Concentration Dependence Of Diffusion Coefficient Research Articles

Influence of concentration-dependent material properties on the fracture and debonding of electrode particles with core–shell structure

Core–shell electrode particle designs offer a route to improved lithium-ion battery performance. However, they are susceptible to mechanical damage such as fracture and debonding, which can significantly reduce their lifetime. Using a coupled finite element model, we explore the impacts of diffusion-induced stresses on the failure mechanisms of an exemplar system with an NMC811 core and an NMC111 shell. In particular, we systematically compare the implications of assuming constant material properties against using Li concentration-dependent diffusion coefficient and partial molar volume. With constant material properties, our results show that smaller cores with thinner shells avoid debonding and fracture regimes. When factoring in a concentration-dependent partial molar volume, the maximum values of tensile hoop stress in the shell are found to be significantly lower than those predicted with constant properties, reducing the likelihood of fracture. Furthermore, with a concentration-dependent diffusion coefficient, significant barriers to full electrode utilisation are observed due to reduced lithium mobility at high states of lithiation. This provides a possible explanation for the reduced accessible capacity observed in experiments. Shell thickness is found to be the dominant factor in precluding structural integrity once the concentration dependency is accounted for. These findings shed new light on the performance and effective design of core–shell electrode particles.

Machine learning-assisted measurement of lithium transport using operando optical microscopy

Diffusion coefficients of electrode materials are often determined using galvanostatic (GITT) or potentiostatic intermittent titration technique (PITT), electrochemical impedance spectroscopy (EIS) or cyclic voltammetry (CV). However, these methods require special care as for each, their formal derivations use quite restrictive assumptions. As an alternative, a machine learning model is developed to extend a previously proposed optical method of studying lithium transport by operando microscopy. The herein reported model enables the measurement of concentration-dependent diffusion coefficients. For this purpose, a python code is developed that determines concentration profiles from RGB images using support vector regression (SVR), a flexible machine learning tool. To evaluate the diffusion coefficient, an inverse Boltzmann-Matano concept is applied. Representing the diffusion coefficient with generalized Redlich-Kister polynomials, concentration profiles are predicted and fit to the measured data. The method is demonstrated here on the example of delithiation of LiMn2O4, but it can, in-principle, be extended to any other battery material showing significant optical response on lithiation, which most of them do.

Численное моделирование водородопроницаемости с концентрационной зависимостью коэффициента диффузии

The paper presents a nonlinear mathematical model of alloys hydrogen permeability for membrane technologies of high-purity hydrogen production. Diffusion processes in the material bulk are taken into account as well as physical and chemical phenomena at the surface: adsorption, desorption and relatively fast dissolution. The iterative computational algorithm and software in Scilab have been developed to model the hydrogen permeability with dynamic boundary conditions and concentration-dependent diffusion coefficient.

Refractive Laser Beam Measuring Diffusion Coefficient of Concentrated Battery Electrolytes

A thorough understanding of electrolyte transport properties is crucial in the development of alternative battery technology. As a key parameter, the diffusion coefficient offers important insights into the behavior of electrolytes, especially for fast charge of high-energy batteries. Existing methods of measurement are often limited by redox species or offer questionable accuracy due to side reactions and/or disruption of the diffusion profile. This work provides a novel optical method for measuring diffusion coefficients of liquid-phase concentrated battery electrolytes without electrochemical reactions. The method relies on the deflection of a refractive laser beam passing through an electrolyte of a minor concentration gradient in a triangular diffusion column. The diffusion coefficient, D, for a range of zinc sulfate electrolytes was successfully extracted by correlating the position of the laser beam to its concentration. Several other physicochemical properties of the same electrolytes are studied to correlate to the concentration-dependent diffusion coefficients, including viscosity, conductivity, and microstructure analysis based on vibrational spectroscopy (Infrared and Raman). Also included is the future application of the triangular column for in situ electrochemical measurements.

