John D. Weeks

Van der waals picture of liquids, solids, and phase transformations.

The van der Waals picture focuses on the differing roles of the strong short-ranged repulsive intermolecular forces and the longer ranged attractions in determining the structure and dynamics of dense fluids and solids. According to this physical picture, the attractive interactions help fix the volume of the system, but the arrangements and motions of molecules within that volume are determined primarily by the local packing and steric effects produced by the repulsive forces. This very useful approach, its limitations, and its successful application to a wide variety of static and dynamic phenomena in condensed matter systems are reviewed.

Dewetting and Hydrophobic Interaction in Physical and Biological Systems

Hydrophobicity manifests itself differently on large and small length scales. This review focuses on large-length-scale hydrophobicity, particularly on dewetting at single hydrophobic surfaces and drying in regions bounded on two or more sides by hydrophobic surfaces. We review applicable theories, simulations, and experiments pertaining to large-scale hydrophobicity in physical and biomolecular systems and clarify some of the critical issues pertaining to this subject. Given space constraints, we cannot review all the significant and interesting work in this active field.

Structure and thermodynamics of the liquid–vapor interface

This paper is concerned with the effects that density fluctuations in different regions of a liquid–vapor interface have on the interfacial thermodynamic and structural properties. The total volume V is divided into a square array of columns whose width is the order of the bulk correlation length. The canonical partition function is written as a sum of constrained partition functions, each describing a system with a given number of particles in each column. Changes in the occupation number of each column (i.e., density fluctuations) are related to changes in position of the local Gibbs dividing surface, and the free energy of such distortions of the Gibbs surface is estimated using macroscopic ideas similar to those used in the capillary wave theory by Buff, Lovett, and Stillinger. Corrections to the interface tension as calculated for a single column with periodic boundary conditions are given. We make a self‐consistent choice of the column width which yields a scaling law originally porposed by Widom. F...

Roles of Repulsive and Attractive Forces in Liquids: The Optimized Random Phase Approximation

The optimized random phase approximation (ORPA) is applied to the calculation of the thermodynamic properties and pair correlation function of simple liquids. General formulas are presented, together with results for the Lennard‐Jones fluid, which are compared with Monte Carlo and molecular dynamic results. Excellent agreement is obtained for the entire single phase fluid region of the phase diagram, except for the critical region and the very low temperature vapor. The theory converges especially rapidly at high densities or at high temperatures. The importance of separating the intermolecular potential in the proper way to obtain most rapid convergence of perturbation theories is discussed. It is concluded that the structure of simple liquids is determined mostly by the rapidly varying parts of the potential. Further, the ORPA provides an accurate theory for calculating the contributions from different forces to the structure and thermodynamics of liquids.

Use of Pseudopotentials in Atomic‐Structure Calculations

Taking the general point of view that the ideas of pseudopotential analysis can be usefully applied to the removal of orthogonality constraints in a wide class of problems, we describe a generalization of the method of pseudopotentials which is applicable to many‐electron systems. The generalized pseudopotential derived herein reduces to the phillips–Kleinman pseudopotential under the one‐electron Hartree–Fock approximation, and a study of its structure helps to clarify some of the properties of one‐electron pseudopotentials. The generalized formalism is then applied to ions with one valence electron, such as Be+ and Mg+, where it suggests a simple model potential which gives a good description of the Rydberg spectra of these ions. The relationship of the pseudopotential to the model potential is discussed. The theory is then applied to atoms with two valence electrons, such as Be and Mg, and it is shown how the use of one‐electron pseudopotentials or model potentials can simplify, for example, the “exact...

Analytical theory of crystal growth

The motion of the crystal–vapor interface is examined by means of the kinetic solid‐on‐solid model, a restricted version of the kinetic Ising model. We formulate an exact kinetic equation for the model and discuss some of the implications of the mean field and random distribution approximations. These methods require numerical integration of a differential‐difference equation and are accurate only in the limit of high temperatures or high deposition rates. We then introduce a new set of approximations which permit the kinetic equations to be solved analytically and discuss their validity. We obtain simple analytic expressions for both the interface width and the growth rate under steady‐state conditions. The qualitative dependence of the interface width on both temperature and deposition rate is correctly described by the theory and the predicted growth rates compare favorably with recent Monte Carlo calculations over a very wide range of temperatures and deposition rates.

Local molecular field theory for effective attractions between like charged objects in systems with strong Coulomb interactions

Strong, short-ranged positional correlations involving counterions can induce a net attractive force between negatively charged strands of DNA and lead to the formation of ion pairs in dilute ionic solutions. However, the long range of the Coulomb interactions impedes the development of a simple local picture. We address this general problem by mapping the properties of a nonuniform system with Coulomb interactions onto those of a simpler system with short-ranged intermolecular interactions in an effective external field that accounts for the averaged effects of appropriately chosen long-ranged and slowly varying components of the Coulomb interactions. The remaining short-ranged components combine with the other molecular core interactions and strongly affect pair correlations in dense or strongly coupled systems. We show that pair correlation functions in the effective short-ranged system closely resemble those in the uniform primitive model of ionic solutions and illustrate the formation of ion pairs and clusters at low densities. The theory accurately describes detailed features of the effective attraction between two equally charged walls at strong coupling and intermediate separations of the walls. Analytical results for the minimal coupling strength needed to get any attraction and for the separation at which the attractive force is a maximum are presented.

Correlation functions in the capillary wave model of the liquid–vapor interface

We study the capillary wave model of the liquid–vapor interface and derive expressions valid in arbitrary dimensions for the density profile and the density–density pair correlation function. The latter is inverted to give an explicit expression for the direct correlation function. We examine the effects of long wavelength density fluctuations on these functions in dimensions d<3 and discuss the applicability of the model to a real liquid–vapor system.

The Roughening Transition

The idea that there could be a “roughening” of the interface of a crystal in equilibrium with its vapor at a particular temperature TR was first suggested by Burton and Cabrera (1949) and further developed in a now classic article by Burton, Cabrera and Frank (BCF) (1951). Representing the crystal surface by a two-dimensional (2D) Ising model they suggested that there would be large fluctations in the surface structure at the Ising model’s critical temperature TC(2D) and a disappearance of the nucleation barrier to crystal growth. Jackson (1953, 1967) further developed and extended these ideas to the case of melt growth and showed that the morphology and growth mechanism of a wide class of crystals could be understood by assuming they were grown above or below the appropriate surface roughening temperature.

Analytic Approach to the Theory of Phase Transitions

An approximation to the first equation of the Kirkwood coupling parameter hierarchy and other model equations for the singlet distribution function are cast into the standard Hammerstein form of nonlinear integral equation. We give a criterion for the existence and uniqueness of solutions of this equation involving the first negative eigenvalue of the kernel, which allows us to establish temperatures and densities where the solution is unique. Multiple solutions of the nonlinear equation are associated with instability of the single phase and thus signal a phase transition. A necessary condition for the existence of other solutions of small norm is given by a bifurcation equation. These new solutions are associated with the freezing transition, and the periodic singlet density of the solid falls naturally out of the theory. The bifurcation equation can be related to the Kirkwood instability criterion, but, in contrast to this, predicts no transition for a system of hard rods when a model kernel is used. T...