High pressure ‘cell’ model of compressed methane

Abstract

The Thomas-Fermi method is used to treat self-consistently a model of compressed methane. Two assumptions underlying the treatment are (i) the use of spherical averaging of the proton potential about the C atom in the methane molecule and (ii) the compressed spherical ‘cell’ model. Within this framework, the equilibrium bond length of CH₄ is calculated as a function of cell volume. The free space bond length given by this model is too large, and so results are presented for R_e/R_e(∞) versus cell volume. The volume is finally converted to an estimated pressure using an empirical equation of state. The relevance of the work to ices in planetary material is pointed out.

Key Words:

• Giant planets
• ices
• statistical theory.