Faraday Discuss. Chem. SOC., 1985, 79, 7-20 Macromolecular Structure and Liquid Crystallinity BY EDWARD T. SAMULSKI Department of Chemistry and Institute of Materials Science, University of Connecticut, Storrs, Connecticut 06268, U.S.A. Received 13th April, 1985 The relationship between low-molar-mass or monomeric liquid crystals and polymeric liquid crystals is explored by examining the historical development of experimental and theoretical aspects of the latter materials. Polymeric liquid crystals are initially contrasted with conventional, non-mesogenic, flexible polymer chains (random coils), and then semi- flexible and rigid-rod polymers are examined. Both thermotropic and lyotropic phases are described, with emphasis placed on the former; in particular, the relationship between dimers and polymers belonging to the semi-flexible category: +(mesogenic core) -(flexible spacer)-+,.The review concludes by drawing attention to the curious behaviour of polypeptide liquid crystals (cholesteric compensation). The underlying theme of the lecture is the need to recognize the synergism and affinity that characterizes research on monomeric and poly- meric liquid crystals. Polymer chemists and physicists have for many years acknowledged in a limited way the relevance of the research effort in liquid crystals to aspects of their own research. They occasionally borrowed nomenclature (‘nematic’ and ‘smectic’) to describe the kinds of supramolecular organization that they presumed must exist in condensed phases of polymers. Some of the early textbooks on high polymers even included a section on the classification of liquid crystals.Today with the increasing interest in ordered, fluid phases composed of macromolecules (polymeric liquid crystals) the research activity in these two formerly distinct areas is becoming synergetic. Subtle phenomena, difficult to investigate in Conventional liquid crystals, are often exaggerated in polymeric liquid crystals. Moreover, the process of extend- ing and refining the modelling of liquid crystals to include polymers is giving us a clearer view of the dominant molecular forces that stabilize the liquid-crystal state. In this lecture I preface a discussion of a few aspects of polymeric liquid crystals that I find particularly intriguing with a brief historical development of the field from my own and necessarily limited perspective.HISTORY Vorlander’s prodigious contribution to liquid-crystal research during the first quarter of this century displayed admirable chemical intuition. Working with little more than the notion that lath-like molecules (I) are predisposed to form liquid- l a t h - l i k e me M LC8 MOLECULAR STRUCTURE AND LIQUID CRYSTALLINITY crystalline melts, he postulated that ‘infinitely long mesogens’ would be compatible with the supramolecular organizational constraints in liquid crystals.’ In addition to this superficial reference to the plausibility of preparing a polymeric liquid crystal (PLC), Vorlander subsequently synthesized a dimer liquid crystal (DLC), a mesogen consisting of two lath-like segments (mesogenic cores) joined together with a flexible alkyl chain (spacer).2 The DLC (11) is currently a subject of active research core - spacer in model compound studies that have a direct bearing on linear, semi-flexible,PLCs (111) composed of polymer chains having the regular alternating sequence: +( mesogenic core) - (spacer)+,. After Vorlander’s early contributions, research mainchain PL C on PLCs in the second quarter of this century was, for all practical purposes, dormant. In fact, until the late 1960s, when the industrial potential of PLCs was recognized, only a very few isolated, albeit significant, discoveries relevant to PLCs were reported.A brief chronology of these contributions follows. Birefringent solutions of rod-like virus particles (lyotropic PLCs) were reported in the late 1930s and early 1940~.