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We develop a multiscale coarse-grain model of the NIST Monoclonal Antibody Reference Material 8671 (NISTmAb) to enable systematic computational investigations of high-concentration physical instabilities such as phase separation, clustering, and aggregation. Our multiscale coarse-graining strategy captures atomic-resolution interactions with a computational approach that is orders of magnitude more efficient than atomistic models, assuming the biomolecule can be decomposed into one or more rigid bodies with known, fixed structures. This method reduces interactions between tens of thousands of atoms to a single anisotropic interaction site. The anisotropic interaction between unique pairs of rigid bodies is precomputed over a discrete set of relative orientations and stored, allowing interactions between arbitrarily oriented rigid bodies to be interpolated from the precomputed table during coarse-grained Monte Carlo simulations. We present this approach for lysozyme and lactoferrin as a single rigid body and for the NISTmAb as three rigid bodies bound by a flexible hinge with an implicit solvent model. This coarse-graining strategy predicts experimentally measured radius of gyration and second osmotic virial coefficient data, enabling routine Monte Carlo simulation of medically relevant concentrations of interacting proteins while retaining atomistic detail. All methodologies used in this work are available in the open-source software Free Energy and Advanced Sampling Simulation Toolkit. [ABSTRACT FROM AUTHOR]

FEASST is an open-source Monte Carlo software package for particle-based simulations. This software, which was released in 2017, has been used to study phase equilibrium, self-assembly, aggregation or gelation in biological materials, colloids, polymers, ionic liquids, and adsorption in porous networks. We highlight some of the unique features available in FEASST, such as flat-histogram grand canonical ensemble, Gibbs ensemble, and Mayer-sampling simulations with support for anisotropic models and parallelization with flat-histogram and prefetching. We also discuss how the challenges of supporting a variety of Monte Carlo algorithms were overcome by an object-oriented design. This also allows others to extend classes, which improves software interoperability, as inspired by LAMMPS classes and user packages. This article describes version 0.25.1 with benchmarks, compilation instructions, and introductory tutorials for running, restarting, and testing simulations, user guidelines, software design strategies, alternative interfaces, and the test-driven development strategy. [ABSTRACT FROM AUTHOR]

Theories of small systems play an important role in the fundamental understanding of finite size effects in statistical mechanics, as well as the validation of molecular simulation results as no computer can simulate fluids in the thermodynamic limit. Previously, a shell particle was included in the isothermal–isobaric ensemble in order to resolve an ambiguity in the resulting partition function. The shell particle removed either redundant volume states or redundant translational degrees of freedom of the system and yielded quantitative differences from traditional simulations in this ensemble. In this work, we investigate the effect of including a shell particle in the canonical, grand canonical, and Gibbs ensembles. For systems comprised of a pure component ideal gas, analytical expressions for various thermodynamic properties are obtained. We also derive the Metropolis Monte Carlo simulation acceptance criteria for these ensembles with shell particles, and the results of the simulations of an ideal gas are in excellent agreement with the theoretical predictions. The system size dependence of various important ensemble averages is also analyzed. [ABSTRACT FROM AUTHOR]

We introduce Gaussian Process Regression (GPR) as an enhanced method of thermodynamic extrapolation and interpolation. The heteroscedastic GPR models that we introduce automatically weight provided information by its estimated uncertainty, allowing for the incorporation of highly uncertain, high-order derivative information. By the linearity of the derivative operator, GPR models naturally handle derivative information and, with appropriate likelihood models that incorporate heterogeneous uncertainties, are able to identify estimates of functions for which the provided observations and derivatives are inconsistent due to the sampling bias that is common in molecular simulations. Since we utilize kernels that form complete bases on the function space to be learned, the estimated uncertainty in the model takes into account that of the functional form itself, in contrast to polynomial interpolation, which explicitly assumes the functional form to be fixed. We apply GPR models to a variety of data sources and assess various active learning strategies, identifying when specific options will be most useful. Our active-learning data collection based on GPR models incorporating derivative information is finally applied to tracing vapor–liquid equilibrium for a single-component Lennard-Jones fluid, which we show represents a powerful generalization to previous extrapolation strategies and Gibbs–Duhem integration. A suite of tools implementing these methods is provided at https://github.com/usnistgov/thermo-extrap. [ABSTRACT FROM AUTHOR]

