Melting transition of Lennard-Jones fluid in cylindrical pores

Three-stage pseudo-supercritical transformation path and multiple-histogram reweighting technique are employed for the determination of solid-liquid coexistence of the Lennard-Jones (12-6) fluid, in a structureless cylindrical pore of radius, R, ranging from 4 to 20 molecular diameters. The Gibbs free energy difference is evaluated using thermodynamic integration method by connecting solid and liquid phases under confinement via one or more intermediate states without any first order phase transition among them. The thermodynamic melting temperature, Tm, is found to oscillate for pore size, R < 8, which is in agreement with the behavior observed for the melting temperature in slit pores. However, Tm for almost all pore sizes is less than the bulk case, which is contrary to the behavior seen for the slit pore. The oscillation in Tm decays at around pore radius R = 8, and beyond that shift in the melting temperature with respect to the bulk case is in line with the prediction of the Gibbs-Thomson equation