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Hard core effects in mean field theories

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The Mathematics of Liquid Crystals

Classically, there have been two different ways to obtain mean field theories for liquid crystals. One is based on short range repulsive forces and the other on long range electrostatic forces. In the former approach, it is the anisotropic shape of the molecules that leads to the anisotropic interaction, and in the latter it is the anisotropy of the molecular charge distribution. In real molecules, both causes of anisotropy will be present and can be expected to contribute to the effective interaction. It is thus desirable to assess the combined effect of anisotropic long range attraction and short range repulsion.

Starting from a long range intermolecular interaction energy, a mean field pair potential can be obtained by averaging over all possible relative positions of two molecules in a fixed relative orientation. The effects of hard core repulsion can be taken into account by an appropriate choice of the domain of integration for the averaging. This involves determining an excluded region, the region that one molecule cannot penetrate due to the hard core repulsion exerted by the other.

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

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