We describe a method for deriving surface functionalization patterns for colloidal systems that can induce self-assembly into any chosen periodic symmetry at a planar interface. The result is a sequence of letters, s ∈ {A,T,C,G}, or a gene, that describes the perimeter of the colloidal object and programs its self-assembly. This represents a genome that is finite and can be exhaustively enumerated. These genes derive from symmetry, which may be topologically represented by two-dimensional parabolic orbifolds; since these orbifolds are surfaces that may be derived from first principles, this represents an ab initio route to colloid functionality. The genes are human readable and can be employed to easily design colloidal units. We employ a biological (genetic) analogy to demonstrate this and illustrate their connection to the designs of Maurits Cornelis (M. C.) Escher. [ABSTRACT FROM AUTHOR]

Variational autoencoders (VAEs) are rapidly gaining popularity within molecular simulation for discovering low-dimensional, or latent, representations, which are critical for both analyzing and accelerating simulations. However, it remains unclear how the information a VAE learns is connected to its probabilistic structure and, in turn, its loss function. Previous studies have focused on feature engineering, ad hoc modifications to loss functions, or adjustment of the prior to enforce desirable latent space properties. By applying effectively arbitrarily flexible priors via normalizing flows, we focus instead on how adjusting the structure of the decoding model impacts the learned latent coordinate. We systematically adjust the power and flexibility of the decoding distribution, observing that this has a significant impact on the structure of the latent space as measured by a suite of metrics developed in this work. By also varying weights on separate terms within each VAE loss function, we show that the level of detail encoded can be further tuned. This provides practical guidance for utilizing VAEs to extract varying resolutions of low-dimensional information from molecular dynamics and Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

Thermodynamic extrapolation has previously been used to predict arbitrary structural observables in molecular simulations at temperatures (or relative chemical potentials in open-system mixtures) different from those at which the simulation was performed. This greatly reduces the computational cost in mapping out phase and structural transitions. In this work, we explore the limitations and accuracy of thermodynamic extrapolation applied to water, where qualitative shifts from anomalous to simple-fluid-like behavior are manifested through shifts in the liquid structure that occur as a function of both temperature and density. We present formulas for extrapolating in volume for canonical ensembles and demonstrate that linear extrapolations of water's structural properties are only accurate over a limited density range. On the other hand, linear extrapolation in temperature can be accurate across the entire liquid state. We contrast these extrapolations with classical perturbation theory techniques, which are more conservative and slowly converging. Indeed, we show that such behavior is expected by demonstrating exact relationships between extrapolation of free energies and well-known techniques to predict free energy differences. An ideal gas in an external field is also studied to more clearly explain these results for a toy system with fully analytical solutions. We also present a recursive interpolation strategy for predicting arbitrary structural properties of molecular fluids over a predefined range of state conditions, demonstrating its success in mapping qualitative shifts in water structure with density. [ABSTRACT FROM AUTHOR]

While ionic liquids have promising applications as industrial solvents, predicting their fluid phase properties and coexistence remains a challenge. Grand canonical Monte Carlo simulation is an effective method for such predictions, but equilibration is hampered by the apparent requirement to insert and delete neutral sets of ions simultaneously in order to maintain charge neutrality. For relatively high densities and low temperatures, previously developed methods have been shown to be essential in improving equilibration by gradual insertion and deletion of these neutral sets of ions. We introduce an expanded ensemble approach which may be used in conjunction with these existing methods to further improve efficiency. Individual ions are inserted or deleted in one Monte Carlo trial rather than simultaneous insertion/deletion of neutral sets. We show how charge neutrality is maintained and show rigorous quantitative agreement between the conventional and the proposed expanded ensemble approaches, but with up to an order of magnitude increase in efficiency at high densities. The expanded ensemble approach is also more straightforward to implement than simultaneous insertion/deletion of neutral sets, and its implementation is demonstrated within open source software. [ABSTRACT FROM AUTHOR]

We present analytic expressions for the second virial coefficient of hard particles in slit and cylindrical pores with arbitrary square-well fluid-fluid and fluid-solid interactions, number of fluid components, and pore sizes. We derive multiple methods to predict the isotherms in confined materials based on the virial expansion and find that the thermodynamic and structural properties calculated from the virial expansion to second order in the dilute limit display excellent qualitative agreement with previous simulation results. [ABSTRACT FROM AUTHOR]

