Faraday Discuss. Chem. SOC., 1985,79, 41-53 Configurational Characteristics and Nematic Order of Semiflexible Thermotropic Polymers BY Do Y. YOON," SERGIO BRUCKNER,~ WILLI VOLKSEN AND J. CAMPBELL SCOTT IBM Research Laboratory, San Jose, California 95193, U.S.A. AND ANSELM C. GRIFFIN Department of Chemistry, University of Southern Mississippi, Hattiesburg, Mississippi 39406, U.S.A. Received 2 1 st January, 1985 The stability and the molecular order of nematic states of thermotropic polymers compris- ing rigid groups connected by flexible spacers are found to be dominated primarily by the characteristics (configurational partition function) of highly extended conformers, which are favoured for packing. Moreover, both the macroscopic consideration of the enthalpies and the entropies of isotropic-nematic transitions and the microscopic probe by deuterium n.m.r.of labelled chains lead to the conclusion that the highly extended conformers are selected preferentially in polymeric nematogens. A number of unique results exhibited by polymer liquid crystals, i.e. strong effects of even-odd character of polymethylene spacers, abnor- malities associated with -C( =O)O- links [compared with -0- and -OC(=O)- links] between rigid (phenylene) groups and polymethylenes and drastic differences between poly- methylene and polyoxyethylene spacers, can all be attributed quantitatively to this conforma- tional ordering, which is the most prominent feature distinguishing polymer liquid crystals from their monomeric counterparts. The orientational order parameters of a nematic polymer measured from both D and H n.m.r.spectra of labelled chains are found to be quite high, ca. 0.8 throughout the nematic region. These findings on conformational order and orienta- tional order of polymer liquid crystals are compared with theoretical predictions based on ideal lattice chains and worm-like chains. The liquid-crystalline state of bulk polymers presents challenging scientific prob- lems as well as new technological applications. The molecular or structural factors controlling its stability over the isotropic state of random chains are directly related to the fundamental question of the packing of long-chain molecules to a high density in the condensed state. It is now well established that polymer chains with sufficient flexibility and negligible orientation-dependent (anisotropic) interactions assume unperturbed random-coil configurations in the undiluted amorphous state, unaffected by the intermolecular interactions.' In this regard, polymer liquid crystals are a clear reminder of the critical importance of intermolecular interactions for chains with incomplete flexibility and/ or appreciable anisotropic interactions. Liquid-crystalline polymers comprising rigid units connected by flexible spacer groups have been studied most prominently in recent years, mainly owing to the presence of well defined isotropic-liquid-crystalline transitions in these polymers.* The rigid groups which normally contain aromatic units introduce both limited flexibility and anisotropic interactions.Therefore these polymers may serve as model 7 IBM World Trade Postdoctoral Fellow.Permanent and present address: Dipartimento di Chimica, Politecnico di Milano, Milan, Italy. 4142 NEMATIC STATES OF THERMOTROPIC POLYMERS \o x o\ 00 v) c? CI - s I o=w 0 n > U WD. Y. YOON et al. 43 systems for trying to understand the packing of real polymer chains in the condensed state.394 For this class of thermotropic polymers it is now well established that the spacer groups play critical roles in determining the stability of the liquid-crystalline state over the isotropic state. This is demonstrated most clearly by the results listed in table 1, namely large oscillations of clearing temperatures, enthal y and entropy changes with the even-odd alternation of polymethylene spacers:-' the abnormal effect of the -C(=O)-0- group between the rigid (phenylene) units and poly- methylene spacers compared with the -0- or OC(=O)- linkages'?' and the rather drastic reduction in the enthalpy and entropy changes effected by polyoxy- ethylene spacers in comparison with polymethylenes." These examples show unambiguously that the spacers are not merely playing the role of solvents, but rather participate actively in the ordering process in the nematic state. Hence the nature of molecular order in nematic polymers and its dependence on chemical structures of polymers are the most pertinent questions.Recently we have investigated the molecular order in polymer liquid crystals by selecting conformations on the basis of chain-sequence extension to match the macroscopic thermodynamic properties of transition enthalpies and entropies as well as the microscopic deuterium n.m.r.spectra of labelled chains.12 The highlights of these studies are summarized in this paper and their detailed descrip- tions will be presented ~eparately.