The crystal structure of tetrahydrofuran deuterate, a clathrate hydrate, has been refined from neutron powder diffraction data at five temperatures in the range 7-265 K. The thermal expansivity was shown to be greater than that of ice Ih in the same range of temperature (T), as observed in previous studies of other clathrates. The overall effect of T has been resolved into contributions from different geometrical parameters in the structure. Thus, an increase in T results in expansion of the host-lattice framework with increases in both the D-D and O-O distances and out-of-plane tilting of water molecules. The greatest dependence on T is exhibited by the D-D distances and the distortion of the hexagonal faces from planarity, which is particularly pronounced in the range 75-140 K. The cage volumes show a complex dependence on T: from 7 to 140 K, the volume of the small cage decreases slightly and that of the large cage increases, and between 140 and 205 K, the trend is reversed. The most pronounced structural changes occur in a similar regime of T as changes in guest dynamics observed in spectroscopic and thermodynamic studies. The temperature dependences of the structure and R(T), when considered along with the relation of R(T) to the degree of anharmonicity in bonding, 34 could be formulated to provide a sensitive test of molecular models of clathrate hydrates.

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The modified Green function appropriate for solution of interior boundary value problems of Laplace's equation in a three-dimensional rectangular parallelepiped, subject to periodic boundary conditions, is developed. This allows the determination of the potential due to an arbitrary continuous charge distribution and its periodic replications in three dimensions. Summation of the eigenfunction expansion by application of the Poisson-Jacobi formula gives a Ewald sum, while application of the Poisson summation formula results in a two-dimensional potential that is perturbed by a rapidly converging Fourier cosine series involving K0 Bessel functions. The latter constitutes a generalization of formulae described by Lekner. Numerical results show that the K0 expansion is more rapidly convergent than the Ewald sum, and could therefore substantially reduce the computational effort involved in the molecular simulation of ionic and polar fluids. The Green function is also shown to be related to the asymptotic behaviour of lattice sums for the screened Coulomb potential, in the limit as the screening constant tends to zero.

In the flow of liquids through porous media, nonlinear effects arise from the dependence of the fluid density, porosity, and permeability on pore pressure, which are commonly approximated by simple exponential functions. The resulting flow equation contains a squared gradient term and an exponential dependence of the hydraulic diffusivity on pressure. In the limiting case where the porosity and permeability moduli are comparable, the diffusivity is constant, and the squared gradient term can be removed by introducing a new variable y, depending exponentially on pressure. The published transformations that have been used for this purpose are shown to be special cases of the Cole-Hopf transformation, differing in the choice of integration constants. Application of Laplace transformation to the linear diffusion equation satisfied by y is considered, with particular reference to the effects of the transformation on the boundary conditions. The minimum fluid compressibilities at which nonlinear effects become significant are determined for steady flow between parallel planes and cylinders at constant pressure. Calculations show that the liquid densities obtained from the simple compressibility equation of state agree to within 1% with those obtained from the highly accurate Wagner-Pruß equation of state at pressures to 20 MPa and temperatures approaching 600 K, suggesting possible applications to some geothermal systems.

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A seafloor process simulator (SPS) has been developed for experimental investigations of the physical, geochemical, and microbiological processes affecting the formation and stability of methane and carbon dioxide hydrates at temperatures and pressures corresponding to ocean depths of 2 km. The SPS is a corrosion-resistant pressure vessel whose salient characteristics are: (i) an operating range suitable for study of methane and carbon dioxide hydrates; (ii) numerous access and observation ports, and (iii) a large (0.0722 m3) internal volume. Initial experiments have shown that the SPS can be used to produce large amounts of high-purity methane hydrate over a wide range of experimental conditions.

The modified Green function appropriate for calculation of coulombic lattice potentials is developed in a spherical harmonic expansion. This is derived from the corresponding Ewald sum in Cartesian coordinates, by applying Gegenbauer's addition theorem for modified spherical Bessel functions to the screened Coulomb potentials resulting from Laplace transformation with respect to the scalar convergence parameter, and Bauer's expansion to the plane waves. It is useful where the charge-density distribution about each nucleus is represented by a spherical harmonic expansion. Radial coefficients of the spherical harmonics are attenuated exponentially, and orthogonality reduces determination of electrostatic lattice potentials to one-dimensional quadratures. This use of the Green function is contrasted with conventional approaches based on point-multipole representations, in which important information on the diffuseness of electronic charge density around the nuclei may be lost in the calculation of multipole coefficients. Possible applications of this result in electronic structure calculations are briefly discussed.