The theoretical framework to evaluate small-angle scattering (SAS) profiles for multi-component macromolecular solutions is re-examined from the standpoint of molecular simulations in the grand-canonical ensemble, where the chemical potentials of all species in solution are fixed. This statistical mechanical ensemble resembles more closely scattering experiments, capturing concentration fluctuations that arise from the exchange of molecules between the scattering volume and the bulk solution. The resulting grand-canonical expression relates scattering intensities to the different intra- and intermolecular pair distribution functions, as well as to the distribution of molecular concentrations on the scattering volume. This formulation represents a generalized expression that encompasses most of the existing methods to evaluate SAS profiles from molecular simulations. The grand-canonical SAS methodology is probed for a series of different implicit-solvent, homogeneous systems at conditions ranging from dilute to concentrated. These systems consist of spherical colloids, dumbbell particles, and highly flexible polymer chains. Comparison of the resulting SAS curves against classical methodologies based on either theoretical approaches or canonical simulations (i.e., at a fixed number of molecules) shows equivalence between the different scattering intensities so long as interactions between molecules are net repulsive or weakly attractive. On the other hand, for strongly attractive interactions, grand-canonical SAS profiles deviate in the low- and intermediate-q range from those calculated in a canonical ensemble. Such differences are due to the distribution of molecules becoming asymmetric, which yields a higher contribution from configurations with molecular concentrations larger than the nominal value. Additionally, for flexible systems, explicit discrimination between intra- and inter-molecular SAS contributions permits the implementation of model-free, structural analysis such as Guinier’s plots at high molecular concentrations, beyond what the traditional limits are for such analysis. [ABSTRACT FROM AUTHOR]

We describe a methodology for extrapolating the structural properties of multicomponent fluids from one thermodynamic state to another. These properties generally include features of a system that may be computed from an individual configuration such as radial distribution functions, cluster size distributions, or a polymer’s radius of gyration. This approach is based on the principle of using fluctuations in a system’s extensive thermodynamic variables, such as energy, to construct an appropriate Taylor series expansion for these structural properties in terms of intensive conjugate variables, such as temperature. Thus, one may extrapolate these properties from one state to another when the series is truncated to some finite order. We demonstrate this extrapolation for simple and coarse-grained fluids in both the canonical and grand canonical ensembles, in terms of both temperatures and the chemical potentials of different components. The results show that this method is able to reasonably approximate structural properties of such fluids over a broad range of conditions. Consequently, this methodology may be employed to increase the computational efficiency of molecular simulations used to measure the structural properties of certain fluid systems, especially those used in high-throughput or data-driven investigations. [ABSTRACT FROM AUTHOR]

We derive an approach for extrapolating the free energy landscape of multicomponent systems in the grand canonical ensemble, obtained from flat-histogram Monte Carlo simulations, from one set of temperature and chemical potentials to another. This is accomplished by expanding the landscape in a Taylor series at each value of the order parameter which defines its macrostate phase space. The coefficients in each Taylor polynomial are known exactly from fluctuation formulas, which may be computed by measuring the appropriate moments of extensive variables that fluctuate in this ensemble. Here we derive the expressions necessary to define these coefficients up to arbitrary order. In principle, this enables a single flat-histogram simulation to provide complete thermodynamic information over a broad range of temperatures and chemical potentials. Using this, we also showhowto combine a small number of simulations, each performed at different conditions, in a thermodynamically consistent fashion to accurately compute properties at arbitrary temperatures and chemical potentials. This method may significantly increase the computational efficiency of biased grand canonical Monte Carlo simulations, especially for multicomponent mixtures. Although approximate, this approach is amenable to high-throughput and data-intensive investigations where it is preferable to have a large quantity of reasonably accurate simulation data, rather than a smaller amount with a higher accuracy. [ABSTRACT FROM AUTHOR]

Virial coefficients are predicted over a large range of both temperatures and model parameter values (i.e., alchemical transformation) from an individual Mayer-sampling Monte Carlo simulation by statistical mechanical extrapolation with minimal increase in computational cost.With this extrapolation method, a Mayer-sampling Monte Carlo simulation of the SPC/E (extended simple point charge) water model quantitatively predicted the second virial coefficient as a continuous function spanning over four orders of magnitude in value and over three orders of magnitude in temperature with less than a 2% deviation. In addition, the same simulation predicted the second virial coefficient if the site charges were scaled by a constant factor, from an increase of 40% down to zero charge. This method is also shown to perform well for the third virial coefficient and the exponential parameter [ABSTRACT FROM AUTHOR]

