Liquid Crystal Phase Behaviour of Attractive Disc-Like Particles

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.

An analytical equation of state for describing isotropic-nematic phase equilibria of Lennard-Jones chain fluids with variable degree of molecular flexibility

“…Other systems for which Type I behaviour was predicted from theory are, for example, hard spherocylinders-, 40,41 hard ellipsoids-, 39,40 and hard disks equipped with isotropic square-well attractions. 42 Type I behaviour was also observed in molecular simulation studies of Gay-Berne fluids 43 or solutions of hard rod-like colloids in a solvent of spherical, ideal polymer particles. Effectively, these colloid-polymer systems can be considered as pseudo one-component systems of attractive colloids due to polymer-induced depletion interactions.…”

“…Therefore, beyond a certain chain length, the vaporliquid equilibrium becomes metastable, and a single isotropicnematic equilibrium is obtained. Disappearing (metastable) vapor-liquid equilibria were predicted in several previous theoretical studies on pure-component systems of attractive mesogens, [39][40][41][42]45 and this phase diagram is classified as Type II. 39 Experimentally, Type II behaviour is observed in solutions of polypeptides in dimethylformamide (DMF).…”

“…47,48 Later, the same behaviour was predicted from several Onsager-based approaches. [39][40][41][42]45 Experimentally, the existence of Type III behaviour is observed for solutions of poly(γ-benzyl-L-glutamate) (PBLG), 46,49,50 polysaccharide Schizophyllan, 51,52 and -hexa-alkylbenzene FIG. 6.…”

Liquid-crystal phase equilibria of Lennard-Jones chains

“…Other more elaborated interaction models have been proposed, e.g. hard-spherocylinder with an attractive square-well potential [28,[62][63][64], hard-disc with an anisotropic square-well attractive potential [27], hard-spherocylinder with an attractive Lennard-Jones potential [65], anisotropic soft-core spherocylinder potential [66,67], and copolymers [68][69][70]. In this work, we focus our study on the isotropic-nematic phase behaviour of linear and partially-flexible Lennard-Jones chain fluids.…”

“…Simulations based on coarse-grained models can access longer time and length scales than their atomistic counterparts, allowing a bulk description of fluids. Coarse-grained models are commonly used to represent a simplified picture of large molecules, such as biomolecules [12][13][14][15][16], polymers [17][18][19][20][21][22], or liquid crystals [23][24][25][26][27][28]. Moreover, simulation results obtained from coarse-grained models can be directly compared with theoretical predictions that are based on a well-defined Hamiltonian, such as the family of perturbation theories developed from the statistical association fluid theory (SAFT) [29][30][31][32][33][34][35][36].…”