Local Diffusion Coefficient Research Articles

Variations in Diffusion Coefficients on Equinox Days at Specified Critical Heights of the Ionosphere at the Equator

This study investigates the local time diffusion coefficient for stable and unstable ( , ) states at the equator (00), "the geographical latitude where the first peak of the magnetic equatorial trough in the ionosphere occurs," during the spring and fall equinoxes (March 21 and September 23). The findings show that the diffusion tensor in a steady state is completely real and has a magnitude equal to the speed of light in a steady state. But in the unsteady state, the diffusion tensor consists of two parts, real and imaginary. The diagonal elements of the real part tensor are of the size of the conductivity in the ionosphere and the elements of the imaginary part are of the size of the speed of sound with about the same magnitude. Furthermore, for all assumed conditions, the diffusion elements form the first peak of the magnetic equatorial trough at 6.00 am local time.

Receptor binding and tortuosity explain morphogen local-to-global diffusion coefficient transition

Morphogens are intercellular signaling molecules providing spatial information to cells in developing tissues to coordinate cell fate decisions. The spatial information is encoded within long-ranged concentration gradients of the morphogen. Direct measurement of morphogen dynamics in a range of systems suggests that local and global diffusion coefficients can differ by orders of magnitude. Further, local diffusivity can be large, which would potentially abolish any concentration gradient rapidly. Such observations have led to alternative transport models being proposed, including transcytosis and cytonemes. Here, we show that accounting for tissue architecture combined with receptor binding is sufficient to hinder the diffusive dynamics of morphogens, leading to an order of magnitude decrease in the effective diffusion coefficient from local to global scales. In particular, we built a realistic in silico architecture of the extracellular spaces of the zebrafish brain using light and electron microscopy data. Simulations on realistic architectures demonstrate that tortuosity and receptor binding within these spaces are sufficient to reproduce experimentally measured morphogen dynamics. Importantly, this work demonstrates that hindered diffusion is a viable mechanism for gradient formation, without requiring additional regulatory control.

Capturing Hydrated Vanadium Ion Dynamics in Ionomer Nanocomposites Used for Redox Flow Batteries.

Herein, we employed high-flux backscattering spectroscopy to capture for the first time the motions of hydrated vanadyl ions in ionomer nanocomposites prepared by both solution-cast and in situ sol-gel condensation methods. Both local and jump diffusion coefficients of the hydrated vanadyl (VO2+) ions as well as the dynamic length scales of ion motions and the fraction of immobile hydrogen atoms were extracted from the scattering spectra. Notably, for solution-cast membranes, the jump and local diffusion coefficients of hydrated VO2+ ions were seen to decrease by over 10- and 4-fold, respectively, with the introduction of 10 mass % silica nanoparticles (SiNPs) compared to their neat counterparts. Further, the VO2+ diffusion coefficients were observed to decrease with thermal annealing, though the impact of annealing was less significant than that seen with the introduction of SiNPs. Finally, in general, thermal annealing and the introduction of SiNPs had no measurable impact on the fraction of immobile hydrogen atoms in both solution-cast and sol-gel ionomer nanocomposites. The data observed in this work, in conjunction with previous structural and chain dynamics studies on hydrated Nafion-SiNP nanocomposites, suggest that a combination of stiffening of the segmental dynamics as well as a decrease in available sulfonic acid groups facilitating transport leads to an overall decrease in mobility of vanadium ions in these ionomer nanocomposites.

