Free energy studies of freezing in slit pores: an order-parameter approachusing Monte Carlo simulation

We report a molecular simulation study of freezing transitions for simple f luids 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. Conventiona l thermodynamic integration methods often fail for confined systems, due to the difficulty in choosing a suitable path of integration. We use a differ ent approach that involves calculating the Landau free energy as a function of a suitable order parameter, using the grand canonical Monte Carlo simul ation method. The grand free energy for each phase can then be obtained by one-dimensional integration of the Landau free energy over the order parame ter. These calculations are carried out for two types of wall-fluid interac tion, a hard wall and a strongly attractive wall modelled on carbon. The gr and 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 struct ure; 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; p hase C corresponds to all the layers being frozen. Our results for the angu lar structure function in the individual molecular layers show strong evide nce 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.