Saupe elastic properties

In view of the desirable molecular design of liquid crystalline phases, the final goal of microscopic theories is not only to predict the temperature dependence of elastic coefficients, but also to reveal relations between the molecular and elastic properties of the mesophases. Since the original work of Saupe in 1960 [241], a large number of microscopic theories have been developed [181-183, 242-270]. The first molecular statistical theories of the Frank elastic constants were formulated by Priest [242] and Straley [243], and a significant. step was made by Poniewierski and Stecki [244,245] who applied density-functional theory in order to relate in a direct quantitative way the elastic constants to characteristic properties of a statistical ensemble of molecules with... 

There are two basic theories to describe the LC state, the continuum theory mainly proposed by Oseen, Zocher, and Frank and the swarm theory supported by researchers such as Bose, Bom, Omstein, Maier, and Saupe [10,11]. The continuum theory models the liquid crystal as an anisotropic elastic medium with properties varying as a function of position. The swarm theory emphasizes molecular interactions and interprets the LC state as the result of a statistically driven thermodynamic equilibrium. In the recent work of de Gennes, Leslie and Ericksen, LC theories integrate aspects of both the continuum theory and the swarm theory [11]. 

Polymers and liquid ciystals are important materials for various research fields. If the two substances are mixed, novel materials which combine the advantageous properties of both may be formed. 1 began to think about this around 1994. Already at that time, this mixed system had attracted attention as an electro-optical material, but from the perspective of basic physical properties, the center of the liquid crystal research up to that point was the phase transition and Uquid crystal stracture of novel low molecular weight liquid crystals. The physics of liquid crystals was based on the Onsager theory, the Maier-Saupe theory, and the elastic theory by Frank. However, the theoretical study of a liquid crystal mixed with other substances had not yet been developed. So, 1 began to think to build theories of phase separations and phase transitions in mixtures of liquid crystals and other substances. Our first paper on the theory of phase separations in the mixture of a polymer and a liquid crystal was published in 1996 [41]. 1 found at a later date that a paper on the same topic by Prof. Kyu of Akron University had been presented already in 1995 [42]. However, there was a difference between the two theories. Kyu s theory has dealt with low molecular weight liquid crystals in an attractive model, whereas our model considered both attractive and repulsive interactions between rodlike liquid crystal molecules and can handle also long rodlike molecules. After that, I had a variety of discussions with Kyu and it was a valuable experience for my research. 

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