William P. Krekelberg

Anomalous structure and dynamics of the Gaussian-core fluid.

It is known that there are thermodynamic states for which the Gaussian-core fluid displays anomalous properties such as expansion upon isobaric cooling (density anomaly) and increased single-particle mobility upon isothermal compression (self-diffusivity anomaly). Here, we investigate how temperature and density affect its short-range translational structural order, as characterized by the two-body excess entropy. We find that there is a wide range of conditions for which the short-range translational order of the Gaussian-core fluid decreases upon isothermal compression (structural order anomaly). As we show, the origin of the structural anomaly is qualitatively similar to that of other anomalous fluids (e.g., water or colloids with short-range attractions) and is connected to how compression affects static correlations at different length scales. Interestingly, we find that the self-diffusivity of the Gaussian-core fluid obeys a scaling relationship with the two-body excess entropy that is very similar to the one observed for a variety of simple liquids. One consequence of this relationship is that the state points for which structural, self-diffusivity, and density anomalies of the Gaussian-core fluid occur appear as cascading regions on the temperature-density plane; a phenomenon observed earlier for models of waterlike fluids. There are, however, key differences between the anomalies of Gaussian-core and waterlike fluids, and we discuss how those can be qualitatively understood by considering the respective interparticle potentials of these models. Finally, we note that the self-diffusivity of the Gaussian-core fluid obeys different scaling laws depending on whether the two-body or total excess entropy is considered. This finding, which deserves more comprehensive future study, appears to underscore the significance of higher-body correlations for the behavior of fluids with bounded interactions.

Generalized Rosenfeld scalings for tracer diffusivities in not-so-simple fluids: mixtures and soft particles.

Rosenfeld [Phys. Rev. A 15, 2545 (1977)] originally noticed that casting the transport coefficients of simple monatomic equilibrium fluids in a specific dimensionless form makes them approximately single-valued functions of excess entropy. This observation has predictive value because, while the transport coefficients of dense fluids can be difficult to estimate from first principles, the excess entropy can often be accurately predicted from liquid-state theory. In this work, we use molecular simulations to investigate whether Rosenfelds observation is a special case of a more general scaling law relating the tracer diffusivities of particles in mixtures to the excess entropy. Specifically, we study the tracer diffusivities, static structure, and thermodynamic properties of a variety of one- and two-component model fluid systems with either additive or nonadditive interactions of the hard-sphere or Gaussian-core form. The results of the simulations demonstrate that the effects of mixture concentration and composition, particle-size asymmetry and additivity, and strength of the interparticle interactions in these fluids are consistent with an empirical scaling law relating the excess entropy to a dimensionless (generalized Rosenfeld) form of tracer diffusivity, which we introduce here. The dimensionless form of the tracer diffusivity follows from knowledge of the intermolecular potential and the transport/thermodynamic behavior of fluids in the dilute limit. The generalized Rosenfeld scaling requires less information and provides more accurate predictions than either Enskog theory or scalings based on the pair-correlation contribution to the excess entropy. As we show, however, it also suffers from some limitations especially for systems that exhibit significant decoupling of individual component tracer diffusivities.

Tuning Density Profiles and Mobility of Inhomogeneous Fluids

Density profiles are the most common measure of inhomogeneous structure in confined fluids, but their connection to transport coefficients is poorly understood. We explore via simulation how tuning particle-wall interactions to flatten or enhance the particle layering of a model confined fluid impacts its self-diffusivity, viscosity, and entropy. Interestingly, interactions that eliminate particle layering significantly reduce confined fluid mobility, whereas those that enhance layering can have the opposite effect. Excess entropy helps to understand and predict these trends.

Structural anomalies of fluids: origins in second and higher coordination shells.

Compressing or cooling a fluid typically enhances its static interparticle correlations. However, there are notable exceptions. Isothermal compression can reduce the translational order of fluids that exhibit anomalous waterlike trends in their thermodynamic and transport properties, while isochoric cooling (or strengthening of attractive interactions) can have a similar effect on fluids of particles with short-range attractions. Recent simulation studies by Yan [Phys. Rev. E 76, 051201 (2007)] on the former type of system and Krekelberg [J. Chem. Phys. 127, 044502 (2007)] on the latter provide examples where such structural anomalies can be related to specific changes in second and more distant coordination shells of the radial distribution function. Here, we confirm the generality of this microscopic picture through analysis, via molecular simulation and integral equation theory, of coordination shell contributions to the two-body excess entropy for several related model fluids which incorporate different levels of molecular resolution. The results suggest that integral equation theory can be an effective and computationally inexpensive tool for assessing, based on the pair potential alone, whether new model systems are good candidates for exhibiting structural (and hence thermodynamic and transport) anomalies.

