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2 BACKGROUND Relatively unhindered rotation about the single bonds in the backbone of most macromolecules means that a random trajectory for the polymer chain is the most common polymer conformation. Features of some special monomers (resonance, stereochemistry, etc.), however, restrict internal degrees of freedom in the polymers such that the mainchain is extended in space along an almost linear trajectory. Extended polymer chains or chain segments can, through excluded volume interactions, lead to long-range orientational ordering of the macromolecules- liquid crystallinity in concentrated solution or in the melt. Liquid crystals (LCs), sometimes also called mesoPhases. were first recognized in low-molar-mass compounds a century ago, and they end oy widespread technological applications because of their unique electro-optical properties. Low-molar-mass LCs are highly anisotropic fluids that exist between the boundaries of the solid state and the conventional isotropic liquid state and exhibit features or both states. ~ macromolecules, orientational ordering of extended polymer chains is sufficient to impart some crystal-like orientational ordering to their fluid phases melts or polymer solutions. Although this orientation is very subtle on a local scale (it is masked by the rapid and complex molecular dynamics characteristic of all fluid phases), time-averaged attributes of these fluids are anisotropic and therefore dramatically different from those same attributes 1: =~ ~ ~ To Ah" ~= c" of in ordinary isotropic liquids. Figure 2.1 exaggerates the "~ between the melt of a conventional random coil polymer (top) and that of a liquid crystalline polymer (LCP) (bottom) in order to pictorially show the long range order in a fluid phase of the LCP. In LOP melts or solutions this average anisotropy has dramatic consequences. When macroscopic uniform alignment of local directors exists, such fluids exhibit bulk anisotropic dielectric, magnetic, optical, transport, etc., properties. Materials formed from polymers that are orientationally organized in the fluid state retain this anisotropy in the solid state and frequently exhibit ultrahigh strength and stiffness (modulus) along the machine direction (parallel to the extended chains) because the organization and confirmational preferences of the chain promote an extended-chain crystal habit. For these 13

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Semi | flexible Ado - chain ~ mer += FIGURE 2.1 Schematic indication of the differences between an isotropic (top) and a liquid crystalline (bottom) polymer fluid.

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15 reasons, LCPs are being increasingly utilized in specialty and high- performance applications. Historical reviews (Economy, 1989; Jackson, 1989; Samulski, 1985; and Dobb and McIntyre, 1984), general introductions (Brows tow, 1988; Chapoy, 1985; Finkelmann, 1987; and S~mulski, 1982) , and contemporary reviews of LOP properties (Calundann et al., 1988; and G. E. Williams, 1987) abound. LCs and LCPs may be divided into two broad categories, according to the principal means of achieving fluidity. Lyotropic LCPs result from the action of a solvent and hence are multicomponent polymer solutions polymer plus solvents). Thermotropic LCPs are produced by heat and may be single (neat polymer) or multicomponent melts. Within each category, three distinctive supr~molecular organizational or structural classes of LCs have been identified: the nematic, smectic, and twisted nematic or cholesteric phases. Structural differentiation of these phases is related to the packing aspect and dimensionality of the translational organization of the molecules. In the examples of these phases we limit consideration to mainchain LCPs. Nematic LCs are distinguished by a unique director (optic axis) in the fluid; the nematic director is established by the parallelism of the long axes of molecules ([average] polymer chain axes). There is no translational order in this nominally uniaxial fluid (Figure 2.2~. Chain parallelism also characterizes the smectic phase, but translational order is also present in the form of long-range stratification normal to the chain axes (Figure 2.39. Mobility of the entire chain within the smectic layers is possible, although this increased translational organization lowers chain mobility relative to nematic phases. (In low-molar-mass LCs bulk fluidity in the smectic structure involves the layers gliding past one another; such a transport mechanism would be sharply attenuated in polymeric analogs, wherein a single semiflexible chain traverses more than one layer; smectics formed from rigid rod polymers with the layer spacing equal to the rod length might exist.) (Wen et al., 1989) In nematic phases chain ends (defects) are randomly distributed in the ordered fluid; there may be a tendency for such defects to segregate between layers in smectic fluids composed of semiflexible chains. Cholesteric LCs are similar to nematics in organization, with the additional feature of a cumulative twist between molecules, a result of the asymmetry of intermolecular forces. This asymmetry is due to the presence of chiral centers in these mesogens. As a result, the local nematic director twists into an inherently biaxial, helicoidal supramolecular structure (Figure 2.4~. Although there is a large number of applications of cholesterics in low-molar-mass LCs that exploit their optical properties (temperature sensors, notch filters, etc.), there is little evidence of widespread use of this biaxial superstructure in LCPs.