A novel measurement method for measuring the concentration-dependent mutual diffusion coefficients based on finite volume method

This paper presents a novel measurement method based on the finite volume method (FVM), which can be used for measuring the concentration-dependent mutual diffusion coefficient D(C) in binary solution. The measurement principle of D was derived by integrating the Fick’s second law in the control volume and establishing discretization equation. By simulating the diffusion process of binary solution, discussed the feasibility of this method. This new method can be used by an experimental system that can monitor changes in concentration distribution, such as optical interferometry. A set of 20 binary mixtures was tested to verify the method. The experimental results showed good agreement with and the literature, which verifies the accuracy of the method. The relative expanded combined uncertainty for the proposed method is estimated to 2.2 %. In addition, D(C) of LiTSFI aqueous solution was measured by the new method based on the digital holographic interferometry system at 288.15 K, 298.15 K and 308.15 K over the mass fraction range of 0 ∼ 0.447 (0 ∼ 2 mol/L). The temperature and concentration influences of D were discussed and a semi-empirical correlation was built.

Retrospective rationalization of disparities between the concentration dependence of diffusion coefficients obtained by boundary spreading and dynamic light scattering.

This study establishes the existence of substantial agreement between published results from traditional boundary spreading measurements (including synthetic boundary measurements in the analytical ultracenrifuge) on two globular proteins (bovine serum albumin, ovalbumin) and the concentration dependence of diffusion coefficient predicted for experiments conducted under the operative thermodynamic constraints of constant temperature and solvent chemical potential. Although slight negative concentration dependence of the translational diffusion coefficient is the experimentally observed as well as theoretically predicted, the extent of the concentration dependence is within the limits of experimental uncertainty inherent in diffusion coefficient measurement. Attention is then directed toward the ionic strength dependence of the concentration dependence coefficient ([Formula: see text]) describing diffusion coefficients obtained by dynamic light scattering, where, in principle, the operative thermodynamic constraints of constant temperature and pressure preclude consideration of results in terms of single-solute theory. Nevertheless, good agreement between predicted and published experimental ionic strength dependencies of [Formula: see text] for lysozyme and an immunoglobulin is observed by a minor adaptation of the theoretical treatment to accommodate the fact that thermodynamic activity is monitored on the molal concentration scale because of the constraint of constant pressure that pertains in dynamic light scattering experiments.

Modelling multicomponent gas diffusion and predicting the concentration-dependent effective diffusion coefficient of coal with application to carbon geo-sequestration

Diffusion of multicomponent gases, which is a complex transport mechanism in coalbed methane (CBM) reservoirs, needs to be accounted for in models of enhanced coalbed methane recovery (ECBM) and geological CO2 storage. We develop a numerical model that accounts for diffusion of free gas, diffusion of adsorbed gas, and competitive sorption. Our model also reflects adsorption-induced swelling and the impact of moisture. The simulator for modelling multicomponent gas diffusion is first validated by comparing its computed concentration field against those yielded by the general-purpose finite element solver COMSOL and the available analytical solutions. The model is then validated against the experimental measurements from the published literature. Subsequently, our simulator is used to model the CO2 Enhanced Coalbed Methane (CO2-ECBM) scenarios. The simulation results quantify the influence of different types of diffusion on the effective diffusion coefficient of coal. We analyse diffusion of methane and carbon dioxide that must be considered when modelling CBM reservoirs and analyse performance-based sensitivity of surface diffusion, moisture, matrix deformation, and pressure. Finally, the model is applied to a CO2 storage case. We calculate the CO2 storage volume and the equilibrium time under various pore pressures. The simulation shows that as pore pressure increases, the amount of CO2 stored increases and the equilibrium time decreases. Overall, this model can be applied to estimate the effective diffusion coefficient, to analyse the impact of rock and gas parameters on multicomponent gas diffusion, to provide insight into the physics of multiple gas transport in coal, and to estimate the feasibility of CO2 storage under various pore pressures.

Single Particle Model with electrolyte for simulating diffusion-limited dynamics during an external short in Li-ion batteries

To mitigate the consequences of a Li-ion battery system failure, a battery management system may only have a few minutes to respond. Rapidly discharging a battery cell significantly reduces the likelihood of thermal runaway, but requires currents comparable to an external short circuit (ESC). Ohmic heating accounts for a large part of the initial heat generation, so the discharge current should be regulated to prevent excessive temperatures. Therefore an accurate and fast model-based controller is needed to implement a fast and safe discharge. This work explores the ability of a Single Particle Model with electrolyte (SPMe) to capture the behavior of a cell undergoing an ESC. This work shows that a reduced-order model with concentration-dependent diffusion coefficients, that were parameterized under nominal operating conditions, can capture the mass transport limitations and resulting current and voltage drops. Additionally, the effects of changes that improve the numerical stability and robustness of the model and high-temperature phenomena on model error are discussed.