Random walks in correlated diffusivity landscapes

In recent years, several experiments have highlighted a new type of diffusion anomaly, which was called Brownian yet non-Gaussian diffusion. In systems displaying this behavior, the mean squared displacement of the diffusing particles grows linearly in time, like in a normal diffusion, but the distribution of displacements is non-Gaussian. In situations when the convergence to Gaussian still takes place at longer times, the probability density of the displacements may show a persisting peak around the distribution’s mode, and the pathway of convergence to the Gaussian is unusual. One of the theoretical models showing such a behavior corresponds to a disordered system with local diffusion coefficients slowly varying in space. While the standard pathway to Gaussian, as proposed by the Central Limit Theorem, would assume that the peak, under the corresponding rescaling, smoothens and lowers in course of the time, in the model discussed, the peak, under rescaling, narrows and stays sharp. In the present work, we discuss the nature of this peak. On a coarse-grained level, the motion of the particles in the diffusivity landscape is described by continuous time random walks with correlations between waiting times and positions. The peak is due to strong spatiotemporal correlations along the trajectories of diffusing particles. Destroying these correlations while keeping the temporal structure of the process intact leads to the decay of the peak. We also note that the correlated CTRW model reproducing serial correlations between the waiting times along the trajectory fails to quantitatively reproduce the shape of the peak even for the decorrelated motion, while being quite accurate in the wings of the PDF. This shows the importance of high-order temporal correlations for the peak’s formation.Graphical abstract

Molecular interaction-based reaction-diffusion coupling within catalytic nanochannels

The nanoconfinement effect on the inner reaction–diffusion coupling is significant, while the underlying common principle remains ambiguous, which is mainly attributed to the lack of a feasible model. Herein, the dynamic reaction density functional theory (DRxDFT) is extended, by involving the position-dependent local diffusion coefficient, to investigate the reaction–diffusion coupling of an irreversible unimolecular isothermal reaction within catalytic nanochannels. The local diffusion coefficient is jointly determined by the pore size and local density. For demonstration, the reaction–diffusion in a rectangle nanochannel is studied by means of DRxDFT, and the predicted steady-state productivities are in excellent agreement with reactive molecular dynamics simulations. The DRxDFT is further applied to analyze the RD coupling within generic catalytic nanochannels. Towards this end, a microscopic effectiveness factor is introduced to identify the dominant role in the competition between reaction and diffusion, with which it is found that the effect of nanochannel size on productivity exhibits a generic opposite trend under reaction-dominated and diffusion-dominated conditions. This work provides a microscopic insight into the coupling of reaction and diffusion in nanoconfinement.

Surface diffusion in narrow channels on curved domains.

We study the transport properties of diffusing particles restricted to confined regions on curved surfaces. We relate particle mobility to the curvature of the surface where they diffuse and the constraint due to confinement. Applying the Fick-Jacobs procedure to diffusion in curved manifolds shows that the local diffusion coefficient is related to average geometric quantities such as constriction and tortuosity. Macroscopic experiments can record such quantities through an average surface diffusion coefficient. We test the accuracy of our theoretical predictions of the effective diffusion coefficient through finite-element numerical solutions of the Laplace-Beltrami diffusion equation. We discuss how this work contributes to understanding the link between particle trajectories and the mean-square displacement.

Molecular-scale insights into confined clindamycin in nanoscale pores of mesoporous silica.

Clindamycin is an antibiotic used to treat a variety of bacterial infections. The sustained release of clindamycin from the drug carrier is an important strategy to prolong the effective antibacterial duration. In this work, the microstructure and dynamics of clindamycin confined into the nanopores of mesopore silica with different pore sizes were studied using molecular dynamics simulation. It is found that there is a layering behavior for clindamycin distribution as a function of distance from the pore surface to the pore center with preferred location near the surface of the nanopore. The radial distribution function between carbonyl oxygen and the silanol groups shows the highest intensity of the first peak with the preferred orientation of carbonyl oxygen pointing toward the pore surface, which suggests the strong interaction between the carbonyl oxygen and the silanol groups on the pore surface. The higher local diffusion coefficients for the clindamycin molecules near the pore surface can be found. In addition, the presence of water can lead to the shift of clindamycin distribution away from the surface and promote the local diffusion of clindamycin near the pore surface. The information in this work will provide the microscopic understanding for the design of the drug carriers for the controlled release of clindamycin.

