Homogeneous nucleation rate of carbon dioxide hydrate formation under experimental condition from Seeding simulations

We investigate the nucleation of carbon dioxide (CO$_2$) hydrates from carbon dioxide aqueous solutions by means of molecular dynamics simulations using the TIP4P/Ice and the TraPPE models for water and CO$_2$ respectively. We work at 400 bar and different temperatures and CO$_2$ concentrations. We use brute force molecular dynamics when the supersaturation or the supercooling are so high so that nucleation occurs spontaneously and Seeding otherwise. We used both methods for a particular state and we get a rate of 10$^{25}\,\text{m}^{-3}\text{s}^{-1}$ for nucleation in a CO$_2$ saturated solution at 255 K (35 K of supercooling). By comparison with our previous work on methane hydrates, we conclude that nucleation of CO$_2$ hydrates is several orders of magnitude faster due to a lower interfacial free energy between the crystal and the solution. By combining our nucleation studies with a recent calculation of the hydrate-solution interfacial free energy at coexistence, we obtain a prediction of the nucleation rate temperature dependence for CO$_{2}$-saturated solutions (the experimentally relevant concentration). On the one hand, we open the window for comparison with experiments for supercooling larger than 25 K. On the other hand, we conclude that homogeneous nucleation is impossible for supercooling lower than 20 K. Therefore, nucleation must be heterogeneous in typical experiments where hydrate formation is observed at low supercooling. To assess the hypothesis that nucleation occurs at the solution-CO$_2$ interface we run spontaneous nucleation simulations in two-phase systems and find, by comparison with single-phase simulations, that the interface does not affect hydrate nucleation, at least at the deep supercooling at which this study was carried out (40 and 45 K). Overall, our work sheds light on molecular and thermodynamic aspects of hydrate nucleation.