Martin Anton van der Hoef

Free energy of the Lennard-Jones solid

We have determined a simple expression for the absolute Helmholtz free energy of the fcc Lennard-Jones solid from molecular dynamics simulations. The pressure and energy data from these simulations have been fitted to a simple functional form (18 parameters) for densities ranging from around 0.94–1.20, and temperatures ranging from 0.1 to 2.0 (values in reduced Lennard-Jones units). The absolute free energy at an arbitrary state point in this range is obtained by integrating over density and temperature from the triple-point. Our result for the free energy is in very good agreement with the values reported in literature previously. Also the melting line obtained from our free energy expression, in combination with an equation of state for the liquid phase, is in excellent agreement with results by Agrawal and Kofke [Mol. Phys. 85, 43 (1995)] obtained via the Gibbs–Duhem integration method.

THREE-BODY DISPERSION CONTRIBUTIONS TO THE THERMODYNAMIC PROPERTIES AND EFFECTIVE PAIR INTERACTIONS IN LIQUID ARGON

The contributions of three-body triple dipole and dipole-dipole-quadrupole dispersion interactions to the thermodynamic properties of liquid argon are examined, using a recently introduced simulation scheme which contains an explicit, quantum mechanical representation of the underlying electronic structure [Mol. Phys. 94, 417 (1998)]. The experimental pressure and energy at a series of liquid densities are shown to be quite accurately reproduced by a combination of the best available pair potential (Aziz) plus these three-body terms. The extent to which these many-body effects can be encompassed by an effective pair potential is then discussed. The nonuniqueness of such an effective potential is reiterated. It is shown that in the dense liquid, the three-body contribution to the effective pair potential ((r)) varies approximately linearly with density and is almost temperature independent. It is shown how the addition of (r) to the Aziz pair potential moves the latter toward the widely used Lennard-Jones (12-6) potential

Gas-solid coexistence of the Lennard-Jones system

Recently, the absolute free energies of the Lennard-Jones system at solid–liquid and solid–gas coexistence were computed from Monte Carlo simulations [J. Chem. Phys. 116, 7145 (2002)]. In this note, we show that the values along the sublimation line are in good agreement with the results from an equation of state published earlier [J. Chem. Phys. 113, 8142 (2000)]. The present values for the thermodynamic properties along the sublimation line are the most accurate reported to date

A novel simulation model for three-body dispersion interactions

We present a novel molecular dynamics simulation technique, which accounts for both two- and three-body dispersion interactions. This technique is a unified approach of molecular dynamics and quantum mechanical variational methods, in the spirit of the Car - Parrinello method (1985 Phys. Rev. Lett. 55 2471). We use a highly simplified model for the electronic structure of the atoms, which is, nevertheless, sufficient to correctly reproduce the London two-body, and the Axilrod - Teller three-body dispersion forces in an appropriate limit. The advantage of this new method is that it allows for a consistent treatment of both dispersion damping and periodic boundary conditions at the pair and three-body levels.

Leakiness of Pinned Neighboring Surface Nanobubbles Induced by Strong Gas–Surface Interaction

The stability of two neighboring surface nanobubbles on a chemically heterogeneous surface is studied by molecular dynamics (MD) simulations of binary mixtures consisting of Lennard-Jones (LJ) particles. A diffusion equation-based stability analysis suggests that two nanobubbles sitting next to each other remain stable, provided the contact line is pinned, and that their radii of curvature are equal. However, many experimental observations seem to suggest some long-term kind of ripening or shrinking of the surface nanobubbles. In our MD simulations we find that the growth/dissolution of the nanobubbles can occur due to the transfer of gas particles from one nanobubble to another along the solid substrate. That is, if the interaction between the gas and the solid is strong enough, the solid–liquid interface can allow for the existence of a “tunnel” which connects the liquid–gas interfaces of the two nanobubbles to destabilize the system. The crucial role of the gas–solid interaction energy is a nanoscopic element that hitherto has not been considered in any macroscopic theory of surface nanobubbles and may help to explain experimental observations of the long-term ripening.

Computer simulations of long-time tails: what's new?

Abstract Twenty five years ago Alder and Wainwright discovered, by simulation, the ‘long-time tails’ in the velocity autocorrelation function of a single particle in fluid [1]. Since then, few qualitatively new results on long-time tails have been obtained by computer simulations. However, within the framework of a lattice gas simulation, we recently developed a technique that makes it possible to ‘measure’ such velocity autocorrelation functions with an efficiency that is at least a factor 106 higher than can be achieved with conventional techniques. This method opens the way for making comparisons with the predictions of mode-coupling theory of long-time tails, to an accuracy which was hitherto not possible. In this paper we describe this method, and review the results on long-time tails that have been obtained. In particular, we present evidence that the functional form of the long-time tail in a two-dimensional fluid is qualitatively different from the simple power law observed by Alder-Wainwright. Su...

Dynamics of Formation of a Vapour Nanobubble Around a Heated Nanoparticle

We study the formation of a nanobubble around a heated nanoparticle in a bulk liquid by using molecular dynamics simulations. The nanoparticle is kept at a temperature above the critical temperature of the surrounding liquid, leading to the formation of a vapor nanobubble attached to it. First, we study the role of both the temperature of the bulk liquid far away from the nanoparticle surface and the temperature of the nanoparticle itself on the formation of a stable vapor nanobubble. We determine the exact conditions under which it can be formed and compare this with the conditions that follow from a macroscopic heat balance argument. Next, we demonstrate the role of dissolved gas on the conditions required for nucleation of a nanobubble and on its growth dynamics. We find that beyond a certain threshold concentration, the dissolved gas dramatically facilitates vapor bubble nucleation due to the formation of gaseous weak spots in the surrounding liquid.

Discrete element study of liquid-solid slurry flows through constricted channels

Discrete element model is used to simulate the flow of liquid-granule mixtures in an inclined channel containing a linear contraction. All the relevant particle/particle and particle/fluid interactions are included in the numerical model. The presence of the contraction induces different steady morphologies of the solid phase or the mixture depending on whether closed or open channels are used. These flows behave quite differently depending on the upstream Froude number and the contraction size ratio. The model is first validated by comparing with the existing results for dry granular (glass particles) chute flows (Vreman et al., 2007). Then simulations of a chute of glass particles in water flowing in a closed channel are compared to the dry granular case. With the same solid flux at the inlet, the hydrodynamic forces in the liquid-solid mixture induce higher particle solid volume fractions in the part of the flow containing the solid phase. The streamwise particle velocity (resp. depth of the solid phase) has the same evolution along the channel with smaller (larger) values than in the dry granular flow case.