Motivations

Clathrate hydrates are a kind of nonstoichiometric crystalline compounds consisting of cavities (or cages) formed by hydrogen-bonded water molecules where guest molecules are trapped.[51] The empty lattice (cavities) is thermodynamically unstable, and its existence is stabilized by hydrogen bond resulting from the enclathration of the trapped solutes in its cages. [51] Methane is one kind of guest molecules that stabilizes the water cages in the clathrate hydrate structure. There are three known common hydrate structures: sI, sII and sH. [51] In type I hydrate, methane clathrate hydrates have attracted much attention because the large amount found in nature can be a potential source of energy.[52] However, it is still unknown for the mechanism of hydrate formation (nucleation). There are many efforts made to better understand the nucleation mechanism of gas hydrates. Sloan et al.,[53-56] in order to describe the kinetic data of gas hydrate formation,[57] proposed a hypothetical model based on the labile cluster hypothesis (LCH), where the mixture of guest molecules and labile cages formed by water and then may combine to form a nucleus. Radhakrishnan et al.[58] argued that the high energy barriers of forming larger aggregates from labile clusters should not exist in a nucleation process. They proposed a local structuring hypothesis (LSH), where a group of the guest molecules are arranged in a configuration similar to that in the clathrate phase as a result of thermal fluctuation. When sufficient gas molecules are solved, the arrangement of the gas cluster also helps the surrounding water molecules re-orientate to form a nuclei. The LSH was later supported by the results of molecular dynamics (MD) simulations from Rodger and co-workers.[59] In 2009, Walsh et al.[60] reported the first unconstrained MD simulations of methane hydrate nucleation on the microsecond time scale. They

(5¹²), also proposed the mutually coordinated guests theory (MCG).[61] When the cluster of MCGs size is larger than the critical size, the nuclei will be favorite to grow to clathrate crystalline structure; otherwise, the nuclei will be fluctuate and then disappeared.[62]

Jacobson et al. studied the nucleation process using MD simulations.[63] They observed the constant formation and dissociation of guest-rich amorphous precursors (the morphology of a blob or cylinder) as a result of thermal fluctuation. As the size of the blob (or cylinder) becomes larger than some critical size, the blob can continue to grow and solved in water then transform into crystalline clathrate. Such two-step nucleation, or the blob hypothesis (BH), was also supported by atomistic MD simulations of Vatamanu and Kusalik.[64]

Although there were a lot of paper discussing the phenomenon of nucleation;

however, the paper studied the interfacial free energy, a crucial parameter in nucleation and growth[45, 65, 66], between hydrate crystalline and water can be counted on fingers[67-69] L.C Jacobson et al. calculated the tension by Gibbs-Thomson equation and showed that the tension of amorphous crystal and crystalline are 32 and 36 mJ/m², respectively.[68] This result is consistent with the experimental results worked by R.

Anderson also using Gibbs-Thomson equation.[67] B.C Knott et al. calculated the interfacial tension by classical nucleation theory, and found that the nucleation rate of homogeneous process is pretty low (310^-111 nuclei cm^-3s^-1). In other words, the homogeneous process is almost impossible reaction path of hydrate nucleation [69]. The curvature of the nuclei in this method theoretically changes during the simulation, but it is treated as constant owing to complication for discussing. Therefore, the value of interfacial energy in this method might not be accurate.

Even if there are handful paper calculating the interfacial free energy between hydrate and water, limited by analysis method, the precision of the interfacial free energy

in other methods comparing to capillary fluctuation theory method is not kind of accuracy and also the further information about hydrate crystalline are not mentioned, for instance, the effect of orientation to hydrate, and kinetic properties. Also, the surfactant, SDS, is verified that can effectively promote the nucleation rate of hydrate forming rate, [48-50] however, the reason that SDS can promote the nucleation rate of CH4 hydrate is still unknown. Though there are some papers claimed that it is caused by the forming SDS micelle,[70-72] but this hypothesis is soon rebelled from several experiments which indicate that SDS would not form the micelle under hydrate forming condition.[73-75]

So far, there is still no any reasonable hypothesis can explain this phenomena. Motivated by these reasons, we use capillary fluctuation method to analyze the CMI between hydrate crystalline and water and also what will be different when SDS adsorb on hydrate interface. In this method, not only the interfacial free energy but also other surface dynamics properties of hydrate crystal can be measured. To get a deeper understanding of the dynamics of the CMI, we analyzed three different systems: ice/water, hydrate/water and SDS/hydrate/water. We show that that relaxation of crystal-melt SW is well described by a double exponential for both two cases. We also show that details of the microscopic dynamics are not important for the relaxation of crystal-melt. Then, we compare the relaxation dynamics of SW for hydrate/water and ice/water with several orientation of CMI. Finally, following the Karma’s theory [33] and several method proposed in [31, 35], we estimate the kinetic coefficient (the constant ratio of crystal growth-rate to degree of supercooling) from our measurements of the CW relaxation dynamics.