Isotropic-nematic phase equilibria of hard-sphere chain fluids—Pure components and binary mixtures

Abstract

The isotropic-nematic phase equilibria of linear hard-sphere chains and binary mixtures of them are obtained from Monte Carlo simulations. In addition, the infinite dilution solubility of hard spheres in the coexisting isotropic and nematic phases is determined. Phase equilibria calculations are performed in an expanded formulation of the Gibbs ensemble. This method allows us to carry out an extensive simulation study on the phase equilibria of pure linear chains with a length of 7 to 20 beads (7-mer to 20-mer), and binary mixtures of an 8-mer with a 14-, a 16-, and a 19-mer. The effect of molecular flexibility on the isotropic-nematic phase equilibria is assessed on the 8-mer+19-mer mixture by allowing one and two fully flexible beads at the end of the longest molecule. Results for binary mixtures are compared with the theoretical predictions of van Westen et al. [J. Chem. Phys. 140, 034504 (2014)]. Excellent agreement between theory and simulations is observed. The infinite dilution solubility of hard spheres in the hard-sphere fluids is obtained by the Widom test-particle insertion method. As in our previous work, on pure linear hard-sphere chains [B. Oyarzún, T. van Westen, and T. J. H. Vlugt, J. Chem. Phys. 138, 204905 (2013)], a linear relationship between relative infinite dilution solubility (relative to that of hard spheres in a hard-sphere fluid) and packing fraction is found. It is observed that binary mixtures greatly increase the solubility difference between coexisting isotropic and nematic phases compared to pure components. C 2015 AIP Publishing LLC. [http://dx

Liquid-crystal phase equilibria of Lennard-Jones chains

“…At constant mole fraction, a maximum in the density of the nematic phase and a maximum in the isotropic-nematic density difference is observed in the range x 2 = 0.4 − 0.6 from simulation results and at x 2 = 0.5 from the theoretical results. Previously, a similar behaviour was found for binary mixtures of linear hardsphere chains [49,104]. With increasing mole fraction of the long component, the driving force for the phase transition increases, which leads to lower coexistence densities.…”

“…A brief explanation of the method is given here, while a detailed description can be found in our previous work [49]. Two forms of the method are distinguished: a constant volume ensemble in which the total volume of the system (the volume of both simulation boxes) remains unchanged, and a constant pressure ensemble in which the pressure of the system is defined and the volume of each simulation box is varied independently.…”

“…In an expanded formulation of the Gibbs ensemble, molecular transfer is performed by a gradual exchange of molecules between phases. Different methods have been proposed for this gradual transfer: configurational-bias insertions/deletions of segments of a tagged molecule [82,84,85], continuous coupling of the intermolecular interactions of a fractional molecule [83,86,87], and discrete coupling of the segments of a fractional molecule [49]. Here, we use the discrete-coupling method for the gradual transfer of a fractional chain molecule.…”

“…Phase equilibria calculations are performed in an expanded version of the Gibbs ensemble [49,82,83]. A brief explanation of the method is given here, while a detailed description can be found in our previous work [49].…”

“…Pair-interaction potentials as hard-sphere [43][44][45][46][47][48][49], hard-ellipsoid [50][51][52], hard-spherocylinders [53][54][55], and the GayBerne potential [56][57][58][59][60][61] are popular for studying liquid crystals. Other more elaborated interaction models have been proposed, e.g.…”