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–1) 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.