~"~-'* DISTRIBUTION OF CHAIN-SEQUENCE EXTENSION The total partition function of a bulk system of chain molecules may be factorized into three contributions by13 where Z,, denotes the steric repulsion, Zen is the orientation-dependent (anisotropic) intermolecular attractions and Zconf represents the configurational degrees of free- dom. Adopting the lattice treatment of Flory and Ronca, l4 the orientation-dependent part of the steric exclusion may be expressed by where X is the ratio between the contour length and the mean diameter of the chain, + is the angle between a chain segment (placed in a lattice cell) and the macroscopic orientation axis and the angle brackets denote averaging over all chain segments.The contribution of anisotropic attractions are likewise described by where T* denotes the magnitude of anisotropic interactions per chain segment of unit axial ratio and the angle brackets with subscript r refer to averaging over the rigid units only, which are the major source of anisotropic attractions. Hence the ordered state is driven by the favourable steric and anisotropic interactions, while sacrificing the configurational degrees of freedom, over the disordered state. Maximization of the steric partition function requires minimizing the value of (sin +), which is averaged over all the chain segments of rigid and flexible groups.This implies that highly anisotropic (extended) configurations will be favoured for the steric-packing consideration. The configurational anisotropy44 NEMATIC STATES OF THERMOTROPIC POLYMERS 0 5 10 15 20 25 dal A Fig. 1. (a) Distribution of chain-sequence extension calculated for polymer I at T = 500 K; the chain sequence refers to a rigid group and a spacer. (b) Orientational correlations of rigid units with the major extension axis and the average conformational energy plotted against the chain-sequence extension; the dashed line denotes the average energy of all conformers. 4.0 2 3.0 E '= 2.0. I h 0 : ' . O - - 0.0 200 - Ti* v 5 loo - 0 1 .o A 8 0.6 9 N mlN I - .0.2 5 10 15 20 25 d,/ 8, Fig. 2.Distributions of chain-sequence extension, orientational correlations of rigid units and the average energy as a function of sequence extension, calculated for polymer I1 at T = 500 K: see caption to fig. 1. here is defined with respect to the major (alignment) axis of chain sequences, which may be identified as the axis along which the total projection of the two rigid groups appended at the ends of a spacer group is maximized. The extension of chain sequence along this axis is therefore a proper measure of the anisotropy of spatial configurations, which is most critical to packing. On the other hand, the anisotropicD. Y. YOON et al. 45 Fig. 3. Distributions of chain-sequence extension, orientational correlations of rigid units and the average energy as a function of sequence extension, calculated for polymer 111 at T = 400 K.The interaction E, denoting the energy of gauche relative to trans state for the O-CH2&CH2-0 bond is taken to be -0.7 kcal mol-'; see caption to fig. 1. Fig. 4. Distributions of chain-sequence extension, orientational correlations of rigid units and the average energy as a function of sequence extension, calculated for polymer IV at T = 360 K; see caption to fig. I .46 NEMATIC STATES OF THERMOTROPIC POLYMERS 1.6 1 1 .o' CI 0.6 5 0 -IN 24 v 0.2 h i? G s 1.2 i;i' 0.8 - N I 0 5 10 15 20 25 da/A Fig. 5. Distributions of chain-sequence extension, orientational correlations of rigid units and the average energy as a function of sequence extension, calculated for polymer V at T = 400 K.The interaction Em denoting the energy of gauche relative to trans state for the O-CH2tCH2-CH, bond is taken to be -0.4 kcal mol-'; see caption to fig. 1. attractions can be maximized by aligning only the rigid groups; the detailed configur- ations of the intervening spacer groups are less critical in this regard. The distribution of chain-sequence extension, d,, calculated in this way employ- ing the rotational isomeric-state models'09" are presented in fig. 1-5 for the five different chain structures, denoted by I-V, as shown in table 1 ; each sequence comprises a rigid group and a spacer. They differ mainly in the even-odd character of the number of spacer bonds and the way the oxygen atoms are placed along the chain backbone; the differences in the rigid groups are inconsequential in these comparisons.Also shown in these figures are the average energies and the orienta- tional correlations of two successive rigid groups along the major extension axis for these conformers falling within a given range of d,. Polymer I exhibits a large fraction of highly extended conformers with the maximum allowed extension d, = 23 A. Orientational correlations of rigid groups exhibit a distinctively bimodal character with all the conformers with d, 3 18 A placing the rigid groups parallel to each other. Among