Model Of Ion Transport Research Articles

Markov Chain-Based Stochastic Modeling of Chloride Ion Transport in Concrete Bridges

Over the last decade, there has been a lot of interest in models for evaluating and predicting the condition of existing bridges in North America due to the large number of them in an advanced state of deterioration. The models have been used to develop optimal strategies to prolong the service life of bridges, allocate limited financial and technical resources and maintain the required level of reliability of the bridges. The main process of deterioration of concrete bridges is corrosion of the reinforcing steel due to chloride ions and models for this type of deterioration can be classified as physical or statistical. The physical models describe the diffusion of chloride ions in concrete and chemical reactions while the statistical models, such as Markov chains, are used to model the progression of states of deterioration of the concrete structures. The physical models are appropriate to analyze deterioration processes for various structures and conditions of exposure but are computationally too demanding for the portfolio analysis of a large number of structures. Markov chain models have been extensively used for the latter purpose but require an extensive historical database to correctly estimate transition probabilities between deterioration states. The objective of this paper is to propose a novel procedure for estimating transition probabilities for Markov chain models by utilizing targeted simulations from physical models. The transition probabilities can be derived from specific climatological regions and concrete properties. The proposed framework provides the required input for portfolio analyses for a large number of different types of structures exposed to different climatological conditions. The procedure is demonstrated with the TransChlor® software and for a group of structures located in Montreal, Canada.

Mathematical Modeling of Ion Transport and Water Dissociation at the Ion-Exchange Membrane/Solution Interface in Intense Current Regimes

At current densities exceeding the limiting current density, H+ and OH− ions are generated at the interface of the ion-exchange membrane with a depleted solution as a result of the dissociation of water molecules. At present, it is generally accepted that water splitting occurs in a thin (a few nanometers) layer inside the membrane, this reaction being catalytic in nature. The mathematical model of ion transport in the diffusion layer near the membrane surface has been constructed and numerically studied under conditions when dissociation and recombination processes involving water molecules and H+ and OH− ions occur simultaneously. It has been shown that in overlimiting current regimes under very high voltages, intense noncatalytic dissociation of water molecules in the extended space charge region of the depleted solution can occur irrespective of the catalytic splitting of water. Since this region has macroscopic dimensions, the rate of noncatalytic water dissociation is comparable with the rate of the corresponding catalytic process. The obtained results significantly supplement modern concepts of the mechanism of generation of H+ and OH− ions in membrane systems, showing that this process can proceed not only in accordance with the conventional mechanism with the catalytic participation of functional groups and/or other compounds, but also via the noncatalytic mechanism that has not been taken into account to the present.

A conceptual review on polymer electrolytes and ion transport models

Abstract This review article provides a deep insight into the ion conduction mechanism in polymer electrolytes (PEs). The concepts of different categories of polymer electrolytes are discussed. The significance of the existence of functional (polar) groups on the backbone of host polymers, which are used in polymer electrolytes, is well explained. The working principle of electrical impedance spectroscopy (EIS) is overviewed. The relationship between impedance plots and equivalent circuits, which are crucial for electrical characterization, is extensively interpreted. Based on the patterns of dc conductivity (σdc) versus 1000/T, the ion transport models of Arrhenius and Vogel–Tammann–Fulcher (VTF) are discussed. Effects of coupling and decoupling between ionic motion and polymer segmental relaxation are analyzed. The important role of dielectric constant on cationic transport in PEs is also explained. The relationships existing between electrical and dielectric parameters are elucidated, which help interpret and understand the ion conduction mechanism. From the reported empirical curves of dc conductivity vs. dielectric constant, the reformulated Arrhenius [ σ d c ( T ) = σ 0 exp ( − E a k B T e ′ ) ] equation is proposed. Finally, other important phenomena, occurring in polymer electrolytes, are shown to be understandable from the dielectric constant studies.

