J. MATER. CHEM., 1991, 1(1), 5-10 Mesogen exhibiting a Ch-A*-A Phase Sequence, a Liquid- crystalline Analogue of the Abrikosov Phase Andrew J. Slaney and John W. Goodby* School of Chemistry, The University, Hull HU6 7RX, UK ~ ~~~ A number of optically active liquid-crystalline compounds have been prepared that have a chlorine atom attached to their asymmetric centres. Many of these materials exhibit unusual properties at their transitions to the liquid state. In this article we report the properties of one of these compounds: S-2-chloro-4-methylpentyl 4’-(4”-n-nonyloxybenzoyloxy)biphenyl-4-carboxylate.From thermal and optical studies it appears that this material undergoes a transition from a cholesteric phase to a smectic A phase via an intermediary twisted phase.The intermediary A* phase is believed to have a structure where there is helical ordering of the molecules occurring in the planes of the molecular layers. Theoretical models suggest that this twist is effected by the inclusion of screw dislocations in the structure of the phase in the form of a lattice of defects. This lattice is thought to be similar in nature to the Abrikosov flux lattice found in superconductors. Keywords: Liquid crystaal; Optical activity; Screw dislocation; Phase transition 1. Introduction In certain circumstances the melting of a cholesteric meso- phase to the isotropic liquid may be mediated via the forma- tion of Blue Phases (BPs). Typically, Blue Phases are detected when the pitch of the cholesteric mesophase is relatively short (54000 A).Although Blue Phases are homogeneous on macroscopic scales larger than the pitch, on smaller, micro- scopic, scales they are thought to be inhomogeneous. The director configuration, that is locally an energy minimum called double twist,’ cannot fill space efficiently and the formation of a periodic array of defects is required in order to stabilize a large-scale homogeneous phase [see Fig. l(a)]. (i) Id (ii) Fig. 1 Schematic representation of some frustrated liquid crystal phases. In each case the twisted structure of the phase is stabilized by defects. (a)The structure of Blue Phase I (02symmetry); (b)the structure of the A* phase (spiral layer order); (c) the structure of a polymer analogue of the A* phase: (i) smectic A polymer, (ii) twisted A* polymer Consequently, Blue Phases are regarded as examples of frus- trated phases.Recently Renn and Lubensky2 showed theoretically that the cholesteric-smectic A phase transition can also be mediated by the formation of a frustrated, intermediary phase. They proposed that at the transition there is competition between the stabilization of the layered structure of the A phase and the desire for the molecules to form a helical macrostructure as in the cholesteric phase. They suggested that this competition can be resolved by the generation of a novel helical smectic A* phase. Subsequently, the phase was described as the liquid-crystalline analogue of the Abrikosov flux phase observed in some supercond~ctors.~~~ Independent of these theoretical studies we showed4 that certain members of the R-and S-l-methylheptyl 4’-(4”-n- alkyloxypropioloyloxy)biphenyl-4-carboxylates exhibit smec- tic A* phases on cooling from the isotropic liquid. X-Ray diffraction, differential scanning calorimetry, thermal optical microscopy, rotary dispersion, and electrical and alignment studies clearly show that this phase has a helical structure combined with a lamellar ordering of the molecule^.^^^ For example, the n-tetradecyloxy homologue4 (14P1 M7) was found to have the following transitions is0 -A*-C*-S3-S4 93.8 89.7 53.4 42.5 where A* is the twisted variant of the A phase, C* is a typical helical, ferroelectric smectic, S3 and S4 are two hitherto unidentified phases, and is0 is the isotropic liquid.Surpris- ingly, the axis of the helix in the A* phase was found to lie in the plane of the layers. The proposed structure for this phase is also shown in Fig. l(b). The twist in the layer structure was suggested to be effected by the formation of defects’ or fluid-like region^.