140.02 and 160.21; ( d ) item 241.01. Prof. E. L.Thomas and Miss B. A. Wood (University of Massachusetts, U.S.A.) said: We thank Sir Charles Frank for the mathematical development of the relation- ship between the molecular director field and the lamellar trajectories in our images. Two main points are brought out by Frank: (i) the (false) impression of ‘orientation domains’ is due to the singularities in the array of lamellae which in fact arise from a continuous underlying molecular-director field ( i. e., there are no molecular-director domain boundaries as defined by surfaces of discontinuous rotation of the molecular director from one domain to the next) although the eye sees apparent domain boundaries in the lamellar trajectories and (ii) the observed textures imply that translational parallelism of the molecular director field is a significant feature in the behaviour of TLCP materials.We accept Frank’s point that the ‘caterpillar’ type arrangement of lamellae (our axial disclinations: see plates 6 and 7 of our paper) are not disclinations of unit strength as we suggested but are as he aptly terms them, ‘lines of confluence’ in the field of lamellar trajectories. The correspondence between Frank’s sinusoidally wrinkled molecular director field (his example 1) and our plate 9 ( a ) is striking. We also accept that the ‘sawtoothed’ molecular trajectories indicated on our plate 4 are drawn unduly straight; Frank’s example 3 can well produce this type of kink band in the field of lamellae without any discontinuities in the molecular-director field [our plate 9(b)].By appropriate choice of the parameters a, b and c the loci of strong curvature in the molecular director field can be restricted to a scale small relative to the width of a kink band, so any degree of sharpness can be produced with mathematically smooth molecular director curves. Note that the experimental determination of the boundary sharpness is limited to a resolution of ca. 100 8, by the inherent size of the lamellae. Evidence for confluences in the molecular-director field is presented in plate 1 of this comment. This micrograph shows sinusoidal lamellar trajectories in a film of the annealed methyl-substituted polymer. Thick dark lines approximately normal to the lamellae occur at inflection points, producing periodic bands. Construction of the orthogonal set of molecular-director trajectories produces the logarithmic singularities of Frank’s example 1 in the centre of each band; the roles of the lamellarGENERAL DISCUSSION 28 1 and the molecular-director field are now exchanged.It remains to understand the origins and inter-relations between the various translationally parallel molecular- director fields. Their nature may reflect the detailed order of the liquid-crystal medium before cessation of flow and subsequent compressive buckling. We stress that the bands ought not to be construed as an intrinsic orientation domain structure of the liquid-crystal medium. Moreover, since banded structures are apparently ubiquitous in flow-oriented liquid-crystal polymers, we suggest that understanding and ultimately controlling the band texture and associated disclinations may assume an importance once reserved for the domain concept in structure-property relations in liquid-crystal polymers.Dr A. H. Windle (University of Cambridge) (communicated): Prof. Thomas has referred to smectic-type organization in thermotropic polymers containing regular lengths of flexible spacer. I should like to ask him if he considers longitudinal positional correlation (or ‘preferred axial stagger’) between the polymer molecules as sufficient justification for the smectic classification. Perhaps it is reasonable in the case of substantial flexible spacers which segregate so as to be alongside like spacers on neighbouring chains and lead to a layer structure within the mesophase. But what if both the rigid and flexible portions of the chains are much shorter and longitudinal correlation still persists? In the extreme, consider a nematic polymer in which there is longitudinal register between monomer units perhaps only 8 A long, but without any long-range positional order in the plane normal to the chains (otherwise it would be a crystal, or at least a plastic crystal). Is that a smectic or a nematic? Prof.E. L. Thomas ( University of Massachusetts, U.S.A.) replied: Chains aligned in the axial direction with no long-range correlation in the lateral direction may be referred to as ‘smectic’ when axial registration is perfect and ‘nematic’ when no axial registration exists. In between these two limits the structure may be referred to as ‘distorted’ smectic.The extent of registration may be quantified by comparing the intermolecular interference function for various layer lines for a uniaxially oriented system. This may be obtained in the following way: if the cylindrically averaged molecular structure factor of the chain is known, then the interchain interference function, Z,, may be obtained by analysis of the scattered intensity distribution of the zeroth-order layer line. Similarly the corresponding inter-chain interference func- tion, Z1, for the first layer line may be determined. Z1 would be a constant for nematic ordering and Z1 = 2, for perfect registration, i.e. smectic ordering.’ In some situations the degree of registration may be defined by a parameter A (see my contribution to the discussion of Prof. Blumstein’s paper).R. Saraf and Y. Cohen, personal communication. Dr A. M. Donald (University of Cambridge) said: Prof. Thomas has presented electron micrographs purporting to show domain structures in a rigid-flexible-spacer spacer main-chain thermotropic polymer. Sir Charles Frank claims these are not ‘domains’ since there need be no abrupt discontinuity in the director field associated with the observed structures. Both these contributions refer to two-dimensional structures. In the thermotropic random copolyester I have been studying in the TEM, the structure cannot always be treated as two-dimensional, which introduces an additional complexity into the problem. The polymer, designated B-N, is based282 GENERAL DISCUSSION shear direction Fig. 4 on hydroxybenzoic anc hydroxynaphthoic acid residues (in the ratio of 7 : 3), and it is upon annealing thin specimens on a rocksalt substrate that a three-dimensional structure develops.When B-N is sheared at 300°C to produce a thin film suitable for the TEM, a banded structure develops. These banded structures, as we have heard in several other presentations, seem to be something of a ubiquitous phenomenon when liquid-crystalline polymers are sheared. The electron microscope is ideally suited to unravelling the underlying molecular trajectory using dark-field techniques, as shown in plate 2. The two dark-field images [plates 2 ( a ) and ( b ) ] are formed from the two wings (ends) of the equatorial arc, and show complementary contrast. The bright-field image [plate 2( c ) ] shows only thickness variations, parallel to the direction of shear, owing to the method of sample preparation.If the objective aperture is moved from the end of the equatorial arc towards the centre, the width of a bright band in the dark-field image increases, showing that there is a smooth variation in the molecular orientation. Fig. 4 shows the molecular trajectory as determined from dark-field micrographs. Three things should be noted in connection with this diagram. First, the TEM provides unambiguous information on the direction of the molecule because direct correlation with the diffraction pattern can be made; the problems associated with optical microscopy because of the possibility of optical biaxiality are sidestepped. Secondly, the distortions involved are mainly bend distortions.The structure does not involve twist distortions at all, which is commonly expected (although I believe without firm evidence for a main-chain thermotropic polymer) to be the lowest- energy distortion. Thirdly, this structure differs from the geometry proposed by Prof. Meyer in his talk. The bands seen here, and in most polymers upon shear, lie perpendicular to the prior shear direction and not parallel. The mechanisms by which they form is still not clear. This banded structure is still essentially a planar structure, but the act of annealing it on a rocksalt substrate leads to a rapid transformation to a very different structure, which at first glance appears to be a ‘domain’ structure. Bright-field contrast is now apparent, with dark ‘veins’ running parallel to the prior shear direction [plate 3( b ) ] .These veins correspond to regions of homeotropy, or near-homeotropy, and look dark because they have a greater cross-section for scattering. In the equatorial dark-field image [plate 3 ( a ) ] , it is apparent that the veins separate regions possessing alternating senses of in-plane misorientation, and the discontinuity appears to be sharp. However, this appearance may be misleading, since the full three-dimensional structure must be considered. Further information on this point can be obtained by tilting the specimen about an axis perpendicular to the prior shear direction. When the specimen is flat the veins are dark, but the contrast elsewhere is fairly uniform [plate 4( a)].Upon tiltingGENERAL DISCUSSION 283 Fig. 5 in one sense alternate ‘domains’ appear dark and light [plate 4(b)]; tilting in the other sense the contrast is reversed [plate 4(c)]. Clearly the veins separate regions which possess opposite senses of molecular tilt out of the specimen plane. Close examination of the appearance of the veins themselves upon such a tilting sequence is also revealing. In plate 5 some rocksalt debris has remained on the specimen surface to act