Thermodynamics of the Nematic Phase

The factor N comes in because we are dealing with a system of N molecul.es. The factor % is required to avoid counting intermolecular interactions twice (pair interactions have been approximated by a single molecule potential 7). The entropy is computed by taking the average value of the logarithm of the distribution function  

At first sight this equation seems unusual with the presence of the second term. The necessity for its existence can be verified immediately in two ways. If we take the derivative (dF/d P2 ) t and set it equal to zero we regain Eq. [5], the self consistency equation for P2 . Thus, as required by thermodynamics, the self-consistent solutions to our problem must be those that represent the extrema of the free energy. Another verification of the correctness of Eq. [8] comes from forming the derivative [d F/dp, Again, as required by thermodynamics, Eq. [6] for the internal energy results. The reason for the appearance of the second term in Eq. [8] is the replacement of pair interactions by temperature-dependent single molecule potentials.  

Tc is usually called a critical temperature, although in much of the liquid-crystal literature it is referred to as the clearing temperature. 

Numerical values of the equilibrium order parameter Pg for various temperatures between zero and 0.22019 v/k have been found on the computer and are presented in Table 1 as an aid to anyone wishing to perform numerical calculations based on this or the Maier-Saupe mean field theory. 

The latent heat of the transition from nematic to isotropic liquid can be calculated from Eq. [6] and the fact that P2 changes from 0.4289 to zero at T  

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