these the conformers with da = 23 A are quite unique in that their (conformational) energy is much lower, by ca. l.Okcalmol-', than the average energy for all the conformers shown by the dotted line in fig.1. They are found to comprise a set of conformers that place every second bond starting from the 0-CH2 (attached to the phenylene oxygen) in the trans state. Owing to the nearly tetrahedral bond geometry involved, all the conformers of this type not only place the successive rigid groups aligned to each other, but also separate them at the same (maximum) extension along this alignment axis regardless of the conformations of the intervening bonds; see the schematic illustration in fig. 6. Polymer I1 with odd-numbered polymethylene spacers, on the other hand, exhibits a very small fraction of highly extended conformers. Furthermore, the relatively extended conformers place the two rigid groups at the ends of a spacer tilted by ca.30" from the major extension axis. Moreover, the relatively extended conformers making up significant enough fractions exhibit energies which are only slightly lower than the average energy. The contrast between the even- andD. Y . YOON et al. 47 'c-c, c-c, t' Fig. 6. Schematic drawings of the spacer conformers exhibiting the maximum extension along the major axis defined by the two rigid units at the ends of the spacer group. The bold lines denote the bonds that assume exclusively ?runs conformations, and the remaining bonds assume the normal conformations according to their statistical weights. The bonds denoted by t" refer to the trans states which are of higher energy than the alternative gauche states. the odd-numbered polymethylene spacers is therefore rather dramatic in these considerations.Polymer 111, which has even-numbered (8) skeletal atoms between linear rigid groups, also exhibits a peak of highly extended conformers and the bimodal distribu- tion of orientational correlations of rigid groups that resemble very closely to those of polymer I. However, a very important difference is noted in the energy of the most extended conformers, which is nearly identical to the average energy in contrast to the large decrease in polymer I. This difference can be traced to the unique feature of the O-CH2+CH2-0 rotation, which favours the gauche state over the trans by ca. 0.4-0.7 kcal m ~ l - ' . ' ~ ~ ' ~ As shown in fig. 6, the highly extended conformers place the O-CH2-&-CH2-0 rotation marked by t* in the trans state exclusively, thereby increasing the energy of these extended conformers.The characteristics of polymer IV are very much the same as those of polymer I. Therefore, the effect of the -OC(=O)- linkage between the phenylene unit and polymethylene spacers is nearly identical to that of the -0- linkage. On the other hand, the -C(=O)O- linkage in polymer V leads to drastically different characteristics, as the results of fig. 5 demonstrate. The population of highly extended conformers is much smaller than that of polymer IV; furthermore, the distribution is skewed toward small values of d,, which is even smaller than that of polymer I1 despite the even-odd difference in polymethylenes. The origin of this drastic change is illustrated in fig. 6; the highly extended conformers of polymer V place the two O-CH2+CH2-CH2 rotations in the trans state, which is of higher energy than the gauche by CQ.0-0.4 kcal mol-1.'6 This situation is completely avoided in polymer IV. This situation is also avoided upon replacing the even-numbered polymethylenes with odd-numbered ones, and hence the polymers with odd- numbered polymethylene spacers do not exhibit this drastic effect."48 NEMATIC STATES OF THERMOTROPIC POLYMERS Comparisons of the characteristics of chain-sequence distributions discussed above with the experimental results of isotropic-nematic transitions of these poly- mers in table 1 show unambiguously the critical importance of highly extended conformers in determining the stability of the liquid-crystalline state of polymers.Furthermore, the enthalpies of the isotropic-nematic transitions seem to reflect directly thn energy of the highly extended conformers, as the comparison of polymer I with polymer I11 demonstrates most strikingly. Therefore, it is obvious that highly extended conformers are selected preferentially in the nematic state. CONFORMATIONAL ORDER The detailed conformational order in the nematic state may then be determined by selecting the conformers on the basis of chain-sequence extension to match the available experimental results. For this purpose we have considered both the macroscopic thermodynamic properties of the enthalpies and the entropies of isotropic-nematic transitions and the microscopic spectroscopic results of deuterium n.m.r. of labelled polymer I.ENTHALPY AND ENTROPY OF THE ISOTROPIC-NEMATIC TRANSITION The enthalpy of the isotropic-nematic transition arises