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We study NaCl ion-pair dissociation in a dilute aqueous solution using computer simulations both for the full system with long-range Coulomb interactions and for a well-chosen reference system with short-range intermolecular interactions. Analyzing results using concepts from Local Molecular Field (LMF) theory and the recently proposed AI-based analysis tool "State predictive information bottleneck" (SPIB), we show that the system with short-range interactions can accurately reproduce the transition rate for the dissociation process, the dynamics for moving between the underlying metastable states, and the transition state ensemble. Contributions from long-range interactions can be largely neglected for these processes because long-range forces from the direct interionic Coulomb interactions are almost completely canceled (90%) by those from solvent interactions over the length scale where the transition takes place. Thus, for this important monovalent ion-pair system, short-range forces alone are able to capture detailed consequences of the collective solvent motion, allowing the use of physically suggestive and computationally efficient short-range models for the dissociation event. We believe that the framework here should be applicable to disentangling mechanisms for more complex processes such as multivalent ion disassociation, where previous work has suggested that long-range contributions may be more important.

We provide a framework for extending equilibrium local molecular field (LMF) theory to a statistical ensemble evolving under a time-dependent applied field. In this context, the self-consistency of the original LMF equation is achieved dynamically, which provides an efficient method for computing the equilibrium LMF potential, in addition to providing the nonequilibrium generalization. As a concrete example, we investigate water confined between hydrophobic or charged walls, systems that are very sensitive to the treatment of long-ranged electrostatics. We then analyze confined water in the presence of a time-dependent applied electric field, generated by a sinusoidal or abrupt variation of the magnitudes of uniform charge densities on each wall. Very accurate results are found from the time-dependent LMF formalism even for strong static fields and for time-dependent systems that are driven far from equilibrium where linear response methods fail.

David Chandler, a major figure in statistical mechanics, spent his career at the University of Illinois Urbana-Champaign, the University of Pennsylvania and the University of California Berkeley. Starting in his graduate work, he made significant advances in many areas of statistical mechanics theory, such as the structure and thermodynamics of simple liquids and nonpolar molecular liquids, the nature of hydrophobic hydration and hydrophobic interactions in aqueous systems, chemical reaction rates, quantum processes in liquids such as electron transfer and the solvation of an excess electron in water, ‘transition path sampling’ (a method for using computer simulations to study chemical reaction rates and other dynamic processes in liquids), and the ‘dynamic facilitation’ theory of the properties of supercooled liquids and the glass transition. He received the Hildebrand Award and the Theoretical Chemistry Award from the American Chemical Society and the Irving Langmuir Chemical Physics Award from the American Physical Society. He was elected to membership in the US National Academy of Sciences and the American Academy of Arts and Sciences.

The response of polar solvents to ions and polar molecules dictates many fundamental molecular processes. To understand such electrostatically-driven solvation processes, one ideally would probe the dielectric response of a solvent to an idealized point test charge or dipole solute, as envisioned in classic continuum treatments of the problem. However, this is difficult in simulations using standard atomically-detailed solvent models with embedded point charges due to possible overlap with the test charge that lead to singular interaction energies. This problem is traditionally avoided for a realistic charged solute by introducing an excluded volume core that shields its embedded point charge or dipole from the charges in the solvent. However, this core introduces additional molecular-scale perturbations of the solvent density that complicate the interpretation of solvent dielectric response. In this work, we avoid these complications through the use of Gaussian-smoothed test charges and dipoles. Gaussian charges and dipoles can be readily inserted anywhere into an atomistic solvent model without encountering infinite energies. If the Gaussian-smoothing is on the scale of molecular correlations in the solvent, both the thermodynamic and dynamic solvation response is linear. Using this observation, we construct accurate predictive theories for solvation free energies and solvation dynamics for insertion of Gaussian charges and dipoles in polar solvents and demonstrate the accuracy of the theories for a widely-used model of water. Our results suggest that Gaussian test charge distributions can be used as an informative probe of dielectric response in molecular models, and our theories can be used to analytically predict the largest component of solvation free energies of charged and polar solutes.

