Transport properties of highly asymmetric hard-sphere mixtures

Modeling the structure and thermodynamics of multicomponent and polydisperse hard-sphere dispersions with continuous potentials

A model system of identical particles interacting via a hard-sphere potential is essential in condensed matter physics; it helps to understand in and out of equilibrium phenomena in complex fluids, such as colloidal dispersions. Yet, most of the fixed time-step algorithms to study the transport properties of those systems have drawbacks due to the mathematical nature of the interparticle potential. Because of this, mapping a hard-sphere potential onto a soft potential has been recently proposed [Báez et al., J. Chem. Phys. 149, 164907 (2018)]. More specifically, using the second virial coefficient criterion, one can set a route to estimate the parameters of the soft potential that accurately reproduces the thermodynamic properties of a monocomponent hard-sphere system. However, real colloidal dispersions are multicomponent or polydisperse, making it important to find an efficient way to extend the potential model for dealing with such kind of many-body systems. In this paper, we report on the extension and applicability of the second virial coefficient criterion to build a description that correctly captures the phenomenology of both multicomponent and polydisperse hard-sphere dispersions. To assess the accuracy of the continuous potentials, we compare the structure of soft polydisperse systems with their hard-core counterpart. We also contrast the structural and thermodynamic properties of soft binary mixtures with those obtained through mean-field approximations and the Ornstein-Zernike equation for the two-component hard-sphere dispersion.

A comprehensive study of the thermal conductivity of the hard sphere fluid and solid by molecular dynamics simulation

This work reports a new set of hard sphere (HS) thermal conductivity coefficient, λ, data obtained by Molecular Dynamics (MD) computer simulation, over a density range covering the dilute fluid to near the close-packed solid, and for a large number of particles (up to N = 13 1072) and long simulation times. The N-dependence of the thermal conductivity is shown to be proportional to N-2/3 to a good approximation over a wide range of system sizes, which enabled λ values in the thermodynamic limit to be predicted accurately. The fluid and solid λ can be represented well by the Enskog theory (ET) formula, λE, times a density-dependent correction term, which is close to unity for the fluid and practically constant for the solid. The convergence of the MD λ data back towards ET in the metastable fluid starts just above the freezing density. For the HS solid and dense fluid it was found that the thermal conductivity is nearly linear in pressure, as has been observed experimentally for a number of solids. Simple excess entropy scaling over the higher density fluid phase region was found, and Rosenfeld's exponential relationship can be fitted to the simulation data for the solid to a high degree of accuracy. The simulation analysis has revealed a number of new trends in the behaviour of the HS thermal conductivity which could be useful in building more accurate models for heat conduction in experimental systems.

Anomalous heat transport in binary hard-sphere gases

Equilibrium and nonequilibrium molecular dynamics (MD) are used to investigate the thermal conductivity of binary hard-sphere fluids. It is found that the thermal conductivity of a mixture can not only lie outside the series and parallel bounds set by their pure component values, but can lie beyond even the pure component fluid values. The MD simulations verify that revised Enskog theory can accurately predict nonequilibrium thermal conductivities at low densities and this theory is applied to explore the model parameter space. Only certain mass and size ratios are found to exhibit conductivity enhancements above the parallel bounds and dehancement below the series bounds. The anomalous dehancement is experimentally accessible in helium-hydrogen gas mixtures and a review of the literature confirms the existence of mixture thermal conductivity below the series bound and even below the pure fluid values, in accordance with the predictions of revised Enskog theory. The results reported here may reignite the debate in the nanofluid literature on the possible existence of anomalous thermal conductivities outside the series and parallel bounds as this Rapid Communication demonstrates they are a fundamental feature of even simple fluids.

