Maier-Saupe theory modified

McMillan s model [71] for transitions to and from the SmA phase (section C2.2.3.21 has been extended to columnar liquid crystal phases formed by discotic molecules [36. 103]. An order parameter that couples translational order to orientational order is again added into a modified Maier-Saupe theory, that provides the orientational order parameter. The coupling order parameter allows for the two-dimensional symmetry of the columnar phase. This theory is able to accormt for stable isotropic, discotic nematic and hexagonal colmnnar phases. 

Recently, phase behaviour of mixtures consisting of a polydisperse polymer (polystyrene) and nematic liquid crystals (p-ethoxy-benzylidene-p-n-butylani-line) was calculated and determined experimentally. The former used a semi-empirical model based on the extended Flory-Huggins model in the framework of continuous thermodynamics and predicted the nematic-isotropic transition. The model was improved with a modified double-lattice model including Maier-Saupe theory for anisotropic ordering and able to describe isotropic mixing. ... 

However, there is not yet semicommercial development of cellulose fibers processed via mesomorphic solutions. The statistical physics of lyotropic LCPs has been dealt with in Ref. 8, but a modified Maier-Saupe theory developed by Picken will be discussed in this chapter. 

The mechanical properties of fibers and films are governed by the orientation distribution of the polymer chains (see Section 6.4.1). Hence the discussion is focused on the development of the orientation of the chains in the polymer solution and on the formation of orientation during spinning of fibers. Good surveys of current theories on the formation of liquid-crystalline phases have been given by Odijk and Ciferri and Marsano." Later in this chapter we shall present a modified Maier-Saupe theory recently developed by Picken of our laboratory." ... 

It has been the merit of Picken (1989, 1990) having modified the Maier-Saupe mean field theory successfully for application to LCPs. He derived the stability of the nematic mesophase from an anisotropic potential, thereby making use of a coupling constant that determines the strength of the orientation potential. He also incorporated influences of concentration and molecular weight in the Maier-Saupe model. Moreover, he used Ciferri s equation to take into account the temperature dependence of the persistence length. In this way he found a relationship between clearing temperature (i.e. the temperature of transition from the nematic to the isotropic phase) and concentration ... 

The Modified Maier-Saupe Mean Field Theory.125... 

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