~ Following this observation Onsager demonstrated that a gas composed of ideal, rigid rods will exhibit a spontaneous transformation from an isotropic to a quasiparallel (nematic) distribution of rods when the density of the gas exceeds a critical value which in turn is an explicit function of the aspect ratio of the This first reasonable model of the nematic-isotropic phase transition was essentially ignored by the modest mainstream of research on conven- tional, low-molar-mass, thermotropic liquid crystals. [Herein I designate such conventional mesogens MLCs (‘monomer’ liquid crystals) irrespective of whether or not such mesogens may be polymerized.] The (Y -helical, rod-like, synthetic polypeptide, poly( y )-benzyl-L-glutamate (PBLG), was shown to form a lyotropic PLC in a variety of common organic solvents in the early 1950s.The initial interest in this seemingly esoteric biopolymer was industrially motivated: Courtaulds Ltd was seeking new fibre-forming polymers and considered synthetic polypeptides because naturally occurring polypeptides ( e.g. wool) exhibit excellent properties.’ Although the anticipated useful properties of PBLG did not materialize, it was comprehensively studied at the Courtaulds Ltd Research Laboratory in Maidenhead and played a significant role in the elucidation of the structural architecture of the ( ~ - h e l i x . ~ . ~ In fact, it was during the preparation of oriented specimeps for i.r.-dichroism studies of the a-helix that the unusual properties of concentrated solutions of PBLG were first noticed.8 Robinson and coworkers then characterized the PBLG liquid crystal, demonstrating that the chiralE.T. SAMULSKI 9 rods (right-handed a-helices) assumed a twisted nematic (cholesteric) supramolecular arrangement in the lyotropic m e s ~ p h a s e . ~ - ~ ~ At roughly the same time and also in England, Flory, using the lattice theory of polymer solutions, replaced flexible chains with rigid rods and demonstrated the formation of an ordered phase above a critical volume fraction of rods that depends on the rod aspect ratio.14 With the exception of isolated comparisons of theory and experiment on the contemporaneous lyotropic polypeptide liquid cry~tals,’~ as in the case of the Onsager model, this advance in the delineation of the role of anisotropic repulsion (steric interactions) in stabilizing mesophases did not gain widespread acceptance.It was largely overshadowed by the mean-field model of Maier and Saupe of the isotropic-nematic phase transition, which implicated anisotropic attraction (dispersion forces) as the source of mesophase stability.16 The latter model influenced the design and synthesis of new classes of thermotropic MLCs into the 1960s and 1970s. The relative importance of repulsive and attractive interactions has been recently reassessed by theorists ;17-19 this reassessment has been reinforced by the discovery of completely aliphatic MLCs (mesogens with negligible polarizability anisotropy).20 In the last decade both the Onsager and Flory models have been re-examined and modified to include the influences of rod flexibility, anisotropic attractive forces, rod length distributions and mixing of rods with random-coil polymers: Flory has recently reviewed these extensions of the lattice theory?l and a modified Onsager model is considered in the review by Grosberg and Khoklov;22 more contemporary approaches to modelling PLCs are available in ref.(23). In the mid 1960s MLCs with a single functional group (e.g. a vinyl group) were polymerized to form a sidechain PLC (IV). Melts of such sidechain polymers W sidechain PLC retained liquid-crystal textures (nematic, smectic and cholesteric) over a well defined temperature range usually in excess of that exhibited by the MLC; i.e. the PLC mesophase relative to the MLC could be ‘stabilized’ uia p~lymerization.~~ I am not aware of a scientifically compelling rationale for synthesizing sidechain PLCs in the 1960s.If activities in Tobolsky’s laboratory at Princeton University were rep- resentative of the times, sidechain PLCs were synthesized only because they could be prepared by non-synthetically inclined students of physical chemistry, e.g. cholesterol acrylate, a commercially available MLC, could be heated into its cholesteric phase, allowing the thermally induced polymerization to proceed ; a solid, dimensionally stable, cholesteric polymer film which reflected irridescent colours was ~btained.