Rate of Lyotropic Nematic Phase Formation: Derivation and Application of Time–Concentration–Temperature–Transformation Diagrams

Abstract

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...

Stochastic kinetics reveal imperative role of anisotropic interfacial tension to determine morphology and evolution of nucleated droplets in nematogenic films

“…Normalized histograms shown in fig. (5) are sharply peaked for κ < 0 and the peak broadens for increasing κ. Also the distributions are correlated in time for κ < 0, although long-ranged elastic interactions are not present in the supercooled isotropic film.…”

“…Many fundamental problems in surface interfacial science are concerned with the morphology of the nucleated phase, its growth rate, the first passage time as well as the kinetic route to equilibrium. Questions about droplet morphology are especially pertinent in studies of nematogenic fluids, where the anisotropy associated with the tensorial structure of the order parameter is one of the important factors in the description of the nucleation process [4,5]. The microstructure of the nucleus is determined by a nontrivial interplay of competing energies: (i) the anisotropic elastic energy associated with deformations of the tensorial order in the bulk, (ii) the anisotropic interfacial tension related to the director anchoring at the interface between the two phases, and (iii) any external forcing that may be present, e.g.…”

A critical review on applications of the Avrami equation beyond materials science

“…Transmissibility or infectiousness of a pathogen ( µ ) causes new infections (SIR) [ 102 , 111 ]. The role of supercooling in materials can be performed by other drivers, such as evaporation-induced supersaturation in a solution [ 112 , 113 ]. CNT assumes that the nuclei of the new phase form through a single step process (JMAK) [ 17 ].…”