The long-ranged nature of the Coulomb potential requires a proper accounting for the influence of even distant electrostatic boundaries in the determination of the solvation free energy of a charged solute. We introduce an exact rewriting of the free energy change upon charging a solute that explicitly isolates the contribution from these boundaries and quantifies the impact of the different boundaries on the free energy. We demonstrate the importance and advantages of appropriately referencing the electrostatic potential to that of the vacuum through the study of several simple model charge distributions, for which we can isolate an analytic contribution from the boundaries that can be readily evaluated in computer simulations of molecular systems. Finally, we highlight that the constant potential of the bulk dielectric phase - the Bethe potential - cannot contribute to the solvation thermodynamics of a single charged solute when the charge distributions of the solvent and solute do not overlap in relevant configurations. But when the charge distribution of a single solute can overlap with the intramolecular charge distribution of solvent molecules, as is the case in electron holography, for example, the Bethe potential is needed when comparing to experiment. Our work may also provide insight into the validity of "extra thermodynamic assumptions" traditionally made during the experimental determination of single ion solvation free energies., 13 pages, 4 figures

The role that van der Waals (vdW) attractive forces play in the hydration and association of atomic hydrophobic solutes such as argon (Ar) in water is reanalyzed using the local molecular field (LMF) theory of those interactions. In this problem, solute vdW attractive forces can reduce or mask hydrophobic interactions as measured by contact peak heights of the ArAr correlation function compared to reference results for purely repulsive core solutes. Nevertheless, both systems exhibit a characteristic hydrophobic inverse temperature behavior in which hydrophobic association becomes stronger with increasing temperature through a moderate temperature range. The new theoretical approximation obtained here is remarkably simple and faithful to the statistical mechanical LMF assessment of the necessary force balance. Our results extend and significantly revise approximations made in a recent application of the LMF approach to this problem and, unexpectedly, support a theory of nearly 40 years ago.

Understanding the nature of ionic hydration at a fundamental level has eluded scientists despite intense interest for nearly a century. In particular, the microscopic origins of the asymmetry of ion solvation thermodynamics with respect to the sign of the ionic charge remains a mystery. Here, we determine the response of accurate quantum mechanical water models to strong nanoscale solvation forces arising from excluded volumes and ionic electrostatic fields. This is compared to the predictions of two important limiting classes of classical models of water with fixed point changes, differing in their treatment of "lone pair" electrons. Using the quantum water model as our standard of accuracy, we find that a single fixed classical treatment of lone pair electrons cannot accurately describe solvation of both apolar and cationic solutes, emphasizing the need for a more flexible description of local electronic effects in solvation processes. However, we explicitly show that all water models studied respond to weak long-ranged electrostatic perturbations in a manner that follows macroscopic dielectric continuum models, as would be expected. We emphasize the importance of these findings in the context of realistic ion models, using density functional theory and empirical models, and discuss the implications of our results for quantitatively accurate reduced descriptions of solvation in dielectric media.

Coulomb interactions play a major role in determining the thermodynamics, structure, and dynamics of condensed-phase systems, but often present significant challenges. Computer simulations usually use periodic boundary conditions to minimize corrections from finite cell boundaries but the long range of the Coulomb interactions generates significant contributions from distant periodic images of the simulation cell, usually calculated by Ewald sum techniques. This can add significant overhead to computer simulations and hampers the development of intuitive local pictures and simple analytic theory. In this paper, we present a general framework based on local molecular field theory to accurately determine the contributions from long-ranged Coulomb interactions to the potential of mean force between ionic or apolar hydrophobic solutes in dilute aqueous solutions described by standard classical point charge water models. The simplest approximation leads to a short solvent (SS) model, with truncated solvent–solvent and solute–solvent Coulomb interactions and long-ranged but screened Coulomb interactions only between charged solutes. The SS model accurately describes the interplay between strong short-ranged solute core interactions, local hydrogen-bond configurations, and long-ranged dielectric screening of distant charges, competing effects that are difficult to capture in standard implicit solvent models.

Long-standing problems associated with long-ranged electrostatic interactions have plagued theory and simulation alike. Traditional lattice sum (Ewald-like) treatments of Coulomb interactions add significant overhead to computer simulations and can produce artifacts from spurious interactions between simulation cell images. These subtle issues become particularly apparent when estimating thermodynamic quantities, such as free energies of solvation in charged and polar systems, to which long-ranged Coulomb interactions typically make a large contribution. In this paper, we develop a framework for determining very accurate solvation free energies of systems with long-ranged interactions from models that interact with purely short-ranged potentials. Our approach is generally applicable and can be combined with existing computational and theoretical techniques for estimating solvation thermodynamics. We demonstrate the utility of our approach by examining the hydration thermodynamics of hydrophobic and ionic solutes and the solvation of a large, highly charged colloid that exhibits overcharging, a complex nonlinear electrostatic phenomenon whereby counterions from the solvent effectively overscreen and locally invert the integrated charge of the solvated object.

