Application of the string method to the study of critical nuclei in capillary condensation

We adopt a continuum description for liquid-vapor phase transition in the framework of mean-field theory and use the string method to numerically investigate the critical nuclei for capillary condensation in a slit pore. This numerical approach allows us to determine the critical nuclei corresponding to saddle points of the grand potential function in which the chemical potential is given in the beginning. The string method locates the minimal energy path (MEP), which is the most probable transition pathway connecting two metastable/stable states in configuration space. From the MEP, the saddle point is determined and the corresponding energy barrier also obtained (for grand potential). Moreover, the MEP shows how the new phase (liquid) grows out of the old phase (vapor) along the most probable transition pathway, from the birth of a critical nucleus to its consequent expansion. Our calculations run from partial wetting to complete wetting with a variable strength of attractive wall potential. In the latter case, the string method presents a unified way for computing the critical nuclei, from film formation at solid surface to bulk condensation via liquid bridge. The present application of the string method to the numerical study of capillary condensation shows the great power of this method in evaluating the critical nuclei in various liquid-vapor phase transitions.