Ginzburg-Landau theory of the liquid-solid interface and nucleation for hard-spheres

The Ginzburg-Landau free energy functional for hard-spheres is constructed using the Fundamental Measure Theory approach to Density Functional Theory as a starting point. The functional is used to study the liquid-fcc solid planer interface and the properties of small solid clusters nucleating within a liquid. The surface tension for planer interfaces agrees well with simulation and it is found that the properties of the solid clusters are consistent with classical nucleation theory.Comment: Replacement 1. Minor changes to figure

Mechanism for the stabilization of protein clusters above the solubility curve: the role of non-ideal chemical reactions

Dense protein clusters are known to play an important role in nucleation of protein crystals from dilute solutions. While these have generally been thought to be formed from a metastable phase, the observation of similar, if not identical, clusters above the critical point for the dilute-solution/strong-solution phase transition has thrown this into doubt. Furthermore, the observed clusters are stable for relatively long times. Because protein aggregation plays an important role in some pathologies, understanding the nature of such clusters is an important problem. One mechanism for the stabilization of such structures was proposed by Pan, Vekilov and Lubchenko and was investigated using a DDFT model which confirmed the viability of the model. Here, we revisit that model and incorporate additional physics in the form of state-dependent reaction rates. We show by a combination of numerical results and general arguments that the state-dependent rates disrupt the stability mechanism. Finally, we argue that the state-depedent reactions correct unphysical aspects of the model with ideal (state-independent) reactions and that this necessarily leads to the failure of the proposed mechanism

Hydrodynamics of an inelastic gas with implications for sonochemistry

The hydrodynamics for a gas of hard-spheres which sometimes experience inelastic collisions resulting in the loss of a fixed, velocity-independent, amount of energy $\Delta$ is investigated with the goal of understanding the coupling between hydrodynamics and endothermic chemistry. The homogeneous cooling state of a uniform system and the modified Navier-Stokes equations are discussed and explicit expressions given for the pressure, cooling rates and all transport coefficients for D-dimensions. The Navier-Stokes equations are solved numerically for the case of a two-dimensional gas subject to a circular piston so as to illustrate the effects of the enegy loss on the structure of shocks found in cavitating bubbles. It is found that the maximal temperature achieved is a sensitive function of $\Delta$ with a minimum occuring near the physically important value of $\Delta \sim 12,000K \sim 1eV$Comment: 35 pages, 9 figure

Velocity correlations and the structure of nonequilibrium hard core fluids

A model for the pair distribution function of nonequilibrium hard-core fluids is proposed based on a model for the effect of velocity correlations on the structure. Good agreement is found with molecular dynamics simulations of granular fluids and of sheared elastic hard spheres. It is argued that the incorporation of velocity correlations are crucial to correctly modeling atomic scale structure in nonequilibrium fluids.Comment: Final corrections after referees' reports. To appear in PR

Atomic-scale structure of hard-core fluids under shear flow

The effect of velocity correlations on the equal-time density autocorrelation function, e.g. the pair distribution function or pdf, of a hard-sphere fluid undergoing shear flow is investigated. The pdf at contact is calculated within the Enskog approximation and is shown to be in good agreement with molecular dynamics simulations for shear rates below the shear-induced ordering transition. These calculations are used to construct a nonequilibrium generalised mean spherical approximation for the pdf at finite separations which is also found to agree well with the simulation data.Comment: 35 pages, 13 figures. To be submitted to PRE. Replacement: More data added to fig 8 and minor improvements to the tex

Properties of non-FCC hard-sphere solids predicted by density functional theory

The free energies of the FCC, BCC, HCP and Simple Cubic phases for hard spheres are calculated as a function of density using the Fundamental Measure Theory models of Rosenfeld et al (PRE 55, 4245 (1997)), Tarazona (PRL 84, 694 (2001)) and Roth et al (J. Phys.: Cond. Matt. 14, 12063 (2002)) in the Gaussian approximation. For the FCC phase, the present work confirms the vanishing of the Lindemann parameter (i.e. vanishing of the width of the Gaussians) near close packing for all three models and the results for the HCP phase are nearly identical. For the BCC phase and for packing fractions above $\eta \sim 0.56$, all three theories show multiple solid structures differing in the widths of the Gaussians. In all three cases, one of these structures shows the expected vanishing of the Lindemann parameter at close packing, but this physical structure is only thermodynamically favored over the unphysical structures in the Tarazona theory and even then, some unphysical behavior persists at lower densities. The simple cubic phase is stabilized in the model of Rosenfeld et al. for a range of densities and in the Tarazona model only very near close-packing

Kinetic Theory and Hydrodynamics of Dense, Reacting Fluids far from Equilibrium

The kinetic theory for a fluid of hard spheres which undergo endothermic and/or exothermic reactions with mass transfer is developed. The exact balance equations for concentration, density, velocity and temperature are derived. The Enskog approximation is discussed and used as the basis for the derivation, via the Chapman-Enskog procedure, of the Navier-Stokes-reaction equations under various assumptions about the speed of the chemical reactions. It is shown that the phenomenological description consisting of a reaction-diffusion equation with a convective coupling to the Navier-Stokes equations is of limited applicability.Comment: Submitted to Journal of Chemical Physic