Liquid crystallinity semiflexible chains

Main Chain Liquid Crystalline Semiflexible Polymers... 

The aromatic semiflexible polyesters can be formed by varying the dicarboxylic multi phenyl acid structure (naphthalene and diphenol) and non-linear aromatic diol (3,4 -dihydroxybenzophenone). 3,4 -dihydroxybenzophenone can be synthesized from 4-methoxy bromobenzene and m-methoxybenzonitrile via multistep reaction, which can be condensed with respective diacid chloride in o-dichlorobenzene at reflux temperature [43]. It is well known that dimethyl siloxane spacer can make a flexible/semiflexible LC polymer. Thermotropic flexible liquid-crystalline main chain polyesters... 

FIGURE 5.7 Schematic Representation of typical, (partially) electroluminescent LC polymer architectures. (a) Rodlike structure, (b) Hairy-rod structure, (c) Combined main-chain-side-chain system, (d) Semiflexible segmented structure, (e) Semiflexible segmented structure with disklike mesogen. (After Weder, C. and Smith, P., Main-chain liquid-crystalline polymers for optical and electronic devices, in Encyclopedia of Materials Science and Technology, Buschow, K.H., Cahn, R.W., Flemings, M.C., Ilschner, B., Kramer, E.J., and Mahajan, S., Eds., Elsevier Science, New York, 2001.)... 

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. 

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.

In the second half of this article, we discuss dynamic properties of stiff-chain liquid-crystalline polymers in solution. If the position and orientation of a stiff or semiflexible chain in a solution is specified by its center of mass and end-to-end vector, respectively, the translational and rotational motions of the whole chain can be described in terms of the time-dependent single-particle distribution function f(r, a t), where r and a are the position vector of the center of mass and the unit vector parallel to the end-to-end vector of the chain, respectively, and t is time, (a should be distinguished from the unit tangent vector to the chain contour appearing in the previous sections, except for rodlike polymers.) Since this distribution function cannot describe internal motions of the chain, our discussion below is restricted to such global chain dynamics as translational and rotational diffusion and zero-shear viscosity. 

This article deals with some topics of the statistical physics of liquid-crystalline phase in the solutions of stiff chain macromolecules. These topics include the problem of the phase diagram for the liquid-crystalline transition in die solutions of completely stiff macromolecules (rigid rods) conditions of formation of the liquid-crystalline phase in the solutions ofsemiflexible macromolecules possibility of the intramolecular liquid-crystalline ordering in semiflexible macromolecules structure of intramolecular liquid crystals and dependence of die properties of the liquid-crystalline phase on the microstructure of the polymer chain. 

In Sect. 3, we will consider the orientational ordering in the solution of semiflexible macromolecules. In general, semiflexible macromolecules can have different flexibility distributions along the chain contour compare, for example, the freely-jointed chain of the long thin rods (Fig. 1 b) and the persistent chain, which is homogeneous along the contour (Fig. lc). We will see what properties of the liquid-crystalline transition do depend on the flexibility distribution along the drain contour and what properties are universal from this point of view. 

Using the results of Sects. 2 and 3, we will consider in Sects. 4 and 5 the intramolecular liquid-crystalline ordering of the segments of one semiflexible chain. 

Thus, in the athermal limit the only difference between the equilibrium free energies of the solutions of separate rods and long chains of rods is due to the translational entropy term. Consequently, we can immediately conclude (analogously to Sect. 2) that the liquid-crystalline transition for the athermal solution of semiflexible chains takes place at 1/p. 

---