Multiscale measurements of gas diffusion coefficient of coal using counter-diffusion and image-based methods

Coal seam gas (CSG), also known as Coalbed Methane (CBM), is an important natural gas resource owing to its abundance and high energy density. During production, the gas desorbs from the coal matrix owing to pressure depletion. It then diffuses primarily within the micropores of the coal matrix toward the coal fractures and then migrates to the wellbore. Therefore, diffusivity plays a significant role in the gas production process, and this process needs to be explicitly characterized. However, experimental gas diffusion measurements are commonly based on coal particles rather than bulk coal samples, and thus, the impacts of coal fractures are typically neglected. This study aims to test the diffusion coefficients of fractured and tight bulk coal samples to provide insights into gas diffusion within the different pores and fractured structures. Diffusion coefficients of bulk coal samples were measured at different diffusion times, confining pressures, and gas pressures using counter-diffusion experiments. The results show that the bulk diffusion coefficient varies with confining pressure and gas pressure, which demonstrates the impacts of internal pore/fracture structure of coal on the diffusivity. The time-dependent diffusion coefficient results show that the diffusion coefficients became constant after 24 h, ranging from 1 × 10−10 m2/s to 2 × 10−10 m2/s. Local diffusion coefficients were obtained using X-ray micro-computed tomography images of krypton gas diffusing through a coal sample. These were higher than the diffusion coefficients of bulk samples, which were in the order of ∼10−9 m2/s. The variations in local diffusion coefficients indicated the heterogeneity of coal, thereby validating the importance of both local and bulk diffusion measurements in coal characterization.

Measurement of Protein and Nucleic Acid Diffusion Coefficients Within Biomolecular Condensates Using In-Droplet Fluorescence Correlation Spectroscopy.

Liquid-liquid phase separation of protein and RNA complexes into biomolecular condensates has emerged as a ubiquitous phenomenon in living systems. These protein-RNA condensates are thought to be involved in many biological functions in all forms of life. One of the most sought-after properties of these condensates is their dynamical properties, as they are a major determinant of condensate physiological function and disease processes. Measurement of the diffusion dynamics of individual components in a multicomponent biomolecular condensate is therefore routinely performed. Here, we outline the experimental procedure for performing in-droplet fluorescence correlation spectroscopy (FCS) measurements to extract the diffusion coefficient of individual molecules within a biomolecular condensate in vitro. Unlike more common experiments such as fluorescence recovery after photobleaching (FRAP), where data interpretation is not straightforward and strictly model dependent, FCS offers a robust and more accurate way to quantify biomolecular diffusion rates in the dense phase. The small observation volume allows FCS experiments to report on the local diffusion coefficient within a spatial resolution of <1μm, making it ideal for probing spatial inhomogeneities within condensates as well as variable dynamics within subcompartments of multiphasic condensates.

Ambipolar Diffusion in the Lower Solar Atmosphere: Magnetohydrodynamic Simulations of a Sunspot

Magnetohydrodynamic (MHD) simulations of the solar atmosphere are often performed under the assumption that the plasma is fully ionized. However, in the lower solar atmosphere a reduced temperature often results in only the partial ionization of the plasma. The interaction between the decoupled neutral and ionized components of such a partially ionized plasma produces ambipolar diffusion. To investigate the role of ambipolar diffusion in propagating wave characteristics in the photosphere and chromosphere, we employ the Mancha3D numerical code to model magnetoacoustic waves propagating through the atmosphere immediately above the umbra of a sunspot. We solve the nonideal MHD equations for data-driven perturbations to the magnetostatic equilibrium and the effect of ambipolar diffusion is investigated by varying the simulation to include additional terms in the MHD equations that account for this process. Analyzing the energy spectral densities for simulations with/without ambipolar diffusion, we find evidence to suggest that ambipolar diffusion plays a pivotal role in wave characteristics in the weakly ionized low density regions, hence maximizing the local ambipolar diffusion coefficient. As a result, we propose that ambipolar diffusion is an important mechanism that requires careful consideration into whether it should be included in simulations, and whether it should be utilized in the analysis and interpretation of particular observations of the lower solar atmosphere.