^^^ Similar results to those found for low molar mass liquid crystals have been reported previously in polymer systemsa6 For example, in cholesteryl-substituted polymethacrylate side- chain polymers, helical smectic A* phases have been found. The structure of the proposed phase is shown in Fig. l(c) (ii). The twist is parallel to the layers and the polymer backbone is believed to coil between the layers.In this case, the stabilization of the helical phase is expected to be critically dependent on the degree of polymerization. Theoretical models2p7 show, for second-order phase tran- sitions of the type described above, that there is competition between the twist penetration distance (A,) and the SA corre-lation length (0.When the ratio AT/( (the Ginzburg parameter) is greater than (J2)- a frustrated phase is predicted. Stabiliz- ation of the phase is proposed to occur through the formation of a lattice of screw dislocations that are described as ‘twist grain boundaries’.2 In this present study we report the discovery of a material that exhibits cholesteric, smectic A*, and Blue phases. Thus, the transitions that bound the upper and lower temperature limits of the cholesteric phase are both mediated by the formation of frustrated phases. 2.Experimental The material synthesized for this study was S-2-chloro-4-methylpentyl 4-(4”-n-nonyloxybenzoyloxy)biphenyl-4-carb-oxylate (902C14M5) Cl which has a similar structure to the first compound reported to exhibit a smectic A* phase.4 The major structural differ- ences between compounds 1 and 2 are the larger dipole at the chiral centre for compound 2 and the greater freedom of rotation of this chiral centre over that in compound 1. The material was prepared by treating the diazonium salt of S-leucine with hydrogen chloride in order to form S-2- chloro-4-methylpentanoic acid. The resulting acid was reduced in the presence of lithium aluminium hydride, and the chiral alcohol formed was then esterified with 4-methoxycarbonoyl- oxy-4’-hydroxybiphenyl in the presence of diethyl azodicar- boxylate.The carbonate-ester produced was purified by column chromatography and then reacted with an ethanol- ammonia mixture in order to remove the protecting carbonate moiety. The resultiiig product, S-2-chloro-4-methylpentyl 4’-hydroxybiphenyl-4-carboxylate,was esterified with 4-n-nonyloxybenzoic acid to give the final liquid crystal 2. The final product was carefully purified by flash chromatog- raphy over silica gel (200-400 mesh) using dichloromethane as the eluant. The collected fractions showed a single compon- ent by thin-layer chromatography. After removal of the solvent the product was recrystallized successively from light petrol (40-60°C) and acetonitrile until constant transition tempera- tures were obtained.The purity of the product was investigated further by normal- and reverse-phase high-pressure liquid chromatography. Normal-phase chromatography was carried out over silica gel (5 pm pore size, 25 x 0.46 cm, Dynamax Scout column) using acetonitrile as the solvent for the mobile phase. Reverse-phase chromatography was performed over octadecylsiloxane (5 pm pore size, 25 x 0.46 cm, ODS Micro- sorb Dynamax 18 column) using both acetonitrile and methanol-water (9:l) as the mobile phase. Detection of the eluting products was made using a Spectroflow 757 UV-VIS detector (i= 254 nm).For both forms of chromatography the material was found to have a chemical purity greater than 99%. The chemical structures of the intermediates and final product were determined by a combination of IR, NMR, and mass spectral analysis; the results for the intermediates and final products were found to be consistent with predicted structures. The transition temperatures (fO.l°C) and initial phase assignments for S-2-chloro-4-methylpentyl 4’-(4”-n-nonyloxy-benzoyloxy)biphenyl-4-carboxylatewere determined by ther- mal optical microscopy using a Zeiss Universal Polarizing J. MATER. CHEM., 1991, VOL. 1 light microscope equipped with a Mettler FP52 microfurnace and FP5 control unit. Alignment, polarization, and tilt-angle studies were carried out using both thin (2 pm) and thick cells (10 pm) constructed from electrically conducting (ITO-coated) glass.The inner surfaces of the thin cells were coated with polyimide, whereas in the thick cells polybutyleneterephthalate was used as the aligning agent. The coated inner surfaces of the cells were unidirectionally