Free Energy Studies of Freezing in Slit Pores: An Order-Parameter Approach using Monte-Carlo Simulation

We report a molecular simulation study of freezing transitions for simple fluids in narrow slit-pores. A major stumbling block in previous studies of freezing in pores has been the lack of any method for calculating the free energy difference between the confined solid and liquid phases. Conventional thermodynamic integration methods often fail for confined systems, due to the difficulty in choosing a suitable path of integration. We use a different approach that involves calculating the Landau free energy as a function of a suitable order parameter, using the grand canonical Monte Carlo simulation method. The grand free energy for each phase can then be obtained by one-dimensional integration of the Landau free energy over the order parameter. These calculations are carried out for two types of wallfluid interaction, a hard wall and a strongly attractive wall modeled on carbon. The grand free energy results for both cases clearly indicate a first order fluid to solid transition. In the case of the attractive carbon wall, there are three phases. Phase A corresponds to all layers having a liquid-like structure; phase B corresponds to the contact layers (the layers adjacent to the two pore walls) being frozen and the rest of the layers being fluid-like; phase C corresponds to all the layers being frozen. Our results for the angular structure function in the individual molecular layers show strong evidence of a transition from a two-dimensional liquid phase to a hexatic phase. This is followed by a transition from the hexatic to a crystal phase.