as a marker. The apparent position of the vein, relative to a piece of rocksalt, moves as the specimen is tilted. Remembering that the darkest contrast will be seen where the molecules lie most nearly parallel to the electron beam direction, plate 5 shows that the molecules change tilt smoothly across the veins.Here again we do not have an abrupt discontinuity in the director field, but in this case a variation confined to a few tens of nanometres. Away from this region, the molecular orientation is sensibly constant over several pm. Is this a domain structure? Not according to Sir Charles’ viewpoint, but for many purposes I feel it is an adequate description to talk in terms of ‘domains’, each possessing a uniform orientation separated by a narrow ‘boundary’ or ‘wall’. The structures seen in this polymer can now be related to those described by Prof. Thomas. If the in-plane molecular orientations are drawn (fig. 5, shear direction vertical), they closely resemble the structure around an axial line in Prof. Thomas’ terminology. This structure leads to a large component of splay.As Sir Charles has pointed out, this splay energy may in thin films be relaxed by a ‘sucking in’, i.e. a local thinning, and this seems to be the case shown in plate 4 of Prof. Thomas’ paper. In contrast to this behaviour, B-N exhibits splay compensation by adopting a three-dimensional structure where locally a positive contribution to the splay energy in one plane is compensated by a negative contribution in an orthogonal plane. Two factors appear to encourage this kind of splay compensation in B-N: first the presence of the rocksalt substrate (veins do not develop in samples of B-N annealed without a substrate), and secondly, the presence of sufficient short chains to permit the homeotropy to develop. B-N, of a higher intrinsic viscosity than used in this study, does not exhibit a vein structure.As has previously been pointed out by Meyer, the elastic constants are going to be molecular-weight-dependent, and more data are urgently needed on this point.284 GENERAL DISCUSSION Y Fig. 6 In attempting to understand the structures and defects of these thermotropic polymers, it is dangerous to draw too many parallels between the rather rigid systems I have examined and the flexible-spacer type of Prof. Thomas' work. However, it is interesting to see where similarities exist, pointing to what must be common phenomena. Clearly the structures that are seen are determined to a large extent by the elastic constants. Both the TEM studies of Thomas and Wood and my own confirm the theoretical predictions that splay distortions are of high energy, but the relative magnitudes of bend and twist are not clear.It would be interesting to know if information on this point can be obtained from a detailed analysis of the decorated disclinations seen in the beautiful micrographs of Thomas and Wood. ' A. M. Donald and A. N. Windle, J. Mater. Sci., 1984, 19, 2085. ' Polymer Liquid Crystals, ed. A. Ciferri, W. R. Krigbaum and R. B. Meyer (Academic Press, New York, 1982), chap. 6. Prof. R. B. Meyer (Brandeis University, U.S.A.) said: The subject of splay compensation has been brought up, Le. the idea that splay in one two-dimensional cross-section of a structure can be compensated by splay in a second plane perpen- dicular to the first. This idea is not new.' My paper in this Discussion effectively used this concept, in describing the splay Frederiks transition.The two-dimensional twist structure which replaces uniform splay is essentially a splay-compensated structure, in that cross sections through it appear to be splay patterns. Once one realizes that apparent splay can be compensated to zero in a three-dimensional structure, the next step is to realize that the structure so created is actually composed of twist. Since the twist elastic constant in polymer nematics can be quite low compared with the splay elastic constant, the energy of splay-compensated structures is also low. ' Polymer Liquid Crystals, ed. A. Ciferri, W. R. Krigbaum and R. B. Meyer (Academic Press, New York, 1982), chap. 6. Dr A. H. Windle (University ofcambridge) (communicated): The issue of banded textures has threatened to surface on several occasions during this meeting.DrGENERAL DISCUSSION 285 Mackley showed us the bands actually forming on relaxation from shear deforma- tion, and Dr Zachariades, in his poster, distinguished between liquid-crystalline polymers which form bands during shear and those in which the bands only appear on relaxation from shear. Now the question of their structural significance has again arisen. The textures which can be seen in thermotropic copolyesters are rich in their variety. However, we have found that shear of the mesophase at rates in the approximate range 5 x lo3 to 5 x lo4 s-l (i.e. hand shear of 10 pm thick specimens), followed by