Simulation and approximate formulae for the radial distribution functions of highly asymmetric hard sphere mixtures

Molecular dynamics simulations of binary sphere mixtures

Explicit simulations of fluid mixtures of highly size-dispersed particles are constrained by numerical challenges associated with identifying pair-interaction neighbors. Recent algorithmic developments have ameliorated these difficulties to an extent, permitting more efficient simulations of systems with many large and small particles of disperse sizes. We leverage these capabilities to perform molecular dynamics simulations of binary sphere mixtures with elastically stiff particles approaching the hard sphere limit and particle size ratios of up to 50, approaching the colloidal limit. The systems considered consist of 500 large particles and up to nearly 3.6×10^{6} small particles with total particle volume fractions up to 0.51. Our simulations confirm qualitative predictions for correlations between large particles previously obtained analytically and for simulations employing effective depletion interactions, but also reveal additional insights into the near-contact structure that result from the explicit treatment of the small particle solvent. No spontaneous crystal nucleation was observed during the simulations, suggesting that nucleation rates in the fluid-solid coexistence region are too small to observe crystal nucleation for feasible simulation system sizes and timescales.

Association Equilibrium for Cross-Associating Chains in a Good Solvent: Crowding and Other Nonideality Effects

Association equilibrium has been studied by molecular dynamics (MD) for mixtures of cross-associating molecules (n-decamer+p-dimer and n-decamer+p-decamer) in a good solvent. Each monomer of n-decamers carries an associative site (n-sticker); each molecule of the second component contains two terminal associative sites (p-stickers). To model the univalent association between the n-sticker and the p-sticker, a technique based on introduction of dummy atoms has been used. We report MD data on the effects of temperature, chain flexibility, and location of the sticker within the chain on the association equilibrium. We find that the presence of nonassociating monomer units of p-chain has a substantial effect on the association equilibrium. This effect is similar to "crowding" in reactive mixtures known to be caused by the presence of inert molecules. Widely used mean field theories of associating chains (e.g., SAFT or Semenov-Rubinstein theory) do not account for the effect of crowding caused by the inert fragments of reactive chains. We introduce simple empirical corrections for crowding that describe association equilibrium in the presence of nonassociating fragment in a chain-like molecule.

Solution of the mean spherical approximation for polydisperse multi-Yukawa hard-sphere fluid mixture using orthogonal polynomial expansions

The Blum-Hoye [J. Stat. Phys. 19 317 (1978)] solution of the mean spherical approximation for a multicomponent multi-Yukawa hard-sphere fluid is extended to a polydisperse multi-Yukawa hard-sphere fluid. Our extension is based on the application of the orthogonal polynomial expansion method of Lado [Phys. Rev. E 54, 4411 (1996)]. Closed form analytical expressions for the structural and thermodynamic properties of the model are presented. They are given in terms of the parameters that follow directly from the solution. By way of illustration the method of solution is applied to describe the thermodynamic properties of the one- and two-Yukawa versions of the model.

Contact values of the particle-particle and wall-particle correlation functions in a hard-sphere polydisperse fluid

The contact values g(sigma,sigma') of the radial distribution functions of a fluid of (additive) hard spheres with a given size distribution f(sigma) are considered. A "universality" assumption is introduced, according to which, at a given packing fraction eta,g(sigma,sigma')=G(z(sigma,sigma')), where G is a common function independent of the number of components (either finite or infinite) and z(sigma,sigma')=[2sigmasigma'/(sigma+sigma')]mu2/mu3 is a dimensionless parameter, mu n being the nth moment of the diameter distribution. A cubic form proposal for the z dependence of G is made and known exact consistency conditions for the point particle and equal size limits, as well as between two different routes to compute the pressure of the system in the presence of a hard wall, are used to express Gz in terms of the radial distribution at contact of the one-component system. For polydisperse systems we compare the contact values of the wall-particle correlation function and the compressibility factor with those obtained from recent Monte Carlo simulations.

Structure of highly asymmetric hard-sphere mixtures: An efficient closure of the Ornstein-Zernike equations

A simple modification of the reference hypernetted chain (RHNC) closure of the multicomponent Ornstein-Zernike equations with bridge functions taken from Rosenfeld's hard-sphere bridge functional is proposed. Its main effect is to remedy the major limitation of the RHNC closure in the case of highly asymmetric mixtures--the wide domain of packing fractions in which it has no solution. The modified closure is also much faster, while being of similar complexity. This is achieved with a limited loss of accuracy, mainly for the contact value of the big sphere correlation functions. Comparison with simulation shows that inside the RHNC no-solution domain, it provides a good description of the structure, while being clearly superior to all the other closures used so far to study highly asymmetric mixtures. The generic nature of this closure and its good accuracy combined with a reduced no-solution domain open up the possibility to study the phase diagram of complex fluids beyond the hard-sphere model.