Nematic-isotropic transition molecular statistical theories

Liquid crystals manifest a number of transitions between different phases uprm variation of temperature, pressure or a craitent of various compounds in a mixture. All the transitions are divided into two groups, namely, first and second order transitions both accompanied by interesting pre-transitional phenomena and usually described by the Landau (phenomenological) theory or molecular-statistical approach. In this chapter we are going to consider the most important phase transitions between isotropic, nematic, smectic A and C phases. The phase transitions in ferroelectric liquid crystals are discussed in Chapter 13. 

The simplest molecular theory of the nematic-isotropic (N-I) transition can be developed in the mean-field approximation. According to the general definition, in the mean-field approximation one neglects all correlations between different molecules. This is obviously a crude and unrealistic approximation but, on the other hand, it enables one to obtain very simple and useful expressions for the free energy. This approximation also appears to be sufficient for a qualitative description of the N-I transition. More precise and detailed theories of the nematic state are based on more elaborate statistical models that will be discussed briefly in Sec. 2.4.3. 

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