Measuring mutual diffusion coefficients in aqueous binary mixtures with unidimensional drying cells.

Chemical diffusion is a mass transport process caused by thermally generated motions of species. In a binary mixture, the diffusion of one species in one direction involves the diffusion of another species in the opposite direction, which corresponds to a single mutual diffusion coefficient. Here, we report a simple and general method to measure such coefficients in binary liquid mixtures, using the PNIPAM/water system as a study case. Experimentally, we show how a simple unidirectional drying cell coupled with a spatially-resolved characterization method such as Raman microscopy can yield concentration gradients developing in between two boundaries of known and constant chemical potential. Acquiring such gradients over time leads to a time-set that is shown to collapse to a single master curve using a change of variable. Such a scaling law offers a self-checking frame for solving analytically the diffusion-advection equation. As a result, we show that a simple analytical formula relates the measured concentration gradient with the concentration-dependent mutual diffusion coefficient. In the PNIPAM/water system, the mutual diffusion coefficient sharply decreases at low water content. Our work thus highlights the importance of considering the concentration-dependence of the mutual diffusion coefficient in complex aqueous solutions and provides a method to measure it.

Improved Subcutaneous Delivery of Ketoconazole Using EpiDerm and HSPiP Software-Based Simulations as Assessed by Cell Viability, Cellular Uptake, Permeation, and Hemolysis In Vitro Studies.

Ketoconazole (KETO) is the drug of choice to control local, systemic, and resistant types of fungal infections. Subcutaneous (sub-Q) delivery offers several benefits. The present study investigated the sub-Q delivery of KETO using HSPiP software based on optimized concentrations of dimethylacetamide (DMA) in binary solvents (DMA + water), in vitro cellular uptake (J774A.1) assays, cellular toxicity (L929), and in vitro hemolysis studies. Results showed that the estimated permeation coefficient (9.6 × 10-3 cm/h) and diffusion coefficient (3.9 × 10-3 cm2/h) of KETO (22.3 mg) in KF3 (300 mg of DMA + water) across EpiDerm were relatively higher as compared to the other formulations [KF1 (11.2 and 150 mg as KETO and DMA, respectively) and KF2 [(22.3 and 300 mg as KETO and DMA, respectively)] due to the increased content of DMA and KETO. HSPiP simulated and predicted the impact of constant and variable diffusion coefficients on the percent drug absorption across EpiDerm and the time needed to achieve equilibrium. The concentration-dependent diffusion coefficient fed into HSPiP predicted that the drug absorption and permeation values were linearly dependent on the square root of time. The HSPiP predicted permeation flux values from KF3, KF2, and KF1 across the EpiDerm were 4.07 × 10-6, 4.01 × 10-6, and 1.1 × 10-6 g/cm2/s, respectively, at respective D range values. The selected K30G (324 mOsm/Kg) showed an optimal pH (6.9) and minimum drug loss (0.01%) over a period of 1 month at room temperature. KG30 was found to be less toxic to normal L292 cells and caused maximum cytotoxicity to candida cells residing within infected macrophage cells (J774A.1 incubated for 24 h), which was attributed to the slow diffusion of K30G compared to DS (the drug solution with an equivalent concentration). KG30 elicited substantial internalization with candida albicans (MTCC 4748) compared to the control group (24 h). Lastly, in vitro hemolysis studies (1 and 5 μg/mL) corroborated the safety of K30G for sub-Q delivery. Therefore, this new formulation and approach for delivering KETO is a promising alternative to conventional products to control fungal infections and, thus, should be further studied in vivo.

