Pair force distributions in simple fluids

On standardised moments of force distribution in simple liquids

The force distribution of a tagged atom in a Lennard-Jones fluid in the canonical ensemble is studied with a focus on its dependence on inherent physical parameters: number density (n) and temperature (T). Utilising structural information from molecular dynamics simulations of the Lennard-Jones fluid, explicit analytical expressions for the dependence of standardised force moments on n and T are derived. Leading order behaviour of standardised moments of the force distribution are obtained in the limiting cases of small density (n → 0) and low temperature (T → 0), while the variations in the standardised moments are probed for general n and T using molecular dynamics simulations. Clustering effects are seen in molecular dynamics simulations and their effect on these standardised moments is discussed.

On the microscopic fluctuations driving the NMR relaxation of quadrupolar ions in water

Nuclear Magnetic Resonance (NMR) relaxation is sensitive to the local structure and dynamics around the probed nuclei. The Electric Field Gradient (EFG) is the key microscopic quantity to understand the NMR relaxation of quadrupolar ions, such as (7)Li(+), (23)Na(+), (25)Mg(2+), (35)Cl(-), (39)K(+), or (133)Cs(+). Using molecular dynamics simulations, we investigate the statistical and dynamical properties of the EFG experienced by alkaline, alkaline Earth, and chloride ions at infinite dilution in water. Specifically, we analyze the effect of the ionic charge and size on the distribution of the EFG tensor and on the multi-step decay of its auto-correlation function. The main contribution to the NMR relaxation time arises from the slowest mode, with a characteristic time on the picosecond time scale. The first solvation shell of the ion plays a dominant role in the fluctuations of the EFG, all the more that the ion radius is small and its charge is large. We propose an analysis based on a simplified charge distribution around the ion, which demonstrates that the auto-correlation of the EFG, hence the NMR relaxation time, reflects primarily the collective translational motion of water molecules in the first solvation shell of the cations. Our findings provide a microscopic route to the quantitative interpretation of NMR relaxation measurements and open the way to the design of improved analytical theories for NMR relaxation for small ionic solutes, which should focus on water density fluctuations around the ion.

Thermodynamic properties and entropy scaling law for diffusivity in soft spheres

The purely repulsive soft-sphere system, where the interaction potential is inversely proportional to the pair separation raised to the power n, is considered. The Laplace transform technique is used to derive its thermodynamic properties in terms of the potential energy and its density derivative obtained from molecular dynamics simulations. The derived expressions provide an analytic framework with which to explore soft-sphere thermodynamics across the whole softness-density fluid domain. The trends in the isochoric and isobaric heat capacity, thermal expansion coefficient, isothermal and adiabatic bulk moduli, Grüneisen parameter, isothermal pressure, and the Joule-Thomson coefficient as a function of fluid density and potential softness are described using these formulas supplemented by the simulation-derived equation of state. At low densities a minimum in the isobaric heat capacity with density is found, which is a new feature for a purely repulsive pair interaction. The hard-sphere and n = 3 limits are obtained, and the low density limit specified analytically for any n is discussed. The softness dependence of calculated quantities indicates freezing criteria based on features of the radial distribution function or derived functions of it are not expected to be universal. A new and accurate formula linking the self-diffusion coefficient to the excess entropy for the entire fluid softness-density domain is proposed, which incorporates the kinetic theory solution for the low density limit and an entropy-dependent function in an exponential form. The thermodynamic properties (or their derivatives), structural quantities, and diffusion coefficient indicate that three regions specified by a convex, concave, and intermediate density dependence can be expected as a function of n, with a narrow transition region within the range 5 < n < 8.

Single particle force distributions in simple fluids

The distribution function, W(F), of the magnitude of the net force, F, on particles in simple fluids is considered, which follows on from our previous publication [A. C. Brańka, D. M. Heyes, and G. Rickayzen, J. Chem. Phys. 135, 164507 (2011)] concerning the pair force, f, distribution function, P(f), which is expressible in terms of the radial distribution function. We begin by discussing the force on an impurity particle in an otherwise pure fluid but later specialize to the pure fluid, which is studied in more detail. An approximate formula, expected to be valid asymptotically, for W(F) referred to as, W(1)(F) is derived by taking into account only binary spatial correlations in the fluid. It is found that W(1)(F) = P(f). Molecular dynamics simulations of W for the inverse power (IP) and Lennard-Jones potential fluids show that, as expected, W(F) and P(f) agree well in the large force limit for a wide range of densities and potential forms. The force at which the maximum in W(F) occurs for the IP fluids follows a different algebraic dependence with density in low and high density domains of the equilibrium fluid. Other characteristic features in the force distribution functions also exhibit the same trends. An exact formula is derived relating W(F) to P(x)(F(x)), the distribution function of the x-cartesian components of the net force, F(x), on a particle. W(F) and P(x)(F(x)) have the same analytical forms (apart from constants) in the low and high force limits.