reasonably prompt cooling to the solid, invariably produces a banded texture.In fact so general is the effect that we tend to use it as a first diagnostic test for a polymeric mesophase! The bands, which are perpendicular to the direction of shear and of period l-lOpm, can be seen between crossed polars (plate 6) and in dark-field TEM, (plate 7), the latter technique confirming that the molecules follow a periodic serpentine path about the shear axis. Prof. Thomas's comments have now focussed our attention on the possibility of out-of-plane components to the molecular trajec- tories. A scanning electron micrograph of sheared N-QT ([HNA],,, with [TA+ HQ]& obtained by Miss Golombok (plate 8), shows that although there is some detectable surface relief associated with the bands, it is very small compared with the in-plane molecular deviations clearly revealed by the path of the fibrillating crack.A. M. Donald and A. H. Windle, J. Muter. Sci., 1983, 18, 1143. Mr B. Reck (University of Mainz, West Germany) said: We prepared recently a new type of liquid-crystalline side-group polymer' having a polyester main chain instead of the commonly used poly( acrylate), poly( methacrylate) or poly( siloxane) structures: e.g. + (CHd 9 I 0 I c=o I 0 LC__Ix This new main-chain structure opens the way to chiral liquid-crystalline side-group polyesters by incorporation of optically active diols, e.g. ( R ) -3-methylhexane-l,6- diol or the diols used in Prof. Chiellini's work. What properties should one expect for such liquid-crystalline side-group polyesters with a chiral main chain? B.Reck and H. Ringsdorf, Makromol. Chem., Rapid Commun., 1985, 6, 291. Prof. E. Chiellini (University of Pisa, Italy) replied: The new series of polymers mentioned by Mr Reck appears interesting and should offer a valid alternative to the synthesis of a large variety of cholesteric polymers with tunable flexibility, length of helical pitch and selective reflections.286 GENERAL DISCUSSION It is hard to predict what will be the characteristic of the cholesteric array in terms of the twisting power related to a rather flexible main chain containing within the repeating chiral unit two asymmetric carbon atoms, of which the closest to the spaced mesogen may assume either one of two possible absolute configurations. By considering, however, that in some of our preferentially chiral liquid-crystal polyesters containing the mesogen in the main chain a cholesteric structure develops even at fairly low enantiomeric excess (10-20%), one may infer that distinct cholesteric structures should occur even with weak asymmetric perturbations.Dr C. Viney (University of Cambridge) said: I would like to add to Dr Gray's work by making some comments about cellulose nitrates (NC). These polymers are further examples of materials in which the molecules are semi-flexible, elongated and chiral, so that they would be expected to form cholesteric mesophases. Such behaviour has indeed been noted in a wide range of solvents.' Another solvent which should be added to the list is tetrahydrofuran (THF). A given volume dissolves a given weight of NC more quickly than acetone or ethanol, and its action is not restricted to a narrow range of polymer degrees of substitution, 0,.For example, acetone requires D, b 2.4 and ethanol requires D, G 2.4, before significant amounts of material can be dissolved. Using NC having M, = 3 x lo6, I obtained the following results for the critical concentration needed for any mesophase texture formation: polymer D, wt% polymer in THF 2.32 2.45 2.72 15 12 7 (Note that measurements of critical concentration can only be of value if the polymer 0, and molecular weight are quoted; this point is usually overlooked in the literature.) The decreasing critical concentration with increasing 0, is consistent with the corresponding expected increase in molecular rigidity.There is, however, another factor which may be important: as the polymer D, increases, so does the chance of neighbouring molecules having any common sequence of substituted monomers; this must increase the ability of the molecules to become ordered. The type of statistical consideration required to model this behaviour has been introduced (for solid-state ordering) in our paper at this Discussion, for the relatively simple case of a copolymer consisting of only two monomer types. In NC the substitution of anhydroglucose units is irregular. The existence of three hydroxy groups per unsubstituted unit means that nitration of the molecule may lead to a particular unit having any one of the following substitutions: unsubstituted; monosubstituted (3 ways) ; disubstituted (3 ways) and trisubstituted.The nitrated polymer therefore effectively consists of up to eight monomer types. However, within the 0, range 2.32-2.72 referred to above, it has been shown2 that increasing the D, has the following