Diffusion in a rough potential: Dual-scale structure and regime crossovers.

<title>Abstract</title> Diffusion in a "rough" potential parameterized by a reaction coordinate q is analyzed for systems that exhibit a coarse-scale structure with barrier height ΔU and period ℓ, superimposed with fine-scale "roughness" of barrier height ΔU′ and small period ℓ′ ≪ ℓ. Numerical solution of the Smoluchowski equation and analytical predictions identify distinct dynamical regimes as a function of the distance |Δq| = |q − q_E| from the stable equilibrium at q = q_E. The physical diffusivity D, set by dissipative effects, can be rescaled to an effective diffusivity D′ that accounts for the fine-scale roughness. This rescaling is strictly valid when |Δq| &lt; Δq_I ∝ (ΔU′/ℓ′ − ΔU/ℓ). Farther than a critical distance Δq_II ∝ ΔU/ℓ, the coarse-scale barriers control activated transport and the dynamics follow Kramers-like escape with an effective diffusivity D′ inferred from the reaction-coordinate trajectory. Closer to equilibrium, the coarse-scale structure induces two diffusive regimes separated by a crossover at Δq_III ∝ 1/ℓ: an initial regime with approximately constant D′ and a near-equilibrium regime where D′ decreases over time for |Δq| &lt; Δq_III. The effective diffusivity obtained here is sensitive to the estimation method used from time series, which depends solely on the fine-scale energy barrier. These results have implications for activated transport in complex media, including protein folding landscapes, colloidal stabilization, and self-assembly.

Chapter 4 - Nuclear magnetic resonance spectroscopy for protein structure, folding, and dynamics

Polymeric materials confining functional molecules are one of the most promising materials for designing nanodevices for energy conversion, e.g., solar cells, fuel cells, and artificial photosynthetic devices that are expected to provide a renewable energy resource. Charge transport (CT) and catalysis by redox molecules in polymeric solid materials are reviewed with a focus on a polyanion film, typically Nafion and other polymeric materials, containing excess water. CT in a polyanion film is evaluated based on the physical displacement (physical diffusion) and charge hopping mechanisms between redox molecules. The mechanism of CT is exhibited to depend on the structure and redox reaction of the center molecules, and the influencing factor on CT is discussed. For the polymeric solid reactor containing excess water, the physical data of CT and molecular transport in the bulk matrix are summarized to demonstrate that the electrochemical reaction in the solid reactor occurs similarly as in an aqueous solution. Recent progress in molecular catalysis for multielectron redox reactions with a focus on water oxidation, reduction of proton, and carbon dioxide is introduced, and the catalytic activity and mechanism in solution and polymeric matrixes are reviewed. A dye-sensitized solar cell was fabricated using polymeric solid materials containing excess organic solution as an electrolyte layer, and its performance similar to a liquid-type solar cell is discussed based on the physicochemical data in the polymeric solid materials. Recent approaches toward construction of an artificial photosynthetic system are reviewed, and, finally, concluding remarks and directions for future research are given.

Fundamental relationships between the thermodynamics and kinetics of protein folding were investigated using chain models of natural proteins with diverse folding rates by extensive comparisons between the distribution of conformations in thermodynamic equilibrium and the distribution of conformations sampled along folding trajectories. Consistent with theory and single-molecule experiment, duration of the folding transition paths exhibits only a weak correlation with overall folding time. Conformational distributions of folding trajectories near the overall thermodynamic folding/unfolding barrier show significant deviations from preequilibrium. These deviations, the distribution of transition path times, and the variation of mean transition path time for different proteins can all be rationalized by a diffusive process that we modeled using simple Monte Carlo algorithms with an effective coordinate-independent diffusion coefficient. Conformations in the initial stages of transition paths tend to form more nonlocal contacts than typical conformations with the same number of native contacts. This statistical bias, which is indicative of preferred folding pathways, should be amenable to future single-molecule measurements. We found that the preexponential factor defined in the transition state theory of folding varies from protein to protein and that this variation can be rationalized by our Monte Carlo diffusion model. Thus, protein folding physics is different in certain fundamental respects from the physics envisioned by a simple transition-state picture. Nonetheless, transition state theory can be a useful approximate predictor of cooperative folding speed, because the height of the overall folding barrier is apparently a proxy for related rate-determining physical properties.