~’ Since these early crude experiments, technologically impor- tant end-uses for sidechain PLCs have been identified: (1) cholesteric PLCs function as tunable-wavelength reflectors and notch filters ;26 (2) sidechain copolymers solubil- ize dichroic dye additives to electro-optic displays;27 (3) they serve as a non- centrosymmetric host matrix for hyperpolarizable guest molecules in non-linear optical devices ;28 (4) lyotropic smectic MLCs can be polymerized to stabilize vesicles10 MOLECULAR STRUCTURE AND LIQUID CRYSTALLINITY in drug-delivery schemes.29 Extensions of the latter to smectic monolayers could stabilize thin organic dielectric layers for microelectronic device fabri~ation.~' Lyotropic sidechain PLCs having amphiphillic sidechains have been prepared and their aqueous phases characterized.26 There have also been efforts to incorporate oblate, disc-like mesogenic cores into theromotropic sidechain P L C S .~ ~ During roughly the same period that sidechain PLCs were first synthesized, linear block copolymers prepared from monomers with distinctly different chemical properties were shown to aggregate into liquid-crystalline textures in the melt or in the presence of a solvent for one of the blocks.32 Block copolymer solids with well developed, microphase-separated morphologies exhibit unique mechanical proper- ties, and preferentially swollen copolymers yield a variety of morph~logies.~~ The development of linear, mainchain PLCs was more intentional and directed. The potential end uses for linear PLCs (high thermal stability and high tensile strength) focused research on these r n a t e r i a l ~ . ~ ~ Expanding on the background provided by research on liquid-crystalline phases formed by biological macromo1ecules,35 in particular, the anomalously low viscosity of the m e ~ o p h a s e ~ ~ relative to the isotropic solution, it would have seemed logical, in retrospect, to design explicitly linear PLCs.Curiously, some polymers subsequently shown to be thermotropic linear PLCs of the semi-flexible polyester type (high aromatic content) were studied in industrial research laboratories in the early 1960s ; ultra-high-strength materials were being sought. However, the liquid-crystalline nature of the fluid phases of these polymers appears to have been o v e r l o ~ k e d . ~ ~ It was not until Stephanie Kwolek rationalized the unusually high tensile strengths exhibited by fibres spun from concentrated solutions of the poly(ary1 amides) that the critical importance of mesophase formation was Dobb and McIntyre have recently reviewed the development of the industrially important PLCS.~' The Kevlar (Du Pont) and Arenka (Akzo) poly(ary1 amide) lyotropic PLCs have received the most notoriety, although commercialization of thermotropic PLCs has just been announced.41 Academic research on mainchain PLCs started in the mid 1970s and has focused on the semi-flexible, alternating copolymer PLCs (111) initially described by Roviello and S i r i g ~ .~ ~ Exaggerated even-odd behaviour (relative to MLCs) of both thermo- dynamic and microscopic properties of these PLCs are associated with the parity of the alkyl spacer segment of the copolymer (re.whether or not there is an even or an odd number of chemical bonds in the spacer). The influence of the parity of the spacer and, more generally, the implications of connecting mesogenic cores via flexible spacers are addressed below and in several of the papers in this Discussion. Table 1 enumerates typical polymers that span a wide range of intrinsic molecular flexibility. The coarse division of the entries in table 1 serves as a mechanism for partitioning the remaining material covered in this lecture. FLEXIBLE POLYMERS In fluid phases (melts and concentrated solutions) of flexible polymers such as those in the first category of table 1, the individual chains are devoid of long-range intramolecular order. An absence of internal order extending beyond a few monomer units is their hallmark, even though such chains are comprised of a continuous succession of covalently joined monomers, each link conforming to exacting bond- length and valence-angle constraints.This is because at typical temperatures charac- terizing polymer fluids (200-500 K) there are very rapid transitions (ca. 10'' s-l) among the rather localized dihedral angle preferences at single covalent bonds. The consequence of this isomerization is that the persistence of orientational correlationE. T. SAMULSKI 11 Table 1. Coarse classification