Interplay of critical Casimir and dispersion forces

Abstract

Using general scaling arguments combined with mean-field theory we investigate the critical (T approximately Tc) and off-critical (T not equal Tc) behavior of the Casimir forces in fluid films of thickness L governed by dispersion forces and exposed to long-ranged substrate potentials which are taken to be equal on both sides of the film. We study the resulting effective force acting on the confining substrates as a function of T and of the chemical potential mu. We find that the total force is attractive both below and above Tc. If, however, the direct substrate-substrate contribution is subtracted, the force is repulsive everywhere except near the bulk critical point (Tc, mu(c)), where critical density fluctuations arise, or except at low temperatures and (L/a)(beta(Delta)(mu))=O(1), with Delta(mu)=mu-mu(c)<0 and a the characteristic distance between the molecules of the fluid, i.e., in the capillary condensation regime. While near the critical point the maximal amplitude of the attractive force if of order of L(-d) in the capillary condensation regime the force is much stronger with maximal amplitude decaying as L(-1). In the latter regime we observe that the long-ranged tails of the fluid-fluid and the substrate-fluid interactions further increase that amplitude in comparison with systems with short-range interactions only. Although in the critical region the system under consideration asymptotically belongs to the Ising universality class with short-ranged forces, we find deviations from the standard finite-size scaling for xi(ln)(xi/xi0(+/-)) >>L even for xi, L>>xi0(+/-), where xi[t=(T-Tc)/Tc-->+/-0,Delta(mu)=0]=xi0(+/-)/t/-nu, is the bulk correlation length. In this regime the dominant finite-size contributions to the free energy and to the force stem from the long-ranged algebraically decaying tails of the interactions; they are not exponentially small in L, as it is the case there in systems governed by purely short-ranged interactions, but exhibit a power law decay in L. Essential deviations from the standard finite-size scaling behavior are observed also within the finite-size critical region L/xi=O(1) for films with thicknesses L less than or approximately equal Lcrit, where Lcrit=xi0(+/-)(16/s/)nu/beta, with nu and beta as the standard bulk critical exponents and with s=O(1) as the dimensionless parameter that characterizes the relative strength of the long-ranged tail of the substrate fluid over the fluid-fluid interaction. We present the modified finite-size scaling pertinent for such a case and analyze in detail the finite-size behavior in this region. The standard finite-size scaling behavior is recovered only for L>>Lcrit.