from both orientational order and conformational order, as is apparent from eqn ( 1 ) and ( 3 ) . The orienta- tional contribution can be estimated according to eqn (3) from the enthalpy of the corresponding monomer and the ratio of the orientational-order parameter of the polymer to that of the monomer, assuming that the conformational ordering is negligible in monomeric nematogens. For the corresponding monomer of polymer I, AHNI = 0.18 kcal mol-' and s == 0.37 at the transition.6 The order parameter, sN1=O.75, of polymer I at the transition12 (see below) then leads to an estimate of ca. 0.74 kcal per mole of repeat unit (mru) for the enthalpy due to orientational ordering; the repeat unit here refers to a rigid group and a spacer.Since this procedure attributes the enthalpy change ofthe monomer entirely to the orientational order and thus neglects any contribution from conformational changes, this estimate represents an upper bound. Comparison with the experimental results then requires the conformational contribution to the enthalpy to be at least 0.8 kcal (mru)-'. From the results of average energy as a function of the sequence extension d, shown in fig. 1 it is obvious that this conformational enthalpy is obtainable, provided that only those conformers with the sequence extension d, = 23 A are selected in the nematic state: see table 2. The entropy change has contributions from the conformational order and the steric (packing) interactions.The conformational contribution can be estimated from Ah AS,=-k lnfN+- TN I (4) where fN is the fractional configurational partition function of the conformers selected in the nematic state, k is Boltzmann's constant, Ah denotes the decrease of the energy of these conformers relative to the average and TNI is the temperature of the isotropic-nematic transition. The steric packing contribution to the entropy is obtained from eqn (2) by averaging the value of sin t,b over the rigid and spacer groups in proportion to the contour length. For this purpose the spacer group isD. Y. YOON et al. 49 Table 2. Calculated and experimental values of enthalpy and entropy changes at the isotropic-nematic transition of polymer I AH/kcal (mru)-' AS/cal (mru)-' K-' ~~ steric interactions - anisotropic interactions 0.74 conformational ordering 0.98 total calculated" 1.72 experimental 1.56 ~~ -3.3 6.3 3 .O 3.2 - All the calculations are carried out at 500 K, taking the axial ratio of the repeat unit to be ca.5.3. Ref. (6). Table 3. Calculated and experimental values of enthalpy and entropy changes at the isotropic-nematic transition of polymer I11 AH/kcal (mru)-' AS/cal (mru)-' K-' steric interactions - anistropic interactions 0.74 total calculated" 0.74 experimental 0.46 conformational ordering 0.0 -3.35 4.76 1.41 1.13 - " All the calculations are carried out at 400 K, taking the axial ratio of the repeat unit to be ca. 4.6. Ref. (10). represented by lattice cells, the length of each approximating the average chain diameter." The total entropy change calculated in this manner for polymer I by selecting only those conformers with the sequence extension d, = 23 A matches very closely the experimental result, as shown by the comparison in table 2.For polymer I11 the orientation-order parameter in the nematic state has not been determined, but the order parameter of the corresponding dimer" is nearly identical to the value, ~ ~ ~ ~ 0 . 4 9 , reported for the dimer of polymer I.6 Hence the orientational contribution to the enthalpy may be taken to be identical to that of polymer I. The transition enthalpy and entropy thus calculated by selecting only those conformers with the maximum sequence extension d, B 20 I$ also match closely the experimental results, as shown in table 3.For this polymer the conforma- tional ordering contributes little to the enthalpy change, whereas this conformational contribution is dominant for polymer I. The large difference in enthalpy changes between polymer I and polymer I11 can therefore be attributed almost entirely to the energies of their extended conformers illustrated in fig. 6. The fact that the entropy change for polymer I1 is much smaller than that for polymer I indicates that the conformational restriction is not so severe for the odd-numbered polymethylene spacers. Good agreement with experimental results for enthalpy and entropy changes is obtained by selecting all the conformers with their sequence extensions d , ~ 18 A. Since all these conformers place the rigid groups tilted by ca.30" from the major extension axis, with their orientational correlations of ca.0.6, the order parameter of the rigid units is expected to decrease accordingly. The estimate of the orientational contribution to the transition enthalpy has thus been reduced from that of polymer I according to eqn ( 3 ) .50 NEMATIC STATES OF THERMOTROPIC POLYMERS I " l 1 " " l l -60 -30 0 30 60 f l k H z Fig. 