We derive a method for extrapolating the grand canonical free energy landscape of a multicomponent fluid system from one temperature to another. Previously, we introduced this statistical mechanical framework for the case where kinetic energy contributions to the classical partition function were neglected for simplicity [N. A. Mahynski et al., J. Chem. Phys. 146, 074101 (2017)]. Here, we generalize the derivation to admit these contributions in order to explicitly illustrate the differences that result. Specifically, we show how factoring out kinetic energy effects a priori, in order to consider only the configurational partition function, leads to simpler mathematical expressions that tend to produce more accurate extrapolations than when these effects are included. We demonstrate this by comparing and contrasting these two approaches for the simple cases of an ideal gas and a non-ideal, square-well fluid. [ABSTRACT FROM AUTHOR]

We present a method for predicting the free energy landscape of fluids at low temperatures from flat-histogram grand canonical Monte Carlo simulations performed at higher ones. We illustrate our approach for both pure and multicomponent systems using two different sampling methods as a demonstration. This allows us to predict the thermodynamic behavior of systems which undergo both first order and continuous phase transitions upon cooling using simulations performed only at higher temperatures. After surveying a variety of different systems, we identify a range of temperature differences over which the extrapolation of high temperature simulations tends to quantitatively predict the thermodynamic properties of fluids at lower ones. Beyond this range, extrapolation still provides a reasonably well-informed estimate of the free energy landscape; this prediction then requires less computational effort to refine with an additional simulation at the desired temperature than reconstruction of the surface without any initial estimate. In either case, this method significantly increases the computational efficiency of these flat-histogram methods when investigating thermodynamic properties of fluids over a wide range of temperatures. For example, we demonstrate how a binary fluid phase diagram may be quantitatively predicted for many temperatures using only information obtained from a single supercritical state. [ABSTRACT FROM AUTHOR]

We demonstrate an extensible flat-histogram Monte Carlo simulation methodology for studying the adsorption of multicomponent fluids in flexible porous solids. This methodology allows us to easily obtain the complete free energy landscape for the confined fluid-solid system in equilibrium with a bulk fluid of any arbitrary composition. We use this approach to study the adsorption of a prototypical coarse-grained binary fluid in "Hookean" solids, where the free energy of the solid may be described as a simple spring. However, our approach is fully extensible to solids with arbitrarily complex free energy profiles. We demonstrate that by tuning the fluid-solid interaction ranges, the inhomogeneous fluid structure inside the pore can give rise to enhanced selective capture of a larger species through cooperative adsorption with a smaller one. The maximum enhancement in selectivity is observed at low to intermediate pressures and is especially pronounced when the larger species is very dilute in the bulk. This suggest a mechanism by which the selective capture of a minor component from a bulk fluid may be enhanced. [ABSTRACT FROM AUTHOR]

Ultrasonic experiments allow one to measure the elastic modulus of bulk solid or fluid samples. Recently such experiments have been carried out on fluid-saturated nanoporous glass to probe the modulus of a confined fluid. In our previous work [G. Y. Gor et al., J. Chem. Phys., 143, 194506 (2015)], using Monte Carlo simulations we showed that the elastic modulus K of a fluid confined in a mesopore is a function of the pore size. Here we focus on the modulus-pressure dependence K(P), which is linear for bulk materials, a relation known as the Tait-Murnaghan equation. Using transition-matrix Monte Carlo simulations we calculated the elastic modulus of bulk argon as a function of pressure and argon confined in silica mesopores as a function of Laplace pressure. Our calculations show that while the elastic modulus is strongly affected by confinement and temperature, the slope of the modulus versus pressure is not. Moreover, the calculated slope is in a good agreement with the reference data for bulk argon and experimental data for confined argon derived from ultrasonic experiments.We propose to use the value of the slope of K(P) to estimate the elastic moduli of an unknown porous medium. [ABSTRACT FROM AUTHOR]