of linear polymer flexibility ; examples ~~ I flexible polymers poly (siloxanes) poly( phosphazines) poly( ethylene) I1 semi-flexible polymers cellulose derivatives: poly(p-phenylene terephthalamide) poly(p-hydroxybenzoic acid) +o@$ A,B-copolymers (regular) f (rigid core) - (flexible spacer)+ ,, I11 rigid rod-like polymers a -helical polypeptides 0 II fNHCH-C+, I R poly(p-phenylenebenzobisthiazole) polyphenyl along such chains is rapidly attenuated.The limited range of intramolecular order is graphically illustrated in fig. 1 for fragments of three flexible polymer chains differing in their chemical constitution. In the figure the bond correlation function, ( P2( bi bj)), a kind of intramolecular order ~arameter;~ is plotted against the separ- ation of a pair of bonds. (P2(6i bj)) = (i(3 cos 0, - 1)) reflects the angular correla- tions between a given bond unit vector bi and a second bond unit vector bj located j - i bonds further along the chain.? The brackets ( ) signify an average over isomerization and may be readily computed using equilibrium statistical mechanics with the rotational isomeric state (r.i.s.) approximation.44 For adjacent bonds 8, ( j = i + l), the supplement of the valence angle, dictates the magnitude of P2( bi bj), and as this angle virtually always exceeds 54.7", the initial value of the bond t The second Legendre polynomial P2( 6, - b,) = i(3 cos 8 , - 1 ) is a cohvenient parameter for expressing the extent of bond orientational correlations. For the extreme situation wherein b, 11 b,, e.g.alternate bond vectors ( j = i + 2k, k = 1 , 2 , 3 . . . ) in an alkyl chain in the all-trans conformation, (P2( b; - b,)) = 1.0. If 8, > 54.7 O (the 'magic angle'), P,(b, - b,) < 0; the extrema -1 is obtained when b , l b , .12 MOLECULAR STRUCTURE AND LIQUID CRYSTALLINITY -0.51- 00 I .O L 1 2 3 4 5 6 7 8 9 1 0 0 -a D -0 * 5 11111111111 ( i -1) Fig. 1. The bond correlation function averaged over rotational isomerization plotted against the distance separating a particular bond pair (j-i): ( a ) an alkyl chain, ( b ) an ethylene oxide chain and (c) a dimethylsiloxane chain. The averages over the respective r.i.s. isomerizations were carried out using nominally accepted statistical weights ;* all non-bonded interactions (excluded volume) were included. 1 2 3 4 5 6 7 8 9 1 0 correlation function (neglecting the self-correlation i = j) is negative. Apart from the peculiar zero at 8, = 54.7 O, ( P2( b bj)) = 0 only when isomerization averages angular correlations to zero.For flexible chains (P2(bi bj)) ---* 0 when the pair of bonds under consideration are sufficiently far removed from one another, i.e. when j - i exceeds the angular correlation 'length'. Returning to fig. 1, we see that for an alkyl chain subjected to generally accepted bond length, valence angle and dihedral angle constraint^,^^ angular correlations become negligible when j - i > 10. The correlations attenuate faster in the ethylene oxide chain because the dihedral angle preference (the largest statistical weight) alternates between gauche at the C-C bonds and trans at the 0-C bonds.& The dimethyl siloxane chain has an alternating valence angle: 8, = (LSi-0-Si) = 37 O and eb = (LO-Si-0) = 70 O. This alternation in 8, together with r.i.s. transitions, causes a loss of angular correlation after only two monomer units.Findings such as those shown in fig. 1 are generally indicative of flexible polymer chains. What does this absence of long-range intrachain order imply about interchain orientational correlations? The latter is the signet of liquid crystals.E. T. SAMULSKI 13 Fig. 2. Schematic drawing of a random-flight conformation of a flexible polymer chain. The insets depict ( a ) positive orientational correlation between two neighbouring chain fragments (parallel chain axes) and ( b ) negative orthogonal correlation. 