The different roles the attractive and repulsive forces play in forming the equilibrium structure of a Lennard-Jones liquid are discussed. It is found that the effects of these forces are most easily separated by considering the structure factor (or equivalently, the Fourier transform of the pair-correlation function) rather than the pair-correlation function itself. At intermediate and large wave vectors, the repulsive forces dominate the quantitative behavior of the liquid structure factor. The attractions are manifested primarily in the small wave vector part of the structure factor; but this effect decreases as the density increases and is almost negligible at reduced densities higher than 0.65. These conclusions are established by considering the structure factor of a hypothetical reference system in which the intermolecular forces are entirely repulsive and identical to the repulsive forces in a Lennard-Jones fluid. This reference system structure factor is calculated with the aid of a simple but accurate approximation described herein. The conclusions lead to a very simple prescription for calculating the radial distribution function of dense liquids which is more accurate than that obtained by any previously reported theory. The thermodynamic ramifications of the conclusions are presented in the form of calculations of the free energy, the internal energy (from the energy equation), and the pressure (from the virial equation). The implications of our conclusions to perturbation theories for liquids and to the interpretation of x-ray scattering experiments are discussed.

We develop a unified and generally applicable theory of solvation of small and large apolar species in water. In the former, hydrogen bonding of water is hindered yet persists near the solutes. In the latter, hydrogen bonding is depleted, leading to drying of extended apolar surfaces, large forces of attraction, and hysteresis on mesoscopic length scales. The crossover occurs on nanometer length scales, when the local concentration of apolar units is sufficiently high, or when an apolar surface is sufficiently large. Our theory for the crossover has implications concerning the stability of protein assemblies and protein folding.

Hydrophobicity manifests itself differently on large and small length scales. This review focuses on large length scale hydrophobicity, particularly on dewetting at single hydrophobic surfaces and drying in regions bounded on two or more sides by hydrophobic surfaces. We review applicable theories, simulations and experiments pertaining to large scale hydrophobicity in physical and biomoleclar systems and clarify some of the critical issues pertaining to this subject. Given space constraints, we could not review all of the significant and interesting work in this very active field.

The van der Waals picture focuses on the differing roles of the strong short-ranged repulsive intermolecular forces and the longer ranged attractions in determining the structure and dynamics of dense fluids and solids. According to this physical picture, the attractive interactions help fix the volume of the system, but the arrangements and motions of molecules within that volume are determined primarily by the local packing and steric effects produced by the repulsive forces. This very useful approach, its limitations, and its successful application to a wide variety of static and dynamic phenomena in condensed matter systems are reviewed.

Room temperature friction experiments on quartzo‐feldspathic rocks obey a velocity dependence of strength which consists of two opposite‐sensed effects. The second of these effects has a negative velocity dependence and evolves over a characteristic displacement. This evolution effect was originally attributed by Dieterich [1978; 1979] to an underlying time‐dependent process but is often described by either of two empirical evolution laws. One depends explicitly on displacement (slip law) and the other retains time dependence (slowness law). The slip law is favored in representing behavior around steady‐state as seen in velocity stepping experiments. However, in this study slide‐hold‐slide tests conducted at different machine stiffnesses show that the evolution effect depends on time, not slip. For the slowness law the coefficient of time‐dependent strengthening b is measured directly in slide‐hold‐slide tests. Existing empirical evolution laws may not be sufficient to describe both near steady‐state and non steady‐state behavior. Provided a more correct form can be found, time‐dependent evolution may improve frictional models of the seismic cycle by reducing the amount of inter‐seismic slip.

The coefficient of friction and velocity dependence of friction of initially bare surfaces and 1-mm-thick simulated fault gouges (< 90 gm) of Westerly granite were determined as a function of displacement to >400 mm at 25øC and 25 MPa normal stress. Steady state negative friction velocity dependence and a steady state fault zone microstructure are achieved after --18 mm displacement, and an approximately constant strength is reached after a few tens of millimeters of sliding on initially bare surfaces. Simulated fault gouges show a large but systematic variation of friction, velocity dependence of friction, dilatancy, and degree of localization with displacement. At short displacement (<10 mm), simulated gouge is strong, velocity strengthening and changes in sliding velocity are accompanied by relatively large changes in dilatancy rate. With continued displacement, simulated gouges become progressively weaker and less velocity strengthening, the velocity dependence of dilatancy rate decreases, and deformation becomes localized into a narrow basal shear which at its most localized is observed to be velocity weakening. With subsequent displacement, the fault restrengthens, returns to velocity strengthening, or to velocity neutral, the velocity dependence of dilatancy rate becomes larger, and deformation becomes distributed. Correlation of friction, velocity dependence of friction and of dilatancy rate, and degree of localization at all displacements in simulated gouge suggest that all quantities are interrelated. The observations do not distinguish the independent variables but suggest that the degree of localization is controlled by the fault strength, not by the friction velocity dependence. The friction velocity dependence and velocity dependence of dilatancy rate can be used as qualitative measures of the degree of localization in simulated gouge, in agreement with previous studies. Theory equating the friction velocity dependence of simulated gouge to the sum of the friction velocity dependence of bare surfaces and the velocity dependence of dilatancy rate of simulated gouge fails to quantitatively account for the experimental observations. EXPERIMENTAL FAULTS of slip when the sample strength is lowest and the friction velocity dependence is the most negative, changes in dilation rate are systematically smaller (Figure 5c, inset c2), similar to the initially bare surface response (Figure 4c). These observations can be quantified by determining the net thickness changes described by tz = AL / AlnV [Marone and Kilgore, 1993] and the changes in dilation rate A(dL / d5)ss / AlnV Example 1 0.004 -> 0.002ß 'o 0.000 -0.002 -ß ß ß ß ß ß b -0.0030 --0.0025-0 _ i i I ß ß ß ß ". ß ß ß ß -0.002-I•1• ß bl ß ß I 100 200 300 400

This paper is concerned with the effects that density fluctuations in different regions of a liquid–vapor interface have on the interfacial thermodynamic and structural properties. The total volume V is divided into a square array of columns whose width is the order of the bulk correlation length. The canonical partition function is written as a sum of constrained partition functions, each describing a system with a given number of particles in each column. Changes in the occupation number of each column (i.e., density fluctuations) are related to changes in position of the local Gibbs dividing surface, and the free energy of such distortions of the Gibbs surface is estimated using macroscopic ideas similar to those used in the capillary wave theory by Buff, Lovett, and Stillinger. Corrections to the interface tension as calculated for a single column with periodic boundary conditions are given. We make a self-consistent choice of the column width which yields a scaling law originally porposed by Widom. Fluctuations in position of the local Gibbs surfaces of widely separated columns cause the total interface width to depend on the system size and strength of an external field while the local width in a single column is proportional to the bulk correlation length. These fluctuations also cause the very long-ranged correlations parallel to the interface predicted by Wertheim. Both the singlet and the pair distributions functions are calculated. An extension of Wertheim’s analysis is given.

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