Three-phase equilibria of hydrates from computer simulation. II. Finite-size effects in the carbon dioxide hydrate

In this work, the effects of finite size on the determination of the three-phase coexistence temperature ($T_3$) of carbon dioxide (CO$_2$) hydrate have been studied by molecular dynamic simulations and using the direct coexistence technique. According to this technique, the three phases involved are placed together in the same simulation box. By varying the number of molecules of each phase it is possible to analyze the effect of simulation size and stoichiometry on the $T_3$ determination. In this work, we have determined the $T_3$ value at 8 different pressures and using 6 different simulation boxes with different numbers of molecules and sizes. In 2 of these configurations, the ratio of the number of water and CO$_2$ molecules in the aqueous solution and the liquid CO$_2$ phase is the same as in the hydrate (stoichiometric configuration). In both stoichiometric configurations, the formation of a liquid drop of CO$_2$ in the aqueous phase is observed. This drop, which has a cylindrical geometry, increases the amount of CO$_2$ available in the aqueous solution and can in some cases lead to the crystallization of the hydrate at temperatures above $T_3$, overestimating the $T_3$ value obtained from direct coexistence simulations. The simulation results obtained for the CO$_{2}$ hydrate confirm the sensitivity of $T_{3}$ depending on the size and composition of the system, explaining the discrepancies observed in the original work by M\'iguez \emph{et al.} Non-stoichiometric configurations with larger unit cells show convergence of $T_{3}$ values, suggesting that finite-size effects for these system sizes, regardless of drop formation, can be safely neglected. The results obtained in this work highlight that the choice of a correct initial configuration is essential to accurately estimate the three-phase coexistence temperature of hydrates by direct coexistence simulations.