Rate of lyotropic nematic phase formation: Derivation and application of time-concentrationerature-transformation diagrams

The effect of both temperature and composition on the rate of transformation of a nematic phase from an isotropic solution is examined from a theoretical standpoint. The kinetics of the transformation are presented as a time-concentrationerature-transformation (TCTT) diagram, analogous to the timeerature-transformation (TTT) diagrams commonly used in metallurgical process design. The transformation is regarded as a nucleated process in which the transformation rate is proportional to the number of stable nuclei, and this in turn depends on a balance between the energy gained by nematic ordering and the energy expended in forming the nematic-isotropic interface. The nematic ordering term is estimated as a function of both concentration and temperature via two different approaches: (i) the lattice theory as described by Flory and Warner and (ii) the Maier-Saupe theory of nematic ordering. Although there are differences in detail, both approaches yield the same qualitative result. The present work provides the details necessary for developing a specific example application of our recently reported generalized system-independent model of nucleation and growth. The TCTT diagram is in essence a phase diagram augmented by kinetic information for nematic ordering, and thus is expected to be a powerful graphical tool in liquid crystal process engineering and other applications.