Insertion of a hard sphere cavity in liquid water breaks translational symmetry and generates an electrostatic potential difference between the region near the cavity and the bulk. Here, we clarify the physical interpretation of this potential and its calculation. We also show that the electrostatic potential in the center of small, medium, and large cavities depends very sensitively on the form of the assumed molecular interactions for different classical simple point-charge models and quantum mechanical DFT-based interaction potentials, as reflected in their description of donor and acceptor hydrogen bonds near the cavity. These differences can significantly affect the magnitude of the scalar electrostatic potential. We argue that the result of these studies will have direct consequences toward our understanding of the thermodynamics of ion solvation through the cavity charging process.

We analyze a recently formulated model in which adsorbed impurities impede the motion of steps in crystals grown from solutions, while moving steps can remove or deactivate adjacent impurities. In this model, the chemical potential change of an atom on incorporation/desorption to/from a step is calculated for different step configurations and used in the dynamical simulation of step motion. The crucial difference between solution growth and vapor growth is related to the dependence of the driving force for growth of the main component on the size of the terrace in front of the step. This model has features resembling experiments in solution growth, which yields a dead zone with essentially no growth at low supersaturation and the motion of large coherent step bunches at larger supersaturation. The transient behavior shows a regime wherein steps bunch together and move coherently as the bunch size increases. The behavior at large line tension is reminiscent of the kink-poisoning mechanism of impurities observed in calcite growth. Our model unifies different impurity models and gives a picture of nonequilibrium dynamics that includes both steady states and time dependent behavior and shows similarities with models of disordered systems and the pinning/depinning transition.

Complementary experimental and theoretical studies presented in this work examine the structure, organization, and solvating properties of methanol at a silica/methanol, solid/liquid interface. Fin...

We use appropriately defined short ranged reference models of liquid water to clarify the different roles local hydrogen bonding, van der Waals attractions, and long ranged electrostatic interactions play in the solvation and association of apolar solutes in water. While local hydrogen bonding in- teractions dominate hydrophobic effects involving small solutes, longer ranged electrostatic and dis- persion interactions are found to be increasingly important in the description of interfacial structure around large solutes. The hydrogen bond network sets the solute length scale at which a crossover in solvation behavior between these small and large length scale regimes is observed. Unbalanced long ranged forces acting on interfacial water molecules are also important in hydrophobic association, illustrated here by analysis of the association of model methane and buckminsterfullerene solutes., 14 pages

Nitriles are important solvents not just for bulk reactions but also for interfacial processes such as separations, heterogeneous catalysis, and electrochemistry. Although nitriles have a polar end and a lipophilic end, the cyano group is not hydrophilic enough for these substances to be thought of as prototypical amphiphiles. This picture is now changing, as research is revealing that at a silica surface nitriles can organize into structures that, in many ways, resemble lipid bilayers. This unexpected organization may be a key component of unique interfacial behavior of nitriles that make them the solvents of choice for so many applications. The first hints of this lipid-bilayer-like (LBL) organization of nitriles at silica interfaces came from optical Kerr effect (OKE) experiments on liquid acetonitrile confined in the pores of sol-gel glasses. The orientational dynamics revealed by OKE spectroscopy suggested that the confined liquid is composed of a relatively immobile sublayer of molecules that accept hydrogen bonds from the surface silanol groups and an interdigitated, antiparallel layer that is capable of exchanging into the centers of the pores. This picture of acetonitrile has been borne out by molecular dynamics simulations and vibrational sum-frequency generation (VSFG) experiments. Remarkably, these simulations further indicate that the LBL organization is repeated with increasing disorder at least 20 Å into the liquid from a flat silica surface. Simulations and VSFG and OKE experiments indicate that extending the alkyl chain to an ethyl group leads to the formation of even more tightly packed LBL organization featuring entangled alkyl tails. When the alkyl portion of the molecule is a bulky t-butyl group, packing constraints prevent well-ordered LBL organization of the liquid. In each case, the surface-induced organization of the liquid is reflected in its interfacial dynamics. Acetonitrile/water mixtures are favored solvent systems for separations technologies such as hydrophilic interaction chromatography. Simulations had suggested that although a monolayer of water partitions to the silica surface in such mixtures, acetonitrile tends to associate with this monolayer. VSFG experiments reveal that, even at high water mole fractions, patches of well-ordered acetonitrile bilayers remain at the silica surface. Due to its ability to donate and accept hydrogen bonds, methanol also partitions to a silica surface in acetonitrile/methanol mixtures and can serve to take the place of acetonitrile in the sublayer closest to the surface. These studies reveal that liquid nitriles can exhibit an unexpected wealth of new organizational and dynamic behaviors at silica surfaces, and presumably at the surfaces of other chemically important materials as well. This behavior cannot be predicted from the bulk organization of these liquids. Our new understanding of the interfacial behavior of these liquids will have important implications for optimizing a wide range of chemical processes in nitrile solvents.

