Quasi-Two-Dimensional Melting in Porous Media: Effect of Multi-layers and Cross-Over in Scaling Behavior

We report molecular simulation and experimental results for simple fluids adsorbed in activated carbon fibers (ACF), where the adsorbed phase consists of either one or two molecular layers. Our molecular simulations involve smooth pore-walls for large system sizes and a systematic system size-scaling analysis. We provide calculations of the Ginzburg parameter to monitor the self-consistency of our finite size simulation results, based on which we establish that for system sizes smaller than 60 molecular diameters, fluctuations are too large to uphold the finite size simulation results. We present scaling analysis and free energy results for a system size of 180 molecular diameters. Our scaling analysis reveals a two-stage melting in our bilayer system consistent with KTHNY scaling for the order parameter correlation functions. Based on the Lee-Kosterlitz scaling of the free energy surface, we establish that the transitions are first order in the thermodynamic limit. Similar results for a monolayer established that the transitions were continuous. We provide scaling arguments to suggest that the change in the order of the transitions in going from a monolayer to bilayer adsorbed system results from the interactions of defects in the multilayers. We also report experimental measurements