3.12 The Folding of Repeat Proteins

Onsager's formalism of nonequilibrium Thermodynamics is employed to analyze competitive diffusion processes pertaining to charge transport through redox polymer electrodes. The validity of reciprocity relations is demonstrated for electron hopping in the case of [Ru(NH3)6]3+/2+ couple on Nafion coated Glassy Carbon (GC) electrodes. The phenomenological coefficients pertaining to electron hopping and physical diffusion are estimated using the experimental data of Cp2FeTMA2+/1+ on Nafion coated GC electrodes. The redox conductivity and transport numbers are expressed in terms of Onsager's coefficients and the calculation of the phenomenological coefficients directly from the charge propagation behavior is demonstrated. The expression for entropy production is shown to yield new insights regarding the interpretation of diffusion coefficients in redox polymeric systems.

The present study aims to estimate effective diahaline turbulent salinity fluxes and diffusivities in numerical model simulations of estuarine scenarios. The underlying method is based on a quantification of salinity mixing per salinity class, which is shown to be twice the turbulent salinity transport across the respective isohaline. Using this relation, the recently derived universal law of estuarine mixing, predicting that average mixing per salinity class is twice the respective salinity times the river run‐off, can be directly derived. The turbulent salinity transport is accurately decomposed into physical (due to the turbulence closure) and numerical (due to truncation errors of the salinity advection scheme) contributions. The effective diahaline diffusivity representative for a salinity class and an estuarine region results as the ratio of the diahaline turbulent salinity transport and the respective (negative) salinity gradient, both integrated over the isohaline area in that region and averaged over a specified period. With this approach, the physical (or numerical) diffusivities are calculated as half of the product of physical (or numerical) mixing and the isohaline volume, divided by the square of the isohaline area. The method for accurately calculating physical and numerical diahaline diffusivities is tested and demonstrated for a three‐dimensional idealized exponential estuary. As a major product of this study, maps of the spatial distribution of the effective diahaline diffusivities are shown for the model estuary.

Dynamics of COVID-19 spreading model with social media public health awareness diffusion over multiplex networks: Analysis and control

Asymmetric diffusion has been observed in different contexts, from transport in stratified and fractured porous media to diffusion of ions and macromolecular solutes through channels in biological membranes. Experimental and numerical observations have shown that diffusion is facilitated in the direction of positive void fraction (i.e., porosity) gradients. This work uses the method of volume averaging in order to obtain effective medium equations for systems with void fraction gradients for passive and diffusive mass transport processes. The effective diffusivity is computed from the solution of an associated closure problem in representative unit cells that allow considering porosity gradients. In this way, the results in this work corroborate previous findings showing that the effective diffusivity exhibits important directional asymmetries for geometries with void fraction gradients. Numerical examples for simple geometries (a section with an obstacle and a channel with varying cross section) show that the diffusion asymmetry depends strongly on the system configuration. The magnitude of this dependence can be quantified from the results in this work.

Effects of heat diffusion and turbulence on detonation development of hydrogen/air mixtures under engine-relevant conditions

Thermodynamic and transport properties of hyperstoichiometric uranium dioxide,UO2+x, constitute a key issue in the application of this material for nuclear fuel since they are closely related to many chemical and physical processes, e.g., diffusion or creep. Starting from a point defect model for UO2+x developed by the authors in a preceding work[1] and quantitatively consistent with some literature experimental measurements of deviation from stoichiometry [2] and electrical conductivity[3],the oxygen and uranium self diffusion processes have been studied in order to appreciate the influence of defects involved in the model and particularly, the two Willis complexes i.e., 2(Oi"Oi''Vȯ)" and 2(Oi"O1''Vȯ)4''. Such a result leads the way to a better understanding of the mechanisms involved in diffusion processes and also helps to define more accurately the nature, as well as the type of the preferential interactions between diffusing impurities and the defects responsible for these transport properties.