The nature of ion solvation has drawn the interest of scientists for over a century, yet a thorough theoretical understanding is still lacking. In this work, we focus on the microscopic origins underlying ionic charge asymmetric and nonlinear response contributions to ion solvation free energies. We first derive an exact expression for the charging component of the ionic free energy, the free energy change when the Coulomb interactions between a fixed ion and the solvent are gradually "turned on". We then introduce the concept of a Gaussian test charge distribution, a generalization of the classical electrostatic point test charge that can be used to probe dielectric response in atomically detailed models. This enables the study of a thermodynamic cycle that isolates a linear and charge-symmetric contribution to the free energy that is well-described by Born-model-like dielectric continuum theories. We give a simple physical derivation of the classic Born model that locally relates the induced charge density in a linear dielectric model to the applied ionic charge distribution. The nonlinear response and charge asymmetric contributions to the ion solvation free energy are then examined in the remaining steps of the cycle and compared to classic thermodynamic cycles for this process using computer simulations. The insights provided by this work will aid the development of quantitative theories for the solvation of charged solutes.

The organization of liquid propionitrile at a hydrophilic silica surface and at the liquid–vapor interface has been studied by molecular dynamics simulations. Analysis has been performed on particle densities and the orientations of different bond vectors. At the silica/liquid interface, propionitrile adopts a lipid-bilayer-like structure in which the carbon–nitrogen bond vector has opposite orientations in two sublayers. To explore the influence of the alkyl group on the interfacial structure, we have also studied the methylene–methyl vector orientations and locations of the methyl groups for molecules in the different sublayers. This analysis reveals that liquid propionitrile forms a compact, entangled bilayer at a silica surface, in contrast to the interdigitated bilayer that has been observed previously for acetonitrile.

Molecular dynamics simulations and vibrational sum frequency generation (VSFG) experiments in the methyl-stretching spectral region have been used to study acetonitrile at the silica/liquid, silica/vapor, and liquid/vapor interfaces. Our simulations show that, at the silica/liquid interface, acetonitrile takes on a considerably different structure than in the bulk liquid. The interfacial structure is reminiscent of a lipid bilayer, and this type of ordering persists for tens of Angstroms into the bulk liquid. This result has important implications for processes involving solid/acetonitrile interfaces, such as heterogeneous catalysis and chromatographic separations. Fitting of VSFG data that have an extremely low nonresonant background contribution provides strong evidence for interfacial populations pointing in opposite directions at these interfaces, in agreement with our simulations. The picture developed from our simulations and experiments reconciles conflicting interpretations of data from previous e...

Understanding the thermodynamic driving forces underlying any chemical process requires a description of the underlying free energy surface. However, computation of free energies is difficult, often requiring advanced sampling techniques. Moreover, these computations can be further complicated by the evaluation of any long-ranged interactions in the system of interest, such as Coulomb interactions in charged and polar media. Local molecular field theory is a promising approach to avoid many of the conceptual and computational difficulties associated with long-ranged interactions. We present frameworks for performing alchemical free energy calculations and non-Boltzmann sampling with local molecular field theory. We demonstrate that local molecular field theory can be used to perform these free energy calculations with accuracy comparable to traditional methodologies while eliminating the need for explicit treatment of long-ranged interactions in simulations.

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 biomolecular systems and clarify some of the critical issues pertaining to this subject. Given space constraints, we cannot review all the significant and interesting work in this active field.

