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− concentration−temperature−transformation (TCTT) diagram, analogous to the time−temperature−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.
■ INTRODUCTIONNucleation and growth theory has been applied to a broad range of phase transformation phenomena that exhibit a competition between favorable transformation energy and unfavorable surface energy. Indeed, classical nucleation theory, originally derived for condensation of vapor to liquid, 1,2 is now commonly taught in introductory materials science courses in terms of the heat treatment of steels. 3−8 Classical nucleation and growth theory applies equally well to crystallization (of ice, 9 proteins from solution, 6,10−13 and colloids 13,14 ), liquid crystalline phase formation, 15−17 and even fields outside of the physical sciences, such as epidemiology. 18 In the case of metallurgical, 3,19,20 ceramic, 21 and mineral 22 phase transformations, the kinetic behavior that results from nucleation and growth is commonly represented on a time−temperature− transformation (TTT) diagram. Such diagrams display contours, often "C" shaped, of constant transformed fraction plotted on the temperature−time plane and are valuable graphical tools for process engineering.An analogous example is found in the transformation from an isotropic solution to a lyotropic nematic liquid crystalline phase, discussed in McEwen 23 and in the present work. The nematic phase becomes thermodynamically favored at a critical mesogen concentration, with the overall free energy becoming more negative as the concentration of the mesogen is further increased. Given this increasing thermodynamic "drive", the number of nuclei and the rate of nematic phase growth should be an increasing function of concentration. However, since increased concentration also reduces m...