Statistical substantiation of the van der Waals theory of inhomogeneous fluids

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.