We try to improve the Thomas−Fermi model for the total energy and electron density of atoms and molecules by directly modifying the Euler equation for the electron density, which we argue is less affected by nonlocal corrections. Here we consider the simplest such modification by adding a linear gradient term to the Euler equation. For atoms, the coefficient of the gradient term can be chosen so that the correct exponential decay constant far from the nucleus is obtained. This model then gives a much improved description of the electron density at smaller distances, yielding in particular a finite density at the nucleus that is in good qualitative agreement with exact results. The cusp condition differs from the exact value by a factor of 2. Values for the total energy of atomic systems, obtained by coupling parameter integration of the densities given by the Euler equation, are about as accurate as those given by the very best Thomas−Fermi−Weizsacker models, and the density is much more accurate. Possibl...

This paper determines the excess free energy associated with the formation of a spherical cavity in a hard sphere fluid. The solvation free energy can be calculated by integration of the structural changes induced by inserting the cavity using a number of different exact thermodynamic pathways. We consider three such pathways, including a new density route derived here. Structural information about the nonuniform hard sphere fluid in the presence of a general external field is given by the recently developed hydrostatic linear response (HLR) integral equation. Use of the HLR results in the different pathways gives a generally accurate determination of the solvation free energy for cavities over a wide range of sizes, from zero to infinity. Results for a related method, the Gaussian Field Model, are also discussed., Comment: 10 pages, 4 figures; submitted to J. Chem. Phys

We have developed a new and general theory of nonuniform fluids that naturally incorporates molecular scale information into the classical van der Waals theory of slowly varying interfaces. Here the theory is applied to the liquid-vapor interface of a Lennard-Jones fluid. The method combines a molecular field treatment of the effects of unbalanced attractive forces with a locally optimal use of linear response theory to approximate fluid structure by that of the associated (hard sphere like) reference fluid. Our approach avoids many of the conceptual problems that arise in the classical theory and shows why capillary wave effects are not included in the theory. The general theory and a simplified version gives results for the interface profile and surface tension for states with different temperatures and potential energy cutoffs that compare very favorably with simulation data.

An understanding of the hydrophobicity of complex heterogeneous molecular assemblies is crucial to characterize and predict interactions between biomolecules. As such, uncovering the subtleties of assembly processes hinges on an accurate classification of the relevant interfaces involved, and much effort has been spent on developing so-called "hydrophobicity maps." In this work, we introduce a novel electrostatics-based mapping of aqueous interfaces that focuses on the collective, long-wavelength electrostatic response of water to the presence of nearby surfaces. In addition to distinguishing between hydrophobic and hydrophilic regions of heterogeneous surfaces, this electrostatic mapping can also differentiate between hydrophilic regions that polarize nearby waters in opposing directions. We therefore expect this approach to find use in predicting the location of possible water-mediated hydrophilic interactions, in addition to the more commonly emphasized hydrophobic interactions that can also be of significant importance., 11 pages, 7 figures in J. Phys. Chem. B (2014)

We study thermodynamic and structural properties of a Lennard-Jones liquid at a state very close to the triple point as the radius of a hard sphere solute is varied. Oscillatory profiles arise for small, molecular sized radii while for large radii smooth interfaces with a ``drying layer'' of low vapor density near the solute are seen. We develop a quantitative theory for this process using a new mean field treatment where the effects of attractive interactions are described in terms of a self-consistently chosen effective single particle field. We modify the usual simple molecular field approximation for the effective field in a very natural way so that exact results (consistent with a given accurate equation of state for the uniform fluid) arise in the ``hydrostatic limit'' of very slowly varying interfaces. Very good agreement with the results of computer simulations for a wide range of solute radii are found., to be published in J.Phys.Chem

In important early work, Stell showed that one can determine the pair correlation function h(r) of the hard-sphere fluid for all distances r by specifying only the “tail” of the direct correlation function c(r) at separations greater than the hard-core diameter. We extend this idea in a very natural way to potentials with a soft repulsive core of finite extent and a weaker and longer ranged tail. We introduce a new continuous function T(r) which reduces exactly to the tail of c(r) outside the (soft) core region and show that both h(r) and c(r) depend only on the “out projection” of T(r): i.e., the product of the Boltzmann factor of the repulsive core potential times T(r). Standard integral equation closures can thus be reinterpreted and assessed in terms of their predictions for the tail of c(r) and simple approximations for its form suggest new closures. A new and very efficient variational method is proposed for solving the Ornstein–Zernike equation given an approximation for the tail of c. Initial applications of these ideas to the Lennard-Jones and the hard-core Yukawa fluid are discussed.