A generic but simple model is presented to evaluate the effect of the heterogeneous surface charge distribution of proteins and zwitterionic nanoparticles on their thermodynamic phase behavior. By considering surface charges as continuous "patches," the rich set of surface patterns that is embedded in proteins and charged patchy particles can readily be described. This model is used to study the fluid phase separation of charged particles where the screening length is of the same order of magnitude as the particle size. In particular, two types of charged particles are studied: dipolar fluids and proteinlike fluids. The former represents the simplest case of zwitterionic particles, whose charge distribution can be described by their dipole moment. The latter system corresponds to molecules/particles with complex surface charge arrangements such as those found in biomolecules. The results for both systems suggest a relation between the critical region, the strength of the interparticle interactions, and the arrangement of charged patches, where the critical temperature is strongly correlated to the magnitude of the dipole moment. Additionally, competition between attractive and repulsive charge-charge interactions seems to be related to the formation of fluctuating clusters in the dilute phase of dipolar fluids, as well as to the broadening of the binodal curve in protein-like fluids. Finally, a variety of self-assembled architectures are detected for dipolar fluids upon small changes to the charge distribution, providing the groundwork for studying the self-assembly of charged patchy particles. [ABSTRACT FROM AUTHOR]

Cubic colloids, sedimented on a surface and immersed in a solution of depletant molecules, were modeled with a family of shapes which smoothly varies from squares to circles. UsingWang-Landau simulations with expanded ensembles, we observe the formation of rhombic lattices, square lattices, hexagonal lattices, and a fluid phase. This systematic investigation includes locating transitions between all combinations of the three lattice structures upon changing the shape and transitions between the fluid and crystal upon changing the depletant concentration. The rhombic lattice deforms smoothly between square-like and hexagonal-like angles, depending on both the shape and the depletant concentration. Our results on the effect of the depletant concentration, depletant size, and colloid shape to influence the stability of the fluid and the lattice structures may help guide experimental studies with recently synthesized cubic colloids. [ABSTRACT FROM AUTHOR]

The fluid phase diagram of trimer particles composed of one central attractive bead and two repulsive beads was determined as a function of simple geometric parameters using flat-histogram Monte Carlo methods. A variety of self-assembled structures were obtained including spherical micelle-like clusters, elongated clusters, and densely packed cylinders, depending on both the state conditions and shape of the trimer. Advanced simulation techniques were employed to determine transitions between self-assembled structures and macroscopic phases using thermodynamic and structural definitions. Simple changes in particle geometry yield dramatic changes in phase behavior, ranging from macroscopic fluid phase separation to molecular-scale self-assembly. In special cases, both self-assembled, elongated clusters and bulk fluid phase separation occur simultaneously. Our work suggests that tuning particle shape and interactions can yield superstructures with controlled architecture. [ABSTRACT FROM AUTHOR]

Using flat-histogram Monte Carlo methods, we investigate the adsorptive behavior of the square-well fluid in two simple slit-pore-like models intended to capture fundamental characteristics of flexible adsorbent materials. Both models require as input thermodynamic information about the flexible adsorbent material itself. An important component of this work involves formulating the flexible pore models in the appropriate thermodynamic (statistical mechanical) ensembles, namely, the osmotic ensemble and a variant of the grand-canonical ensemble. Two-dimensional probability distributions, which are calculated using flat-histogram methods, provide the information necessary to determine adsorption thermodynamics. For example, we are able to determine precisely adsorption isotherms, (equilibrium) phase transition conditions, limits of stability, and free energies for a number of different flexible adsorbent materials, distinguishable as different inputs into the models. While the models used in this work are relatively simple from a geometric perspective, they yield non-trivial adsorptive behavior, including adsorption-desorption hysteresis solely due to material flexibility and so-called "breathing" of the adsorbent. The observed effects can in turn be tied to the inherent properties of the bare adsorbent. Some of the effects are expected on physical grounds while others arise from a subtle balance of thermodynamic and mechanical driving forces. In addition, the computational strategy presented here can be easily applied to more complex models for flexible adsorbents. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We have calculated the pair correlation functions for several binary mixtures composed of simple solutes in a Lennard-Jones solvent. In particular, we have studied the solute-solute pair correlation functions and their dependence on the total density, the solvent Lennard-Jones parameters, and on the solute-solute energy parameter. All the results were obtained from solving the Percus–Yevick equations, as well as from Monte Carlo simulations. The relevance of these results to the problem of hydrophobic interactions is also discussed. [ABSTRACT FROM AUTHOR]