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16 FIGURE 2.2 An absence of translational order in the idealized nematic. FIGURE 2.3 Smectic stratification (lateral registration) in a polymer mesophase.

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FIGURE 2.4 Helicoidal cholesteric structure in a mainchain LOP.

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18 MACROMOLECULAR DESIGN AND SYNTHESIS Thermotropics Mainchain (linear) LCPs are generally synthesized by condensation polymerization involving transesterification (Jackson, 1989) (Figure 2.5~. The growth step is an ac~dolysis reaction yielding an ester connecting link accompanied by the loss of acetic acid. The polymerization is usually conducted in the melt, although in some cases the use of an inert suspending medium is reported. The reaction in the melt is carried out either to completion or first to low molecular-weight-oligomer followed by solid state polymerization to high molecular weight. This general approach is employed for the important high-temperature all-aromatic polymers such as Xydar~ (Amoco), Spectral (Hoechst-Celanese), Victrex~ SRP (ICI), and presumably the recent polymers announced by Du Pont and Granmont/Montedison. j CHi O~O 6 CH, + CHIN O6 OlI ~ HO 6 4~ 6 0lI | T0~0346U' ~t Polyester FIGURE 2.5 Condensation polymerization involving acidolysis. In one commercial case of an aliphatic- aromatic thermotropic LOP- the lower-use-temperature polymer X7G (Eastman) - this condensation step is preceded by the reaction of acetoxybenzoic acid with polytethylene terephthalate) (PET) in an acidolysis reaction in which the PET chain is cleaved. This results in one chain capped with a carbophenyl carboxylic acid moiety and the other capped with an acetoxyphenyl moiety. This is then followed by the acidolysis reaction of the acetoxy and carboxyl end groups, with loss of acetic acid accompanied by other acidolysis reactions. This sequence in short rebuilds the molecular weight with accompanying insertion of oxyphenylcarbonyl mer sequences.

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19 Typical copolyester LCPs are shown in Figure 2.6. Patented Aromatic LOP Polyesters Amoco (Carbons) t A <3~ fo~o] J ~ 3~ . touch o o . ~C , ~_ Hoec~Cehne~e t ~ _ ~ c: to - }~44~c) _fo~] .~ DuPont - J hobo-a83 lo~~3} . - -3} ~ 0 0 Jeff> I is ~ 5 r~~ r OnzmonMo~e~bon t~ ~ ~ j- ~ o ~ :- ~ 04 l J ~ _ FIGURE 2.6 Representative potential thermotropic copolyesters.

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20 LvotroDics The lyotropic LCPs are prepared by solution polycondensation (Figure 2.7~. For many of the extended chain polyamides, solution polymerization in amide solvents is the preferred method. For example, poly~p-phenylene terephthalamide) is synthesized by reacting the appropriate aromatic diamine, p-phenylenediamine in this case, with terephthaloyl chloride in an amphoteric solvent, such as N-methyl-2-pyrrolidone containing a solubility-enhancing salt. Lyotropic LC polyamides, depending on their composition, may be spun directly from their reaction media, or they may be isolated, redissolved, and spun from solutions containing strongly interacting acids, such as sulfuric acid, oleum, etc. The use of a phosphorylation method for the preparation of aromatic polyamides involves the direct condensation of aromatic amino acids or aromatic diamines with aromatic diacids in the presence of an aryl phosphite and organic base. Typical unit structures that yield polyamide lyotropic LCPs are shown in Figure 2.8. C16 6C1 . = H2N~NH2 ~ . ~ iNN-~ 8 . FIGURE 2.7 Synthesis of polyarylamides.

