Equation of State of a Model Methane Clathrate Cage

Abstract

We investigate the behavior of a model methane clathrate cage under high hydrostatic pressures. The methane clathrate cage consists of 20 water molecules forming 12 pentagonal faces, with a methane molecule positioned at the cage center. The clathrate compound is located inside a fullerene-type arrangement of 180 He atoms to simulate an isotropic pressure. Different pressures are simulated by decreasing the radius of the He array. The minimal energy of the total system for each configuration is calculated by using density functional theory. The variation of the energy with the volume of the imprisoned clathrate cage leads to the proposal of a (cold) equation of state in the pressure range [0,60] GPa. The elastic parameters of the state equation are found in agreement with equivalent quantities measured on clathrates in their sI conformation. Special attention is given to the distribution of the confined atoms and the eventual symmetry lost from the clathrate cage with the pressure, as the clathrate cage constitutes a basic structural unit of the crystal. Finally, the strengths and limitations of the model are discussed.

Pressure-Induced Metallization of Li+-Doped Hydrogen Clusters

“…These studies were restricted to use less than a dozen atoms in the building of the unit cell because the computational cost of the ab initio methods gives little chance to explore alternative arrangements with different numbers of atoms that could lead to other geometries in the conformation of the unit cell. In this regard, similar investigations have been carried out using hydrogen clusters, the finite-size counterpart of crystals, − and for other systems of energetic interest . In particular, it was shown that hydrogen molecules are capable of self-assemblimg, leading to stable clusters with geometries that depend of both the number of hydrogen molecules and the thermodynamic conditions of pressure and temperature .…”

“…We pay attention to their structural and electronic properties by comparing with the isoelectronic and stable cluster H 26 , constituted by hydrogen solely, with the extra H 2 particle replacing He and Li + . The expressions that determine the pressure and volume from the basic mechanical variables of position, velocity, and force are discussed briefly; nevertheless, they have been discussed a number of times and can be found elsewhere …”

Effect of Guest Size on the Mechanical Properties and Molecular Structure of Gas Hydrates from First-Principles

“…Furthermore, only one other first-principles theoretical study exists on the mechanical and thermal properties of sII gas hydrates. First-principles modeling has been successfully implemented in many previous gas hydrate studies. − These methods provide the benefit of a thoroughly controlled environment, eliminating impurities and structural defects, where an in-depth investigation into the properties and structure of gas hydrates at the atomistic scale is facilitated. The goal of this paper is to fill the aforementioned gaps in hydrate literature by presenting the elastic and acoustic properties of several sII gas hydrates from hydrocarbon formers (i.e., methane, ethane, propane, and isobutane), using first-principles simulations.…”

Microscopic pressure-cooker model for studying molecules in confinement

“…Then, by following standard rules of analytical mechanics, the Lagrangian equations of motion are obtained. The model provides a formal framework for the previous studies of the hydrogen gas under the effects of pressure and temperature [4][5][6][7][8][9][10][11]. Contrary to other proposed models, the present model includes a representation of the medium surrounding the system of the confined particles by a direct inclusion of such properties as the structure and rigidity of the container, the viscosity of the fluid forming the surrounding medium, etc., described in terms of mechanical and statistical mechanics axioms.…”