We use discontinuous molecular dynamics and grand-canonical transition-matrix Monte Carlo simulations to explore how confinement between parallel hard walls modifies the relationships between packing fraction, self-diffusivity, partial molar excess entropy, and total excess entropy for binary hard-sphere mixtures. To accomplish this, we introduce an efficient algorithm to calculate partial molar excess entropies from the transition-matrix Monte Carlo simulation data. We find that the species-dependent self-diffusivities of confined fluids are very similar to those of the bulk mixture if compared at the same, appropriately defined, packing fraction up to intermediate values, but then deviate negatively from the bulk behavior at higher packing fractions. On the other hand, the relationships between self-diffusivity and partial molar excess entropy (or total excess entropy) observed in the bulk fluid are preserved under confinement even at relatively high packing fractions and for different mixture compositions. This suggests that the excess entropy, calculable from classical density functional theories of inhomogeneous fluids, can be used to predict some of the nontrivial dynamical behaviors of fluid mixtures in confined environments. [ABSTRACT FROM AUTHOR]

Computer simulations are employed to obtain subcritical isotherms of small finite sized systems inside the coexistence region. For all temperatures considered, ranging from the triple point up to the critical point, the isotherms gradually developed a sequence of sharp discontinuities as the system size increased from ∼8 to ∼21 molecular diameters. For the smallest system sizes, and more so close to the critical point, the isotherms appeared smooth, resembling the continuous van der Waals loop obtained from extrapolation of an analytic equation of state outside the coexistence region. As the system size was increased, isotherms in the chemical potential-density plane developed first two, then four, and finally six discontinuities. Visual inspection of selected snapshots revealed that the observed discontinuities are related to structural transitions between droplets (on the vapor side) and bubbles (on the liquid side) of spherical, cylindrical, and tetragonal shapes. A capillary drop model was developed to qualitatively rationalize these observations. Analytic results were obtained and found to be in full agreement with the computer simulation results. The analysis shows that the shape of the subcritical isotherms is dictated by a single characteristic volume (or length scale), which depends on the surface tension, compressibility, and coexistence densities. For small reduced system volumes, the model predicts that a homogeneous fluid is stable across the whole coexistence region, thus explaining the continuous van der Waals isotherms observed in the simulations. When the liquid and vapor free energies are described by means of an accurate mean-field equation of state and surface tensions from simulation are employed, the capillary model is found to describe the simulated isotherms accurately, especially for large systems (i.e., larger than about 15 molecular diameters) at low temperature (lower than about 0.85 times the critical temperature). This implies that the Laplace pressure differences can be predicted for drops as small as five molecular diameters, and as few as about 500 molecules. The theoretical study also shows that the extrema or apparent spinodal points of the finite size loops are more closely related to (finite system size) bubble and dew points than to classical spinodals. Our results are of relevance to phase transitions in nanopores and show that first order corrections to nucleation energies in finite closed systems are power laws of the inverse volume. [ABSTRACT FROM AUTHOR]

We present a methodology based on grand-canonical transition-matrix Monte Carlo and finite-size scaling analysis to calculate surface tensions in binary mixtures. In particular, mixture transition-matrix Monte Carlo is first used to calculate apparent, system-size-dependent free-energy barriers separating coexisting fluid phases. Finite-size scaling is then used to extrapolate these values to the infinitely large system limit to determine the true thermodynamic surface tension. A key distinction of the methodology is that it yields the entire isothermal surface-tension curve for a binary mixture in a relatively small number of simulations. We demonstrate the utility of the method by calculating surface-tension curves for three binary Lennard-Jones mixtures. While we have only examined the surface tension of simple fluids in this work, the method is general and can be extended to molecular fluids as well as to determine interfacial tensions of liquid-liquid interfaces. [ABSTRACT FROM AUTHOR]

We present a method for directly locating density-driven phase transitions in multicomponent systems. Phase coexistence conditions are determined through manipulation of a total density probability distribution evaluated over a density range that includes both coexisting phases. Saturation quantities are determined through appropriate averaging of density-dependent mean values of a given property of interest. We discuss how to implement the method in both the grand-canonical and isothermal-isobaric semigrand ensembles. Calculations can be conducted using any of the recently introduced flat-histogram techniques. Here, we combine the general algorithm with a transition-matrix approach to produce an efficient self-adaptive technique for determining multicomponent phase equilibrium properties. To assess the performance of the new method, we generate phase diagrams for a number of binary and ternary Lennard-Jones mixtures. [ABSTRACT FROM AUTHOR]

