Nematic stability and the alignment-induced growth of anisotropic micelles

Abstract

In this paper we treat for the first time a phenomenon in micellized soap solutions which arises uniquely from their being colloidal suspensions whose « particles » do not maintain their integrity. In particular we focus on the growth of anisotropic aggregates which is attendant upon their long-range orientational ordering. We consider a simple analytical form for the free energy per molecule and compare explicitly the sizes of rod-like micelles in coexisting isotropic (I) and nematic (N) phases. The coupling between growth and alignment is shown to limit the stability of finite-size, partially-ordered aggregates : the nematic phase is confined to a highly restricted concentration range, because its micelles can only survive (i.e. remain finite) if they are small. The roles of translational and rotational degrees of freedom, and of cosurfactant effects, are also considered : both are shown to enhance the stability range of the nematic. Within Onsager's theory for the long-range alignment of rod-like particles, we conclude further that : (i) the growth of micelles at the I → N transition is driven largely by the orientational « entropy of mixing » — bigger rods allow this entropy loss to be minimized; and (ii) the nematic order parameter and the ratio of coexisting sizes are essentially universal, with the average volume fraction at the transition scaling as the reciprocal of the average aggregation number