The hexagonal phase of wormlike micelles

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Abstract
A mean-field description is presented for the nematic and hexagonal ordering of intrinsically polydisperse semiflexible wormlike micelles interacting via a hard core volume exclusion potential. The predicted phase diagram is determined by two parameters, controlling the intrinsic rigidity of the micelles and their size in the isotropic phase before a liquid crystalline phase emerges. Increasing the micellar flexibility destabilizes the nematic phase, which disappears in favor of the hexagonal phase when the ratio of the persistence length and the diameter of the micelles is reduced to less than a certain minimum value. The minimum rigidity required to stabilize a nematic depends on whether the micelles in the isotropic phase can be viewed as rodlike or not. For micelles on average longer than roughly a persistence length, we find a nematic phase provided the persistence length is greater than about thirteen times the micelle diameter. For increasingly shorter rods, this value goes up; the nematic phase is ‘‘squeezed’’ out and we find a direct transition from the isotropic to the hexagonal phase over a larger flexibility range.