consequences: the partial D, for primary substitution [substitution on the C(6) site] tends to unity, while the number of 6-monosubstituted units tends to zero. This means that what is effectively a random copolymer of eight monomer types at 0,=2.32 becomes a random copolymer of only three monomer types at D, = 2.72. The increased likelihood of local longitudinalGENERAL DISCUSSION 287 register between sections of adjacent molecules must contribute to the lowering of the critical concentration required for lyotropic mesophase formation.D. G. Gray, J. Appl. Polym. Sci., Appl. Polym. Symp., 1983,37, 179. * D. T. Clark, P. J. Stephenson and F. Heatley, Polymer, 1981, 22, 1 1 12. Dr R. R. Luise (Du Pont, WiZmington, D.C., U.S.A.) said: Since anisotropic cellulosic solutions generally have low clearing temperatures, if one dares, one may try to heat one’s solutions above their clearing points, and then cool back to the liquid-crystalline state. In this way, one may obtain the undisturbed equilibrium state, which is more likely to be cholesteric. Dr M. R. Mackley (University of Cambridge) said: Concerning the spinning of mesophase carbonaceous pitch described in Dr Singer’s contribution, does the mechanism for the onion-skin effect have any relation to the skin-core effect observed for thermotropic polymers that we reported in our paper? Dr L. S.Singer ( Union Carbide, Parma, U.S.A.) replied: I do not think that there is any direct connection between the onion-skin mesophase pitch fibre structure which I showed and the skin-core structure discussed in the paper by Alderman and Mackley. Our structure was apparently uniform throughout. The mechanism for the development of the onion-skin structure is not fully understood, but U.S. Patents by Nazem (4376747) and Riggs (4504454) do discuss the matter of transverse fibre structure in considerable detail. Prof. G. C. Berry (Carnegie-MeZZon Uniuersity, U.S.A.) asked: Can Dr Singer provide any information on the dynamic shear moduli (i.e. G’ and G’’) for torsion about the axis of carbon fibres, especially as these might depend on the suprastructure described in his lecture? Dr L.S. Singer ( Union Carbide, Parma, U.S.A.) responded: The dynamic torsion behaviour has been studied by Fischbach and coworkers on a variety of carbon-fibre types, including PAN, rayon, isotropic pitch and mesophase pitch. The most recent detailed study of mesophase-pitch-based carbon fibres was made by Fischbach and Srinivasagopalan.’ They found that, qualitatively, all the fibres behave similarly ; however, the effective torsional moduli are consistent with differences in the micro- structure of the fibres. D. B. Fischbach and S. Srinivasagopalan, Proc. 5rh London Inr. Carbon and Graphite Con$, Imperial College, London, 1978 (Society of Chemical Industry), vol. I, pp. 389-397. Prof. E. L. Thomas (University of Massachusetts, U.S.A.) said: Can Dr Singer tell us how to tailor the spinning process so as to produce fibres with onion-skin texture and fibres with radial texture? Dr L. S. Singer (Union Carbide, Parma, U.S.A.) replied: Yes and no. The development of orientation and texture in fibres spun from liquid-crystal systems such as mesophase pitch is determined by the intrinsic structural and rheological properties of the pitch and the flow-orientation forces during spinning. As one might expect, the phenomena are either not well understood, proprietary, or both. Two recent U.S. patents by Nazem (4 376 747) and Riggs (4 504 454) are relevant.3 Bb molecular director fields. Plate 1. Bright-field electron micrographs illustrating some of the types of lamellar trajectories and their associatedPlate 2. ( a ) and ( 6 ) : Dark-field images of an as-sheared sample of B-N. The images were formed from the two wings of the equatorial arc and show complementary contrast. (c) The corresponding bright field image.Plate 3. Equatorial dark-field ( a ) and bright-field (6) images of B-N annealed for 10 min on a rock salt substrate at 300 "C.Plate 4. Bright-field images of B-N annealed for 10 min at 300 "C on a rocksalt substrate: ( u ) flat; (6) tilted through +24"; (c) tilted through -24" about the horizontal axis, which is perpendicular to the prior shear direction.Plate 5. Three bright-field micrographs showing changes in the apparent position of veins relative to rocksalt debris, on tilting the specimen about the horizontal axis (shear direction vertical): ( a ) 0"; ( b ) -24" and (c) +24". Plate 6. Banded texture in B-ET. The shear axis is horizontal (C. Viney).Plate 7. Dark-field TEM micrograph showing bands perpendicular to the shear direction. They cannot be seen clearly in bright field.' Plate 8. A sample of a copolyester (N-QT) sheared (bottom left to top right) to produce banded texture, seen in the SEM. The fibrillations reveal the sinusoidal trajectory of the molecules about the shear axis.