Liquid crystalline polymers, theoretical

X-ray scattering is a powerful tool for the study of structures of liquid crystalline polymers. Theoretically, X-ray scattering from a given material can be treated as the Fourier transform of electron density of the material. For a nematic liquid crystalline polymer, the Fourier transform can be considered as the convolution of electron density of a long, hard rod and a layer of randomly... 

These results demonstrate that side-chain liquid crystalline polymers can be synthesized by polymer analogous reactions from theoretically any polymer backbone. When the polymer backbone is rigid, as in the case of PPO, a long spacer is required both to decrease the Tg of the parent polymer and to partially decouple the... 

The distinct properties of liquid-crystalline polymer solutions arise mainly from extended conformations of the polymers. Thus it is reasonable to start theoretical considerations of liquid-crystalline polymers from those of straight rods. Long ago, Onsager [2] and Flory [3] worked out statistical thermodynamic theories for rodlike polymer solutions, which aimed at explaining the isotropic-liquid crystal phase behavior of liquid-crystalline polymer solutions. Dynamical properties of these systems have often been discussed by using the tube model theory for rodlike polymer solutions due originally to Doi and Edwards [4], This theory, the counterpart of Doi and Edward s tube model theory for flexible polymers, can intuitively explain the dynamic difference between rodlike and flexible polymers in concentrated systems [4]. 

The growing interest in liquid-crystalline polymers has stimulated many theoretical and experimental studies of their solutions, and the results have already been summarized by many authors. For instance, the statistical thermodynamic theories were reviewed by Flory [5], Odijk [6], Semenov and Khokhlov [7], Ciferri et al. [8], and Vroege and Lekkerkerker [9], while the dynamical theories were discussed by Doi and Edwards [4] and Moscicki [10]. 

In the present article, we focus on the scaled particle theory as the theoretical basis for interpreting the static solution properties of liquid-crystalline polymers. It is a statistical mechanical theory originally proposed to formulate the equation of state of hard sphere fluids [11], and has been applied to obtain approximate analytical expressions for the thermodynamic quantities of solutions of hard (sphero)cylinders [12-16] or wormlike hard spherocylinders [17, 18]. Its superiority to the Onsager theory lies in that it takes higher virial terms into account, and it is distinctive from the Flory theory in that it uses no artificial lattice model. We survey this theory for wormlike hard spherocylinders in Sect. 2, and compare its predictions with typical data of various static solution properties of liquid-crystalline polymers in Sects. 3-5. As is well known, the wormlike chain (or wormlike cylinder) is a simple yet adequate model for describing dilute solution properties of stiff or semiflexible polymers. 

Figure 6 shows the phase diagrams plotting temperature T vs c for PHIC-toluene systems with different Mw or N [64], indicating c( and cA to be insensitive to T, as is generally the case with lyotropic polymer liquid crystal systems. This feature reflects that the phase equilibrium behavior in such systems is mainly governed by the hard-core repulsion of the polymers. The weak temperature dependence in Fig. 6 may be associated with the temperature variation of chain stiffness [64]. We assume in the following theoretical treatment that liquid crystalline polymer chains in solution interact only by hardcore repulsion. The isotropic-liquid crystal phase equilibrium in such a solution is then the balance between S and Sor, as explained in the last part of Sect. 2.2. 

Figures 7 and 8 display such plots for various lyotropic liquid-crystalline polymer systems, which range in q from 5.3 to 200 nm. As expected, most data points come close to the theoretical curve. This finding suggests that liquid crystallinity of stiff-chain or semiflexible polymer solutions has its main origin in the hard-core repulsion of the polymers.

Fig. 12a-c. Polymer concentration dependence of the orientational order parameters S for three liquid-crystalline polymer systems a PBLG-DMF [92,93] b PHIC-toluene [94] c PYPt-TCE [33], Marks experimental data solid curves, theoretical values calculated from the scaled particle theory. The left end of each curve gives the phase boundary concentration cA... 

This value is, therefore, mentioned as the theoretical maximum of a it remains an open question what the significance of V is in such a case, thinking of our spheres For liquid-crystalline polymers values round a = 1.5 are indeed being found. 

Introduction of ring-opening metathesis as a versatile polymerisation technique (ROMP) by Chauvin and Herisson Nobel Prize Chemistry to Paul J. Flory for his fundamental achievements, both theoretical and experimental, in the physical chemistry of the macromolecules Fully aromatic polyamides developed Aramids, being lyotropic liquid crystalline polymers of high strength, due to extended molecular chains (Morgan and Kwolek)... 

The virtually universal even-odd behavior of both melting and clearing temperatures for liquid crystalline polymers having polymethylene spacers has not yet been explained theoretically, but similar trends have also been observed for low molecular weight LC compounds with alkyl terminal groups. Of course, odd-even effects are... 

Theoretical Aspects of Liquid Crystals and Liquid Crystalline Polymers... 

The purpose of this chapter is to explain theoretically the formation of liquid crystal phases in polymer systems and to provide the basic concepts for designing and synthesizing liquid crystalline polymers. Liquid crystalline polymers combine features of both polymers and liquid crystals, thus we discuss the materials from two sides liquid crystallinity and polymer properties. Theoretical descriptions have encountered many difficulties in the past. One is that the present theoretical understanding of neither polymers or liquid crystals is complete. 

The Flory theory discussed in the next section is another important theory on rigid liquid crystalline polymers. Because of its clear picture of the lattice model and the incorporation of the Onsager theory, it has become a basic method for the theoretical study of liquid crystalline polymers. As a result of the constant efforts of Flory and his co-workers, the theory has been applied to binary and poly-disperse systems and also includes the soft interactions. 

A comparison of the theoretical expectations of worm-like liquid crystalline polymers and experimental data is made in Figure 2.14. The abscissa is the ratio of total length to persistence length L/l the ordinate is the critical volume fraction in the unit of the ratio of molecular diameter to persistence length. The theoretical expectation is taken from Khokhlov et aVs theory (Khokhlov Semenov, 1982 Odijk, 1986) on the worm-like chains. 

In tracing back the history of the liquid crystalline polymer itself, the German scientist D. Vorlander should be mentioned. It was he who first pointed out that the long shape of the polymer does not prevent the polymer from exhibiting liquid crystallinity. The polymeric liquid crystallinity was first found in the tobacco mosaic virus in solution around 1940, and later found in the poly-peptide solution. The initial theoretical basis for the rigid liquid crystalline polymer is attributed to the... 

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