0 5 10 h / A Fig. 3. The chain-axis (chord) Correlation function is shown as a function of chain separation rrj; [after ref. (SO) and (51)]. The nature of interchain organization in condensed, fluid phases (and also, mechanically equilibrated rubbers or glasses) composed of linear, flexible polymers is less readily accessible. There is, of course, no evidence for macroscopic order.On a smaller scale, i.e. on the order of the scale of the overall chain dimensions, neutron-scattering data indicate that the polymer chains assume a random-flight trajectory (fig. 2).48 On the submacromolecular scale, information about orienta- tional correlations between chain fragments is difficult to obtain. There seems to be a strong temptation to impose short-range order on the larger-scale randomness, i.e. to suggest that locally, chains pack with their chain axes aligned approximately parallel [fig. 2( a)]. Such local nematic-like ordering seems ‘intuitively’ proper for prolate chain fragments.Experimental data extrapolated from low-molar-mass fluids is not unequivocal on short-range order; studies of n-alkanes sug est only very weak orientational order characterized by a correlation length <10 !?’ Computer experiments (molecular dynamics and Monte Carlo calculations) relevant to this point corroborate this view but suggest that orientational correlations between nearest-neighbour chain fragments, insofar as they are detectable, have proximate segments orthogonal on average [fig. 2( b ) ] , i e . the chain-axis angular correlation function averaged over all pairs I and J of chain fragments at a given Eeparation rlJ, p2( Cl C’), is negative when the fragments contact each other (fig. 3) ; P2( C, CJ)14 MOLECULAR STRUCTURE AND LIQUID CRYSTALLINITY tends to positive values (+0.05) for rZJ = 5 - 6 A, before becoming negligible at separations on the order of 10 81.50,51 In sum, the random-chain configuration, together with minimal short-range interchain correlations, ensure that fluid phases of flexible polymers are isotropic on all scales.Does this imply that further consider- ation of flexible polymers in the context of mesophase formation should be discon- tinued? Apparently not. Several polymers in this category merit further study. (1) Poly(ethy1ene) melts at high pressures are purported to form mesophases ; extended-chain crystals are derived from the quenched melts.52 (2) Poly( diethylsiloxane) exhibits anomalous behaviour above its melting point; the term viscous-crystalline was applied to the ordered fluid pha~e.’~ Curiously, there may be an MLC analogue of the poly( siloxane) ‘mesophase’: the dimer of di-isobutyl silanediol exhibits a me~ophase.’~ (3) Poly(phosphazines), a new class of flexible elastomers with good thermal stability, clearly manifest mesophases above Tg.” Clearly, further studies of flexible polymers directed at the supramolecular organizational attributes of these polymers are warranted.SEMI-FLEXIBLE POLYMERS Much of the current research activity focuses on thermotropic, semi-flexible polymers. In industrial research laboratories, primary structures of the types shown in the first and second entries under semi-flexible polymers in table 1 are tuned (monomer stereochemistry or ratios of co-monomers are varied) to yield melt- processible materials which retain desirable properties for specific end-uses (thermal stability, high modulus etc.).In academic laboratories, semi-flexible PLCs with a regular, alternating copolymer primary structure, +(core) - (spacer)+,, are being studied. There are a variety of straightforward synthetic routes to such PLCs utilizing thoroughly characterized components (known mesogenic cores of MLCs). Addi- tionally, the ready availability of spacer homologues with variable length provides an entrt! to even-odd phenomena in this class of PLCs. Not surprisingly (especially if Vorlander’s work on DLCs is considered), all of the even-odd phenomena (oscillations in TNI, AS,, etc.) are exaggerated in PLCs relative to those observed in MLCs.Hence studies of these PLCs afford a unique opportunity to refine our understanding of one of the more subtle effects that has intrigued researchers working on liquid crystals since their discovery a century ago. Griffin rekindled interest in the polymer precursor DLCs and suggested that they may play a pivotal role in contrasting PLC and MLC b e h a ~ i o u r . ~ ~ This simple oligomer has the essential distinguishing feature of the polymer: connectivity between two mesogenic cores via covalent bonds, which in turn enables the direct coupling of orientational correlations between two mesogenic cores. Recently, considerable emphasis has been placed on the role of DLCs as models for PLCS.’