Fluid interface in two dimensions close to the critical point
Journal
Physica A: Statistical Mechanics and its Applications
Journal Volume
172
Journal Issue
1-2
Pages
53-76
Date Issued
1991
Author(s)
Abstract
Theoretical and computer simulation results for the equilibrium structure of the interface between two-dimensional fluid phases near the critical point are described. In the theoretical analysis, the equilibrium interface is assumed, in accord with current ideas, to consist of an intrinsic interface of the nonclassical van der Waals type, broadened by long-wavelength capillary wave fluctuations. It is found that in two dimensions of space, the interfacial thickness is very sensitive to the choices of the external field and of the intrinsic interface. For an intrinsic interface with a thickness proportional to the bulk correlation length ξ, the critical exponent ω describing the divergence of the interfacial thickness as the critical point is approached depends on the scale of the external field relative to ξ, and ranges from ω = 9/ 32 to ω = 17/ 32, in contrast to the prediction ω = 1 of nonclassical van der Waals theory. For a linear external field (gravity), the interfacial thickness is found to exhibit a crossover with change of critical exponent from capillary wave behavior at low and near critical temperatures to van der Waals behavior at temperatures very close to the critical temperature. An estimate of the order of magnitude of the crossover temperature is made by combining available experimental data and theory. In the currently accessible temperature range, the capillary wave prediction prevails, in contrast to the case of three-dimensional fluids. Computer simulations are performed for continuous fluids using the method of molecular dynamics. The interfacial thickness between two-dimensional fluid phases, in which the particles interact with a Lennard-Jones potential, is determined as a function of temperature in the absence of an external field. The number of particles ranges from 242 to 1024. Due to the smallness of the interfacial areas studied, long-wavelength capillary waves are strongly suppressed, and the results for the interfacial thickness are found to be consistent with the prediction of the nonclassical van der Waals theory of the intrinsic interface. © 1991.
Type
journal article