Liquid crystalline order in self-assembling systems: Orientation dependence of the particle size distribution

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Abstract
Proteins and surfactants can associate reversibly into large asymmetric aggregates that can form liquid crystalline phases. A general theoretical treatment is given of such systems, allowing for spherical aggregates of arbitrary diameter and composition that can grow indefinitely in one direction to form rods, or in two directions to form disks. Assuming that interparticle interactions may be approximated by hard-core repulsions, a fine-mesh lattice model is used to derive the configurational free energy. Assuming further a simple phenomenological form for the intraparticle interactions, the equilibrium size and orientation distribution may be expressed in terms of a small number of parameters. The distribution function is a generalization of the well-known most probable distribution for linear condensation polymers in ideal solutions. The generalization allows for the unequal growth of particles in different orientations under the influence of interparticle repulsions.