7. Traces of the deuterium n.m.r. spectra of the labelled polymer I, with C,0D20 spacers, at various temperatures in the nematic region reached by heating the sample through the crystalline-nematic transition. DEUTERIUM N.M.R. SPECTRA OF LABELLED POLYMER I The chain conformations in the nematic state have also been investigated with the microscopic probe of deuterium n.m.r.spectra of polymer I in which the protons of the spacer groups are replaced by deuterium.12 The deuterium n.m.r. quadrupole splitting for each C-D bond in the aligned nematic state can be approximated taking the fast motion limit:I8 where e2qQ/h ( = 174 kHz) is the quadrupolar coupling coiistant, s denotes the (orientational) order parameter of chain segments with respect to the director of the nematic domain, 4 represents the angle between the C-D bond and the alignment axis of chain segments and the angle brackets denote averaging over all the allowed conformations. The deuterium n.m.r. spectra of the labelled polymer I, (C10D200C6H4- COOC6H40C10D200C6H400CC6H40)x, in the nematic temperature region are shown in fig. 7. The central peak, whose intensity increases with temperature, reflects the presence of the isotropic phase coexisting with the nematic phase, owing to the relatively low average molecular weight and the polydispersity of the sample.Aside from this central peak, the five distinguishable CD, groups of the polymer exhibit only one quadrupole splitting throughout the nematic range, thereby indicating severe restrictions on the chain conformations for the ordinarily flexible C10D20 group. This deuterium n.m.r. result may also be analysed by selecting the conformers on the basis of chain-sequence extension. All the conformers with d, b 18 8, place the two successive rigid groups parallel to each other, so that the alignment axis of chain segments virtually coincides with the phenylene-0 bond in fig.6.The deuterium n.m.r. spectra thus calculated according to eqn (5) for the three groups of conformers, which differ in the minimum allowed sequence extension, are plotted in fig. 8. Only those conformers with d, = 23 8, exhibit one quadrupole splitting, in agreement with experimental results. Adding the conformers with d, = 21 8, leads to three quadrupole splittings, and further addition of less extended conformersD. Y. YOON et al. 51 - f l k H z Fig. 8. The deuterium n.m.r. spectra calculated for the labelled polymer I by including only those conformers whose sequence extensions d, fall in the range indicated: ( a ) 23, ( b ) 221 18 A. The orientational-order parameter is taken to be 1 in these calculations. -60 -30 0 30 60 and (c) with d, 2 18 A leads to larger separation of two external splittings.Therefore, the chain conformations consistent with the deuterium n.m.r. spectra of labelled polymer I is in good agreement with the conclusion drawn above on the basis of the enthalpy and entropy changes at the isotropic-nematic transition. This excellent agreement may also be taken as evidence confirming our procedure of estimating the enthalpy and entropy changes. ORIENTATIONAL ORDER The orientational-order parameter of polymer I can be determined from the magnitude of the deuterium n.m.r. quadrupole splittings according to eqn ( 5 ) , once the general profile is matched by the specific conformations as described above. The order parameters thus obtained at different temperatures while the sample is heated (filled circles) or cooled (open circles) are plotted in fig.9. Since the alignment axis of these conformers are taken to coincide with the phenylene-0 bond, the proton n.m.r. dipolar splittings of the same labelled polymer, which are dominated by the interactions of the vicinal protons of the phenylene group, can also be used to determine the order parameters fromlg 3 y2h ~ I T rL-H 28, =-- S where y is the gyromagnetic ratio of the proton, h is Planck’s constant and TH-H denotes the distance between two vicinal protons of the phenylene group. Taking TH-H to be 2.45 A leads to a value of 24.5 kHz for the case of perfect alignment. The experimental results of the proton n.m.r. dipolar splittings in the nematic state of labelled polymer I, obtained while the sample is heated through the crystalline- nematic transition, are shown in fig.10, and the order parameters determined from these spectra are plotted in fig. 9 as filled triangles. Excellent agreement between the results deduced from deuterium quadrupole splittiilgs and proton dipolar splittings further confirms our interpretation of deuterium n.m.r. spectra in terms of the specific nematic conformations described above.52 NEMATIC STATES OF THERMOTROPIC POLYMERS 0.9 0.8 S 0.7 0.6 170 180 190 200 210 220 T / "C Fig. 9. Orientational-order parameter of the labelled polymer I in the nematic state plotted against temperature. 