Excess-entropy scaling for gas diffusivity in nanoporous materials

Understanding dynamics in coarse-grained models. IV. Connection of fine-grained and coarse-grained dynamics with the Stokes-Einstein and Stokes-Einstein-Debye relations

Applying an excess entropy scaling formalism to the coarse-grained (CG) dynamics of liquids, we discovered that missing rotational motions during the CG process are responsible for artificially accelerated CG dynamics. In the context of the dynamic representability between the fine-grained (FG) and CG dynamics, this work introduces the well-known Stokes-Einstein and Stokes-Einstein-Debye relations to unravel the rotational dynamics underlying FG trajectories, thereby allowing for an indirect evaluation of the effective rotations based only on the translational information at the reduced CG resolution. Since the representability issue in CG modeling limits a direct evaluation of the shear stress appearing in the Stokes-Einstein and Stokes-Einstein-Debye relations, we introduce a translational relaxation time as a proxy to employ these relations, and we demonstrate that these relations hold for the ambient conditions studied in our series of work. Additional theoretical links to our previous work are also established. First, we demonstrate that the effective hard sphere radius determined by the classical perturbation theory can approximate the complex hydrodynamic radius value reasonably well. Furthermore, we present a simple derivation of an excess entropy scaling relationship for viscosity by estimating the elliptical integral of molecules. In turn, since the translational and rotational motions at the FG level are correlated to each other, we conclude that the "entropy-free" CG diffusion only depends on the shape of the reference molecule. Our results and analyses impart an alternative way of recovering the FG diffusion from the CG description by coupling the translational and rotational motions at the hydrodynamic level.

Artificial neural network prediction of self-diffusion in pure compounds over multiple phase regimes

Artificial neural networks (ANNs) were developed to accurately predict the self-diffusion constants for pure components in liquid, gas and super critical phases. The ANNs were tested on an experimental database of 6625 self-diffusion constants for 118 different chemical compounds. The presence of multiple phases results in a heavy skew in the distribution of diffusion constants and multiple approaches were used to address this challenge. First, an ANN was developed with the raw diffusion values to assess what the main drawbacks of this direct method were. The first approach for improving the predictions involved taking the log 10 of diffusion to provide a more uniform distribution and reduce the range of target output values used to develop the ANN. The second approach involved developing individual ANNs for each phase using the raw diffusion values. Results show that the log transformation leads to a model with the best self-diffusion constant predictions and an overall average absolute deviation (AAD) of 6.56%. The resultant ANN is a generalized model that can be used to predict diffusion across all three phases and over a diverse group of compounds. The importance of each input feature was ranked using a feature addition method revealing that the density of the compound has the largest impact on the ANN prediction of self-diffusion constants in pure compounds.

Diffusion of colloidal particles in model porous media

Using video microscopy and simulations, we study the long-time diffusion of colloidal tracers in a wide range of model porous media composed of frozen colloidal matrices with different structures. We found that the diffusion coefficient of a tracer can be quantitatively determined by the structures of porous media. In particular, a universal scaling relation exists between the dimensionless diffusion coefficient of the tracer and the structural entropy of the system. This universal scaling relation is an extension of the scaling law previously discovered for the diffusion of colloidal particles in fluctuating media.

Protein Solvent Shell Structure Provides Rapid Analysis of Hydration Dynamics

The solvation layer surrounding a protein is clearly an intrinsic part of protein structure-dynamics-function, and our understanding of how the hydration dynamics influences protein function is emerging. We have recently reported simulations indicating a correlation between regional hydration dynamics and the structure of the solvation layer around different regions of the enzyme Candida antarctica lipase B, wherein the radial distribution function (RDF) was used to calculate the pairwise entropy, providing a link between dynamics (diffusion) and thermodynamics (excess entropy) known as Rosenfeld scaling. Regions with higher RDF values/peaks in the hydration layer (the first peak, within 6 Å of the protein surface) have faster diffusion in the hydration layer. The finding thus hinted at a handle for rapid evaluation of hydration dynamics at different regions on the protein surface in molecular dynamics simulations. Such an approach may move the analysis of hydration dynamics from a specialized venture to routine analysis, enabling an informatics approach to evaluate the role of hydration dynamics in biomolecular function. This paper first confirms that the correlation between regional diffusive dynamics and hydration layer structure (via water center of mass around protein side-chain atom RDF) is observed as a general relationship across a set of proteins. Second, it seeks to devise an approach for rapid analysis of hydration dynamics, determining the minimum amount of information and computational effort required to get a reliable value of hydration dynamics from structural data in MD simulations based on the protein-water RDF. A linear regression model using the integral of the hydration layer in the water-protein RDF was found to provide statistically equivalent apparent diffusion coefficients at the 95% confidence level for a set of 92 regions within five different proteins. In summary, RDF analysis of 10 ns of data after simulation convergence is sufficient to accurately map regions of fast and slow hydration dynamics around a protein surface. Additionally, it is anticipated that a quick look at protein-water RDFs, comparing peak heights, will be useful to provide a qualitative ranking of regions of faster and slower hydration dynamics at the protein surface for rapid analysis when investigating the role of solvent dynamics in protein function.

