Abstract
We employ a generalized van der Waals-Onsager perturbation theory to construct a free energy functional capable of describing the thermodynamic properties and orientational order of the isotropic and nematic phases of attractive disc particles. The model mesogen is a hard (purely repulsive) cylindrical disc particle decorated with an anisotropic square-well attractive potential placed at the centre of mass. Even for isotropic attractive interactions, the resulting overall inter-particle potential is anisotropic, due to the orientation-dependent excluded volume of the underlying hard core. An algebraic equation of state for attractive disc particles is developed by adopting the Onsager trial function to characterize the orientational order in the nematic phase. The theory is then used to represent the fluid-phase behaviour (vapour-liquid, isotropic-nematic, and nematic-nematic) of the oblate attractive particles for varying values of the molecular aspect ratio and parameters of the attractive potential. When compared to the phase diagram of their athermal analogues, it is seen that the addition of an attractive interaction facilitates the formation of orientationally-ordered phases. Most interestingly, for certain aspect ratios, a coexistence between two anisotropic nematic phases is exhibited by the attractive disc-like fluids.
Highlights
Liquid crystals [1,2,3] are intermediate phases with characteristics that lie between the fully positionally- and orientationally-ordered crystal and the disordered liquid states
The fluid-phase diagrams of attractive cylindrical discs of various aspect ratios with square-well attractive interaction are calculated by equating the pressure and chemical potential of the coexisting phases at a given temperature
We present a closed-form equation of state for the description of the thermodynamic properties and orientational ordering of attractive hard-core cylindrical-disc fluids, which serves as a basic model for thermotropic discotic liquid crystals
Summary
Liquid crystals [1,2,3] are intermediate (meso) phases with characteristics that lie between the fully positionally- and orientationally-ordered crystal and the disordered liquid states. The Onsager view that repulsive (excluded volume) interactions are of key importance in the formation of orientationally ordered phases is widely accepted In his pioneering work on nematic LCs [8], Onsager proposed the well-accepted free energy functional for nematic states and demonstrated that the isotropic-nematic phase transition can be driven by entropy alone. As has already been mentioned, purely repulsive discotic particles have been shown to exhibit columnar phases in the higher density region This was first demonstrated by Veerman and Frenkel [25,74] with simulations of the hard cut-sphere system; columnar order was subsequently found in systems of oblate hard spherocylinders [32]. By using the Onsager trial function to describe the degree of orientational order in the nematic phase, the free energy and equation of state for the nematic state can be expressed in closed algebraic form, which allows a straightforward superimposition of contributions from intermolecular interactions such as chiral, dipolar and associating interactions, or the extension to other types of dispersive intermolecular potentials (e.g., Lennard-Jones, Mie, Yukawa)
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