Shape anisotropy and ordered phases in reversibly assembling lyotropic systems

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Abstract
When a fluid composed of sufficiently asymmetric hard particles is compressed, purely entropic effects give rise to phases possessing long-range orientational and, in some cases, translational order. The various ordered phases observed in conventional lyotropic liquid-crystal systems are commonly described in terms of such a hard-particle model. Here we study the liquid-crystal phases observed in reversibly assembling lyotropics (i.e., systems in which amphiphilic monomers form asymmetric aggregates) within the framework of a hard-particle model. These self-assembling systems are complicated by a variable and polydisperse aggregate size distribution, which is both concentration and temperature dependent, and is coupled to the orientational and translational ordering of the system. Our approach employs a phenomenological description of aggregate assembly, in conjunction with a scaled particle treatment of fluid configurational entropy and a cell description of periodic columnar and smectic density modulations. Cases of rodlike and disklike aggregates are considered. The calculated phase diagram for the rodlike (disklike) system displays a low-temperature nematic phase intervening between a low-concentration isotropic phase and a high-concentration columnar (smectic) phase. With increasing temperature the region of nematic stability narrows and finally terminates at an isotropic-nematic-columnar (smectic) triple point above which there is a direct isotropic to columnar (smectic) transition. This general phase diagram is characteristic of a number of experimental systems in which the aggregates are restricted to either rod- or disklike geometries. The calculated concentration dependence of the aggregate size distribution, orientational order parameter, and periodic columnar and smectic spacings are also reported and compared with specific experimental results.