~-~O Blumstein and Thomas dramatically illustrated that, relative to MLCs, the even-odd entropy change accompanying the nematic-isotropic transition as a func- tion of the number of bonds in the spacer is highly amplified in PLCS.~’ Generally speaking, ASNI for spacers having an even number of bonds (even spacer-chain parity) is ca. 1-2 J mru-’ K-’ {mru = mol of repeat unit, i.e.f-(core)-(spacer)+} roughly independent of the spacer chain length and the degree of polymerization; i.e. ASNI is about the same for MLCs and for DLCs and PLCs having even spacer parity. For odd parity, ASNI = 6-10 J mru-’ K-’ in DLCs and is roughly a factor of two larger in PLCs. For odd-parity spacers the difference between the magnitudes of the DLC and the PLC ASNI values can be rationalized. Roughly speaking, each mesogenic core in the PLC is coupled to two nearest-neighbour cores via spacerE. T.SAMULSKI 15 chains, whereas in the DLC, orientational coupling exists with only a single, covalently bonded core. The large even-odd oscillation of ASNI may also be rationalized in a qualitative manner. In nematic phases, the long-range orientational order encourages mesogenic molecules to align on average parallel to the local director, n. This has significant conformational consequences for the spacer chains when two mesogenic cores are covalently coupled: successive pairs of cores in dimers or polymers will strive, within the conformational constraints of the spacer, to keep their respective core axes parallel to n in the nematic phase. For odd-parity spacers, extended, conformationally ordered spacers (in the extreme, the all-trans conformation of aliphatic spacers) are ideally accommodated in the nematic, and, as a consequence, at the nematic- isotropic transition there will be a substantial contribution from spacer conforma- tional disordering to ASNI.This is not the case for even-parity spacers; the valence angles (approximately tetrahedral) conspire against extended spacer conformations, as such conformations disrupt coparallel juxtapositioning of successive cores ( i.e. in the extreme all-trans conformation, successive cores make an angle of 109.5 O with each other). The uniaxial nematic constraint favours a conformationally disordered spacer, and there is a correspondingly smaller contribution to ASNl for even-parity spacers. The relative magnitudes of different contributions to ASNI have been considered in a more quantitative manner.62-65 We find that for ester-linked spacers, when the calculated spacer conformational contribution is subtracted from experimental values of AS" in the PLC, this difference (ca.1 J mru-' K-' for even-parity spacers and ca. 3 J mru-' K-' for odd) lies in the range of ASNI values determined for MLCs without large alkyl chains.65 Deuterium nuclear magnetic resonance (d.m.r.) gives a more detailed picture of the spacer conformation and delineates the differences between a DLC and a PLC.66 In nematic phases the d.m.r. spectrum of a multiply labelled molecule is a superposition of quadrupolar splittings A v,, the magnitudes of which reflect the efficacy of the molecular motion (rigid-body reorientation, libration and internal isomerization) for averaging the electric field gradient at the ith deuteron; i.e.d.m.r. is a direct measure of the averaging of the orientation of the C-D bond vectors relative to the nematic director. For flexible alkyl chains the number of Av, resolved in the quadrupolar splitting pattern reflects the degree of differential averaging of the electric field gradient at the various methylene segments and is determined by the facility of isomerization at the respective positions along the chain.67 Fig. 4 shows the temperature dependence of the d.m.r. spectra of a neat DLC and a polymer in a PLC-MLC eutectic mixture, each having deuterium-labelled spacer chains: -O(CD2),o-O--. The behaviour of the former is reminiscent of that exhibited by n-alkanes (dissolved in nematic solvents) and alkyl chains appen- ded to conventional MLCs.On lowering the temperature the nematic order increases, yielding larger Avi. This increase in the Avi always occurs in MLCs with the relative Avi diverging at low temperature. When the DLC is contrasted with the polymer eutectic, the widths of both the PLC and DLC quadrupolar