Chemical potential of a test hard sphere of variable size in hard-sphere fluid mixtures

A detailed comparison between the Boublík-Mansoori-Carnahan-Starling-Leland (BMCSL) equation of state of hard-sphere mixtures is made with Molecular Dynamics (MD) simulations of the same compositions. The Labík and Smith simulation technique [S. Labík and W. R. Smith, Mol. Simul. 12, 23-31 (1994)] was used to implement the Widom particle insertion method to calculate the excess chemical potential, βμ₀^ex, of a test particle of variable diameter, σ₀, immersed in a hard-sphere fluid mixture with different compositions and values of the packing fraction, η. Use is made of the fact that the only polynomial representation of βμ₀^ex which is consistent with the limits σ₀ → 0 and σ₀ → ∞ has to be of the cubic form, i.e., c₀(η)+c¯₁(η)σ₀/M₁+c¯₂(η)(σ₀/M₁)²+c¯₃(η)(σ₀/M₁)³, where M₁ is the first moment of the distribution. The first two coefficients, c₀(η) and c¯₁(η), are known analytically, while c¯₂(η) and c¯₃(η) were obtained by fitting the MD data to this expression. This in turn provides a method to determine the excess free energy per particle, βa^ex, in terms of c¯₂, c¯₃, and the compressibility factor, Z. Very good agreement between the BMCSL formulas and the MD data is found for βμ₀^ex, Z, and βa^ex for binary mixtures and continuous particle size distributions with the top-hat analytic form. However, the BMCSL theory typically slightly underestimates the simulation values, especially for Z, differences which the Boublík-Carnahan-Starling-Kolafa formulas and an interpolation between two Percus-Yevick routes capture well in different ranges of the system parameter space.

Pseudo hard-sphere potential for use in continuous molecular-dynamics simulation of spherical and chain molecules

We present a continuous pseudo-hard-sphere potential based on a cut-and-shifted Mie (generalized Lennard-Jones) potential with exponents (50, 49). Using this potential one can mimic the volumetric, structural, and dynamic properties of the discontinuous hard-sphere potential over the whole fluid range. The continuous pseudo potential has the advantage that it may be incorporated directly into off-the-shelf molecular-dynamics code, allowing the user to capitalise on existing hardware and software advances. Simulation results for the compressibility factor of the fluid and solid phases of our pseudo hard spheres are presented and compared both to the Carnahan-Starling equation of state of the fluid and published data, the differences being indistinguishable within simulation uncertainty. The specific form of the potential is employed to simulate flexible chains formed from these pseudo hard spheres at contact (pearl-necklace model) for m(c) = 4, 5, 7, 8, 16, 20, 100, 201, and 500 monomer segments. The compressibility factor of the chains per unit of monomer, m(c), approaches a limiting value at reasonably small values, m(c) < 50, as predicted by Wertheim's first order thermodynamic perturbation theory. Simulation results are also presented for highly asymmetric mixtures of pseudo hard spheres, with diameter ratios of 3:1, 5:1, 20:1 over the whole composition range.

DynamO: a free O(N) general event-driven molecular dynamics simulator

Molecular dynamics algorithms for systems of particles interacting through discrete or "hard" potentials are fundamentally different to the methods for continuous or "soft" potential systems. Although many software packages have been developed for continuous potential systems, software for discrete potential systems based on event-driven algorithms are relatively scarce and specialized. We present DynamO, a general event-driven simulation package, which displays the optimal O(N) asymptotic scaling of the computational cost with the number of particles N, rather than the O(N) scaling found in most standard algorithms. DynamO provides reference implementations of the best available event-driven algorithms. These techniques allow the rapid simulation of both complex and large (>10(6) particles) systems for long times. The performance of the program is benchmarked for elastic hard sphere systems, homogeneous cooling and sheared inelastic hard spheres, and equilibrium Lennard-Jones fluids. This software and its documentation are distributed under the GNU General Public license and can be freely downloaded from http://marcusbannerman.co.uk/dynamo.

Crystallization of hard disks induced by a temperature gradient

While uniform temperature has no effect on equilibrium properties of hard-core systems, its gradient might substantially change their behavior. In particular, in hard-disk system subject to temperature difference ΔT disks are repelled from the hot boundary of the system and accumulate at the cold one. Using event-driven molecular dynamics simulations we show that for sufficiently large ΔT or coverage ratio ρ∗, crystal forms at the cold boundary. In this spatially inhomogeneous system a significant decrease of diffusivity of disks clearly marks the stationary interface between liquid and crystal. Such a behavior is also supported through calculation of the radial distribution function and the bond order parameter. Simulations show that for this nonequilibrium system the equipartition of energy holds and velocity obeys the Boltzmann distribution.