The isotropic-nematic phase transition: the Onsager theory revisited

Dave C. Williamson

Physica A: Statistical Mechanics and its Applications, 1995, vol. 220, issue 1, 139-164

Abstract: A simple Monte Carlo annealing technique is proposed for the minimisation of the Onsager-Helmholtz free energy functional at the level of the second virial coefficient. Random changes are made to vary a discrete representation of the single particle distribution function f(θ) in order to determine the minimum of the free energy surface. The annealing technique gives results of comparable accuracy to other commonly used minimisation methods. The main advantage of the annealing technique is that it is not necessary assume a particular functional form for f(θ). It is also easy to extend the method to include higher virial coefficients and to mixtures. We anticipate that this type of technique could be of quite general use for a number of problems involving the minimisation of functionals.

Date: 1995
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:220:y:1995:i:1:p:139-164

DOI: 10.1016/0378-4371(95)00113-L

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