Ronald Lovett

General Restriction on the Distribution of Ions in Electrolytes

The rigorous second‐moment condition previously derived for “primitive‐model” electrolyte ion atmospheres in equilibrium is generalized to arbitrary mixtures of electrolytes of unrestricted charge species. No special assumptions regarding the nature of solvent dielectric behavior are required, and the condition remains valid even in the presence of specific chemical interactions that lead to complex ion formation.

The structure of the liquid–vapor interface

A formal derivation is presented for the equilibrium relation between the singlet density in a fluid and the direct correlation function and for the equivalent relation involving the pair number density. It is shown that this relation is equivalent to the macroscopic condition for hydrostatic equilibrium when the singlet density varies sufficiently slowly to permit the introduction of local thermodynamics. Some aspects of the usage of this in the determination of the singlet density in the liquid–vapor transition region are discussed.

Computer simulation study of the local pressure in a spherical liquid–vapor interface

The pressure profiles across a liquid–vapor interface introduced previously [J. Chem. Phys. 106, 635 (1997)] have been evaluated with the aid of molecular dynamics simulations for a system of particles interacting via a (truncated and shifted) Lennard-Jones potential. This investigation extends earlier results [J. Chem. Phys. 106, 645 (1997)] to spherical interfaces. Further evidence is found that, for the range of curvatures investigated, the surface tension is curvature independent while the investigation of larger curvatures is prevented by the considerable noise found on the liquid side of the interface.

Kinetic instabilities in first order phase transitions

Linear stability analysis is used to show that an homogeneous system in the early ’’aging’’ stage of a first order phase transition is unstable to heterogeneous development. A detailed analysis appropriate to precipitation out of a solution is presented although only the most general features of a first order phase transition are actually necessary. A linear dispersion relation is constructed which can also be applied to an initially heterogeneous system and which predicts heterogeneous development in general agreement with observed Liesegang ring formation.

On the stability of a fluid toward solid formation

A traditional search for solidlike singlet densities in a system with a fluidlike pair distribution function is undertaken. The analysis is based upon a nonlinear integral equation relating the direct correlation function and the singlet density in contrast with previous analyses based upon similar relations between the singlet and pair number densities. An investigation is also made of the mechanical stability of such a system and it is found that a solidlike solution and mechanical instability appear simultaneously. Numerical analysis shows that the three‐dimensional hard sphere system remains stable at all densities but that an additional attractive pair interaction produces a physically reasonable instability.

When does a pair correlation function fix the state of an equilibrium system

The classical demonstrations that a unique single particle external field is associated with each equilibrium single particle density field (Hohenberg and Kohn, Mermin) are reinterpreted in the language of functional Legendre transformations. This picture is readily extended to the pair distribution function problem and the extension offers a context for understanding how the singlet and pair number densities fix the state of a system. It is shown that one can be sure that there are closure relations to integral equations in general and that in principle the correct closure relation fixes not only the distribution functions but also the complete thermodynamic state of a system. It also follows that a correctly closed integral equation possesses a unique solution. Integral equations for the radial distribution function alone, however, are typically produced by projecting out the singlet density field and for this reason they provide an incomplete characterization of the system. The failure to specify a uni...

The local pressure in a cylindrical liquid–vapor interface: A simulation study

The equilibrium force distribution, or the local pressure in an interface as defined in a companion paper, has been determined from molecular dynamics simulations of a Lennard-Jones fluid. Both a cylindrical and a planar interface are considered. Limited evidence is found that the surface tension could be independent of the curvature of the interface.

A molecular theory of the Laplace relation and of the local forces in a curved interface

Equilibrium in a two-phase system, a liquid in equilibrium with its vapor, for example, is characterized by the constancy throughout the system of the temperature and the chemical potential and a relation between the pressures of the phases, the Laplace relation of macroscopic thermodynamics. We give a molecular expression for this latter relation in terms of a local pressure defined as the thermodynamic response to a local volume change and we show that this local pressure is the same as the local force distribution in an interface. The macroscopic characteristics of the two-phase system, including the bulk pressures, the surface tension and the location of the surface of tension are all determined by this local pressure function. As shown in a companion paper this function can easily be determined by numerical simulation.

Phase instability and the direct correlation function integral equation

Extensive searches for the equilibrium liquid–solid coexistence line have been based on the identification of this line with the bifurcation points in integral equations such as the lowest order Kirkwood lambda coupling equation, the lowest order Born and Green equation, and a similar relation between the direct correlation function and the singlet density. In applications where these integral equations should be identical, different results have been found. The difference is explained by noting that additional, implicit approximations have always been introduced. A new formulation free of such approximations is given, and it is shown that the general condition for bifurcation to occur is simply expressed in terms of the direct correlation function and has a simple physical interpretation: An approximation free search for bifurcation points will identify points of liquid instability and not points of liquid–solid coexistence.

The constraint on the integral kernels of density functional theories which results from insisting that there be a unique solution for the density function

All predictive theories for the spatial variation of the density in an inhomogeneous system can be constructed by approximating exact, nonlinear integral equations which relate the density and pair correlation functions of the system. It is shown that the set of correct kernels in the exact integral equations for the density is on the boundary between the set of kernels for which the integral equations have no solution for the density and the set for which the integral equations have a multiplicity of solutions. Thus arbitrarily small deviations from the correct kernel can make these integral equations insoluble. A heuristic model equation is used to illustrate how the density functional problem can be so sensitive to the approximation made to the correlation function kernel and it is then shown explicitly that this behavior is realized in the relation between the density and the direct correlation function and in the lowest order BGYB equation. Functional equations are identified for the kernels in these...