splitting patterns increase on lowering the temperature (increasing nematic order), but at comparable reduced temperatures the PLC Aui converge to and coalesce at some limiting value Avo = 80 kHz. Two idealized, limiting cases wherein an odd-parity spacer assumes the all- trans conformation are conceivable: ( 1 ) successive cores (and alternate bonds of the spacer) are aligned exactly parallel to the nematic director resulting in the C-D bond vectors making an angle of 109.5 O relative to n and (2) the major axis of the all-trans conformation is aligned parallel to n yielding C-D bond-vector orienta-16 MOLECULAR STRUCTURE AND LIQUID CRYSTALLINITY 50 kHz c---------$ Fig.4. Temperature dependence of the quadrupolar splittings associated with deuterium- labelled spacer chains in (a) a DLC, and ( b ) a labelled PLC in a eutectic mixture containing a MLC [see ref. (66)]. tions that are normal to n. The calculated quadrupolar splittings Av = l$q &-,,I corresponding to these two limiting cases are Av( 1) = 83.9 kHz and Av(2) = 126 kHz, respectively ( q = 168 kHz). These two extremes would, in conjunction with experi- mental measurements, enable determinations of the order parameters for the molecular director Sm ( i) = A vo/ A v( i).For the two idealized cases above we find Sm( 1) = 0.95 and Sm(2) = 0.63. X-ray measurements of the azimuthal scattering intensity from aligned, quenched PLCs with odd spacer parity yield S,,, values in the nematic phase ranging from 0.6 to 0.72.68 Proton n.m.r. measurements yield mesogenic-core order parameters that span a slightly larger range, 0.7-0.8.64*69 Clearly neither of the above limiting cases applies in a fluid phase, and even at the lowest temperatures in the PLC eutectic (fig. 4) the magnitude of Avo implies that there is still considerable mobility of the C-D bond vectors. The observed coales- cence (Avi ---* Avo) as the temperature is lowered suggests that, concomitant with the increased nematic order, the averaging of the C-D bond-vector orientation (methylene mobility) becomes independent of the methylene segment’s proximity to the mesogenic cores.Similar findings were reported for a different PLC earlier.7o The marked differences in the d.m.r. data for the DLC and the PLC (fig. 4) reflect the distinctly different abilities of the spacer chain to accommodate the increasing orientational constraints imposed on the mesogenic cores in the respective oligomers, and raise additional questions about the relationship of the dimer mesophase to that of the polymer. Are the d.m.r. measurements in the PLC simply showing the annealing out of the chain-end ‘defects’ as the temperature is lowered? (Note that ‘hairpin’ bends do not increase the number of defects in a DLC and both bent and extended DLC conformers would accommodate increasing nematic order.) Moreover, in semi-flexible, linear PLCs, certain deformations requiringE.T. SAMULSKI 17 chain ends (splay) may actually drive conformational transitions in the spacer to produce hairpin defects. As the d.m.r. observations clearly show averaged conforma- tional differences between the dimer and the polymer, it would be interesting to ascertain the critical degree of polymerization (the mesogenic-core angular correla- tion length) above which the spacer dynamics of the oligomer crosses over to behaviour characteristic of the polymer. The calculations used to simulate spectra such as shown in fig. 4 also afford an opportunity to extract predicted values of the core-order parameter (the ‘nematic order’) in a homologous series. At the N-I transition, the predicted values of the core order oscillate with spacer parity in the range from ca.0.35 for even parity to ca. 0.65 for odd parity.65 Such an oscillation is observed experimentally. 