Equilibrium Phase Transitions in a Porous Medium

Static critical phenomena of a three-dimensional Ising model confined in a porous medium made by spinodal decomposition have been studied using large-scale Monte Carlo simulations. We thus examine the influence of the geometry of Vycor-like materials on phase transitions. No surface interactions (preference of the Vycor-like material for one phase above the other) are taken into account. We find that the critical temperature depends on the average pore size D as Tc(D)=Tc(∞)-c/D. The critical exponents are independent of pore size: we find ν=0.8±0.1, γ=1.4±0.1, β=0.65±0.13. No divergence is observed for the specific heat, indicating α≤0. All data for all pore sizes can be collapsed well with the scaling function for the magnetic susceptibility χL−γ/ν=χ̃(tL1/ν), where t=T/Tc(D)-1. These critical phenomena are consistent with those computed for the randomly site-diluted Ising model. Experimental realizations of our numerical experiments are discussed.