The relaxation process of viscous flow may be visualized as the sudden shifting of some small patch on one side of a shear surface with respect to the neighboring material on the other side of the shear surface. Any shear surface will divide a mosaic of such patches lying on the two sides of the surface. Except for the simplest systems, this mosaic of patches will be heterogeneous and can be described by groups each characterized by its mean relaxation time βn, by xn the fractional area of the shear surface which the group occupies and by αn, a characteristic shear volume divided by kT. The resulting generalized expression for viscosity is η= ∑ n=1nxnβnαnsinh−1βnṡβnṡ,where ṡ is the rate of shear. This equation is applied to masticated natural rubber, polystyrene, X-672 GR-S, X-518 GR-S rubber, and Vistanex LM-S polyisobutylene. All applications give good agreement with experiment. The known criticisms of Eyring's simple relaxation theory for viscous flow are reviewed, and are apparently taken care of in this general treatment.

A new perturbation theory which is reliable over a wide fluid region is presented. The new theory reduces to the theory of Weeks, Chandler, and Anderson at densities near or below the triple point density of a simple fluid but it can also accurately predict thermodynamic properties at higher densities near the freezing line of the fluid. This is done by employing an optimized reference potential whose repulsive range decreases with increase in density. Thermodynamic properties for Lennard-Jones, exponential-6, and inverse nth-power (n=12, 9, 6, and 4) potentials have been calculated from the new theory. Comparison of the calculated data with available Monte Carlo simulations and additional simulations carried out in this work shows that the theory gives excellent thermodynamic results for these systems. The present theory also gives a physically reasonable hard-sphere diameter over the entire fluid range.

The hard-sphere radial distribution functions, gHS(r/d,η), for the face-centered cubic and hexagonal close-packed phases have been computed by the Monte Carlo method at nine values of the packing fraction, η[=(π/6)ρd3], ranging from 4% below the melting density to 99% of the close-packed density. The Monte Carlo data are used to improve available analytic expressions for gHS(r/d,η). By utilizing the new gHS(r/d,η) in the Henderson and Grundke method [J. Chem. Phys. 63, 601 (1975)], we next derive an expression for yHS(r/d,η) [=gHS(r/d)exp{βVHS(r)}] inside the hard-sphere diameter, d. These expressions are employed in a solid-state perturbation theory [J. Chem. Phys. 84, 4547 (1986)] to compute solid-state and melting properties of the Lennard-Jones and inverse-power potentials. Results are in close agreement with Monte Carlo and lattice-dynamics calculations performed in this and previous work. The new gHS(r/d,η) shows a reasonable thermodynamic consistency as required by the Ornstein–Zernike relation. As an application, we have constructed a high-pressure phase diagram for a truncated Lennard-Jones potential. From this study, we conclude that the new gHS(r/d,η) is an improvement over available expressions and that it is useful for solid-state calculations.

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We have developed a new perturbation theory that extends our earlier perturbation theory of fluids to solids and that is reliable over a wide solid region. Characteristic features of this new theory are the use of an optimized reference potential whose repulsive range shrinks with density and its ability to deal with both harmonic and anharmonic thermodynamic properties on equal footing. Thermodynamic properties of face-centered-cubic crystals are computed from the new theory for the Lennard-Jones system, the exponential-6 system, and the inverse nth-power (n=12, 9, 6, and 4) systems. Monte Carlo simulations are also performed to supplement available data. A comparison of theory and computer simulation shows excellent agreement, except for the softest repulsive system (n=4). The agreement extends from an anharmonic region near the melting line to a harmonic region, where the hard-sphere reference system achieves close to 92% of the close-packed density. Beyond this region errors in the analytic fits to the hard-sphere radial distribution functions used in this work make an accurate test of the new theory difficult. Since the present formulation is the same for both solid and fluid phases, we used the theory to compute the melting and freezing data of the aforementioned model systems. Agreement with the corresponding Monte Carlo data is satisfactory. Comparison with other theoretical models of solids is also discussed.