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21 N~C HAN\ HE \, A\ ASH N C~C\ FIGURE 2 . 8 Lyotropic polyamide unit structures . b~c\ of \ C1 N~N~ HE \ H O ~-C V ~ H \ OH N ':~C H: ~ ~ C Con ~0 C Poly(p-phenylene-2, 6-benzobisthiazole) (PBZT) (Figure 2.9) and poly(p- phenylene-2,6-benzobisoxazole) (PBO) were initially prepared at the Air Force Materials Laboratory at Wright-Patterson Air Force Base (see Wolfe, 1988, for a review). PBZT was prepared by the reaction of 2,5-diamino-1,4-benzene- dithiol dihydrochloride with terephthalic acid in polyphosphoric acid. PBO is similarly derived from 4,6-diamino-1,3-benzenediol dihydrochloride. The procedure also works well for A-B type monomers, such as 3-amino-4- mercaptobenzoic acid and 3-~mino-4-hydroxybenzoic acids (Chow et al., 19899. The preparation of "molecular complexes" from blends of polymers derived from A-A+B-B monomers and polymers derived from A-B types has also been reported (Wolfe, 1988~.

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22 HX~HH2 H2~-XH r ~ H064/ \~6oH t............ ,X~N~ i~v l N~X~ -n X = 0,S Poly(p phenylene-2 ,6-benzobis " X "azole) rPBX] ~. FIGURE 2.9 Synthesis of PBX polymers. Sidechain Thermotropic LCPs While most of the interest in LCPs is focused on mainchain a-- important class of LCPs contains the mesogenic groups as an appendage (meso~enic core) on the polymer sidechain LCPs (see Attard and Williams, . ~ ~ ~ TV ~ ~w . Synthetic routes to sidechain LCPs have traditionally +~ ~ I ^~.rN polymers, an an appendage ~ car 1986, ~ ., involved polymerization of a vinyl monomer (e.g., acry~ate or mernacry~are under free radical conditions in solution (Figure 2.10~. (The only real difficulty with this reaction is encountered when radical reactive groups are located elsewhere in the monomer.) It is also possible to produce sidechain LCPs through polycondensation. For example, malonate monomers can be converted to polyesters in a polyesterification reaction (Figure 2.11~. This reaction is of special interest for radical reactive groups such as nitroaromatics and stilbenes, which have application in nonlinear optics. Polycondensation of combined sidechain and mainchain LCPs can also be utilized. r - -~

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23 ] mesogea spacer AIBN O= ~solvent ~ FIGURE 2.10 Preparation of sidechain LCPs by free radical polymerization. litOgOlit ~ HO _~OH ID \_~oL IS ( 0~)4 L ~ FIGURE 2.11 Preparation of sidechain LCPs by polyesterification. - ~s

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38 ELECTRO-OPTICAL PROPERTIES Herein the focus is on nonlinear optical (NL0) properties of organic systems involving LCPs. There are, however, a number of recent phenomena (generally linear electro-optic) that employ conventional polymers or LCPs together with low-molar-mass LCs. The latter (guest) is dispersed in the host polymer matrix as a microemulsion and the director responds to an applied field thereby changing the refractive index difference between the guest LC and polymer (LCP) host. The phenomena may be adapted to light attenuation and optical switching (roan et al., 1986; Drzaic, 1986~. In the cases of NL0 phenomena, readers may readily sense the intensity of interest in organic polymeric systems, in general (Boyd, 1989), and in LCPs (Williams, 1987), in particular. Relevant aspects of second- and third-order NL0 processes are reviewed here so that readers may consider the potential of LCPs in this active research area, one that is anticipated to yield technologically important advances In the future (Williams, 1987~. Second-Order NLO Processes There are basically two categories of second-order NL0 processes: (a) the linear electro-optic or Pockels effect and (b) parametric processes such as second-harmonic generation (SHG) and sum or difference frequency generation. In the former a d.c. electric field is applied to a medium, which responds by altering its refractive index in proportion to the applied field. In the latter the electric field associated with incident light produces polarization components at other frequencies, which can act as a source of electromagnetic radiation at those frequencies. For a material to exhibit significant second-order NLO responses it must have a noncentrosymmetric structure. In the case of polymers this implies that a polar symmetry axis must be introduced into a medium that would otherwise be nonpolar because of orientational averaging. Electric field poling of thermoplastic polymers at elevated temperatures (above the glass transition temperature, Tg) leads to the introduction of a polar axis (by biasing molecular dipoles in the direction of the applied field) (Meredith et al., 1982; Le Barny et al., 1987; DeMartino, 1988~. This induced polarity can be retained by cooling the polymer to well below its To. The main advantage of introducing liquid crystallinity into polymers for second-order NL0 applications is the enhancement in the degree of polar molecular alignment it can provide; up to - factor of 5 under certain processing conditions. The origin of this enhancement is the effect of the local anisotropic potential associated with the liquid crystalline director on the orientational distribution function of the nonlinear chromophore. Enhanced alignment translates into up to a factor of 5 larger nonlinear coefficient, which in turn can increase the efficiency of processes such as second-harmonic generation by over an order of magnitude For third-order NL0 materials uniaxial alignment associated with the liquid . crystalline director can have a similar enhancement in the coefficient by removing the spatial averaging effects of an isotropic environment on the direction of largest nonlinearity in the chromophore. For commercial applications the stability of retained alignment is of primary concern since