We present a novel computational methodology for determining fluid-phase equilibria in binary mixtures. The method is based on a combination of highly efficient transition-matrix Monte Carlo and histogram reweighting. In particular, a directed grand-canonical transition-matrix Monte Carlo scheme is used to calculate the particle-number probability distribution, after which histogram reweighting is used as a postprocessing procedure to determine the conditions of phase equilibria. To validate the methodology, we have applied it to a number of model binary Lennard-Jones systems known to exhibit nontrivial fluid-phase behavior. Although we have focused on monatomic fluids in this work, the method presented here is general and can be easily extended to more complex molecular fluids. Finally, an important feature of this method is the capability to predict the entire fluid-phase diagram of a binary mixture at fixed temperature in a single simulation. [ABSTRACT FROM AUTHOR]

We present a kinetic theory of homogeneous bubble nucleation based on explicit calculation of the single-molecule evaporation and condensation rates as a function of the size of the vapor embryo. The surface condensation rate is calculated from the kinetic theory of gases, and the surface evaporation rate is related to the rate of escape of molecules from a potential well in the field established by the liquid-vapor interface. Equality of these rates corresponds naturally to the critical bubble. While the interface plays a crucial role in this respect, the kinetic nucleation theory does not invoke an explicit surface tension. The nucleation rate is derived from a population balance and depends only on the ratio of the evaporation to condensation rates. In contrast to classical theory, a nontrivial trend captured by the present theory is the increase in nucleation rate with decreasing temperature at fixed degree of metastability. Comparison with classical nucleation theory reveals markedly different supersaturation dependencies of the nucleation rate, while the predicted sizes of the critical bubble are in good agreement. [ABSTRACT FROM AUTHOR]

Reports on a computational study of homogeneous liquid-vapor nucleation in the Lennard-Jones fluid. Use of the umbrella sampling Monte Carlo simulations to calculate free energy barriers to homogeneous liquid-vapor nucleation; Decrease in calculated free energy barriers with increased superheating.

The residual multiparticle entropy (RMPE) of two- and three-dimensional fluids changes sign near the freezing line, providing a quasiuniversal “one-phase” rule for the location of the liquid-solid transition. We present new simulation results for d-dimensional hard-sphere fluids (d=1-5) which show, however, that this freezing criterion fails in other spatial dimensions. The results also call into question the idea that a change in sign of the RMPE implies the emergence of a new kind of local structural order in the fluid. [ABSTRACT FROM AUTHOR]

Cylindrical or rod-like particles are promising materials for the applications of fillers in nanocomposite materials and additives to control rheological properties of colloidal suspensions. Recent advances in particle synthesis allows for cylinders to be manufactured with short-ranged attractions to study the gelation as a function of packing fraction, aspect ratio and attraction strength. In order to aid in the analysis of small-angle scattering experiments of rod-like particles, computer simulation methods were used to model these particles with specialized Monte Carlo algorithms and tabular superquadric potentials. The attractive interaction between neighboring rods increases with the amount of locally-accessible surface area, thus leading to patchy-like interactions. We characterize the clustering and percolation of cylinders as the attractive interaction increases from the homogenous fluid at relatively low attraction strength, for a variety of aspect ratios and packing fractions. Comparisons with the experimental scattering results are also presented, which are in agreement. [ABSTRACT FROM AUTHOR]

We used flat-histogram sampling Monte Carlo to study capillary phase transitions in deformable adsorbent materials. Specifically, we considered a pure adsorbate fluid below its bulk critical temperature within a slit pore of variable pore width. The instantaneous pore width is dictated by a number of factors, such as adsorbate loading, reservoir pressure, fluid-wall interaction, and bare adsorbent properties. In the slit pores studied here, the bare adsorbent free energy was assumed to be biparabolic, consisting of two preferential pore configurations, namely, the narrow pore and the large pore configurations. Four distinct phases could be found in the adsorption isotherms. We found a low-pressure phase transition, driven primarily by capillary condensation/evaporation and accompanied by adsorbent deformation in response. The deformation can be a relatively small contraction/expansion as seen in elastic materials, or a large-scale structural transformation of the adsorbent. We also found a high-pressure transition driven by excluded volume effects, which tends to expand the material and thus results in a large-scale structural transformation of the adsorbent. The adsorption isotherms and osmotic free energies can be rationalized by considering the relative free energy differences between the basins of the bare adsorbent free energy. [ABSTRACT FROM AUTHOR]

