Recent theoretical work on the microscopic structure and surface tension of the liquid-vapour interface of simple (argon-like) fluids is critically reviewed. In particular, the form of pairwise intermolecular correlations in the liquid surface and the capillary wave treatment of the interface are examined in some detail. It is argued that conventional capillary wave theory, which leads to divergences in the width of the density profile, is unsatisfactory for describing all the equilibrium aspects of the interface. The density functional formalism which has been developed to study the liquid-vapour interface can also be profitably applied to other problems in the statistical mechanics of non-uniform fluids; here a new generalization of the ‘linear’ theory of spinodal decomposition is formulated and by considering a ‘nearly uniform’ fluid, some useful results for the long-wavelength behaviour of the liquid structure factor of various monatomic liquids are obtained. Some other topics of current inte...

The nature of the liquid-vapour interface and other topics in the statistical mechanics of non-uniform, classical fluids

Publisher Summary This chapter focuses on measurements and theories pertaining to homogeneous nucleation under cooled liquids and glasses that transform to phases of the same composition. The dynamical model describing the cluster evolution appears to be quantitatively correct. Although there are some experimental and theoretical difficulties with the classical theory, there are also many approaches to rectify these problems. At present, there are no experiments that can demonstrate or can refute conclusively the validity of the classical theory in the regime where it is expected to be valid. This is partially because of a lack of knowledge of the correct values for the parameters that are fit by the theory. Better measurements of the steady-state and time-dependent nucleation rates and the free-energy difference as a function of temperature, and the design of new experiments such as the multistep annealing treatments discussed in the chapter are used to test more rigorously nucleation theories. Time-dependent nucleation and the interface kinetics are incorporated into the field-theoretic approaches to give theories that are as widely applicable and, hence, testable as the classical theory.

Crystal Nucleation in Liquids and Glasses

Canonical molecular dynamics (MD) and Monte Carlo (MC) simulations for liquid/vapor equilibrium in truncated Lennard-Jones fluid have been carried out. Different results for coexistence properties (orthobaric densities, normal and tangential pressure profiles, and surface tension) have been reported in each method. These differences are attributed in literature to different set up conditions, e.g., size of simulation cell, number of particles, cut-off radius, time of simulations, etc., applied by different authors. In the present study we show that observed disagreement between simulation results is due to the fact that different authors inadvertently simulated different model fluids. The origin of the problem lies in details of truncation procedure used in simulation studies. Care has to be exercised in doing the comparison between both methods because in MC calculations one deals with the truncated potential, while in MD calculations one uses the truncated forces, i.e., derivative of the potential. The truncated force does not uniquely define the primordial potential. It results in MD and MC simulations being performed for different potential models. No differences in the coexistence properties obtained from MD and MC simulations are found when the same potential model is used. An additional force due to the discontinuity of the truncated potential at cut-off distance becomes crucial for inhomogeneous fluids and has to be included into the virial calculations in MC and MD, and into the computation of trajectories in MD simulations. The normal pressure profile for the truncated potential is constant through the interface and both vapor and liquid regions only when this contribution is taken into account, and ignoring it results in incorrect value of surface tension.

https://web.mst.edu/~hale/argonMC/References/JCP.1999.Trokhymchuk.LJ.liq.sim.Tc.pots..pdf

Computer simulations of liquid/vapor interface in Lennard-Jones fluids: Some questions and answers

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...

Structure and thermodynamics of the liquid–vapor interface

Monte Carlo or molecular dynamics simulations involve the numerical determinations of the statistical thermodynamics and related structural, energetic and (in the case of molecular dynamics) dynamic properties of an atomic or molecular assembly on a high-speed digital computer. Applications to molecular systems range from the study of the motions of atoms or groups of atoms of a molecule or macromolecule under the influence of intramolecular energy functions to the exploration of the structure and energetics of condensed fluid phases such as liquid water and aqueous solutions based on intermolecular potentials. The quantities determined in a typical Monte Carlo or molecular dynamics simulation include the average or mean configurational energy (thermodynamic excess internal energy), various spatial distribution functions for equilibrium systems, and time-correlation functions for dynamical systems, along with detailed structural and energetic analyses thereof. Diverse problems in structural and reaction chemistry of molecules in solution, such as solvation potentials, solvent effects on conformational stability and the effect of solvent on chemical reaction kinetics and mechanism via activated complex theory also require a particular knowledge of the configurational free energy, which in principle follows directly from the statistical thermodynamic partition function for the system. Considerations on free energy in molecular simulations take a distinctly different form for intramolecular and intermolecular degrees of freedom. For the intramolecular case, the problem involves vibrational and librational modes of motion on the intramolecular energy surface. We will discuss briefly a t the end of this paper the harmonic and quasiharmonic approximation used to compute vibrational contributions to the free energy, but we will restrict the focus herein to the intermolecular case, where the particles of the system undergo diffusional motion and a harmonic or quasiharmonic treatment breaks down. These considerations apply also in the case of a flexible molecule, where conformational transitions are effectively an intramolecular “diffusional mode.” Conventional Monte Carlo and molecular dynamics procedures for diffusional modes, although firmly grounded in Boltzmann statistical mechanics and dynamics, do not proceed via the direct determination of a partition function because of well-known

Free energy simulations.

A new Monte Carlo method for calculating the surface tension of a liquid is described. The method is based on a direct evaluation of the free energy required to create a surface, unlike earlier Monte Carlo calculations which evaluated the surface stress. It is applied to the 6:12 fluid in conditions close to the triple point for argon. The calculated surface tension agrees within statistical uncertainty with previous Monte Carlo estimates, but the statistical uncertainty of the present method is much lower. Agreement with experimental data for argon is not good, as should be expected; estimates of the effects of using a correct pair potential and particularly of including three‐body interactions indicate that they would lead to good agreement.

J. A. Barker

Papers

A new Monte Carlo method for calculating surface tension