Quantum Statistical Theory of Atoms in Hydroquinone Clathrates

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Abstract
A quantum statistical mechanical theory of clathrates is presented. This theory, like the van der Waals theory, idealizes a clathrate as (1) a lattice having properties unaffected by the extent of occupancy of its cavities by guest atoms, and (2) a system of independent cavities randomly occupied by guest atoms. Within a cavity, the guest atom is assumed to move in the cell potential Φ(x, y, z)= ∑ q=x,y,zVq[ρqtan2(πq/2γq)−1],rather than in the sphericalized Lennard-Jones—Devonshire cell potential used in the van der Waals theory. The corresponding Schrödinger equation is exactly soluble and the energy eigenvalues are easily incorporated into a convenient quantum statistical mechanical formalism, valid at both low and high temperature, for the ``guest'' contribution to thermodynamic functions. With an assumed cubical cell symmetry, shown to be not unreasonable, one of the three parameters can be approximately determined by structural data on the β-hydroquinone lattice. After adjusting the remaining two parameters to fit some data, the thermodynamic predictions are found to be in satisfactory agreement with all other thermodynamic data on rare-gas hydroquinone clathrates. The energy of the transition from ground to first excited state for the motion of guest atoms is in very good agreement with experimental data.

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