Composition and concentration anomalies for structure and dynamics of Gaussian-core mixtures.

We report molecular dynamics simulation results for two-component fluid mixtures of Gaussian-core particles, focusing on how tracer diffusivities and static pair correlations depend on temperature, particle concentration, and composition. At low particle concentrations, these systems behave like simple atomic mixtures. However, for intermediate concentrations, the single-particle dynamics of the two species largely decouple, giving rise to the following anomalous trends. Increasing either the concentration of the fluid (at fixed composition) or the mole fraction of the larger particles (at fixed particle concentration) enhances the tracer diffusivity of the larger particles but decreases that of the smaller particles. In fact, at sufficiently high particle concentrations, the larger particles exhibit higher mobility than the smaller particles. Each of these dynamic behaviors is accompanied by a corresponding structural trend that characterizes how either concentration or composition affects the strength of the static pair correlations. Specifically, the dynamic trends observed here are consistent with a single empirical scaling law that relates an appropriately normalized tracer diffusivity to its pair-correlation contribution to the excess entropy.

Impact of surface roughness on diffusion of confined fluids

Using event-driven molecular dynamics simulations, we quantify how the self diffusivity of confined hard-sphere fluids depends on the nature of the confining boundaries. We explore systems with featureless confining boundaries that treat particle-boundary collisions in different ways and also various types of physically (i.e., geometrically) rough boundaries. We show that, for moderately dense fluids, the ratio of the self diffusivity of a rough wall system to that of an appropriate smooth-wall reference system is a linear function of the reciprocal wall separation, with the slope depending on the nature of the roughness. We also discuss some simple practical ways to use this information to predict confined hard-sphere fluid behavior in different rough-wall systems.

Relation Between Pore Size and the Compressibility of a Confined Fluid

When a fluid is confined to a nanopore, its thermodynamic properties differ from the properties of a bulk fluid, so measuring such properties of the confined fluid can provide information about the pore sizes. Here, we report a simple relation between the pore size and isothermal compressibility of argon confined in such pores. Compressibility is calculated from the fluctuations of the number of particles in the grand canonical ensemble using two different simulation techniques: conventional grand-canonical Monte Carlo and grand-canonical ensemble transition-matrix Monte Carlo. Our results provide a theoretical framework for extracting the information on the pore sizes of fluid-saturated samples by measuring the compressibility from ultrasonic experiments.

Osmotic virial coefficients for model protein and colloidal solutions: Importance of ensemble constraints in the analysis of light scattering data

Protein-protein interactions in solution may be quantified by the osmotic second virial coefficient (OSVC), which can be measured by various experimental techniques including light scattering. Analysis of Rayleigh light scattering measurements from such experiments requires identification of a scattering volume and the thermodynamic constraints imposed on that volume, i.e., the statistical mechanical ensemble in which light scattering occurs. Depending on the set of constraints imposed on the scattering volume, one can obtain either an apparent OSVC, A(2,app), or the true thermodynamic OSVC, B(22)(osm), that is rigorously defined in solution theory [M. A. Blanco, E. Sahin, Y. Li, and C. J. Roberts, J. Chem. Phys. 134, 225103 (2011)]. However, it is unclear to what extent A(2,app) and B(22)(osm) differ, which may have implications on the physical interpretation of OSVC measurements from light scattering experiments. In this paper, we use the multicomponent hard-sphere model and a well-known equation of state to directly compare A(2,app) and B(22)(osm). Our results from the hard-sphere equation of state indicate that A(2,app) underestimates B(22)(osm), but in a systematic manner that may be explained using fundamental thermodynamic expressions for the two OSVCs. The difference between A(2,app) and B(22)(osm) may be quantitatively significant, but may also be obscured in experimental application by statistical uncertainty or non-steric interactions. Consequently, the two OSVCs that arise in the analysis of light scattering measurements do formally differ, but in a manner that may not be detectable in actual application.

Available states and available space: static properties that predict self-diffusivity of confined fluids

Although density functional theory provides reliable predictions for the static properties of simple fluids under confinement, a theory of comparative accuracy for the transport coefficients has yet to emerge. Nonetheless, there is evidence that knowledge of how confinement modifies static behavior can aid in forecasting dynamics. Specifically, molecular simulation studies have shown that the relationship between excess entropy and self diffusivity of a bulk equilibrium fluid changes only modestly when the fluid is isothermally confined, indicating that knowledge of the former might allow semi-quantitative predictions of the latter. Do other static measures, such as those that characterize free or available volume, also strongly correlate with single-particle dynamics of confined fluids? Here, we study this issue for both the single-component hard-sphere fluid and hard-sphere mixtures. Specifically, we use molecular simulations and fundamental measure theory to study these systems at approximately

Model for the free-volume distributions of equilibrium fluids

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