buffed prior to construction in order to induce a homogeneous, planar alignment of the liquid crystal. Electrical contacts were made directly to the internal surfaces of the glass so that the polarization direction and tilt angle measurements could be studied in an applied electric field in a Linkam THM 600 hot-stage attached to a polarizing microscope. The values of the tilt angles are reported to within &lo. Temperatures and heats of transition were determined by differential scanning calorimetry using a Perkin-Elmer DSC- Lab I calorimeter in conjunction with a thermal analysis data station (TADS).As a check on instrumental accuracy an indium standard was run at 10.0”C min-’. The measured latent heat, 28.36 J g-’, compared well with that normally obtained for indium of 28.45 J g-’. The material was studied at various heating and cooling rates (1, 2, 5 and 10°C min-’), in both aluminium and graphite pans. Miscibility studies were performed by weighing out the individual mixture components onto a glass slide and heating them into their isotropic liquids. The materials were then mixed thoroughly and allowed to cool into their liquid- crystalline phases. Phase identification was then carried out in the usual manner.3. Results 3.1 Thermal Optical Microscopy S-2-chloro-4-methylpentyl 4’-(4”-n-nonyloxybenzoyloxy)bi-phenyl-4-carboxylate (902C14M5) was found to have the following phases and transition temperatures m.p. is0 -+ BPIII-+ BPI[ -+ BPI 74.9 150.2 149.9 148.6 -+ Ch -+ A* + A -+ C* -+ recryst. 145.8 145.4 144.6 121.0 41.8 where m.p. is the melting point (/“C), is0 is the isotropic liquid, and recryst. is the recrystallization temperature. On cooling the compound between untreated glass plates, the transition from the isotropic liquid to Blue Phase I11 was very difficult to detect optically. However, the transitions to Blue Phase 11, and subsequently to Blue Phase I were very clear and characterized by the formation of an iridescent platelet defect texture. Further cooling resulted in the forma- tion of an iridescent cholesteric phase (pitch xO.4-0.5 pm).This phase was identified from its focal-conic and Grandjean plane textures. Upon slow cooling (O.l°C min-’) the choles- teric phase transformed into a smectic A phase via the intermediary chiral smectic A* modification. The transition was characterized by the formation of filaments, thus produc- ing a vermis texture. The filaments grew rapidly from the Grandjean plane texture on cooling (Fig. 2). Rotation of the polarizer showed that the intermediary phase was helical.? This was confirmed by the observation of pitch bands perpen- dicular to the long axes of the filaments. As the temperature t Professor H.Stegemeyer recently communicated to us that he and W. U. Muller have also observed a similar phenomenon occurring at the cholesteric to smectic A phase transition in mixtures of cholesteryl oleyl carbonate and cholesteryl chloride. Their results are reported in W. U. Muller, Ph.D. Thesis, University of Berlin, 1974. J. MATER. CHEM., 1991, VOL. 1 Fig. 2 The formation of the A* phase of 902C14M5 on cooling from the cholesteric phase. The cholesteric phase appears in its Grandjean plane texture at the top (x 50) was slowly lowered the filaments formed a homeotropic texture. Only on certain occasions was a typical focal-conic texture of the A phase observed (Fig. 3). The filament texture of the A* phase4 obtained for S-1-methylheptyl 4'-(4-n- tetradecyloxypropioyloxy)biphenyl-4-carboxylate (Fig.4) can be compared with that for the compound under investigation as shown in Fig. 5. Further cooling produced a transition to a normal chiral smectic C* phase, which exhibited both broken focal-conic and plane textures. The plane texture of the phase also appeared somewhat iridescent. Furthermore, as the tempera- ture was lowered the phase showed some abnormal changes in its plane texture; these were assumed to be due to a large variation in tilt angle with respect to temperature (see later). Free-standing films of 902C14M5 prepared in the smectic A phase exhibited a normal homeotropic texture. Cooling produced a schlieren texture at the transition to the helical chiral C* phase.Upon further cooling this texture quickly Fig. 3 The filament texture of