We relate properties of an anisotropic continuum model of a two-dimensional vicinal surface to those of a model with fluctuating and interacting steps. We show that analysis of the fluctuations of an individual step in the array provides information about the length scale on which the surface has reached equilibrium and can be used to estimate fundamental step parameters from locally equilibrated surfaces. Monte Carlo simulations of a stable vicinal surface using the terrace–step–kink model agree with the theoretical predictions. We further apply this analysis to steps on an unstable surface during reconstruction-induced faceting and show that it can be used to determine whether the faceting process is in the nucleation or spinodal decomposition regime.

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.

The structure of a nonuniform Lennard-Jones (LJ) liquid near a hard wall is approximated by that of a reference fluid with repulsive intermolecular forces in a self-consistently determined external mean field incorporating the effects of attractive forces. We calculate the reference fluid structure by first determining the response to the slowly varying part of the field alone, followed by the response to the harshly repulsive part. Both steps can be carried out very accurately, as confirmed by MC simulations, and good agreement with the structure of the full LJ fluid is found., 4 pages, 3 figures

Surface reconstruction on sufficiently wide terraces on a vicinal surface can cause the formation of step bunches. We consider this process in the nucleation regime using a two-dimensional (2D) dynamical model that describes both surface reconstruction and the effects of the growth of a reconstructed facet on the motion of neighboring steps. When there is local mass transport, we show that the growth of a reconstructed facet can induce the growth of a similar facet nearby, leading to regular arrangements of flat facets separated by step bunches and to other characteristic 2D step patterns.

The stability of fault slip is sensitive to the way in which frictional strength responds to changes in slip rate and in particular to the effective velocity dependence of steady state friction Δμss/Δ ln V. This quantity can vary substantially with displacement, temperature and slip rate. To investigate the physical basis for this behavior and the possible influence of shear heating, we slid initially bare granite surfaces in unconfined rotary shear to displacements of hundreds of millimeters at normal stresses, σn of 10 and 25 MPa and at room temperature. We imposed step changes in slip rate within the range 10−2 to 103.5 μm/s and also monitored frictional heating with thermistors embedded in the granite. The transient response of μ to slip rate steps was fit to a rate- and state-dependent friction law using two state variables to estimate the values of several parameters in the constitutive law. The first 20 mm of slip shows rising friction and falling Δμss/Δ ln V; further slip shows roughly constant friction, Δμss/Δ ln V and parameter values, suggesting that a steady state condition is reached on the fault surface. At V ≤ 10 μm/s, Δμss/Δ ln V = −0.004 ± 0.001. At higher rates the response is sensitive to normal stress: At σn = 25 MPa granite shows a transition to effective velocity strengthening (Δμss/Δ ln V = 0.008 ± 0.004) at the highest slip rates tested. At 10 MPa granite shows a less dramatic change to Δμss/Δ ln V ≈ 0 at the highest rates. The maximum temperature measured in the granite is ∼60°C at 25 MPa and 103.5 μm/s. Temperatures are in general agreement with a numerical model of heat conduction which assumes spatially homogeneous frictional heating over the sliding surface. The simplest interpretation of our measurements of Δμss/Δ ln V is that the granite is inherently velocity weakening (∂μss/∂ ln V 0 mimics velocity strengthening. These results have implications for the frictional behavior of faults during earthquakes. High slip rates may cause a switch to effective velocity strengthening which could limit peak coseismic slip rate and stress drop. For fluid-saturated faults, strengthening by this mechanism may be partly or fully offset by weakening due to thermal pressurization of a poorly drained pore fluid.

We discuss the ramifications of Widom's idea that attractive intermolecular forces essentially cancel in dense uniform liquids. This idea was used directly in the WCA theory of uniform liquids, where the structure of the liquid is approximated by that of a simpler reference fluid with purely repulsive intermolecular forces. To take account of the unbalanced attractive forces found in nonuniform fluids, Weeks, Selinger, and Broughton (WSB) developed a new method where the structure is related to that of a nonuniform reference fluid in an external field chosen to yield a self-consistent description of correlations induced by the repulsive forces and a mean field treatment of the attractive forces. Using simulations, we provide a quantitative test of the accuracy of both methods for the uniform fluid at different points in the phase diagram by relating correlation functions in the uniform fluid to those in a nonuniform fluid with a particle fixed at the origin. We find that at high densities the WSB approach can correct most of the small errors in the structure of the WCA reference fluid. At lower densities the WSB method provides a considerable improvement over the WCA theory. A simplified version of the WSB method is presented that is of comparable accuracy.

