471365 Exploring the Free Energy Landscape of Gas Hydrate Nucleation By Forward Flux Sampling
Here we present an advanced computational strategy based on forward flux sampling (FFS)1 to overcome the limit of the direct molecular simulation. Through this strategy, we pursue a quantitative, “first principle” description on the key factors contributing to the crystallization of hydrate. To facilitate the application of FFS in studying methane hydrate formation, we developed an effective order parameter based on the topological analysis of the tetrahedral network2. The order parameter capitalizes the signature of hydrate structure, i.e., polyhedral cages, and is capable of efficiently distinguishing hydrate from ice and liquid water while allowing the formation of different hydrate phases, i.e., sI, sII, and amorphous. The quality of the developed order parameter was subsequently verified by the rigorous pB histogram analysis, i.e., committor probability analysis, which indeed showed that the order parameter describes well the reaction coordinates of hydrate nucleation.
Employing the developed method, we explicitly explore hydrate nucleation on its nucleation rate, free energy landscape, and structural evolution, for different guest species, and under conditions where spontaneous hydrate nucleation becomes too slow to occur in direct simulation.
First, analyzing the obtained large ensemble of hydrate nucleation trajectories, we show hydrate formation, on average, is facilitated by a gradual transition from amorphous to crystalline structure, which provides the direct support to the two-step nucleation mechanism of gas hydrate. Importantly, the analysis also reveals the diversity of hydrate nucleation behaviors. In particular, there also exist nucleation pathways where hydrate crystallizes directly into crystalline phase, without necessarily going through the amorphous stage. The diversity of hydrate nucleation pathways highlights the complexity of hydrate nucleation, and calls for further study for hydrate nucleation mechanism under various conditions.
Second, we obtained the free energy landscape along the nucleation pathway through combining the FFS and backward fluxing sampling (BFS)3. Since the stationary distribution as a function of the order parameter is calculated independent of nucleation theory, the obtained free energy profile can be used to test the applicability of the classical nucleation theory (CNT). Interestingly, the calculated free energy profile for homogeneous ice nucleation was found to fit perfectly against CNT, a result supporting our previous studies4,5 demonstrating the classical nature of ice nucleation. In comparison, the calculated free energy profile for hydrate nucleation shows noticeable deviation from the CNT, particularly at small cluster sizes. The difference may not be surprising, and can be attributed to the non-classical nucleation pathways of hydrate and the irregular shape of hydrate nucleus. Nevertheless, the differences aside, the CNT was found to describe the free energy landscape of hydrate nucleation reasonably well, despite its non-classical nature.
The work is supported by NSF through award CBET-1264438.
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