the A* phase and the focal-conic texture of the smectic A phase of 902C14M5. Filaments form at the transition as shown around an air bubble in the plate (x 50) Fig. 5 The filament texture of S-2-chloro-4-methylpentyl 4-(4"-n-nonyloxybenzoyloxy)biphenyl-4-carboxylate(902C14M5) (x 50) gave way to a plane texture. From this texture the twist rotation of plane-polarized light through the sample was found to be laevo(f). Hence the direction of the helix was catagorised as right-handed. As the chiral centre is removed from the rigid core by an even number of atoms (8,even parity), the material can be classified as See with a negative inductive effect at the chiral centre (-1).This result is in agreement with the previously reported hypothesis. Heating of the free-standing film to a temperature close to the transition to the cholesteric phase resulted in the formation of a droplet which was supported by a film of smectic A. The droplet was clearly in the cholesteric phase, but at the edges the filament texture of the chiral smectic A* phase was observed. The temperature differentials in the oven caused the fila- ments in the free-standing film to grow at the edge of the droplet at which point they transformed back into the A phase. At the centre of the film the A phase was thought to be converted into the cholesteric phase, thereby producing a convectional current in the film.Spiral growth of the filaments consequently resulted in the rapid rotation of the droplet on the surface of the film. At higher temperatures the droplet underwent a transition into Blue Phase I, at which point the rotation ceased. 3.2 Thermal Investigations The material (902C14M5) was studied by differential scanning calorimetry at various heating and cooling rates. Typical thermograms are shown in Fig. 6 and 7 for heating and 0.5 BPJJ -+ BPmor IS0 Fig. 6 Differential scanning calorimetry thermogram for the initial Fig. 4 The filament texture of S-l-methylheptyl4-(4-n-tetradecyloxy-heating cycle of 902€14M5. Heating rate= 2°C min-'; samplepropioloyloxy)biphenyl-4-carboxylate(14PlM7) (x 50) weight =6.24 mg 8 0.8 smectic A \7 0.6 2\ -g 0.4 c c Q).c 0.2 0 TI"C Fig.7 Differential scanning calorimetry thermogram for the first cooling cycle of 902C14MS. Cooling rate = 2°C min- '; sample weight = 6.24 mg cooling rates of 2°C min- In these figures only the transitions occurring near the clearing points are shown. The heating cycle (Fig. 6) shows five peaks over a 6°C temperature range. These phase changes were found to corre- spond to the A to A*, A* to Ch, Ch to BPI, BPI to BPII, and BPI1 to BPI11 or isotropic liquid transitions. The fact that the BPI1 to BPI11 transition could not be detected at all is in agreement with results obtained by more sensitive techniques.* The A* to cholesteric, cholesteric to BPI and BPll to BPlll or isotropic transitions appeared to be first order; the order of the A to A* and BPI to BPI1 transitions could not be gauged by this technique.The fourth differential suggests that both phase changes could be first order, but it remains a possibility that the A to A* transition is in fact second order. The cooling cycle showed a slight depression in transition temperature due to decomposition and supercooling. In this case the transition to the cholesteric mesophase from BPI supercools substantially (Fig. 7) with respect to the other phase changes. This is in agreement with thermal optical studies. Once again the isotropic to BPI,, BPll to BPI, and A* to A transitions can be seen clearly. The BPI to cholesteric phase change, however, is amalgamated with the cholesteric to A* transition.For heating cycles, the sample was either heated slowly (5°C min-') from room temperature, or preheated to 130°C and then slowly heated (2°C min-') through the phase transitions to a temperature of 165°C. The second method was generally found to produce better results because it reduced the possibility of thermal decomposition of the sam- ple. Cooling cycles were simply the reverse of heating runs. In order to investigate the extent of the decomposition of the specimen, thermal cycles were also made using graphite pans. The results obtained were found to be almost identical to those observed for aluminium pans. Thus, the results