The isotropic-nematic and nematic-nematic phase transition of binary mixtures of tangent hard-sphere chain fluids: An analytical equation of state

Abstract

An analytical equation of state (EoS) is derived to describe the isotropic (I) and nematic (N) phase of linear-and partially flexible tangent hard-sphere chain fluids and their mixtures. The EoS is based on an extension of Onsager's second virial theory that was developed in our previous work [T. van Westen, B. Oyarzún, T. J. H. Vlugt, and J. Gross, J. Chem. Phys. 139, 034505 (2013)]. Higher virial coefficients are calculated using a Vega-Lago rescaling procedure, which is hereby generalized to mixtures. The EoS is used to study (1) the effect of length bidispersity on the I-N and N-N phase behavior of binary linear tangent hard-sphere chain fluid mixtures, (2) the effect of partial molecular flexibility on the binary phase diagram, and (3) the solubility of hard-sphere solutes in I-and N tangent hard-sphere chain fluids. By changing the length bidispersity, two types of phase diagrams were found. The first type is characterized by an I-N region at low pressure and a N-N demixed region at higher pressure that starts from an I-N-N triphase equilibrium. The second type does not show the I-N-N equilibrium. Instead, the N-N region starts from a lower critical point at a pressure above the I-N region. The results for the I-N region are in excellent agreement with the results from molecular simulations. It is shown that the N-N demixing is driven both by orientational and configurational/excluded volume entropy. By making the chains partially flexible, it is shown that the driving force resulting from the configurational entropy is reduced (due to a less anisotropic pairexcluded volume), resulting in a shift of the N-N demixed region to higher pressure. Compared to linear chains, no topological differences in the phase diagram were found. We show that the solubility of hard-sphere solutes decreases across the I-N phase transition. Furthermore, it is shown that by using a liquid crystal mixture as the solvent, the solubility difference can by maximized by tuning the composition. Theoretical results for the Henry's law constant of the hard-sphere solute are in good agreement with the results from molecular simulation. © 2014 AIP Publishing LLC.

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.…”

“…For details on the equations for calculating the different contributions, the reader is referred to the work of van Westen et al [71]. Details on the development of the different contributions to the equation of state can be found elsewhere [81,[102][103][104][105].…”

“…The extension of the equation of state to mixtures is straightforward, and can be obtained from Ref. [104] (chain contribution) and Ref. [105] (dispersion contribution).…”

“…Table . densities is observed, with larger deviations at lower temperatures corresponding to a larger concentration of the short chains. This effect is expected since the description of the hard-chain reference fluid that underlies the perturbation theory becomes less accurate for shorter chain lengths [104].…”

“…With increasing mole fraction of the long component, the driving force for the phase transition increases, which leads to lower coexistence densities. However, the addition of a small amount of the long component to a pure fluid of the short component leads to a dramatic increase in the orientational order of the system (due to induced order [104]). As a result, the density of the nematic phase increases.…”