Maier-Saupe-Flory-Huggins free energy

A theoretical phase diagram for mixtures of polymer and liquid crystals has been calculated by combining Flory-Huggins free energy for isotropic mixing (10) and Maier-Saupe free energy for nematic ordering (11.12) as follows ... 

Figure 1 depicts the experimental cloud points and the nematic-isotropic transition temperatures in comparison with the theoretical phase diagram of the PMMA-OH/E7 PDLC system. The phase diagram calculation was carried out based on the combined Flory-Huggins (FH) and Maier-Saupe (MS) free energies using r = 2.25 and a = -4.0. The b value was estimated from the critic temperature using x = a + (Xc-a)Tc /T. 

In this section we consider a general model that has broad applicability to phase transitions in soft materials the Landau theory, which is based on an expansion of the free energy in a power series of an order parameter. The Landau theory describes the ordering at the mesoscopic, not molecular, level. Molecular mean field theories include the Maier-Saupe model, discussed in detail in Section 5.5.2. This describes the orientation of an arbitrary molecule surrounded by all others (Fig. 1.5), which set up an average anisotropic interaction potential, which is the mean field in this case. In polymer physics, the Flory-Huggins theory is a powerful mean field model for a polymer-solvent or polymer-polymer mixture. It is outlined in Section 2.5.6. 

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