Non-monotonous Lattice Distortion Model for Gas Hydrates.

Gas hydrate forms when the hydrogen bonded crystal structure of water entraps small-sized gas molecules at relatively low temperature and high pressure. Experimental and spectroscopic studies prove that the inclusion of guest into an empty cavity leads to distortion of hydrate lattice via either contracting or expanding the cavity that 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 size of the guest. Addressing this research gap, we propose the lattice distortion 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 a spin-component scaled modification in second order Møller-Plesset (SCS-MP2) perturbation theory applied with the Dunning's basis set. The half-counterpoise method with the Pauling point correction factor is used to deal with the basis set superposition (BSSE) and completeness (BSCE) errors. As an estimate of degree of lattice distortion, the reference chemical potential difference (RCPD) is calculated by applying linear regression analysis to the experimental data of hydrate phase equilibrium. We identify a non-monotonous 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 the larger guest expands the cavity during encapsulation. This apart, for the first time, we report RCPD (771.5475 J·mol-1) for undistorted sII-type hydrate lattice as the minimum of the lattice distortion curve. The proposed model is validated with the phase equilibrium data of nitrogen, oxygen, cyclopropane, propane and isobutane hydrates having wide range of guest size.