Skin permeability prediction with MD simulation sampling spatial and alchemical reaction coordinates

A molecular-level understanding of skin permeation may rationalize and streamline product development, and improve quality and control, of transdermal and topical drug delivery systems. It may also facilitate toxicity and safety assessment of cosmetics and skin care products. Here, we present new molecular dynamics simulation approaches that make it possible to efficiently sample the free energy and local diffusion coefficient across the skin’s barrier structure to predict skin permeability and the effects of chemical penetration enhancers. In particular, we introduce a new approach to use two-dimensional reaction coordinates in the accelerated weight histogram method, where we combine sampling along spatial coordinates with an alchemical perturbation virtual coordinate. We present predicted properties for 20 permeants, and demonstrate how our approach improves correlation with ex vivo/in vitro skin permeation data. For the compounds included in this study, the obtained log KPexp-calc mean square difference was 0.9 cm2 h−2.

Quasilinear theory for inhomogeneous plasma

This paper presents quasilinear theory (QLT) for a classical plasma interacting with inhomogeneous turbulence. The particle Hamiltonian is kept general; for example, relativistic, electromagnetic and gravitational effects are subsumed. A Fokker–Planck equation for the dressed ‘oscillation-centre’ distribution is derived from the Klimontovich equation and captures quasilinear diffusion, interaction with the background fields and ponderomotive effects simultaneously. The local diffusion coefficient is manifestly positive-semidefinite. Waves are allowed to be off-shell (i.e. not constrained by a dispersion relation), and a collision integral of the Balescu–Lenard type emerges in a form that is not restricted to any particular Hamiltonian. This operator conserves particles, momentum and energy, and it also satisfies the$\smash {H}$-theorem, as usual. As a spin-off, a general expression for the spectrum of microscopic fluctuations is derived. For on-shell waves, which satisfy a quasilinear wave-kinetic equation, the theory conserves the momentum and energy of the wave–plasma system. The action of non-resonant waves is also conserved, unlike in the standard version of QLT. Dewar's oscillation-centre QLT of electrostatic turbulence (Phys. Fluids, vol. 16, 1973, p. 1102) is proven formally as a particular case and given a concise formulation. Also discussed as examples are relativistic electromagnetic and gravitational interactions, and QLT for gravitational waves is proposed.

Robust Interior Penalty Discontinuous Galerkin Methods

A new variant of the IPDG method is presented, involving carefully constructed weighted averages of the gradient of the approximate solution. The method is shown to be robust even for the most extreme simultaneous local mesh, polynomial degree and diffusion coefficient variation scenarios, without resulting into unreasonably large penalization. The new IPDG method, henceforth termed as robust IPDG (RIPDG), offers typically significantly better error behaviour and conditioning than the standard IPDG method when applied to scenarios with strong mesh/polynomial degree/diffusion local variation, especially when the underlying approximation space does not contain a sufficiently rich conforming subspace. The latter is of particular importance in the context of IPDG methods on polygonal/polyhedral meshes. On the other hand, when using uniform meshes, constant polynomial degree for problems with constant diffusion coefficients the RIPDG method is identical to the classical IPDG. Numerical experiments indicate the favourable performance of the new RIPDG method over the classical version in terms of conditioning and error.

New Framework for Computing a General Local Self-Diffusion Coefficient Using Statistical Mechanics.

Widely applicable, modified Green-Kubo expressions for the local diffusion coefficient (Dl) are obtained using linear response theory. In contrast to past definitions in use, these expressions are statistical mechanical results. Molecular simulations of systems with anisotropic diffusion and an inhomogeneous density profile confirm the validity of the results. Diffusion coefficients determined from different expressions in terms of currents and velocity correlations agree in the limit of large systems. Furthermore, they apply to arbitrarily small local regions, making them readily applicable to nanoscale and inhomogeneous systems where knowledge of Dl is important.