Surface reconstruction can generate effective attractive interactions between steps on vicinal surfaces, leading to the formation of step bunches. Modified repulsive interactions arise from the fluctuations of a step in the asymmetric environment at the edge of the step bunch. These are determined by a mapping to the ground state energy of a quantum particle between two rigid walls in an external field. This yields an edge energy term that controls the dynamics of faceting and causes wider step spacings at the edge of the bunch, in agreement with Monte Carlo simulations. [S0031-9007(97)03948-3]

The rate of thermal decay of a metastable sawtooth morphology on Si(111) is greatly accelerated by the application of a bulk direct current in the “uphill” direction. STM measurements of the rate are compared with a mesoscopic theory of surface mass transport incorporating an effective surface electromigration force on the diffusing species. Quantitative agreement with the experimental observations is obtained for an effective charge ≤ 0.01 electron charge at 900°C.

We study two-dimensional models of step flow in which the local velocity of a step is expressed as a function of its neighboring terrace widths and the local curvature of the step. Repulsive step interactions modify the velocity functions at short distances and prevent step crossing. When the velocity of a step depends mainly on the width of the terrace behind, the resulting asymmetry in the velocity functions can make the uniform step train unstable towards step bunching. Typically, during growth or evaporation, the surface will develop characteristic patterns where slowly moving fairly straight bunches coexist with fast-moving, strongly bent single steps that cross from one bunch to another. The bunching and debunching processes happen simultaneously. These general features have been seen in recent experiments on the current-induced step bunching of Si (111) surfaces. The same qualitative behavior persists in a wide class of microscopic models that require a much more complicated description.

The potential energy between molecules is often represented as a sum of pairwise additive potentials for all atom pairs in both molecules. Such atomistic potentials encode much physical and chemical information, and in particular give an accurate representation of the molecular shape. However, the number of terms in the sum for a pair of molecules goes as N2 where N is the number of atoms in a molecule, and thus grows rapidly inefficient for large N. Starting with an atomistic pairwise additive potential for Copper Phthalocyanine (CuPc), a planar tile‐shaped molecule with 57 atoms, we determine a simpler reduced intermolecular potential consisting of a sum of effective pair interactions between 13 appropriately chosen ‘‘interaction sites’’ on each molecule. This potential reproduces many qualitative features of the full atomistic potential model for CuPc including the very anisotropic molecular shape, but is much easier to evaluate numerically, requiring only 1% as much computation time as the full atomis...

The coefficient of friction and velocity dependence of friction of initially bare surfaces and 1-mm-thick simulated fault gouges ( 400 mm at 25°C 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 (

We extend the terrace-step-kink model of crystal growth to impure solutions where the impurities act as barriers to step motion. The effects of supersaturation, step curvature, step repulsions, and impurities on step motion are treated in a unified free energy framework. The model reproduces several features seen in experiments on growth of potassium dihydrogen phosphate crystals, wherein a dead zone at low supersaturations and a recovery of crystal growth by motion of large coherent step bunches at larger supersaturations are observed. We identify a key feature of solution growth that leads to these effects.

Structural and thermodynamic properties of a nonuniform liquid are related to those of a reference fluid with purely repulsive intermolecular forces in an external field. A new equation for that field derived from the Yvon-Born-Green hierarchy permits a self-consistent description of correlations induced by the exact repulsive forces and a mean field treatment of the attractive forces. Predictions of the theory for drying effects at repulsive walls and for the liquid-vapor interface are compared to molecular dynamics simulations.

Instabilities in step structure induced by direct-current heating have been measured using STM on Si(111) surfaces with an equilibrium step separation of approximately 1500 A. The two-dimensional structure of kinetically formed step bunches and associated “crossing arrays” of single-height steps shows qualitatively good agreement with predictions of a generalized theory of step-flow instability. Quantitative analysis of the structures is consistent with the theory. The result provides the first experimental determination of an effective anisotropy ratio governing kinetic step bunching. The measured value of this anisotropy ratio is 0.20 ± 0.03.

