Advances in generalised van der Waals approaches for the isotropic-nematic fluid phase equilibria of thermotropic liquid crystals - An algebraic equation of state for attractive anisotropic particles with the Onsager trial function

Mario Franco-Melgar (1) , Andrew J. Haslam (1) , George Jackson (1)

1 Chemical Engineering

In this contribution we provide a review and reformulation of perturbation theories (generalised van der Waals approaches) for the description of the fluid phase behaviour and orientational ordering transitions of thermotropic nematic liquid crystals. Free energy functionals of the basic Onsager form are used as the platform for the development of a general formulation which reduces to the specific forms of the various theories that have found common use. A novel closed analytical description of the thermodynamic properties and degree of nematic order is then obtained by employing the Onsager trial function to represent the orientational distribution function in terms of a single parameter. The latter essentially constitutes an algebraic equation of state for the nematic phase appropriate for use in engineering applications. The description of ordering transitions with scaled-Onsager theories and suitable trial functions has already been illustrated by its application to systems of hard spherocylinders (HSCs), indicating that the approach provides an excellent representation of the orientational order of the hard-core (athermal) system [M. Franco Melgar, A. J. Haslam, and G. Jackson, Mol. Phys. 106, 649 (2008)]. Here, the hard-body model is extended to account for attractive interactions (treated at the van der Waals level) of a general isotropic/anisotropic form (e.g., Lennard-Jonesium, square-well (SW), Maier-Saupe (MS) etc.).

Mots clés: Physical Sciences

Mario Franco-Melgar, Andrew J. Haslam, George Jackson. Advances in generalised van der Waals approaches for the isotropic-nematic fluid phase equilibria of thermotropic liquid crystals - An algebraic equation of state for attractive anisotropic particles with the Onsager trial function. Molecular Physics, 2009, 107 (22), pp.2329-2358. ⟨10.1080/00268970903352335⟩. ⟨hal-00530832⟩