Melting Point of a Confined Fluid within Nanopores: The Composition Effect on the Gibbs-Thomson Equation

The Gibbs-Thomson (GT) equation finds that the shift in the freezing/melting temperature under confinement with respect to its bulk counterpart is inversely proportional to the pore size. This century old relation successfully elaborates the freezing experiments of many fluids (e.g., water, molten salt), while it fails in quantitatively predicting the phase stability of the nonstoichoimetric crystals (e.g., gas hydrates). Based only on the crystal/liquid coexistence, we here revisit the GT equation to treat the multicomponent compounds within a slit confined geometry. In addition to the interfacial energy contribution, the extended GT equation accounts for the excess free energies associated with the composition variations upon the freezing/melting transition. Using the direct coexisting method (DCM), we first probe the melting temperatures of a face-centered cubic (fcc) crystal confined in slit pores as well as its bulk counterpart. The melting temperature under confinement is shown to be depressed compared to the bulk. We then turn to estimate the parameters entering the GT equation using several independent molecular simulations. The melting temperature depression observed in the DCM simulations is found to be well described by the GT equation if used with accurate estimates of the pore/crystal and pore/liquid interfacial tensions. Finally, using the above molecular modeling strategies, we show that the GT equation with the composition correction successfully predicts the shifted melting temperature of methane hydrate confined in porous solids. For such nonstoichoimetric compounds under confinement, accounting for the composition effects is of utmost importance as it exhibits a non-negligible contribution to the GT description. The extended GT equation can be expected to investigate the capillary freezing of the nonstoichoimetric compound in nanopores and to provide a better understanding of the pore body.