Orientational and thermodynamic properties of rod - plate mixtures

Abstract

The molecular-statistical model of a fluid composed of rectangular parallelepipeds, that is continuous in translations and discrete in orientation distribution, is employed in calculations relating to regions corresponding to the stability of uniaxial and biaxial nematic phases in model mixtures of uniaxial rod-like and plate-like particles, interacting via steric repulsion. The calculations are performed taking into account three-particle correlations. It is shown that for fixed overall mole fraction, the value of the configurational Gibbs free energy of a biaxial phase is equal to that of a system with a miscibility gap containing two uniaxial nematic phases, one rich in rod-like molecules and the other in plate-like ones. The results of the present study are compared with those of studies of related model systems.

Enhancement by Polydispersity of the Biaxial Nematic Phase in a Mixture of Hard Rods and Plates

“…At the conclusions of his work, Alben mentions that a N + -N − phase separation might replace the B phase, but does not considers this possibility in his analysis. A similar phase behavior has later been obtained by other authors using different models [2,3,4,5]. They take into account the effect of having free (rather than restricted to a lattice) rotations and/or translations.…”

Structure and thermodynamics of platelet dispersions

“…A second-order virial approximation [Eq. ( 54), without the last term] has been used to investigate the phase diagram of binary mixtures of rods and platelets [166,167]. It has been found that mixing rods and platelets can stabilize a biaxial nematic phase in which the symmetry axes of particles of different species point along mutually perpendicular directions.…”

A generalisation of the Onsager trial-function approach: describing nematic liquid crystals with an algebraic equation of state

“…In some cases qualitative differences in the types of phase behaviour are seen when compared with the full numerical solution particularly for mixtures (see the studies on mixtures of rod and disk-like particles [137][138][139][140]). The simple model of Zwanzig [88] (in which only the three cartesian orientations of the orientational distribution function are considered) have also found popular use owing to the tractable nature of the free energy [141][142][143][144][145][146][147][148][149][150][151][152][153][154]. As a final remark on the general use of trial functions, one should mention that in addition to being a useful ingredient in providing a representation of the thermodynamic properties of the isotropic-nematic transition, the Onsager, Gaussian and related trial functions have been used to analyse and describe the degree of orientational order determined experimentally [155][156][157][158][159][160].…”