Article

# Phase diagram of mixtures of hard colloidal spheres and discs: a free-volume scaled-particle approach.

Van't Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute, Utrecht University, Padualaan 8, 3584CH Utrecht, The Netherlands.

The Journal of Chemical Physics (Impact Factor: 3.12). 03/2004; 120(5):2470-4. DOI: 10.1063/1.1637573 Source: PubMed

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**ABSTRACT:**Scaled particle theory for a binary mixture of hard discorectangles and for a binary mixture of hard rectangles is used to predict possible liquid-crystal demixing scenarios in two dimensions. Through a bifurcation analysis from the isotropic phase, it is shown that isotropic-nematic demixing is possible in two-dimensional liquid-crystal mixtures composed of hard convex bodies. This bifurcation analysis is tested against exact calculations of the phase diagrams in the framework of the restricted-orientation two-dimensional model (Zwanzig model). Phase diagrams of a binary mixture of hard discorectangles are calculated through the parametrization of the orientational distribution functions. The results show not only isotropic-nematic, but also nematic-nematic demixing ending in a critical point, as well as an isotropic-nematic-nematic triple point for a mixture of hard disks and hard discorectangles.Physical Review E 10/2005; 72(3 Pt 1):031703. · 2.31 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We report the results of a comprehensive study of the rheological properties of a series of mixed colloid systems where the shape of one of the components has been varied systematically. Specifically we have measured the oscillatory, transient (creep) and continuous steady shear flow behaviour of a 2.5 wt% dispersion in water of a well-characterised hectorite clay modified by the addition of a series of aluminasol colloidal particles whose shape varies systematically from rod (boehmite) to platelet (gibbsite) to sphere (alumina-coated silica), all having essentially the same smallest dimension, which is similar to that of the hectorite. The particle characterisation and rheological properties of the pure components have recently been reported in Part I of this series (Soft Matter, 2007, 3, 1145). The mixtures show the same general behaviour as the pure systems, displaying a complex yield space transition from an elastoviscous gel at low applied stresses to a viscous, weakly elastic, shear-thinning liquid at high stresses. The unifying theme of this work is that the addition of 0.25 wt% of the minor component in all cases results in dramatic enhancements to the dispersion rheological properties. At the same time the magnitude of this effect depends on the shape of the particles. Shear moduli, low stress viscosities and effective yield stresses all increase in the additive order rods < platelets < spheres, with enhancements for the latter being up to a factor of 500 and typically 20. At the same time the critical failure strains for the gels decreased in the same order – the strongest gels are also the most fragile in this sense. The physicochemical factors underlying this behaviour are discussed and a simple qualitative model described. While no complete explanation or model can be proposed at this stage, the study provides a quantitative model-system baseline for mixed colloidal dispersions already used for industrial applications (e.g. oilwell-drilling fluids) and suggests ways in which such fluids may be optimised and controlled.Soft Matter 01/2008; · 4.15 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**A completely generalized version of an inhomogeneous scaled particle theory (I-SPT) for hard particle fluids confined by hard walls is presented, whereby the reversible work of cavity insertion can be determined for a cavity of any radius located at any distance from the hard wall. New exact and approximate conditions on the central function Ḡ of I-SPT are developed, where Ḡ is related to the average value of the anisotropic density of hard-sphere centers at the surface of the cavity. The predictions of the work of insertion and the form of Ḡ are quite accurate up to moderate bulk densities as compared to molecular simulation results. The accuracy of I-SPT begins to decline at high densities, due to limitations of certain needed approximations required for a complete description of Ḡ. Finally, interesting insights into the origin of depletion effects between a hard-sphere solute and the hard wall are generated via this version of I-SPT. The oscillatory nature of depletion forces, exhibiting both attractive and repulsive domains, is found to arise from the interplay between bulk SPT and I-SPT relations.Physical Review E 03/2011; 83(3 Pt 1):031126. · 2.31 Impact Factor

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