Summary When hydrogen is stored underground in porous media, mixing of remaining hydrocarbon gas with hydrogen occurs. One of the major processes enhancing gas mixing is molecular diffusion, which depends on subsurface conditions (pressure and temperature), phase saturation, gas composition, and rock properties (porosity and tortuosity). Also, molecular diffusion of hydrogen through water-saturated caprock might lead to hydrogen losses during underground storage. Limited data is available describing the hydrogen-methane diffusion through reservoir rocks. Moreover, minor attention was given to the influence of temperature and water saturation on effective diffusion. To evaluate these effects, a series of experiments were carried out using an unsteady state method with fixed volumes. In this experimental setup, methane diffusing into a hydrogen-filled view cell is measured using infrared light spectroscopy. Diffusion through 100% water-saturated rock was measured using the pressure decay method. In this experiment, the partial pressure of the gas diffusing into saturated rock was measured and converted to concentration change. 3D numerical models were constructed to determine the diffusion coefficients by matching observed concentration changes. The measured bulk and effective hydrogen-methane diffusion coefficients within the temperature range of 28–100°C follow the kinetic gas theory. In both sets of experiments, the diffusion coefficient is proportional to temperature to the power of 3/2. Deviations from predicted diffusion coefficient values are smaller than 5%. Diffusion of gases (nitrogen, hydrogen, and methane) in water and formation brine was measured and found to be several orders of magnitude smaller than gas-gas diffusion. Hydrogen diffusion in 100% water-saturated Berea rock revealed a slow diffusion process. This indicates minor diffusive transport of hydrogen through water-saturated rocks (e.g., caprock shales). The results of effective hydrogen-methane diffusion measurements through partially saturated rock samples (40% and 60% water saturation) prove that water reduces effective pore space for gas mixing and, thus, the diffusion coefficient reduces with increasing water saturation. The data show that the effective tortuosity needs to increase with water saturation increase. Also, it was found that gas diffusivity is affected by saturation hysteresis. Several experiments were performed with a core sample saturated with the imbibition process revealing slower diffusion through a core plug in comparison to the drainage saturation process. Having obtained reliable hydrogen effective diffusion coefficients through saturated rock samples, the analytical equations and numerical models were developed to quantify diffusive hydrogen losses into the caprock. It is estimated that the amount of hydrogen losses due to diffusion accounts for 0.09% of cushion gas volume for case-study reservoirs during 30 years of underground hydrogen storage (UHS) operations. It was also shown that the introduction of hydrogen diffusion into the full-field simulation model might not be plausible due to the requirement of small grid sizes to minimize numerical dispersion effects. The study contributes a high-quality data set of effective diffusion coefficients with temperature, pressure, and water saturation. It is crucial to assess hydrogen losses through caprock and hydrogen-hydrocarbon gas mixing within the reservoir between high- and low-permeability layers. We also show an example of hydrogen loss assessment and point out the slow process of diffusion into caprock.

The objective of this work was to evaluate the influence of the amount of broken kernels in relation to the whole grains (0, 15, and 30%) and moisture content (5, 10, and 15% wet basis) on some physical properties of soybeans (bulk density, porosity, and angle of repose) using response surface methodology. In addition, the effective thermal diffusivity (αef) was determined and empirical models were proposed to improve equipment design and drying and storage operations of soybeans. The results indicated that the moisture content changes and the addition of broken kernels in the whole soybeans caused increases in bulk density (from 673 ± 2 to 693 ± 3 kg/m3) and angle of repose (from 26.6 ± 0.3 to 31.2 ± 0.3 °) and decrease in porosity (from 45.1 ± 0.1 to 41.3 ± 0.4%). The effective thermal diffusivity values increased with increasing moisture content and the addition of broken kernels, in the range of 5.7 × 10−8 to 9.5 × 10−8 m2/s. The proposed empirical model for determination of effective thermal diffusivity was predictive and significant (p &lt; .05).Practical applicationsThe presence of split and broken soybeans has been a problem due to the lack of uniformity of stored grain mass, causing significant loss of quality and difficulty in operational handling. In this way, the knowledge of the engineering properties of soybeans is a key factor in determining the design of the drying, storage, aeration, processing, and handling systems. Bulk density is needed for the design of drying and aeration systems. Porosity can affect the rate of heat and mass transfer during aeration and drying operations and the design of hoppers for processing machinery and bulk grain storage requires angle of repose data. In addition, the thermal diffusivity elutes the heating rate of grains stored in steel silos.

