Crossover from capillary wave to van der Waals regime for fluid interfaces in two dimensions very close to the critical point

摘要

An analytic expression is derived for the interfacial profile of a liquidndash;vapor or a liquidndash;liquid phase equilibrium by assuming, in accord with current ideas, that the equilibrium interface consists of an intrinsic interface of the nonclassical van der Waals type broadened by capillary wave fluctuations. It is shown that in two dimensions of space, the interfacial thickness exhibits a crossover with change of critical exponent from capillary wave behavior at low and nearhyphen;critical temperatures, to van der Waals behavior at temperatures very close to the critical temperature. The location of the crossover temperature is determined by the ratio of the critical amplitudes of the roothyphen;mean squared interfacial thickness and the bulk correlation length. From available experimental data and theory, an estimate of the order of magnitude of the critical amplitude ratio is made, from which the crossover is found to occur in the temperature range 3times;10minus;4K(Tcminus;T)0.3 K. In the currently accessible temperature range, the capillary wave prediction prevails, in contrast to the case of threehyphen;dimensional systems.