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39 critical device characteristics are determined by the stability of parameters related to alignment. Liquid crystallinity can assist in the retention of local alignment because of its highly anisotropic contribution to the local orientational potential energy (D. J. Williams, 1987~. An alternative approach to inducing noncentrosymmetry might be to introduce chirality and the other structural requirements of the ferroelectric smectic c* mesophase into a polymeric structure containing chromophores capable of producing a nonlinear response (Goodby and Leslie, 1984~. Because of its complexity, this approach has not yet been fully examined or exploited, but it may be fruitful for achieving high degrees of order with excellent stability. Most devices designed to take advantage of the Pockels effect operate by retarding the phase of light propagating through the medium with the field- induced refractive index change. One figure of merit (FOM) quantifying the suitability of a material for a particular electro-optic or integrated optic application (Alferness, 1982) is FOM ~ Xf21/n( + 1) where x`2, is the first nonlinear coefficient, n the refractive index, and the dielectric constant of the electro-optical material. This FOM determines the trade-off between the electric field and path length required to achieve a particular degree of phase retardation. For very-high-speed devices where electric fields are applied via microwave transmission lines, an additional factor emerges. Here the velocity of the microwave pulse Vm = C/E~ must match that of light, Ve = C/n, in the medium over the interaction length required for a given amount of phase retardation to occur (DeMartino et al., 1987~. From these considerations a large refractive index would favor phase retardation. For high-bandwidth devices operating in the traveling wave mode, n2 approximately equals of the electrodes at optical frequenc ies . For electro-optic materials such as LiNbO3, n2 and E are very different, so that velocity matching can only be achieved over short distances (Lytel et al., 1988~. From a device design point of view, if the phase retardation must be achieved over short distances, much higher voltages are required. A thorough discussion of device-dependent requirements for electro-optic materials is beyond the scope of this report, but a general list of requirements and desirable characteristics compared to the properties of currently existing materials is presented in Chapter 3. For second-harmonic generation, a separate FOM is required that leads to additional desirable material characteristics. Consider the fraction of power converted to the harmonic frequency, P(2~/P(~), over a certain region in a crystal. It is proportional to the following factors: P2 '/p`~' ~ ~x`2, /n3~/~3/2] P(~)L f(AkL/2) where n, A, and are, respectively, the refractive index, dipole moment, and dielectric constant of the nonlinear materials, and f(AkL/2) is a phase mismatch factor that is periodic in character and whose amplitude is reduced by increasing periodicity. The periodicity of this function is determined by

