Correlations in the liquid–vapor interface
15 Sep 1976-Journal of Chemical Physics (American Institute of PhysicsAIP)-Vol. 65, Iss: 6, pp 2377-2381
TL;DR: In this article, a liquid-vapor system in a gravitational field is examined using the grand canonical distribution functions ρs(r1,r2) and direct correlation functions cs(r 1, r2) for a nonuniform system.
Abstract: A liquid–vapor system in a gravitational field is examined using the grand canonical distribution functions ρs(r1...rs) and direct correlation functions cs(r1...rs) for a nonuniform system. The limit of zero field is taken under the assumption that ρ1(z) approaches a limit representing a two‐phase system. The limiting behavior is discussed in terms of an infinite continuous matrix calculated from c2(r1,r2) and ρ1(z). The vanishing of eigenvalues in zero field implies the appearance of long‐ranged correlations. The correlations are shown to be in the horizontal directions, confined to the interface, and macroscopic in range. The situation in an interface is briefly contrasted with the effect of a rigid wall in order to illustrate the fact that spontaneous symmetry breaking rather than the inhomogeneity of ρ1(z) is responsbile for the long‐ranged correlations. The invariance properties of a system in a gravitational field are used to give a new derivation of the conventional choice of the dividing surface. A microscopic expression for the surface tension is used to calculate the range of the interfacial correlations.
Citations
More filters
TL;DR: In this paper, 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.
Abstract: 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...
2,202 citations
TL;DR: In this paper, the authors considered the effects of density fluctuations in different regions of a liquid-vapor interface on the interfacial thermodynamic and structural properties of the system, and the canonical partition function was written as a sum of constrained partition functions, each describing a system with a given number of particles in each column.
Abstract: 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...
359 citations
TL;DR: In this article, the authors review some recent theoretical and computer simulation studies of simple atomic fluids adsorbed at structureless substrates and place emphasis on phase transitions, especially the various types of wetting transition, which is associated with capillary wave-like fluctuations in a continuously growing wetting film.
Abstract: Reviews some recent theoretical and computer simulation studies of simple atomic fluids adsorbed at structureless substrates. Emphasis is placed on phase transitions, especially the various types of wetting transition. Criticality is associated with capillary-wave-like fluctuations in a continuously growing wetting film. This is of a subtle nature, which is best understood in terms of the pairwise correlation function of the fluid. Other surface phase transitions, such as prewetting and layering, occur out of bulk coexistence. Theory suggests that for sufficiently attractive substrates a sequence of first-order transitions, corresponding to the growth of new adsorbed liquid layers, should occur as the pressure of the bulk gas increases towards saturation at temperatures not too far above the bulk triple point. The extent to which such behaviour is found in adsorption experiments is discussed. The authors also argue that a simple fluid confined between two parallel hard-walls can exhibit surprisingly rich equilibria.
285 citations
TL;DR: The statistical mechanics of inhomogeneous systems are usefully discussed from at least two complementary approaches: (i) the virial route, in which calculations of the structure and the thermodynamic properties are based on knowledge of the intermolecular forces in conjunction with the distribution function hierarchy, and (ii) the fluctuation theory route, based on formal results linking the equilibrium structure and properties of a system to its response to a change in external field.
Abstract: The statistical mechanics of inhomogeneous systems is usefully discussed from at least two complementary approaches: (i) the virial route, in which calculations of the structure and the thermodynamic properties are based on knowledge of the intermolecular forces in conjunction with the distribution function hierarchy, and (ii) the fluctuation theory route, based on formal results linking the equilibrium structure and properties of a system to its response to a change in external field. This paper makes use of both of these approaches to discuss the properties of a fluid in the presence of a strong localized external field. Particular attention is paid to the limiting case when the external field acts as a hard wall. Fluctuation theory yields a unified approach to interfaces stabilized by one body external fields of arbitrary strength, the strength determining the stability of the interfacial boundary with respect to wave-like fluctuations; with the weak field limit identified as a free fluid-fluid interfa...
238 citations
TL;DR: Mise au point. Rappel des equations fondamentales et des conditions d'etude as mentioned in this paper, and mise-au-point of a modele basique.
Abstract: Mise au point. Rappel des equations fondamentales et des conditions d'etude. Donnees sur le modele de l'ion ponctuel et la theorie de Gouy-Chapman, sur les theories de la double couche pour les electrolytes modeles primitifs, sur la comparaison de la theorie avec des simulations dans le cas des electrolytes symetriques et enfin sur la mise au point d'un modele basique
235 citations
References
More filters
TL;DR: In this paper, the chemical potentials of the components of gas mixtures and liquid solutions are obtained in terms of relatively simple integrals in the configuration spaces of molecular pairs, and the molecular pair distribution functions appearing in these integrals are investigated in some detail, in their dependence upon the composition and density of the fluid.
Abstract: Expressions for the chemical potentials of the components of gas mixtures and liquid solutions are obtained in terms of relatively simple integrals in the configuration spaces of molecular pairs. The molecular pair distribution functions appearing in these integrals are investigated in some detail, in their dependence upon the composition and density of the fluid. The equation of state of a real gas mixture is discussed, and an approximate molecular pair distribution function, typical of dense fluids, is calculated. Applications of the method to the theory of solutions will be the subject of a later article.
2,946 citations
TL;DR: It is shown that Boltzmann’s equation in the kinetic theory of gases follows as a particular case, and that, in equilibrium conditions, the theory gives results consistent with statistical mechanics.
Abstract: This paper outlines a general theory whose object is to provide a basis from which all the equilibrium and dynamical properties of liquids can be investigated. A set of multiform distribution functions is defined, and the generalized continuity equations satisfied by these functions are derived. By introducing the equations of motion, a set of relations is obtained from which the distribution functions may be determined. It is shown that Boltzmann’s equation in the kinetic theory of gases follows as a particular case, and that, in equilibrium conditions, the theory gives results consistent with statistical mechanics. An integral equation for the radial distribution function is obtained which is the natural generalization of one obtained by Kirkwood for ‘rigid spherical molecules’. Finally, it is indicated how the theory may be applied to solve both equilibrium and dynamical problems of the liquid state.
493 citations
TL;DR: Statistical evaluation of low-order distribution functions and thermodynamic properties of nonuniform equilibrium flow is presented in this paper, where the authors consider the case of non-uniform flow.
Abstract: Statistical evaluation of low order distribution functions and thermodynamic properties of nonuniform equilibrium flow
232 citations
TL;DR: In this article, a statistical expression for the surface tension of a liquid-vapor interface is derived, which contains the density profile and the direct correlation function in the vicinity of the interface.
Abstract: We derive a statistical mechanical expression for the surface tension of a liquid-vapor interface. It contains the density profile and the direct correlation function in the vicinity of the interface. When a local Ornstein-Zernike approximation is made on the direct correlation function, the surface-tension theory of Fisk and Widom is obtained.
231 citations
TL;DR: A formal derivation 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 is presented in this article.
Abstract: 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.
223 citations