New types of phase behaviour in binary mixtures of hard rod-like particles

Abstract

The phase behaviour of binary mixtures of hard rod-like particles has been studied using Parsons—Lee theory (Parsons, J. D., 1979, Phys. Rev. A, 19, 1225); Lee, S. D., 1987, J. Chem. Phys., 87, 4972). The stability of the isotropic-nematic (I-N) transition with respect to isotropic—isotropic (I-I), and nematic—nematic (N-N) demixing is investigated. The individual components in the mixtures are modelled as hard cylinders of diameters Di and lengths Li (i = 1,2). The aspect ratios ki = Li/Di of the components are kept fixed (with values of k 1 = 15 and k 2 = 150), and the phase behaviour of the mixtures is studied for varying diameter ratios d = D 1/D 2. When the diameter ratio is relatively large, e.g., for values of d = 50, component 1 may be considered a large colloidal particle, while the second component plays the role of a weakly interacting solvent. This mixture exhibits only an I-N phase transition which is driven by the excluded volume interaction between the large particles (no I-I or N-N demixing is seen). A decrease in the diameter ratio enhances the contribution of the smaller component to the free energy (especially in terms of the unlike excluded volume term), and I-I as well as N-N demixing transitions are observed. The character of the N-N transition is rather unusual, a single region bounded by a lower critical point (in the pressure—composition plane) is seen for a diameter ratio of d = 3.2, while two demixed nematic regions bounded by lower and upper critical points are observed for d = 3.13. A further decrease in the diameter ratio (e.g., to d = 3) leads to systems with a phase behaviour in which the two demixed N-N regions meet, giving rise to a large demixed region with very strong fractionation in composition, and no N-N critical points. The I-I demixing transition is always accompanied by a lower critical point and occurs for systems with intermediate size (diameter) ratios. A diameter ratio of d = 4.5 corresponds to systems with significant like and unlike excluded volume interactions, and in this case the I-N transition takes place over the whole composition range with weak fractionation and one azeotropic point. Surprisingly, the coexisting nematic phase is of lower packing fraction than the isotropic phase for some of the compositions, i.e., an inversion of packing fraction takes place. In addition to this, the longer rods can be less ordered that the shorter rods for certain values of the composition.