were found to be both reproducible, and consistent from one form of specimen holder to another.3.3 Electrical and Alignment Studies The material (902C14M5) was investigated using two types of cell: one with a glass-plate separation of 2 pm and the other with a separation of 10 pm. The material was introduced into the cells by capillary action while in its isotropic phase. In each case the material was allowed to cool slowly into its smectic C* phase before an electrical field was applied. Good alignment was obtained in the 2 pm cell by this method; J. MATER. CHEM., 1991, VOL. 1 however, for the thicker cell the alignment was of a poorer q~ality.~The inferior quality of the alignment in the thicker cell was primarily due to the pitch of the cholesteric mesophase being considerably shorter than the cell plate separation.In the thinner cell this was not the case as the pitch was comparable to the cell spacing gap. The tilt angle was determined as a function of temperature in both cells." The results obtained were found to be essen- tially consistent, with the tilt angle being slightly higher in the 2 pm cell (ca. 2", which is outside the experimental error). The tilt angle was found to saturate at a value close to 35", as shown in Fig. 8, and the polarization direction was deter- mined to be Ps(+) from the switching direction relative to the polarity of the applied electric field. The result for the polariz- ation direction obtained is in agreement with previous hypo theses. Switching in both cells was found to become complex as the voltage was increased.Hydrodynamic instabilities and electrical breakdown were found to occur in thick cells when the electric field intensity was increased above the relatively low level of ca. 2 V pm-l. Twist walls and splayed states were clearly visible in thick cells where switching occurred with poor contrast. Cumulative switching sometimes resulted in no contrast between the switched states at all; however, the switching process was detected from the transitory responses seen on polarity reversal. It appears that cumulative pulses result in the reorientation of the layers via hydrodyn-amic instabilities, hence only a transitory response is seen as the material is switched. This tends to suggest that the layers are relatively weak or poorly defined in this particular smectic C* phase. Observations of the alignment of the material on cooling from the isotropic liquid provided only a few examples where filaments were obtained at the transition to the A phase.This may have been because the surface forces were strong enough to prevent the formation of a helical structure. 3.4 Phase Miscibility Studies In order to identify conclusively the phase occurring between the A and cholesteric phases a miscibility study was attempted 40 60 120 140 TI% Fig. 8 Plot of the tilt angle as a function of temperature in the ferroelectric smectic C* phase of 902C14M5 [Set' Ps(+)]. The angle was measured optically in a cell with a 2 pm plate separation.A d.c. field of f10 V was applied to the specimen to induce polarization reversal J. MATER. CHEM., 1991, VOL. 1 CH, 160 1160 ts,* / smectic A / 1 601 4 60 I4O 0 20 40 60 80 100 100 ‘10 A 100OlO B composition (YO) Fig. 9 Miscibility phase diagram of binary mixtures (wto/o) between S-1-methylheptyl 4-(4-pentadecyloxypropioloyloxy)biphenyl-4-carb-oxylate (A) and S-2-chloro-4-methylpentyl 4(4”-n-nonyloxybenzoyl-oxybiphenyl-4-carboxylate(B) with S-1 -methyl heptyl 4’-(4”-n-pentadecyloxypropioloyloxy)-biphenyl-4-carboxylate (1 5PlM7), which was reported as exhi- biting a smectic A* phase.5 The phase diagram is shown in Fig. 9 for weighed mixtures of the two compounds. The figure shows that the C* phase of both materials is continuously miscible across the phase diagram, thus confirming the presence of a C* phase with a right-hand helix in the test material.The cholesteric phase was found to be present across half of the composition range. The temperature range of the cholesteric phase decreased as the amount of the standard material 15PlM7 was increased. At the lower temperature boundary of the cholesteric phase, filaments were formed at the transition to the smectic A phase. The temperature range for which the filaments were found to