Diffusion of molecules through nanopores under confinement: Time-scale bridging and crowding effects via Markov state model

Passive transport of molecules through nanopores is characterized by the interaction of molecules with pore internal walls and by a general crowding effect due to the constricted size of the nanopore itself, which limits the presence of molecules in its interior. The molecule-pore interaction is treated within the diffusion approximation by introducing the potential of mean force and the local diffusion coefficient for a correct statistical description. The crowding effect can be handled within the Markov state model approximation. By combining the two methods, one can deal with complex free energy surfaces taking into account crowding effects. We recapitulate the equations bridging the two models to calculate passive currents assuming a limited occupancy of the nanopore in a wide range of molecular concentrations. Several simple models are analyzed to clarify the consequences of the model. Eventually, a biologically relevant case of transport of an antibiotic molecule through a bacterial porin is used to draw conclusions (i) on the effects of crowding on transport of small molecules through biological channels, and (ii) to demonstrate its importance for modelling of cellular transport.

Prediction of local diffusion coefficient based on images of fractured coal cores

Diffusion is a transport phenomenon in coal that plays a significant role in the productivity of coal seam gas (CSG) reservoirs. The diffusion coefficient quantifies the extent of gas diffusion in a coal sample. Diffusion coefficient is commonly measured as a bulk value for a core; however, it can vary spatially in a core, and its local variation is commonly ignored. We present an automated method to calculate local diffusion coefficients of krypton in a coal core using 3D microcomputed X-ray tomography (micro-CT) images. Fractures are identified from greyscale micro-CT images automatically and compared with the conventional watershed segmentation method. Local diffusion coefficients within the matrix are calculated automatically considering different fluid states. As gas within a coal core may be in the free state or adsorbed state, our method calculates the total diffusion coefficient taking into account the state of the fluid. We observe a variation of diffusion coefficient with time suggesting that as the gas accesses different regions of the pore matrix the diffusion rate changes. 3D diffusion coefficient maps are generated from the automated calculation, which shows the heterogeneity of the coal sample. The fractions of free and adsorbed gases are calculated, which allows further analysis of their individual impact on transport. Additionally, the proposed method can be applied to other fractured materials for automated diffusion coefficient measurements.

Fractal microstructure effects on effective gas diffusivity of a nanoporous medium based on pore-scale numerical simulations with lattice Boltzmann method

The interaction between gas diffusion and complex microstructures of a nanoporous medium is important to gas diffusion in shale formation, but this interaction is complex and has not been fully understood. Those approaches based on fractal theory can well describe the fractal multiscale microstructure with simple boundaries. The lattice Boltzmann method (LBM) can consider the effects of complex microstructures at one scale. This study proposes a combination approach of fractal theory and LBM to simulate the gas diffusion process in fractal multiscale microstructures of a nanoporous medium. In this study, the gas diffusion in a complex microstructure at base scale is numerically simulated by the LBM and the gas diffusion in finer microstructures is described through a diffusion equation with a local gas diffusion coefficient. First, a microstructure of a nanoporous medium is reconstructed by a random reconstruction algorithm. Then, a local gas diffusion coefficient is proposed based on fractal theory to consider the effects of coupling molecular diffusion and Knudsen diffusion with the fractal structures of a nanoporous medium on the gas diffusion in finer microstructures. This local gas diffusion coefficient is validated by experimental data and introduced into the governing equation of gas diffusion. The LBM simulation is verified with experimental data and two other model results on the effective gas diffusivity of a nanoporous medium. Finally, key parameters for the effective gas diffusivity of a nanoporous medium are identified through sensitivity analysis. It is found that the effective gas diffusivity in a microstructure is higher for a smaller range of Knudsen number. Bigger pore diameter fractal dimension and smaller tortuosity fractal dimension represent lower gas diffusion resistance and have higher effective gas diffusivity. This combination approach provides a powerful tool to estimate the effective gas diffusivity in a complex nanoporous medium.