Toxicant Deposition and Transport in Alveolus: A Classical Density Functional Prediction

The deposition and transport of toxicants on pulmonary surfactant are important processes in human health and medical care. We have introduced classical density functional theory (CDFT) to provide insight into this process. Nine typical toxicants in PM2.5 were considered, and their free energy and structural information have been examined. The free energy profile indicates that PbO, As₂O₃, and CdO are the three toxicants most easily deposited in the pulmonary alveolus, which is consistent with survey data. CuO appears to be the easiest toxicant to transport through the surfactant. Structural analysis indicates that the toxicants tend to pass through the surfactant with rotation. The configuration of the pulmonary surfactant was examined by extending our previous work to polymer systems, and it appears that both the configurational entropy and the direct interaction between the surfactant and the toxicant dominate the configuration of the pulmonary surfactant.

Perspective: Excess-entropy scaling

This article gives an overview of excess-entropy scaling, the 1977 discovery by Rosenfeld that entropy determines properties of liquids like viscosity, diffusion constant, and heat conductivity. We give examples from computer simulations confirming this intriguing connection between dynamics and thermodynamics, counterexamples, and experimental validations. Recent uses in application-related contexts are reviewed, and theories proposed for the origin of excess-entropy scaling are briefly summarized. It is shown that if two thermodynamic state points of a liquid have the same microscopic dynamics, they must have the same excess entropy. In this case, the potential-energy function exhibits a symmetry termed hidden scale invariance, stating that the ordering of the potential energies of configurations is maintained if these are scaled uniformly to a different density. This property leads to the isomorph theory, which provides a general framework for excess-entropy scaling and illuminates, in particular, why this does not apply rigorously and universally. It remains an open question whether all aspects of excess-entropy scaling and related regularities reflect hidden scale invariance in one form or other.

Molecular Dynamics Simulations for Loading-Dependent Diffusion of CO2, SO2, CH4, and Their Binary Mixtures in ZIF-10: The Role of Hydrogen Bond

The loading-dependent diffusion behavior of CH₄, CO₂, SO₂, and their binary mixtures in ZIF-10 has been investigated in detail by using classical molecular dynamics simulations. Our simulation results demonstrate that the self-diffusion coefficient D_i of CH₄ molecules decreases sharply and monotonically with the loading while those of both CO₂ and SO₂ molecules initially display a slight increase at low uptakes and follow a slow decrease at high uptakes. Accordingly, the interaction energies between CH₄ molecules and ZIF-10 remain nearly constant regardless of the loading due to the absence of hydrogen bonds (HBs), while the interaction energies between CO₂ (or SO₂) and ZIF-10 decease rapidly with the loading, especially at small amounts of gas molecules. Such different loading-dependent diffusion and interaction mechanisms can be attributed to the relevant HB behavior between gas molecules and ZIF-10. At low loadings, both the number and strength of HBs between CO₂ (or SO₂) molecules and ZIF-10 decrease obviously as the loading increases, which is responsible for the slight increase of their diffusion coefficients. However, at high loadings, their HB strength increases with the loading. Similar loading-dependent phenomena of diffusion, interaction, and HB behavior can be observed for CH_4, CO₂, and SO₂ binary mixtures in ZIF-10, only associated with some HB competition between CO₂ and SO₂ molecules in the case of the CO₂/SO₂ mixture.