Interface‐resolved direct numerical simulations (DNSs) of chemical vapor infiltration (CVI) have been performed over a range of furnace‐operating conditions (Thiele moduli) and for practical woven preform geometries. A level‐set method is used to resolve the geometry of the initial preform at tow scale. The interface between the vapor and solid phase is then evolved in time through the entire CVI densification cycle, fully resolving the time‐varying topology between the two phases. In contrast to previous level‐set methods for CVI simulation, the physical reaction and diffusion processes govern the level‐set movement in the current approach. The surface deposition kinetics is described by the usual one‐step model. In this paper, the DNS data are used to study the evolving porosity, surface‐to‐volume ratio, and flow infiltration properties (permeability and effective diffusivities). Comparisons are made to popularly‐assumed structure functions and the standard, Kozeny–Carmen porous media model commonly employed in modeled CFD simulations of CVI. The virtual DNS experiments reveal a Thiele modulus and preform geometry (fabric layup) dependence which the existing microstructural and infiltration models are not able to describe throughout the entire densification process. The DNS‐based, woven geometry‐specific correlations can be applied directly to mean‐field, furnace‐scale CFD simulations.

Optimizing the water management in proton exchange membrane fuel cells (PEMFCs) is paramount to improving their performance at high current densities. Numerical models describing the physical processes in the PEMFC are an important tool to analyze and understand experimental results and optimize the performance with respect to material properties and operating conditions. Macro-scale models of PEMFCs describing two-phase flow have previously been developed (1, 2). These models rely on effective transport properties and morphological information of the porous layers, such as pore size distribution (PSD), to accurately describe the physical processes. These properties are often estimated using empirical correlations (1). Microstructural modeling provides a feasible alternative to estimate the required transport properties based on the morphology of the porous layers. Microstructural models describing gas transport and liquid water intrusion have previously been developed for gas diffusion layers (GDLs) (3) and micro-porous layers (MPLs) (4). For catalyst layers (CLs), microstructural models describing the transport and electrochemical reactions under dry conditions are available in literature (5, 6). However, very few studies (7, 8) have accounted for liquid water intrusion in the CLs and the corresponding effect on the transport properties and electrochemical performance. The aim of this work is to develop numerical models to simulate liquid water intrusion in the fuel cell CLs and study the corresponding effect on the transport properties and performance. A focused ion beam-scanning electron microscopy (FIBSEM) CL reconstruction is used to study gas and charge transport and liquid water intrusion in the CL. Liquid water intrusion in the CL is simulated using a full morphology based model. In-situ μ-CT data was used to validate the liquid water intrusion model. The validated model will be used to simulate liquid water intrusion in CLs with different modes of injection such as nucleation (8), PSD based (7) and boundary based (9). The obtained saturation distributions in the CLs would be used as meshes for continuum simulations to study the changes in the effective diffusivity and electrochemical performance of the CLs. For the electrochemical simulations, charge transport is simulated in an ionomer film and oxygen transport is simulated in the ionomer, pores and liquid water. Figure 1a shows a schematic of a single pore with ionomer film and the reaction boundary. Since FIBSEM does not provide any information about the ionomer, carbon or platinum, it is assumed that the ionomer forms a thin film at pore-solid interface. This film is digitally reconstructed based on the composition of the CL. The reaction is simulated at the ionomer-solid interface assuming that the solid interface corresponds to platinum particles. The numerical framework for the microscale simulations has been developed in the open-source package OpenFCST (10). The current results show that the different modes of water injection result in different threshold saturations, i.e., the saturation at which percolating pore volume for gas transport is lost. The effective diffusivity of oxygen reduces with an increase in saturation. Electrochemical simulations on partially saturated CLs are underway.