occur was determined to be independent of the concentration of the two components in the binary mixture. This suggests that the formation of filaments is not due to impurity effects. Once the concentration of the standard material had reached a level of more than 50% by weight in the binary mixtures, the cholesteric phase was no longer observed.Furthermore, the filaments also disappeared and the transition from the isotropic to the smectic A phase (5-50% by weight of 902C14M5 region of the phase diagram) took place in a normal fashion with the formation of typical focal-conic defects. In the region of 95-100% of the standard material, 15PlM7, the smectic A* phase was again found. On cooling of this phase a direct transition to the smectic C* phase occurred, without the formation of an intermediary A phase. The phase diagram exemplifies a number of points. First the A* phase is only seen accompanying a cholesteric-to-smectic A phase change or in close proximity to a transition to a C* phase. Secondly, the filaments observed are not due to phase separation caused by chemical impurities as some- times observed in other systems.’’ Thirdly the A*-C* tran-sition temperatures are depressed on adding the test material to the standard.Consequently, the A* phase abruptly disap- pears, suggesting that the A* phase is stabilized by the adjacent helical C* phase. Thus, continuous miscibility of the A* phase across the phase diagram for the two materials is probably not practical for these two types of material. This is because in the centre of the figure there is no cholesteric phase, and the C* phase is depressed too much to affect the formation of a smectic A* phase; hence miscibility of the A* phases fails.4. Discussion The optical and thermal results indicate that a novel phase mediates the cholesteric to smectic A phase transition in S-2-chloro-4-methylpentyl 4-(4-n-nonyloxybenzoyloxy)bi-phenyl-4-carboxylate. The defect texture of this phase is almost identical to that observed for the chiral smectic A* phase of S-1-methylheptyl 4’-(4”-n-tetradecyloxypropioloyloxy)bi-phenyl-4-carboxylate. Optical studies show that the intermedi- ary phase is indeed helical, and therefore fundamentally different in nature from the normal smectic A phase. The growth of filaments to give a uerrnis texture shows that the phase has long-range order and is not a cholesteric phase. Pitch bands normal to the long axes of the filaments, similar to those observed for 14PlM7, show that the helical axis of the phase possibly runs parallel to the long axes of the filaments, as shown in Fig.10. These observations are all consistent with the formation of an intermediary A* phase. Alternatively, the growth of the filaments can appear to be limited in the direction perpendicular to their long axes. Coalescence of the filaments (edge-to-edge) did not take place readily, thereby suggesting that a fluid-like defect region bounds the sides of the filament. Thermal studies clearly show enthalpies of transition for the various phases described. Transitions to, from, and between Blue Phases (I and 11)are all first order, a result that is consistent with heat-capacity studies.* The A*-A transition may be first or second order in nature; neither possibility is precluded by theory.” It is surprising that transitions such as these are clearly discernable by differential scanning calor- imetry.However, they are reproducible and consistent from one sample holder to another. Confirmation of the classification of the A* phase by miscibility was not found. This may be due to the selection of the standard material as the cholesteric phase disappears in the middle of the phase diagram and the fact that the A phase has an extended temperature range due to the depression of the A-C* transition temperatures. Therefore, neither the cholesteric nor the smectic C* phase is able to influence phase formation in the centre of the phase diagram.Unfortunately, as examples of the new A* phase are limited, a range of miscibility standards is not yet available in order to try to alter the ranges of the cholesteric and A* phases in the centre of the phase diagram. So, although miscibility studies do not show continuous miscibility of the two A* phases, neither