Hydrogen-bonded liquid-crystalline supramolecules

Some rigid molecules are known to undergo liquid crystallization when H-bonded with each other. A typical example is a binary mixture of low-mass molecules R(Ay and R Bg, each carrying at least one rigid part A or B capable of pairwisely forming mesogenic core when associated. Dimer, trimer, main-chain type, side-chain type. 

For the orientational free energy, we employ the conventional molecular field theory of Maier and Saupe [66], or its extension by McMillan [67], which includes both orientational ordering of the mesogenic cores and translational ordering of their centers of mass. It is given by 

In contrast to conventional liquid crystals, A m changes depending on the temperature and composition, and should be decided by the equilibrium condition. The symbol jj expresses the nematic order parameter defined by 

The averages ( ) refer to the statistical weight for orientation of each mesogenic core, whose partition function Z is defined by 

By using this statistical weight, the definitions (6.110) and (6.111) become self-consistent coupled equations to find these order parameters. We solve the equations with equilibrium conditions for vm, and then by substitution find the chemical potential of each component as functions of the temperature and composition [65]. 

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