Complex spatiotemporal dynamics of a harvested prey–predator model with Crowley–Martin response function

The formation of spatiotemporal patterns is one of the most important part in the prey–predator dynamical system. In this paper, we investigate the local dynamics as well as the Turing structure through diffusion-driven instability by taking more general Crowley–Martin response function in the prey–predator system with the effect of linear harvesting of prey and predator. All the feasible equilibrium points are extracted. Boundedness, persistence, local and global stability, and Hopf bifurcation are established for some suitable parametric conditions. The parametric space for which the Turing spatial structure takes place is found out. Different kinds of patterns are demonstrated depending on the ecological parameters of the local system and diffusion coefficients.

Homogenization of Continuum-Scale Transport Properties from Molecular Dynamics Simulations: An Application to Aqueous-Phase Methane Diffusion in Silicate Channels.

Silica-based materials including zeolites are commonly used for wide-ranging applications including separations and catalysis. Substrate transport rates in these materials can significantly influence the efficiency of such applications. Two factors that contribute to transport rates include (1) the porosity of the silicate matrix and (2) nonbonding interactions between the diffusing species and the silicate surface. These contributions generally emerge from disparate length scales, namely, "microscopic" (roughly nanometer-scale) and "macroscopic" (roughly micron-scale), respectively. Here, we develop a simulation framework to estimate the simultaneous impact of these factors on methane mass transport in silicate channels. Specifically, we develop a model of methane transport using homogenization theory to obtain transport parameters valid at length scales of hundreds to thousands of nanometers. These parameters implicitly reflect interactions taking place at fractions of a nanometer. The inputs to the homogenization analysis are data from extensive molecular dynamics simulations that incorporate atomistic-scale interactions, processed to yield local diffusion coefficients and mean force potentials. With this model, we demonstrate how nuances in silicate hydration and silica/methane interactions impact methane diffusion rates in silicate materials, including the effects of silicate surface chemistry such as the presence of silanol groups. The molecular dynamics simulations indicate that methane diffusivity at the silica surface is lower than the bulk-like rates observed at the center of channels of sufficient width. However, potentials of mean force generally evidence attractive methane/silica interactions that enhance diffusion overall. By simultaneously accounting for both of these effects, we show that the effective diffusion coefficient for the nanoporous silicate can be approximately double the value of estimates assuming fully bulk-like behavior in the channel. This study therefore demonstrates the importance of determining diffusion coefficients and potentials of mean force at an atomistic level when estimating transport properties in bulk materials. Importantly, we provide a simple homogenization framework to incorporate these molecular-scale attributes into bulk material transport estimates. This hybrid homogenization/molecular dynamics approach will be of general use for describing small-molecule transport in materials with detailed molecular interactions.

Characterization of Pectin-Based Gels: A 1H Nuclear Magnetic Resonance Relaxometry Study.

Rare sugars are monosaccharides and their derivatives that are not commonly found in nature. d-Allulose is a rare sugar that is C-3 epimer of fructose and presents an alternative to sucrose with potential health benefits. In this study, different amounts of sucrose, d-allulose, and soy protein isolate (SPI) were used to prepare a set of pectin gels. The effect of these ingredients on the gels was studied at both a molecular level, by 1H nuclear magnetic resonance (NMR) relaxometry, and a macroscopic level, through the assessment of viscoelastic properties as well as hardness and moisture content measurements. The NMR dispersion profiles were analyzed considering relaxation mechanisms associated with rotational and translational diffusion motions of mono- and disaccharides as well as bound water molecules. Significant variations of the local diffusion coefficient for the studied formulations were evidenced by the model fitting analysis. The viscosity trends observed within each group of samples having the same amount of SPI were mostly in agreement with the diffusion coefficients obtained from the NMR relaxometry. The observed discrepancies could be explained considering hardness and moisture content results, which put into evidence the fact that decreasing the moisture (mainly free water) affects the macroscopic properties of the systems, such as hardness and viscosity, but not the local diffusion processes probed by NMR relaxometry. These findings show the importance of combining both micro- and macroscopic information to analyze the different properties of food products.