The effect of concentration on the rate of formation of liquid crystal and crystalline phases

Abstract

In certain instances the rates of growth of a lyotropic phase from isotropic solutions of biological polymers is observed to be concentration dependent. Such behaviour is rationalised in this paper by treating lyotropy as a nucleated phenomenon and by considering the free energy requirements of stable nuclei. The relative number of stable nuclei from which phase growth can occur depends on both the free energy and the interfacial energy differences between the isotropic and the anisotropic state. Adopting the Flory lattice approach to quantify the former, and using a realistic value for the latter, an expression is derived which predicts that the rate of phase formation passes through a maximum as the concentration of the isotropic solution is increased. This result is analogous to the time–temperature relation that describes nucleated solidification and solid-state transformations in metals. The conditions under which mesogen crystallisation will occur are also discussed in terms of the relative rate of nucleation for this process compared with that of liquid crystal formation.