In this paper, we present a computer molecular dynamic simulation study of the crystal-melt interface for three different systems: TIP4P/Ice model of water and sI hydrate with TIP4P/Ice model, also SDS on hydrate with water, and OPLS_AA model. We focus on both the thermodynamics properties and the dynamics of surface waves for both Ih and sI hydrate crystal.
First, we generate an initial configuration in which a crystal slab is surrounded by its melt. The box geometry allows for the study of long wavelength capillary waves without having a prohibitively large number of molecules in the system (see Figure. 4 for an example). Then, we perform molecular dynamics simulations in the NV T ensemble at the melting temperature. The overall density of the system is comprised in between the coexistence densities of the fluid and the crystal phases, which guarantees that the system stays at coexistence throughout the NVT simulation. The area of the box side parallel to the interface (s and v directions) is chosen in such way that the solid phase is free of any stress.
Once we run the molecular dynamics simulations, we analyze the thermodynamics property (equation (37)) and dynamic autocorrelation function of the surface wave modes (equation (40)). To calculate both thermodynamics property and dynamics profile, we first obtain a function that describes the position of the interface, which we do by identifying the outermost crystalline particles of the solid slab. We show a feasibility of using F4 order parameter to identify the interface location of CMI system. In ref.[31], it mentioned that simulations were not affected by the choice of the parameters needed to locate the interface or by the geometry of the box or the system size.
The average interfacial free energies of Ih and sI hydrate for different orientation are 29.24mN/m2 and 34.60 mN/m2, respectively. The results are in good agreement with other simulation methods and experimental works. Furthermore, we show that the effect of different orientations for sI hydrate to interfacial free energy is only 3%. To the best of our knowledge, this result has never been reported before our work in both the experiment and simulation field.
We also examine in detail the shape of the dynamic autocorrelation function as a function of the wave-vector q, and using a double exponential function describes the relaxation dynamics of crystal-melt surface waves and performs well for our system. This implies that there are two distinct time scales, fast and slow, involved in the relaxation of crystal-melt surface waves. The slow time scale is due to the recrystallization-crystal-melting occurring at the interface, and is governed by capillary forces. The fast relaxation is due to a combination of processes that readily alter the shape of the interface. We speculate these may be related to Rayleigh waves, sub-diffusion of the fluid and the attachment/detachment of particles to/from the crystal phase.
As the length scale of the capillary wave modes increases (or q decreases), the relaxation becomes increasingly dominated by the slow process and can be just described by a single exponential. Within the uncertainty of our data, we see that the characteristic time for the slow relaxation process is related to q by the power law: τ ∝ q-2 for all systems.
We compare the relaxation dynamics of different systems in diffusive time units. We see that the crystal-melt interface of water relaxes about thirty times faster than that of sI hydrate crystal. We ascribe this difference to the presence of complicate hydrogen bond network and cage-like configuration of hydrate.
Furthermore, the kinetic coefficient of Ih/water obtained by CFT is same as both other simulation work and experiment work at the region degree of subcooling
approaching to zero. In sI methane-hydrate/water system, the kinetic coefficient by CFT in this work is larger than other simulation and experiment work, about 30 times. The reason presumes that it is caused by the enormous methane concentration at the interface region whose concentration is same as methane-hydrate phase, however, we still cannot explain the fact that why the methane concentration is high within two layer thickness above the interface.
Last, we have already tried to calculate the interfacial free energy of hydrate/water with SDS adsorbing on the hydrate surface, however, that the SDS molecule will detach from the interface during the simulation cause failure to measure the interfacial free energy. The detaching phenomena should no happened according to other simulation work which calculate the adsorption free energy profile of SDS on hydrate interface. We still do not know the reason why that happened in the CMI system. However, there is a single run successfully shows that SDS could reduce the stiffness (interfacial free energy) of hydrate crystal, then according to CNT, the nucleation rate is faster almost 100 times than that without SDS.
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