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Density Functional Theory for Hard-Body Models of Liquid Crystals

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The Mathematics of Liquid Crystals

Hard-body models for lyotropic liquid crystalline phases date back to Onsager (1949) who showed that a fluid of hard rods can exhibit a transition from an isotropic to a nematic phase that is driven purely by entropy. Onsagers treatment is based on a second-virial description of the free energy that is accurate in the (Onsager) limit of very long thin rods (spherocylinders). For shorter spherocylinders and for smectic and crystalline phases, as well as for treating inhomogeneous fluids, e.g. situations arising at interfaces between phases and in anchoring and wetting at substrates, it is necessary to develop theories in which the ensemble averaged one-body particle density depends on both the orientation and the position of the particles. Density Functional Theory (DFT), developed first for simple fluids with spherical particles, is one such theory and it has emerged as powerful means of tackling phase transitions and the structure and thermodynamics of inhomogeneous fl uids. This lecture will provide an overview of the basics of DFT before focusing on the successful geometry-based Fundamental Measure Theory (FMT) approach introduced originally by Rosenfeld (1989) for hard-sphere mixtures. FMT for spheres has as its starting point the incorporation of the exact second virial contribution into the free energy functional. Attempts to extend the ideas of FMT to hard bodies of arbitrary shape were made by Rosenfeld (1994, 1995). These failed to yield a stable nematic phase for spherocylinders, partly because they did not include the correct Onsager limit. In recent years there has been renewed effort to develop improved FMT that go towards capturing this limit. I shall describe progress for a variety of model colloidal liquid crystalline fluids including hard spherocylinders, mixtures of hard spheres and rods, and hard thin platelets. If time permits I shall mention some recent applications of Dynamical DFT to non-equilibrium properties.

This talk is part of the Isaac Newton Institute Seminar Series series.

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