0, Results determined from the deuterium n.m.r. quadrupole splittings in the nematic state reached by heating through the crystalline-nematic transition; 0, deuterium n.m.r.results in the nematic state cooled from the isotropic state; A, results from the proton n.m.r. dipolar splittings for the sample heated through the crystalline-nematic transition. The solid line is drawn through the experimental points to extrapolate to the clearing temperature. L 202 197 187 172 I I I 1 I I 1 f / k H z Fig. 10. Traces of the proton n.m.r. spectra from the labelled polymer I with C,0D20 spacers obtained at the nematic temperatures indicated when the sample is heated through the crystalline-nematic transition. -30 -20 -10 0 10 20 30 The orientational-order parameter of the nematic state of polymer I is ca. 0.8 throughout the nematic range and extrapolates to ca. 0.75 at the isotropic-nematic transition. This is in close agreement with the results of Martins et aL2' on polymer IV, determined from the proton n.m.r.dipolar splittings of unlabelled polymer. These results from n.m.r. measurements represent the order parameters of the nematic phase aligned in the applied field. In this regard the n.m.r. methods are preferable to other methods such as diamagnetic anisotropy, i.r. dichroism etc. that average over the entire sample, since these methods may overlook the possibility of coexisting isotropic phase and/or the nematic domains which have not been aligned properly, leading to lower estimates of nematic-order parameters.D. Y. YOON et al. 53 Table 4. Calculated and experimental values of enthalpy and entropy changes at the isotropic-nematic transition of polymer I1 AH/kcal (mru)-' AS/cal (mru)-' K-' steric interactions - anisotropic interactions 0.27 conformational ordering 0.40 total calculated" 0.67 experimental 0.92 -Oh3 - 2.15 1.52 2.0 " All the calculations are carried out at 500 K, taking the axial ratio of the repeat unit to be CQ.5.0. Ref. (7). DISCUSSION The conformational order in nematic polymers is found to be severely restricted to the highly extended configurations, indicating the dominant effect of steric packing interactions. This finding is also consistent, qualitatively at least, with the result of Monte Carlo simulations on cubic-lattice chains which show the ordered state to exhibit nearly perfect order both in conformation and orientation. In this regard, the presence of significant fractions of gauche bonds in the nematiqstate of polymer I may be attributed to the different geometrical features of polymethylene chains and thus points to the shortcomings of the cubic-lattice model in representing the diverse configurations of real chains.The orientational-order parameter, sNI == 0.75, at the isotropic-nematic transition of polymer I is rather high, falling in the upper limit of the predictions of worm-like chains.13 However, it is still substantially lower than the perfect alignment predicted for the lattice chains. This deviation may be related to the fact that real chain conformations exhibit departures from the strictly lattice-like characteristics owing to the appreciable range, ca. 20°, in the allowed torsional' angles around each rotational isomeric state of polymethylene chains.I6 Therefore both conformational order and orientational order of polymer liquid crystals are likely to depend on subtle details of chain configurations of real polymers. P. J. Flory, Faraday Discuss. Chem. SOC., 1979, 68, 14. P. J. Flory, Proc. R. SOC. London, Ser. A, 1984,234,73; Proc. Natl Acad. Sci. USA, 1982,79,4510. D. Y. Yoon and A. Baumgartner, Macromolecules, 1984, 17, 2864. A. C. Griffin and S. J. Havens, J. Polym. Sci., Polym. Phys. Ed., 1981, 19, 951. G. Sigaund, D. Y. Yoon and A. C. Griffin, Macromolecules, 1983, 16, 875. A. Blumstein and 0. Thomas, Macromolecules, 1982, 15, 1264. A. Blumstein, S. Vilasager, S. Ponrathnam, S. B. Clough and G. Maret, J. Polym. Sci., Polym. Phys. Ed., 1982, 20, 877. W. Volksen, D. Y. Yoon, S. Bruckner and J. C. Scott, work in preparation. S. Bruckner, J. C. Scott, D. Y. Yoon and A. C. Griffin, Macromolecules, in press. * See, for example, C. K. Ober, J-I. Jin and R. W. Lenz, Adv. Polym. Sci., 1984, 59, 103. ' A. C. Griffin and D. Y. Yoon, work in preparation. 10 l 1 D. Y. Yoon and S. Bruckner, Macromolecules, 1958, 18, 651. l 3 G. Ronca and D. Y. Yoon, J. Chem. Phys., 1982,76, 3295. l4 P. J. Flory and G. Ronca, Mol. Crysf. Liq. Cryst., 1979, 54, 289. I s P. J. Flory and G. Ronca, Mol. Cryst. Liq. Cyst., 1979, 54, 311. l 6 P. J. Flory, Statistical Mechanics of Chain Molecules (Interscience, New York, 1969), chap. V. '' E. Riande, J. Guzman and M. A. Llorente, Macromolecules, 1982, 52, 298. A. D. Buckingham and K. A. McLauchlan, Prog. Nucl. Magn. Reson. Spectrosc., 1967, 2, 63. l9 F. Volino, A. F. Martins and A. J. Dianoux, Mol. Cryst. Liq. Cryst., 1981, 66, 37. *' A. F. Martins, J. B. Ferreira, F. Volino, A. Blumstein and R. B. Blumstein, Macromolecules 1983, 12 16, 279.