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40 the mismatch in momentum Ak of the fundamental and harmonic waves. A FOM for harmonic conversion is given by FOM = (X ~ ~ /n (~/e ~ I Here it is clear that low-refractive- index materials have a considerable advantage relative to high-index materials, and the quadratic dependence of power conversion efficiency on xt2, puts a tremendous premium on that factor. The input power P(~) and interaction length L are parameters to be played off against the material FOM. Other factors such as birefringence and geometrical optical factors limit the length over which the interaction can be maintained. In waveguided structures designed for optimized propagation of fundamental and harmonic fields, the dependence on interaction length L becomes quadratic, and optical fields can be propagated over long distances, leading to high conversion efficiencies (Zyss and Chemla, 1987~. Because of the lack of materials with suitable properties, as well as processes to fabricate them into suitable waveguides, the potential technological advantages of waveguide SHG have yet to be realized. Third-Order NLO Processes _ Third-order nonlinear processes arise from the nonlinearity in the polarization response of all dielectric media, including conj ugated organic systems . The x-electrons in conjugated organic systems , being loosely bound, contribute much more strongly to the nonlinear response than the more tightly bound core electrons (Rustagi and Ducuing , 1974~. Third-order processes fall into two basic categories. The first is analogous to the Pockels effect, where the refractive index change is quadratically dependent on the applied field, which can be at d.c. or optical frequencies. This can lead to a variety of interesting effects that are manifested in various device designs, including bistable switches, power limiters, and optically driven modulators (Stegeman et al., 19883. The second category of processes involves the interaction of optical fields at different frequencies, where energy can be exchanged between field components in a manner similar to second-order parametric processes. The fields can all be at the same frequency (in contrast to second-order processes, where one of the fields must be at the harmonic, sum, or difference frequency) or at different frequencies. Third- harmonic generation, degenerate four-wave mixing, and real-time holography are examples of such effects (Shen, 1984~. If one of the frequencies or any combination of them matches a resonant process in the molecule or medium, large enhancements in nonlinear response can be achieved. In this case dissipation of thermal energy and the temporal response of the resonant process place constraints on the utility of the process. Momentum conservation must be maintained and can be controlled by the interaction geometry. There is no symmetry restriction for third-order processes, unlike the case for second-order processes, so they are exhibited by all media. In conjugated polymers, where electron oscillations are much larger in the chain direction than perpendicular to it, nonlinear responses are extremely large.

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41 Nonresonant third-order nonlinearities are larger in polymers such as polyacetylene (Sinclair et al., 1987), polydiacetylene (Sauteret et al., 1976), and other conjugated polymers than in any other class of materials, including inorganic semiconductors. The response parallel to the chain direction suggests that macroscopic orientation of the polymer should result in a considerably larger response than in an isotropic system. The enhancement factor can be shown to be a factor of five. Conjugated liquid crystalline maincha~n polymers are also known to exhibit high degrees of shear-induced uniaxial alignment, and the expected increases in nonlinear coefficients in appropriate directions have been observed (Rao et al., 1986~. All optical signal processing applications based on third-order NLO fall into two basic categories: parallel and serial. There are two approaches to parallel processing that enable the massive parallelism and interconnectivity of optics to contribute to optical computing and information processing (Gibbs, 19861. The first of these involves the use of simple spatial patterns combined with the switching behavior of nonlinear etalon devices to perform computational functions; these devices are simply miniature resonant cavities where the thickness, refractive index, and reflectivity of the internal surfaces are chosen to provide a destructive interference condition and therefore low transmission through the device. The nonlinear contribution to the refractive index of the medium, as illustrated by the equations below, causes the transmission characteristics to be light-intensity-dependent and capable of exhibiting bistable behavior. The second approach to parallel processing involves the formation of transient holograms generated by two counter-propagating beams in a bulk nonlinear medium to alter the information content of a third beam interacting with the grating thereby producing a new fourth beam. An example of information processing by this method is associative memory (Yariv and Kwong, 1986~. Here an optical mode of a resonator containing a hologram with many messages and a nonlinear medium can selectively amplify a particular message, given only partial information from an input beam. For these applications the primary requirement is for large X(3), where xt3~/~ - n2nO~OC2/3 in MKS units and n = nO ~ n2I where nO is the material refractive index, n2 is the light-intensity-dependent refractive index, and I is the light intensity and ~ is the absorption coefficient. A large value of n2 maximizes the response of the material to small amounts of energy. Because of the inherent parallelism, high degrees of information throughput are generated, and response times in the nanosecond to millisecond time frame are useful. Because of their extremely large resonant nonlinearities, GaAlAs multiple quantum wells and photorefractive crystals such as BaTiO3 have a tremendous functional advantage for this class of applications. Investigations of NLO

