Self-diffusion coefficients and shear viscosity of inverse power fluids: from hard- to soft-spheres

Abstract

Molecular dynamics computer simulation has been used to compute the self-diffusion coefficient, D, and shear viscosity, eta(s), of soft-sphere fluids, in which the particles interact through the soft-sphere or inverse power pair potential, phi(r) = epsilon(sigma/r)(n), where n measures the steepness or stiffness of the potential, and epsilon and sigma are a characteristic energy and distance, respectively. The simulations were carried out on monodisperse systems for a range of n values from the hard-sphere (n --> infinity) limit down to n = 4, and up to densities in excess of the fluid-solid co-existence value. A new analytical procedure is proposed which reproduces the transport coefficients at high densities, and can be used to extrapolate the data to densities higher than accurately accessible by simulation or experiment, and tending to the glass transition. This formula, DX(c-1) proportional, variant A/X + B, where c is an adjustable parameter, and X is either the packing fraction or the pressure, is a development of one proposed by Dymond. In the expression, -A/B is the value of X at the ideal glass transition (i.e., where D and eta(s)(-1) --> 0). Estimated values are presented for the packing fraction and the pressure at the glass transition for n values between the hard and soft particle limits. The above expression is also shown to reproduce the high density viscosity data of supercritical argon, krypton and nitrogen. Fits to the soft-sphere simulation transport coefficients close to solid-fluid co-existence are also made using the analytic form, ln(D) = alpha(X)X, and n-dependence of the alpha(X) is presented (X is either the packing fraction or the pressure).

Communication: Pseudoisomorphs in liquids with intramolecular degrees of freedom

“…Simple atomic systems studied for many years by computer simulations include the Lennard-Jones (LJ) pairpotential system, the hard-sphere system, the Yukawa (screened Coulomb) system, inverse power-law systems, etc [10][11][12][13][14]. Several molecular models are also simple in the sense that they have lines in the thermodynamic phase diagram, so-called isomorphs, along which the dynamics is invariant to a good approximation in suitably reduced units [15][16][17].…”

Microscopic relationship between colloid–colloid interactions and the rheological behaviour of suspensions: a molecular dynamics-stochastic rotation dynamics investigation

“…This model has been investigated before, e.g. Hoover et al reported its phase behaviour [13], and more recently, Heyes et al studied the transport properties of fluids modelled with inverse power law interactions, from n = 4 up to the hard-sphere limit (n → ∞) [5]. The solvent was modelled with the stochastic rotation dynamics, or multi-particle collision dynamics method, first proposed by Malevanets and Kapral [14].…”

“…These studies focused on the dependence of the viscosity on the strain rate and the observation of shear thinning [2,3], as well as the rationalisation of the shear thinning in terms of the equilibrium structure of the fluid [4]. Additional studies investigated the dependence of the shear viscosity with the thermodynamic state, namely, density and pressure, considering different particle interactions [5]. Hydrodynamic interactions have also been studied using Stokesian dynamics [6], revealing the hydrodynamic origin of shear thickening.…”

The EXP pair-potential system. II. Fluid phase isomorphs

“…The EXP pair potential has not been studied much on its own right, in fact even less than other purely repulsive pair potentials like the family of inverse-power law pair potentials [2][3][4][5][6][7][8][9]. In most cases, the exponential function appears as a term in mathematically more involved potentials, for instance: 1) giving the repulsive part of the Born-Meyer pair potential from 1932 [10] or in embedded-atom models of metals [11,12], 2) multiplied by a Coulomb term to give the Yukawa (screened Coulomb) potential [13,14], or 3) giving the attractive long-ranged part in a model that rigorously obeys the van der Waals equation of state in one dimension [15].…”