ON A MAPPING BETWEEN HARD-CORE POTENTIAL MODELS FOR NEMATOGENS AND CONTINUOUS ONES

Abstract

Hard-core nematogenic models can be studied using Onsager’s theory, and, on the other hand, continuous interaction potentials can be investigated using the molecular field approach pioneered by Maier and Saupe. Comparison between these treatments shows a certain formal similarity, reflecting their common variational root; on this basis, hard-core potential models can be mapped on separable continuous ones, via their excluded volume. As a specific example, we have, therefore, considered hard spherocylinders and hence the continuous potential model(s) [Formula: see text] here uj denotes the unit vector defining particle orientation, xj denotes the coordinate vector of its center of mass, and ∊ is a positive quantity setting temperature and energy scales(i.e. T*=kBT/∈). The |sin| function can be expanded in a series of Legendre polynomials of even order, with a dominant P2 term; particles’ centers of mass were associated with a simple-cubic lattice, the function ɸ(r) was truncated at nearest-neighbor separation, and values of the two parameters p and q were chosen so as to make contact with the Lebwohl-Lasher lattice model, i.e. [Formula: see text]. The resulting pair potential was studied by molecular field theory and by computer simulation; molecular field theory predicts a first-order transition at [Formula: see text], whereas the result obtained by simulation was [Formula: see text]; comparison with the Lebwohl-Lasher model shows that the higher-order interactions contained in the potential tend to increase the transition temperature towards its molecular field limit.