Diffusion-limited C-rate: A criterion of rate performance for lithium-ion batteries

Rate performance is one of the important indexes of lithium-ion batteries. However, the discharge capacity would sometimes collapse after a critical C-rate, which is related to a classic concept termed the diffusion-limited C-rate (DLC). In this work, DLC is revisited using the Pseudo-Two-Dimensional model. The DLC analytical model is improved by incorporating the concentration-dependent liquid diffusion coefficient and shows good effectiveness compared with the simulation results. Subsequently, the impact of rate-limiting factors on the rate performance is examined to determine the effective scope of the proposed DLC model. Based on the adjustment of resistance ratios and time constant ratios of different kinetic processes, we find that the rate performance below DLC is hardly limited by electronic transports and charge transfer processes while the discharge capacity below DLC may be severely decayed if the solid-state diffusion in the electroactive particles is too slow. DLC helps identify the ‘knee’ on discharge capacity curves with discharge C-rate, which is a criterion of rate performance in some scenarios.

Optical measurement of concentration-dependent diffusion coefficient by tracing diffusion image width

ObjectiveRepeated experiments at different concentrations are necessary to measure the concentration-dependent liquid diffusion coefficient D(C), this process is arduous and time consuming using traditional methods. MethodsIn order to overcome the limitation, the self-designed liquid-core cylindrical lens were used as the diffusion cell and imaging element, considering one observed altitude on the focal plane of the self-designed liquid-core cylindrical lens, the variation in the diffusion image width reflects the experimental time-varying concentration profile Cez, t), D(C) over the whole concentration range was calculated by the comparison between calculated concentration profiles Cn(z, t)s and above experimental values by changing the observed altitudes. ResultThe D(C) of urea aqueous solution was measured with D(C) = 1.3872 × (1–0.0399 ×C-0.0031 ×C2-0.0002 ×C3) × 10−5 cm2/s, this is similar to literature values and verifiable via image simulations. Comparing with traditional measurement method, this approach requires one experiment and significantly reduces experimental workloads, further improving D(C) measurement technology.

Plasma Charge Carrier Attachment Induced Transport in Solid Ionic Materials

Lithium aluminum germanium phosphate of the stoichiometric formula Li1.5Al0.5Ge1.5(PO4)3 has been studied by means of the femtosecond laser plasma charge attachment induced transport (fs-plasma CAIT) [1]. The technique is based on attaching polarity selected charge carriers from a plasma to the front side of a sample, which induces transport of mobile charge carriers in the bulk of this sample. First, in a conductivity study, an activation energy of 0.73 eV for lithium ion transport has been measured by means of proton attachment. Second, a constant-voltage attachment experiment employing deuterium ions has been performed and subsequently analyzed by time-of-flight secondary ion mass spectrometry. The resulting concentration depth profile revealed a replacement of native lithium ions by deuterons in the first 350 nm of the sample. A theoretical analysis of the profile by means of the Nernst−Planck−Poisson equations provides access to the concentration dependent diffusion coefficient and the unique site energy distribution of the natively contained lithium ions. A full width at half-maximum of 113 meV for the SED of the Li+ ions is determined. The approach discussed can be applied to many more materials, where the potential energy landscape affects the function.More recent efforts in studying solid state ionic materials by means of the Plasma-CAIT technique will also be presented.[1] Jan L. Wiemer, Martin Schäfer, and Karl-Michael Weitzel, J. Phys. Chem. C, 125, 4977−4985, (2021) Figure 1

Spatiotemporal measurement of concentration-dependent diffusion coefficient

We introduce a method to measure the concentration-dependent diffusion coefficient from a sequence of images of molecules diffusing from a source toward a sink. Generally, approaches measuring the diffusion coefficient, such as fluorescence recovery after photobleaching (FRAP), assume that the diffusion coefficient is constant. Hence, these methods cannot capture the concentration dependence of the diffusion coefficient if present. Other approaches measure the concentration-dependent diffusion coefficient from an instantaneous concentration profile and lose the temporal information. These methods make unrealistic assumptions, are not robust, and lead to 100% error. We introduce an image analysis framework that utilizes spatial and temporal information in a sequence of concentration images and numerically solves the general form of Fick's second law using radial basis functions (RBF) to measure the concentration-dependent diffusion coefficient. We term this approach as concentration image diffusimetry (CID). Our method makes no assumptions about the sink and source size and the diffusion dependence on concentration. CID is superior to existing methods in estimating spatiotemporal changes and concentration-dependent diffusion. CID also provides a statistical uncertainty quantification on the measurements using a bootstrapping approach, improving the reliability of the diffusion measurement. We assessed CID's performance using synthetically generated images. Our analysis suggests that CID accurately measures the diffusion coefficient with less than 2% error for most cases. We validated CID with FRAP experimental images and showed that CID agrees with established FRAP algorithms for samples with a constant diffusion coefficient. Finally, we demonstrate the application of CID to experimental datasets of a concentration gradient-driven protein diffusion into a tissue replicate. In conclusion, this work presents an image-based methodology that uses the spatial and temporal changes of concentration fields to measure the concentration-dependent diffusion coefficient.

