High-order virial coefficients and equation of state for hard sphere and hard disk systems

Dipolar colloids in apolar media: direct microscopy of two-dimensional suspensions

Spherical colloids, in an absence of external fields, are commonly assumed to interact solely through rotationally-invariant potentials, u(r). While the presence of permanent dipoles in aqueous suspensions has been previously suggested by some experiments, the rotational degrees of freedom of spherical colloids are typically neglected. We prove, by direct experiments, the presence of permanent dipoles in commonly used spherical poly(methyl methacrylate) (PMMA) colloids, suspended in an apolar organic medium. We study, by a combination of direct confocal microscopy, computer simulations, and theory, the structure and other thermodynamical properties of organic suspensions of colloidal spheres, confined to a two-dimensional (2D) monolayer. Our studies reveal the effects of the dipolar interactions on the structure and the osmotic pressure of these fluids. These observations have far-reaching consequences for the fundamental colloidal science, opening new directions in self-assembly of complex colloidal clusters.

Fifth to eleventh virial coefficients of hard spheres

Virial coefficients B(n) of three-dimensional hard spheres are reported for n=5 to 11, with precision exceeding that presently available in the literature. Calculations are performed using the recursive method due to Wheatley, and a binning approach is proposed to allow more flexibility in where computational effort is directed in the calculations. We highlight the difficulty as a general measure that quantifies performance of an algorithm that computes a stochastic average and show how it can be used as the basis for optimizing such calculations.

An asymptotically consistent approximant method with application to soft- and hard-sphere fluids

A modified Padé approximant is used to construct an equation of state, which has the same large-density asymptotic behavior as the model fluid being described, while still retaining the low-density behavior of the virial equation of state (virial series). Within this framework, all sequences of rational functions that are analytic in the physical domain converge to the correct behavior at the same rate, eliminating the ambiguity of choosing the correct form of Padé approximant. The method is applied to fluids composed of "soft" spherical particles with separation distance r interacting through an inverse-power pair potential, φ = ε(σ∕r)(n), where ε and σ are model parameters and n is the "hardness" of the spheres. For n < 9, the approximants provide a significant improvement over the 8-term virial series, when compared against molecular simulation data. For n ≥ 9, both the approximants and the 8-term virial series give an accurate description of the fluid behavior, when compared with simulation data. When taking the limit as n → ∞, an equation of state for hard spheres is obtained, which is closer to simulation data than the 10-term virial series for hard spheres, and is comparable in accuracy to other recently proposed equations of state. By applying a least square fit to the approximants, we obtain a general and accurate soft-sphere equation of state as a function of n, valid over the full range of density in the fluid phase.

New virial equation of state for hard-disk fluids

Although many equations of state of hard-disk fluids have been proposed, none is capable of reproducing the currently calculated or estimated values of the first eighteen virial coefficients at the same time as giving very good accuracy when compared with computer simulation values for the compressibility factor over the whole fluid range. A new virial-based expression is here proposed which achieves these aims. For that, we use the fact that the currently accepted estimated values for the highest virial coefficients behave linearly with their order, and also that virial coefficients must have a limiting behaviour that permits the closest packing limit in the compressibility factor to be also adequately reproduced.