68i71 Also, in a PLC we might expect that linking successive cores together via the spacer could very well amplify biaxial librations of the mesogenic core. Hence it would be of interest to determine explicitly the biaxiality of the ordering of a PLC core and ascertain if, relative to MLCs and D L C S , ~ ~ there is a pronounced even-odd oscilla- tion in ( S , - S,,,,), and thereby refine the measurements of the ‘nematic order’ derived from n.m.r. studies. RIGID-ROD POLYMERS All of the rigid-rod polymers (the last entries in table 1) are thermally intractable, i.e.they chemically degrade at temperatures below their melting points. As a consequence, these polymers must be solubilized in order to exhibit mesophase formation. The severe solvent requirements (usually strong acids) have not, however, deterred research on these systems, as the potential reward (high thermal stability and ultra-high-strength fibres) is considerable. I will confine my remarks about this class of PLCs to the system with which I am most familiar, the lyotropic polypeptide mesophase. Building on the comprehen- sive characterization of this PLC by Robinson et a L y 3 in the 1960s and 1970s we subjected the PBLG mesophase to the kinds of investigations that were carried out with thermotropic MLCs.In every respect the lyotropic PBLG liquid crystals exhibited all of the qualities of a thermotropic MLC. The only difference between the polymer mesophase and MLCs was the expanded timescale for phenomena in the former. However, this is merely a consequence of the attenuated transport properties of polymer fluids relative to ordinary The PBLG liquid crystal could act as a nematic solvent for n.m.r.:3-75 its twist viscosity coefficient was determined,76 and, with measurements of its diamagnetic ani~otropy,~~ DuPrC deter- mined the critical magnetic field for untwisting the cholesteric structure and measured the first elastic constant in a PLC.78 Much earlier, Tobolsky and I showed the effect of liquid-crystal texture on the morphology of solid polymer films cast from cholesteric and nematic PBLG lyotropic phases.79 The cholesteric texture in PBLG solutions continues to fascinate me; Robinson demonstrated that the cholesteric pitch could be varied continuously and indepen- dently by controlling (1) rod length (molecular weight), (2) rod concentration, (3) temperature and (4) the solvent comp~sition.’~ Perhaps the most intriguing observa- tion in PBLG mesophases is that the cholesteric pitch can be compensated at a given temperature by merely adjusting the composition of the achiral solvent mixture.This observation that the solvent medium in which the PBLG rods were embedded could dictate the sense of the cholesteric twist prompted my brother and I to consider McLachlan’s formulation of the van der Waals-Liftshitz forces between dielectric particles embedded in a dielectric medium as a candidate for describing this unusual18 MOLECULAR STRUCTURE AND LIQUID CRYSTALLINITY choI e s t e r i c is0 t ropic Fig.5. Schematic representation of the transformation of tightly packaged, liquid-crystalline (cholesteric) DNA to an unravelled, isotropic suspension of random coils. compensation phenomenon.80 Osipovsl has recently reconsidered this approach, and, in an elegant extension of the model, he has accounted for multiple inversions of cholesteric sense observed experimentally in PBLG liquid crystals.82 It would be interesting to determine if this approach might be extended to include ther- motropic MLCs, as it may be readily parametrized in terms of specific molecular attributes (the excess polarizability of the particle relative to the medium).Finally, I want to close by speculating about the implications of polymer mesomorphism in biological systems. Ever since seeing B ~ u l i g a n d ’ s ~ ~ conjecture about and experimental evidence for packaging DNA in chromosomes with a concentrated, cholesteric structure, I have been intrigued by the possibility that a mesophase transition (cholesteric to isotropic) coupled with a macromolecule transi- tion (helix to random-coil) might be involved in the highly synchronous expression of genetic information during the life-cycle of a cell. Such a coupled transition is schematically shown in fig. 5. This would be a highly cooperative transition, as demonstrated by recent theoretical modeling of ‘induced rigidity’: stiffening of a polymer chain during the pretransition stage of the isotropic-nematic liquid-crystal tran~ition.’~ I thank the U.S.National Institutes of Health (NIH grant AM17497) for support for my research program. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 D. Vorlander, Z. Phys. Chem., 1923, 105, 211. D. Vorlander, Z. Phys. Chem., TeiZA, 1927, 126, 449. F. C. Bawden and N. W. 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