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42 properties of organic systems, being in a much earlier stage, have not yet demonstrated similar advantage. Serial applications of third-order nonlinear optics involve the use of the intensity-dependent refractive index in waveguided structures to perform rapid switching of bit streams between two or more optical channels. The importance of such devices can be appreciated by realizing that optical fibers can be utilized to transmit information at rates approaching 1 THz. This rate is beyond the capabilities of known light detectors and will require all- optical signal processing before light signals are converted to electronic ones. In waveguides, long interaction lengths can be used to generate phase retardations needed for switching applications so that the premium for materials is put on the speed of the nonlinear response and the optical losses in the material caused by linear optical processes. The decay times of nonlinear responses in semiconductors and quantum well structures, as well as the response time in photorefractive materials, are in general too slow for this type of application. Polymeric materials exhibiting extremely large nonlinearities (albeit much smaller than the resonant nonlinear responses of the inorganic materials that makes them more suitable for parallel processing) may offer the best hope for this important class of applications ' additional gains can be made in their properties (Stegeman et al., 1987~. REFERENCES Alferness, R. C. 1982. Waveguide electrooptic modulators. IEEE Trans. MTT 30 ( 8 ): 1121- 1137 . Admundson, K. R., D. S. Kalika, M. R. Shen, X. M. Yu, M. M. Denn, and J. A. Reimer. 1987. Influence of degree of polymerization on phase separation and rheology of a thermotropic liquid crystal polymer. Mol. Cryst. Liq. Cryst. A153:271-280. Admundson, K. R. 1989. Investigation of the morphology of liquid crystalline polymers using nuclear magnetic resonance spectroscopy . PhD . dissertation, U. of Cali., Berkeley. Attard, G. S. and G. Williams. 1986. Liquid-crystalline side-chain polymers. Chemistry in Britain 22~10~:919-924. Bodaghi, H., T. Kitao, J. E. Flood, J. F. Fellers, and J. L. White. 1984. Poly~p-phenylene terephthalamide) films formed from extrusion and coagulation of liquid crystalline sulphuric acid solutions. Characterization of orientation and void structure, annealing, and upgrading of film mechanical propert~es. Polym. Eng. and Sci. 24~4~:242- 251. Boyd, G. T. 1989. Applications requirements for nonlinear-optical devices and the status of organic materials. J. Opt. Soc. Am. B6~4~:685-692.

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43 Browstow, W. 1988. Polymer liquid-crystals and their blends. Kunststoffe (German Plastics) 78~5~:411-419. Calundann, G., M. Jaffe, R. S. Jones, and H. Yoon. 1988. Fibre Reinforcements for Composite Materials, A. R. Bunsell, ed. New York: Elsevier . Chandrasekhar, S. 1977. Liquid Crystals. New York: Cambridge Univ. Press. Chapoy, L. L. 1985. Recent Advances in Liquid Crystal Polymers. New York: Elsevier Appl. Sci. Pub. Chow, A. W., S. P. Bitler, P. E. Penwell, D. J. Osbourne and J. F. Wolfe. 1989. Synthesis and solution properties of extended chain poly(2,6- benzothiazole) and poly(2,5-benzoxazole). Macromolecules 22~99:3S14- 3520. De Gennes, P. G. 1971. The Physics of Liquid Crystals. Oxford: Clarendon Pres s . DeMartino, R. N. 1988. U. S. Patent 4,779,961. DeMartino, R. N., D. Haas, G. Khanarian, T. Leslie, H. T. Man, J. Riggs, M. Sansone, J. Stamatoff, C. Teng, and H. Yoon. 1987. P. 65 in Nonlinear Optical Properties of Polymers: Materials Research Society Proceedings, Vol. 109, A. J. Heeger, J. Ornstein, and D. R. Ulrich, eds. Pittsburgh: Material Research Society. DeTeresa, S. J., R. S. Porter, and R. J. Farris. 1985. A model for the compressive buckling of extended chain polymers. J. Mater. Sci. 20(5):1645-1659. Doane, J. W., N. A. Vaz, B. G. Wu, and S. Zumer. 1986. Field controlled light scattering from nematic microdroplets. Appl. Phys. Lett. 48(4):269-271. Dobb, M. G. and J. E. McIntyre. 1984. Properties and applications of liquid- crystalline main-chain polymers. Pp. 61-98 in Liquid Crystal Polymers II/III, M. Gordon, ed. Berlin: Springer-Verlag. Dobb, M. G. 1985. The production, properties and structure of high- performance poly~p-phenylene terephthal~ide) fibres. Pp. 673-704 in Handbook of Composites, Vol. 1: Strong Fibers, W. Watt and B. V. Petrov, eds. New York: Elsevier Sci. Pub. Dowell, F. 1989. Prediction and design of 1st super-strong liquid- crystalline polymers. J. Chem. Phys. 91~2) :1326-1338. Drzaic, P. S. 1986. Polymer dispersed nematic liquid-crystal for large area displays and light valves. J. Appl. Phys. 60~6~: 2142-2148.

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