Thermodynamic Route to Efficient Prediction of Gas Diffusivity in Nanoporous Materials

We report an efficient computational procedure for rapid and accurate prediction of the self-diffusivity of gas molecules in nanoporous materials by implementing the transition state theory for intercage hopping at infinite dilution with the string method in conjunction with the excess-entropy scaling for predicting gas diffusion coefficients at finite loadings. The theoretical procedure has been calibrated with molecular dynamics simulations for the diffusion coefficients of methane and hydrogen gases in representative nanoporous materials including metal organic frameworks and zeolites. Combined with the classical density functional theory for calculating the excess entropy of gas molecules in micropores, the theoretical procedure enables efficient computation of both thermodynamic and transport properties important for design and screening of nanostructured materials for gas storage and separation.

Entropy prediction for H2 adsorption in metal-organic frameworks

Entropy is an important thermodynamic property and serves as a bridge connecting equilibrium and non-equilibrium systems, which provides a basic understanding of various practical phenomena. In this study, classical density functional theory was introduced to efficiently predict entropy. The theory was applied to a high-throughput prediction of entropy and excess entropy for H2 adsorption in metal-organic frameworks. It seems that the entropy screening and uptake screening are generally equivalent at high temperature. Based on the entropy screening, the best hydrogen storage materials have been identified. The correlations between entropy and thermodynamic properties, such as uptake, isosteric heat and adsorption degree, were examined and are explained. The results imply that among the tested thermodynamic properties, the correlation between entropy and isosteric heat is the strongest.

Development of 3-dimensional time-dependent density functional theory and its application to gas diffusion in nanoporous materials

An entropy scaling based TDDFT has been proposed and applied to diffusion in a nanoporous material.

How Local and Average Particle Diffusivities of Inhomogeneous Fluids Depend on Microscopic Dynamics

Computer simulations and a stochastic Fokker-Planck equation based approach are used to compare the single-particle diffusion coefficients of equilibrium hard-sphere fluids exhibiting identical inhomogeneous static structure and governed by either Brownian (i.e., overdamped Langevin) or Newtonian microscopic dynamics. The physics of inhomogeneity is explored via the imposition of one-dimensional sinusoidal density profiles of different wavelengths and amplitudes. When imposed density variations are small in magnitude for distances on the scale of a particle diameter, bulk-like average correlations between local structure and mobility are observed. In contrast, when density variations are significant on that length scale, qualitatively different structure-mobility correlations emerge that are sensitive to the governing microscopic dynamics. Correspondingly, a previously proposed scaling between long-time diffusivities for bulk isotropic fluids of particles exhibiting Brownian versus Newtonian dynamics [Pond et al. Soft Matter 2011, 7, 9859-9862] cannot be generalized to describe the position-dependent behaviors of strongly inhomogeneous fluids. While average diffusivities in the inhomogeneous and homogeneous directions are coupled, their qualitative dependencies on inhomogeneity wavelength are sensitive to the details of the microscopic dynamics. Nonetheless, average diffusivities of the inhomogeneous fluids can be approximately predicted for either type of dynamics based on knowledge of bulk isotropic fluid behavior and how inhomogeneity modifies the distribution of available volume. Analogous predictions for average diffusivities of experimental, inhomogeneous colloidal dispersions (based on known bulk behavior) suggest that they will exhibit qualitatively different trends than those predicted by models governed by overdamped Langevin dynamics that do not account for hydrodynamic interactions.

Tuning structure and mobility of solvation shells surrounding tracer additives

Molecular dynamics simulations and a stochastic Fokker-Planck equation based approach are used to illuminate how position-dependent solvent mobility near one or more tracer particle(s) is affected when tracer-solvent interactions are rationally modified to affect corresponding solvation structure. For tracers in a dense hard-sphere fluid, we compare two types of tracer-solvent interactions: (1) a hard-sphere-like interaction, and (2) a soft repulsion extending beyond the hard core designed via statistical mechanical theory to enhance tracer mobility at infinite dilution by suppressing coordination-shell structure [Carmer et al., Soft Matter 8, 4083-4089 (2012)]. For the latter case, we show that the mobility of surrounding solvent particles is also increased by addition of the soft repulsive interaction, which helps to rationalize the mechanism underlying the tracer's enhanced diffusivity. However, if multiple tracer surfaces are in closer proximity (as at higher tracer concentrations), similar interactions that disrupt local solvation structure instead suppress the position-dependent solvent dynamics.