do they preclude it. One interesting point that is brought out by miscibility studies is the need for pretran- sitional effects to be present before the A* can be stabilized. Purity studies show the material to be better than 99% helix axis -filament structure Fig. 10 The structure of filaments that grow in a typical defect texture at the cholesteric to A transition chemically pure. However, our initial studies show that the optical purity of the compound is ca.95% of the S isomer and 5% of the R isomer. Miscibility studies show that the formation of filaments is not dependent on chemical purity as in other systems.” However, there are some indications that the formation of filaments, and hence the temperature range of the A* phase, may be dependent on optical purity. Similarly, this is thought to be the case with Blue Phases where the temperature range of the phases are suspected to be dependent on optical purity.I3 Certainly, as the optical purity decreases towards formation of the racemate the helical A* phase diappears because the twist can no longer be stabilized. It is not clear, however, what happens with increas- ing optical purity. Preliminary studies suggest that increasing the optical purity also appears to reduce the temperature range of the phase.This hints at the possibility that the optical isomer in lower concentration stabilizes the formation of the phase. This could be achieved possibly by the migration of this isomer to the cores of the defects; thus the cores in this phase would become populated by the racemic species. This would have the effect of lowering the interfacial energy between the defect and smectic A-like region [see Fig. l(b)]. If the cores of the screw dislocations are populated by the racemic form, this means that the other regions in the phase will be enriched in the predominant optical isomer. Thus, the phase would be inhomogeneous with respect to the concen- tration of enantiomers.Such an outcome would be difficult to accept, but it should be remembered that enantiomers have been shown to be inhomogeneous in other systems.14 5. Conclusion We believe that S-2-chloro-4-methylpentyl 4’-(4”-n-nonyloxy-benzoyloxy)biphenyl-4-carboxylate ex hi bi ts a choles teric- smectic A*-smectic A phase sequence. This sequence has been theoretically predicted by Renn and Lubensky to occur at all cholesteric to smectic A phase transitions. Indeed, examination J. MATER. CHEM., 1991, VOL. 1 of other related materials shows the presence of the A* phase in all materials where the chirality of the material is strong and the layer ordering weak. The authors are extremely grateful to J. S. Patel (Bell Com- munications) and A.Samra (RSRE) for supplying them with aligned cells and to M. Turner for detailed HPLC studies. We would also like to thank Drs. J. S. Patel, R. Pindak and P. Styring for stimulating discussions and for their interest in this work. We are also indebted to the SERC for their financial support to A.J.S. References 1 S. Meiboom, J. P. Sethna, P. W. Anderson and W. F. Brinkman, Phys. Rev. Lett., 1981, 46, 1216. 2 S. R. Renn and T. C. Lubensky, Phys. Rev. A, 1988,38, 2132. 3 G. Srajer, R. Pindak, M. A. Waugh, J. W. Goodby and J. S. Patel, Phys. Rev. Lett., 1990, 64, 13. 4 J. W. Goodby, M. A. Waugh, S. M. Stein, E. Chin, R. Pindak and J. S. Patel, Nature (London), 1989, 337, 449. 5 J. W. Goodby, M. A. Waugh, S. M. Stein, E. Chin, R. Pindak and J. S. Patel, J. Am. Chem. SOC., 1989, 111, 8199. 6 Ya. S. Freidzon, Ye. G. Tropsha, V. V. Tsukruk, V. V. Shilov, V. P. Shibaev and Yu. S. Lipatov, J. Polym. Chem. (USSR), 1987, 29, 1371. 7 P. G. de Gennes, Solid State Commun., 1972, 10, 753. 8 R. N. Kleinman, D. J. Bishop, R. Pindak and P. Taborek, Phys. Rev. Lett., 1984, 53, 2137. 9 J. S. Patel and J. W. Goodby, J. Appl. Phys., 1986, 59, 2355; J. S. Patel, T. M. Leslie and J. W. Goodby, Ferroelectrics, 1984, 59, 137. 10 J. W. Goodby, E. Chin, T. M. Leslie, J. M. Geary and J. S. Patel, J. Am. Chem. SOC.,1986, 108, 4729. 11 R. B. Meyer and P. Palffy-Muhoray, personal communication. 12 T. C. Lubensky, personal communication. 13 P. Taborek, J. W. Goodby and P. E. Cladis, Liq. Cryst., 1989, 4, 21. 14 J. F. Dreiding, personal communication. Paper 0/02342F; Received 25th May, 1990