Isotropic−Nematic Density Inversion in a Binary Mixture of Thin and Thick Hard Platelets

Abstract

We study the phase behavior of a binary mixture of thin and thick hard platelets, using Onsager's second virial theory for binary mixtures in the Gaussian approximation. Higher virial terms are included by rescaling the excluded volume part of the Onsager free energy using a modified form of the Carnahan-Starling free energy for hard spheres (Parsons' approach). Our calculations provide a simple explanation for the isotropicnematic (I-N) density inversion, as experimentally observed in systems of polydisperse gibbsite platelets by Van der Kooij et al. (J. Phys. Chem. B 2001, 105, 1696. In these systems, a nematic upper phase was found to coexist with an isotropic bottom phase. We confirm the original conjecture of the authors, which states that the phenomenon originates from a pronounced fractionation in thickness between the phases, such that the thick platelets are largely expelled from the nematic phase and preferentially occupy the isotropic phase. Our calculations show that the inverted state is found in a major part of the I-N coexistence region. In addition, a nematic-nematic demixing transition is located at sufficiently high osmotic pressures for any thickness ratio L 2 /L 1 > 1. The N-N coexistence region is bounded by a lower critical point which shifts toward lower values as the thickness ratio is increased. At high thickness ratios (L 2 /L 1 > 3.3), a triphasic coexistence is found at which two nematic phases coexist with an isotropic phase. We show that the demixing transition is driven by a small O(L/D) contribution to the excluded volume entropy.

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

“…We devote the remainder of this section to obtaining approximate solutions of Eqs. (27) and (28). The first integral (Eq.…”

“…The first integral (Eq. (27)) was approximated by Onsager in the Appendix of his seminal paper from 1949. 9 Since from Onsager's analysis it is difficult to subtract for which cases his approximation is justified, we will here go through his derivation in a bit more detail and put some emphasis on the assumptions made.…”

Global fluid phase behavior in binary mixtures of rodlike and platelike molecules

“…A drawback of the Onsager theory is that it is justified only for very long and thin particles as the virial expansion is described only up to second order in his approach. The extension of the Onsager theory to binary mixtures is straightforward, and it has been applied to a number of systems including rod-rod, 28 -31 plate-plate, 32 and rod-plate 22,23,25 binary mixtures. Isotropic-nematic, nematic-nematic, and isotropic-isotropic phase coexistence, as well as reentrant phenomena are commonly seen in these systems.…”

“…It is interesting to note that upper critical pressures have been obtained for nematic demixing in mixtures of hard rodlike particles, [29][30][31] while lower critical pressures are seen as the limit of nematic demixing in mixtures platelike particles. 32 In hard rod-plate mixtures, the nematic directors of the rod-rich and plate-rich coexisting phases are always perpendicular to each other, so that high-pressure nematic-nematic critical points have not been observed. Furthermore, the large rod-plate excluded volume means that the region of nematic-nematic separation is very wide in composition.…”

The effect of size ratio on the sphere structure factor in colloidal sphere-plate mixtures

“…33 For monodisperse hard rods, this theory proved successful in accounting for the isotropic-to-nematic phase transition [34][35][36][37] and it was then extended to study mixtures of such particles, 38 also including smectic phases. [39][40][41] For hard discs, the Parsons theory has also been applied, 42,43 but, as it reduces to Onsager theory 44 for thin particles, it does not describe the isotropic-nematic phase transition too well in the thin platelet limit.…”