Statistical substantiation of the van der Waals theory of inhomogeneous fluids

Abstract

Computer experiments on simulation of thermodynamic properties and structural characteristics of a Lennard-Jones fluid in one- and two-phase models have been performed for the purpose of checking the base concepts of the van der Waals theory. Calculations have been performed by the method of molecular dynamics at cutoff radii of the intermolecular potential r(c,1)=2.6sigma and r(c,2)=6.78sigma. The phase equilibrium parameters, surface tension, and density distribution have been determined in a two-phase model with a flat liquid-vapor interface. The strong dependence of these properties on the value of r(c) is shown. The p,rho,T properties and correlation functions have been calculated in a homogeneous model for a stable and a metastable fluid. An equation of state for a Lennard-Jones fluid describing stable, metastable, and labile regions has been built. It is shown that at T > or =1.1 the properties of a flat interface within the computer experimental error can be described by the van der Waals square-gradient theory with an influence parameter kappa independent of the density. Taking into account the density dependence of kappa through the second moment of the direct correlation function will deteriorate the agreement of the theory with data of computer simulation. The contribution of terms of a higher order than (nablarho)(2) to the Helmholtz free energy of an inhomogeneous system has been considered. It is shown that taking into account terms proportional to (nablarho)(4) leaves no way of obtaining agreement between the theory and simulation data, while taking into consideration of terms proportional to (nablarho)(6) makes it possible to describe with adequate accuracy all the properties of a flat interface in the temperature range from the triple to the critical point.

Interfacial tensions of industrial fluids from a molecular‐based square gradient theory

“…Theoretically, the influence parameter can be computed from its molecular definition (i.e., integration of the direct correlation function of the homogeneous fluid), but the available theories for the two-body direct correlation function between two species in homogeneous fluids are not completely developed, as the results still exhibit poor performance when compared to experimental or molecular dynamics results. [72][73][74][75] 48,53,71,and78 ). Mixtures add another dimension of complexity, whereas the corresponding binary (cross) influence parameter must then be determined, usually in an empirical fashion through simple geometric mixing rules or by fitting to binary experimental data.…”

Inclusion of Corrections of the Highest Order of Smallness in the Van der Waals Capillarity Theory

“…In the case of a plane interface, the excess, surface part of the functional of grand thermodynamic potential Ω s has the form [2,6,8] , (1) , (2) where A is the area of the interface, p is the pressure, µ is the chemical potential, ρ is the number density, and T is the temperature; the subscript s indicates the quantities relating to the equilibrium coexistence of phases. The function ψ takes into account the effect of nonuniform distribution of particles in the system and, in the general case, depends on various derivatives of one-particle density ρ(z) (square of gradient , Laplacian ∆ρ, and so on).…”

“…The influence coefficient κ 1 may be obtained within statistical treatment [4,8], , (4) where c(r) and h(r) denote the direct and complete correlation functions, respectively, or this coefficient κ 1 may be calculated by the experimental data on surface tension on a plane interface [6][7][8].…”

“…The validity of the Van der Waals capillarity theory in the region of lower temperatures when the density gradients are high is disputable. The results of molecular-dynamic calculations [8] of the properties of a plane interphase layer in LennardJones systems demonstrated the need for inclusion into the free energy functional of terms of a higher order of smallness than the square of density gradient. The inclusion of these terms makes it possible to describe the entirety of the properties of a plane liquid-vapor interface in the temperature range from the triple to critical point.…”

Gradient theory computation of the radius-dependent surface tension and nucleation rate for n-nonane clusters

“…4 Theoretical foundations of the gradient theory and the related statistical physics background are given in the books by Rowlinson and Widom, 5 Davis,6 and Kalikmanov. 7 A recent study of the gradient theory with comparison to molecular simulations was given by Baidakov et al 8 The gradient theory is closely related to the density functional theory, first applied to gas-liquid nucleation by Oxtoby and Evans. 9 Both theories are based on the mean-field approximation.…”