Calculation of gas concentration-dependent diffusion coefficient in coal particles: Influencing mechanism of gas pressure and desorption time on diffusion behavior

To investigate the effects of equilibrium pressure and desorption time on gas diffusion in coal particles, we described the time-varying diffusion process by introducing an indeterminate function of desorption time. Using gas desorption data, we established an analytical model for calculating the gas diffusion coefficient under the different desorption times. The analytical solution of the concentration-dependent diffusion model is equivalent to that of the unipore diffusion model at the initial desorption time. Still, the diffusion coefficient decreased with the decrease of gas equilibrium pressure and the extension of desorption time. Additionally, the numerical method compared adsorbed and free gas effects on gas desorption. The results demonstrated that the diffusion coefficient considered adsorbed gas was more significant than the analytical solution's. The diffusion coefficient in the free gas system was overestimated due to the change of diffusion distance and decreased to the actual value over desorption time. However, the attenuation rate of diffusion coefficients in the adsorbed gas system positively correlates with gas pressure. The concentration gradient of free gas is the driving force for gas diffusion. The simulation and experimental results show that the free to total gas ratio has a strong linear relationship with the diffusion coefficient, which explains the influencing mechanism of gas pressure and desorption time on the gas diffusion.

The effect of concentration-dependent diffusion on double-diffusive instability

The article studies the stability of a two-layer miscible system to the double-diffusive instability. The system is placed in a vertical Hele–Shaw cell and is composed of two homogeneous aqueous solutions initially separated by a narrow transient zone. We have restricted our consideration to the initially stable density stratification that precludes the Rayleigh–Taylor instability. The main objective of the study is to elucidate the effect of a concentration-dependent diffusion coefficient, which has been commonly ignored by researchers. Assuming linear dependence of the diffusion coefficient of each solute and using Picard's iteration scheme, we have derived a closed-form analytical expression for the time-dependent density profile. This permits the stability boundary to be established for a two-layer system with respect to the double-diffusive instability by taking into account the effect of a concentration-dependent diffusion coefficient. The obtained analytical result has been substantiated by the results of direct numerical simulation. The experiments have shown that a successive increase in the concentrations of both solutes, with their ratio remaining unchanged, can lead to opposite results. In the case of a NaNO3-H2SO4 pair, the two-layer system, being stable at low concentrations, becomes unstable as the concentrations proportionally increase, giving rise to convective motion in the form of salt fingers. On the contrary, a two-layer system consisting of LiCl and NaNO3 solutions is stabilized with increasing concentrations of dissolved substances. A further increase in the concentrations of these substances causes mechanical equilibrium breaking and subsequent formation of the so-called diffusive-layer convection. The experimental results are in good agreement with the theoretical predictions.

Preparation of infrared axial gradient refractive index lens based on powder stacking and the sintering thermal diffusion method

The gradient refractive index (GRIN) lens is widely used in the visible band, but it is still elusive in the infrared band. In this paper, we propose a new method of fabricating chalcogenide GRIN by spark plasma sintering (SPS) technology based on powder stacking and sintering thermal diffusion. We replaced Se in Ge11.5As24Se64.5 glass with S and prepared several Ge11.5As24Se(64.5-x)Sx glasses as infrared transmission GRIN materials. The maximum refractive index difference (Δn) of the matrix glass is 0.18. The effects of heat treatment temperature and time on diffusion depth and concentration-dependent thermal diffusion coefficient were investigated. The diffusion depth of 100 µm was demonstrated under the condition of 400 °C-48 h by this method. The thickness of the glass layer can be well controlled by powder stacking. The obtained GRIN glass is highly transparent in the near- and mid-infrared wavelength region.

