Homogenous nucleation rate of CO₂ hydrates using transition interface sampling

Carbon dioxide and water can form solid clathrate structures in which water cages encapsulate the gas molecules. Such hydrates have sparked much interest due to their possible application in CO₂ sequestration. How the solid structure forms exactly from the liquid phase via a homogenous nucleation process is still poorly understood. This nucleation event is rare on the molecular timescale even under moderate undercooling or supersaturation conditions because of the large free energy barrier toward crystallization, rendering a brute force simulation of hydrate nucleation unfeasible for moderate undercooling or supersaturation. Here, we perform transition interface sampling simulations to quantify the homogenous nucleation rate for CO₂ hydrate formation using accurate atomistic force fields at 500 bars for three different temperatures between 260 and 273 K. Collecting more than 100 000 pathways comprising roughly two milliseconds of simulation time, we computed a nucleation rate in the amorphous phase of ∼10²¹ nuclei s⁻¹ cm⁻³ for a temperature of 260 K and a rate of ∼10¹² nuclei s⁻¹ cm⁻³ for a temperature of 265 K. For a temperature of 273 K, we find that the hydrate forms an sI crystalline phase with a rate of order of ∼10¹ nuclei s⁻¹ cm⁻³. We compare these rates to classical nucleation theory estimates as well as experiments, and to nucleation rate estimates for methane hydrates and discuss possible causes of the observed differences. Our findings shed light on the kinetics of this important clathrate and should assist in future hydrate formation investigation.