We respond to a Comment on our recent paper [J. Chem. Phys.128, 161101 (2008)] regarding the connection between the change in sign of the residual multiparticle entropy and the freezing transition. [ABSTRACT FROM AUTHOR]

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, A2,app, or the true thermodynamic OSVC, B22osm, 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 A2,app and B22osm 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 A2,app and B22osm. Our results from the hard-sphere equation of state indicate that A2,app underestimates B22osm, but in a systematic manner that may be explained using fundamental thermodynamic expressions for the two OSVCs. The difference between A2,app and B22osm 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. [ABSTRACT FROM AUTHOR]

Density-functional theory is used to study homogeneous bubble nucleation in the stretched Lennard-Jones liquid. We show that the ratio of density-functional to classical nucleation theory free energy barriers should scale with the quantity Δμ/Δμ[sub spin], the difference in chemical potential between the bulk superheated and the saturated liquid divided by the chemical potential difference between the liquid spinodal and the saturated liquid. The critical bubble changes from classical near coexistence (sharp interface, uniform density that decreases with penetration into the coexistence region) to nonclassical beyond Δμ/Δμ[sub spin]approx. 0.5 (diffuse interface, increasing density with increasing penetration into the metastable region). The density at the center of the bubble, the mean bubble density, the bubble size, the interfacial thickness, and the free energy cost of forming a critical bubble all scale with Δμ/Δμ[sub spin] in temperature-independent fashion. This precise measure of the degree of metastability should emerge as a natural parameter in data correlation, as well as in the development of improved theories of nucleation. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We use Monte Carlo simulations to investigate the thermodynamic behavior of soft porous crystal (SPC) adsorbents under the influence of an external barostat. We consider SPCs that naturally exhibit polymorphism between crystal forms of two distinct pore sizes. In the absence of barostatting, these crystals may be naturally divided into two categories depending on their response to stress applied by the adsorbate fluid: those which macroscopically deform and change the volume of their unit cell ("breathing") and those which instead undergo internal rearrangements that change the adsorbate-accessible volume without modifying the unit cell volume ("gate-opening"). When breathing SPCs have a constant external pressure applied, in addition to the thermodynamic pressure of the adsorbate fluid, we find that the free energy difference between the crystal polymorphs is shifted by a constant amount over the entire course of adsorption. Thus, their relative stability may be easily controlled by the barostat. However, when the crystal is held at a fixed overall pressure, changes to the relative stability of the polymorphs tend to be more complex. We demonstrate a thermodynamic analogy between breathing SPCs held at a fixed pressure and macroscopically rigid gate-opening ones which explains this behavior. Furthermore, we illustrate how this implies that external mechanical forces may be employed to tune the effective free energy profile of an empty SPC, which may open new avenues to engineer the thermodynamic properties of these polymorphic adsorbents, such as selectivity.

We use flat-histogram Monte Carlo simulations to study how changing the flexibility of soft porous crystals (SPCs) affects their selective adsorption of a binary, size-asymmetric supercritical fluid. Specifically, we consider mesoporous SPCs which have multiple minima in their free energy profiles as a function of pore size such that they are capable of exhibiting polymorphism between a narrow and large pore phase. While specific fluid-pore interactions determine the shape of both pores' selectivity curve as a function of adsorbate pressure, an individual pore tends to selectively adsorb a species based on the size of the adsorbate molecule relative to itself, thereby shifting the pore's selectivity curve relative to its polymorph. By controlling the flexibility of a SPC, the relative thermodynamic stability of the two pore phases may be varied, thereby changing the overall selectivity of the SPC during adsorbate loading. We investigate this for two classes of SPCs: one representative of "gate-opening" materials and another of "breathing" materials. For gate-opening materials, this control is much more salient than in breathing ones. However, for the latter, we illustrate how to tune the free energy profile to create materials which breathe multiple times during adsorption/desorption.

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.