Physics-based modeling of sodium-ion batteries part II. Model and validation

Sodium-ion batteries (SIBs) have recently been proclaimed as the frontrunner 'post lithium' energy storage technology. This is because SIBs share similar performance metrics with lithium-ion batteries, and sodium is 1000 times more abundant than lithium. In order to understand the electrochemical characteristics of SIBs and improve present-day designs, physics-based models are necessary. Herein, a physics-based, pseudo-two-dimensional (P2D) model is introduced for SIBs for the first time. The P2D SIB model is based on Na3V2(PO4)2F3 (NVPF) and hard carbon (HC) as positive and negative electrodes, respectively. Charge transfer in the NVPF and HC electrodes is described by concentration-dependent diffusion coefficients and kinetic rate constants. Parametrization of the model is based on experimental data and genetic algorithm optimization. It is shown that the model is highly accurate in predicting the discharge profiles of full cell HC//NVPF SIBs. In addition, internal battery states, such as the individual electrode potentials and concentrations, can be obtained from the model at applied currents. Several key challenges in both electrodes and the electrolyte are herein unraveled, and useful design considerations to improve the performance of SIBs are highlighted.

Physical Origin of the Differential Voltage Minimum Associated With Lithium Plating in Li-Ion Batteries

The main barrier to fast charging of Li-ion batteries at low temperatures is the risk of short-circuiting due to lithium plating. In-situ detection of Li plating is highly sought after in order to develop fast charging strategies that avoid plating. It is widely believed [1,2,3] that Li plating after a single fast charge can be detected and quantified by using a minimum in the differential voltage (DV) signal during the subsequent discharge, which indicates how much lithium has been stripped. In this work, [4] a pseudo-2D physics-based model is used to investigate the effect on Li plating and stripping of concentration-dependent diffusion coefficients [5] in the active electrode materials. A new modelling protocol is also proposed, in order to distinguish the effects of fast charging, slow charging and Li plating/stripping. The model predicts that the DV minimum associated with Li stripping is in fact a shifted and more abrupt version of a minimum caused by the stage II-stage III transition in the graphite negative electrode. Therefore, the minimum cannot be used to quantify stripping. Using concentration-dependent diffusion coefficients yields qualitatively different results to previous work [2,3]. This knowledge casts doubt on the utility of DV analysis for detecting Li plating.[1] Mathias Petzl and Michael A. Danzer, J.Power Sources vol. 254, pp. 80-87, 2014.[2] Xiao-Guang Yang et al., J. Power Sources vol. 395, pp. 251-261, 2018.[3] Dongsheng Ren et al., J. Electrochem. Soc. vol. 165 (10), pp. A2167-A2178, 2018.[4] Simon E. J. O’Kane et al., J. Electrochem. Soc. vol. 167, pp. 090540, 2020.[5] Madeleine Ecker et al., J. Electrochem. Soc. vol. 162 (9), pp. A1836-A1848, 2015.[6] Ian D. Campbell et al., J. Electrochem. Soc. vol. 166 (4), pp. A725-A739, 2019. Figure 1

Protein Transport upon Advection at the Air/Water Interface: When Charge Matters.

The formation of dense protein interfacial layers at a free air-water interface is known to result from both diffusion and advection. Furthermore, protein interactions in concentrated phases are strongly dependent on their overall positive or negative net charge, which is controlled by the solution pH. As a consequence, an interesting question is whether the presence of an advection flow of water toward the interface during protein adsorption produces different kinetics and interfacial structure of the adsorbed layer, depending on the net charge of the involved proteins and, possibly, on the sign of this charge. Here we test a combination of the following parameters using ovalbumin and lysozyme as model proteins: positive or negative net charge and the presence or absence of advection flow. The formation and the organization of the interfacial layers are studied by neutron reflectivity and null-ellipsometry measurements. We show that the combined effect of a positive charge of lysozyme and ovalbumin and the presence of advection flow does induce the formation of interfacial multilayers. Conversely, negatively charged ovalbumin forms monolayers, whether advection flow is present or not. We show that an advection/diffusion model cannot correctly describe the adsorption kinetics of multilayers, even in the hypothesis of a concentration-dependent diffusion coefficient as in colloidal filtration, for instance. Still, it is clear that advection is a necessary condition for making multilayers through a mechanism that remains to be determined, which paves the way for future research.