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Soft Matter and Biological Physics

Eur. Phys. J. E 4, 51-57

Representation of pair correlations in nematics

L. Longa1,2, G. Cholewiak2, R. Trebin1 and G.R. Luckhurst3.

1  Institut für Theoretische und Angewandte Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70550 Stuttgart, Germany
2  Instytut Fizyki, Uniwersytet Jagiellonski, Reymonta 4, Kraków, Poland
3  Department of Chemistry and Southampton Liquid Crystal Institute, University of Southampton, Southampton, SO17 1BJ, United Kingdom


(Received 11 April 2000 and Received in final form 19 July 2000)

A complete expansion of equilibrium pair correlation functions for a uniaxial nematic phase composed of axially symmetric, non-polar and chiral molecules is proposed. Full advantage is taken of the symmetry of the nematic state and of the molecules. The explicit analysis and classification of the terms involving spherical harmonics with indices not exceeding 4 is given and illustrated using computer simulations for the nematic phase of a Gay-Berne mesogen. The theory is contrasted with the commonly used approach employing invariants that describe orientational correlations in molecular fluids. The role of the new representation in obtaining a correct understanding of a variety of observables, like the elastic constants, is demonstrated. In particular, the long-standing puzzle concerning the splay-bend degeneracy is resolved.

61.30.Cz - Theory and models of liquid crystal structure.
61.30.-v - Liquid crystals.
05.70.Ce - Thermodynamic functions and equations of state.

© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2001