We have examined in detail the structure and properties of the liquid-vapor interface for the two-dimensional Widom-Rowlinson model in its low-temperature regime. Various simplifying features permit the deduction of several basic results. Included among these are (1) unambiguous definition of capillary wave modes with upper wavelength cutoff proportional to ~ 1 l ’ ~ (el = liquid density); (2) wavelength dispersion of bare surface tension; and (3) nonmonotonic intrinsic density profile (i.e., that with vanishing capillary wave amplitudes). In an Appendix we show how many of these results can be extended to the three and higher dimensional cases.

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.

We study in detail the impurity mechanism suggested by Frank for step bunching instabilities on crystal surfaces during crystal growth and evaporation. A two-dimensional model in which the impurities are treated microscopically is proposed. We perform a numerical simulation of the model and show that it leads to step bunching. In this paper we examine the large line tension limit, where the step train remains effectively one dimensional. Using a mean-field theory, we express the velocity of a step in terms of the widths of adjacent terraces and the parameters of the microscopic model. It is shown that the theory is valid over a wide range of physical parameters, and only outside this range does one have to use a more complicated exposure time formalism. We compare the velocity function predicted by the theory with results from Monte Carlo simulations of the two-dimensional model and find remarkable agreement. Our theory predicts a logarithmic growth of the average terrace width with time for noninteracting impurities, in agreement with Monte Carlo simulations. Lastly, we suggest new physical realizations of the impurity mechanism. We illustrate the robustness of the idea by considering generalized impurities, which are created by the kinetic process itself without involving an external impurity source. In some of these cases a power-law coarsening of the terrace widths may arise.

Laboratory studies of the frictional behavior of rocks can provide important information about the strength and sliding stability of natural faults. We have conducted friction experiments on antigorite and lizardite serpentinites, rocks common to both continental and oceanic crustal faults. We conducted both velocity-step tests and timed-hold tests on bare surfaces and gouge layers of serpentinite at room temperature. We find that the coefficient of friction of lizardite serpentinite is quite low (0.15–0.35) and could explain the apparent low stresses observed on crustal transform faults, while that of antigorite serpentinite is comparable to other crustal rocks (0.50–0.85). The frictional behavior of both types of serpentinite is well described by a two-mechanism model combining state-variable-dominated behavior at high slip velocities and flow-dominated behavior at low velocities. The two-mechanism model is supported by data from velocity-step tests and timed-hold tests. The low velocity behavior of serpentinite is strongly rate strengthening and should result in stable fault creep on natural faults containing either antigorite or lizardite serpentinite.

Using concepts from perturbation and local molecular field theories of liquids we divide the potential of the SPC/E water model into short and long ranged parts. The short ranged parts define a minimal reference network model that captures very well the structure of the local hydrogen bond network in bulk water while ignoring effects of the remaining long ranged interactions. This deconstruction can provide insight into the different roles that the local hydrogen bond network, dispersion forces, and long ranged dipolar interactions play in determining a variety of properties of SPC/E and related classical models of water. Here we focus on the anomalous behavior of the internal pressure and the temperature dependence of the density of bulk water. We further utilize these short ranged models along with local molecular field theory to quantify the influence of these interactions on the structure of hydrophobic interfaces and the crossover from small to large scale hydration behavior. The implications of our findings for theories of hydrophobicity and possible refinements of classical water models are also discussed.

The Dieterich-Ruina state-variable friction laws do a good job describing results of rock friction experiments, and fault models based on them are able to mimic natural seismicity in many respects. To be useful for modeling earthquakes, high velocities must be successfully modelled. Ruina gave a formula for steady state frictional strength with a constant (usually negative) slope on a logarithmic plot that does not agree with recent observations of friction of a variety of materials at velocities greater than 30 to 100 μms−1. This steady state function, termed the “log-linear function,” with inertia neglected, does not recover from instability and, consequently, cannot give predictions of stress drop or peak velocities during unstable slip. Adding inertia yields stress drops that are too large to match experimental observations. This paper explores the consequences for unstable slip when inertia is considered and when the steady state function is altered at high velocity. Two steady state functions are considered: one that has no dependence on velocity at high slip velocity (“zero-slope”) and one that has a positive velocity dependence at high velocity (“positive-slope”). Inclusion of inertia and use of these modified steady state functions improve the results of simulations in terms of qualitatively reproducing many aspects of unstable sliding, but the positive-slope function yields the best quantitative agreement with experimental observations. Use of the modified steady state functions predicts that stress drop during unstable sliding should decrease with increasing loading velocity and at sufficiently high load point velocity there will be a transition to stable sliding, a result that is observed experimentally.