Nonmonotonous Lattice Distortion Model for Gas Hydrates.

A gas hydrate forms when the hydrogen-bonded crystal structure of water entraps the small-sized gas molecules at a relatively low temperature and high pressure. Experimental and spectroscopic studies prove that the inclusion of a guest into an empty cavity leads to the distortion of the hydrate lattice via either the contraction or expansion of the cavity, which depends on the size and functional group of the guest. However, the existing lattice distortion theories represent only the expansion phenomena, and consequently, the degree of distortion is reported as a monotonous function of the size of the guest. Addressing this research gap, we propose the lattice distortion by using the statistical thermodynamics based model, in association with the modified Patel-Teja equation of state, and an ab initio quantum mechanical methodology for cavity potential calculations. To accurately capture the guest-host interactions, we propose the spin-component-scaled modification in the second order Møller-Plesset (SCS-MP2) perturbation theory applied with Dunning's basis set. The half-counterpoise method with the Pauling point correction factor is used to handle the basis set superposition (BSSE) and completeness (BSCE) errors. As an estimate of the degree of lattice distortion, the reference chemical potential difference (RCPD) is calculated by applying linear regression analysis to the experimental data of the hydrate phase equilibrium. We identify a nonmonotonous lattice distortion model, in which RCPD first decreases, and then increases, with the guest size. This result shows that the small guest contracts the cavity and that the larger guest expands the cavity during encapsulation. Therefore, for the first time, we report the RCPD (794.0913 J mol) for the undistorted sII-type hydrate lattice as the minimum of the lattice distortion curve. The proposed model is validated with the phase equilibrium data of methane, nitrogen, oxygen, cyclopropane, propane, and isobutane hydrates that have a wide range of guest sizes.