Critical point shifts in films

Abstract

Critical behavior in thin films is discussed with attention to the example of phase separation in binary fluid mixtures between parallel plates. The analyses focus on the dependence of the shift in critical temperature ΔTc, critical field, etc., on the film thickness D, and on the nature of the walls as modeled by a surface field or chemical potential h1 which acts near the walls and leads to preferential adsorption of one of the bulk phases. Mean field theory for an Ising/lattice-gas model is utilized and the resulting asymptotic scaling functions for the shifts ΔTc etc. are computed within Landau theory by analytic and numerical methods. Series analyses for simple cubic lattice Ising model films with h1=0 are used to estimate universal features of three-dimensional systems: specifically, if ξ(ΔT) is the bulk correlation length, determined, say, via scattering experiments, at ΔT=T−T∞c≳0 then the shift ratio D/ξ(‖ΔTc‖) is about 2.89 for h1=0 but 4.61 for h1→∞, compared with mean field values π and 5.0699. Crossover effects for small nonzero h1 may lead to 10%–15% errors in estimating the exponent for the decay of ΔTc with D. The relation of the theory to recent experiments and the connection with wetting phenomena are discussed briefly.