Ion transport studies in nanocomposite polymer electrolyte membrane of PVA–[C4C1Im][HSO4]–SiO2

The paper reports the effect of SiO2 nano-filler on structural, thermal, and ion transport properties of polymer electrolyte system comprising polyvinyl alcohol (PVA) and 1-butyl-3-methylimidazolium hydrogen sulfate [C4C1Im][HSO4] ionic liquid. The addition of SiO2 nano-filler results into enhancement in amorphicity and thermal stability and lowering of glass transition temperature of the membranes. A detailed investigation of possible interactions among the constituents PVA, [C4C1Im][HSO4] and SiO2, and cation–anion and anion–anion pairs of [C4C1Im][HSO4] in the polymer electrolyte and their dissociation due to SiO2 filler has been carried out in the membranes using Fourier transform infra-red (FTIR) and Raman spectroscopy. The membranes show maximum room temperature ionic conductivity as 9.9 × 10−3 S cm−1 for 6 wt.% of the nano-filler which is about four times higher than the membrane without nano-filler and an order higher than pure [C4C1Im][HSO4]. With temperature, the ionic conductivity shows VTF behavior in the temperature range 40–120 °C. On the basis of FTIR and ion transport results, a model for ion transport in the membranes is proposed.

Electrochemical-mechanical coupled modeling and parameterization of swelling and ionic transport in lithium-ion batteries

The intercalation and aging induced volume changes of lithium-ion battery electrodes lead to significant mechanical pressure or volume changes on cell and module level. As the correlation between electrochemical and mechanical performance of lithium ion batteries at nano and macro scale requires a comprehensive and multidisciplinary approach, physical modeling accounting for chemical and mechanical phenomena during operation is very useful for the battery design. Since the introduced fully-coupled physical model requires proper parameterization, this work also focuses on identifying appropriate mathematical representation of compressibility as well as the ionic transport in the porous electrodes and the separator. The ionic transport is characterized by electrochemical impedance spectroscopy (EIS) using symmetric pouch cells comprising LiNi1/3Mn1/3Co1/3O2 (NMC) cathode, graphite anode and polyethylene separator. The EIS measurements are carried out at various mechanical loads. The observed decrease of the ionic conductivity reveals a significant transport limitation at high pressures. The experimentally obtained data are applied as input to the electrochemical-mechanical model of a prismatic 10 Ah cell. Our computational approach accounts intercalation induced electrode expansion, stress generation caused by mechanical boundaries, compression of the electrodes and the separator, outer expansion of the cell and finally the influence of the ionic transport within the electrolyte.

Oral Furosemide Therapy in Patients with Exudative Retinal Detachment Due to Hypertensive Retinopathy-IV

Introduction: Hypertensive retinopathy is a condition characterized by a spectrum of retinal vascular signs in people with elevated blood pressure. This condition can be accompanied by exudative retinal detachment in hypertensive retinopathy grade IV. Furosemide is considered as a diuretic agent to force fluid absorption across the retinal epithelium. This is consistent with a model for ion transport in the isolated RPE, in which active furosemide-inhibitable transport of chloride from retina to choroid for a significant fraction of the short-circuit current. Objectives: To report the efficacy of oral furosemide in patients with exudative retinal detachment due to hypertensive retinopathy-IV. Case presentation: We reported two young patients, first patient with chronic kidney disease complained with decreased of visual acuity to 20/100 in the right and 20/200 in the left eye. The second patient with preeclampsia suddenly experienced bilateral visual loss to counting finger on both eyes. Those patients showed sub-retinal fluid, macular star and cotton wool spots in both retina. Macular edema was seen by optical coherence tomography (OCT) examination in both eyes. Both cases were diagnosed as hypertensive retinopathy grade IV with exudative retinal detachment. Oral furosemide 40 mg once a day was given. On the first patient visual acuity improve to 20/80 on both eyes and on the second patient visual acuity improve to 20/400 on both eyes. Ocular ultrasonography (USG) examination showed significant decrease of exudative retinal detachment with in the 17 days. Conclusion: Furosemide is diuretic agent and might be effective in resolution of exudative retinal detachment followed by improvement of visual acuities in patient with hypertensive retinopathy grade IV.

Кристаллофизическая модель ионного переноса в нелинейно-оптических кристаллах KTiOPO-=SUB=-4-=/SUB=-

AbstractThe ionic conductivity along the principal axes a, b, and c of the unit cell of the nonlinear-optical high-resistance KTiOPO_4 single crystals (rhombic syngony, space group Pna 2_1), which are as-grown and after thermal annealing in vacuum, has been investigated by the method of impedance spectroscopy. The crystals were grown from a solution-melt by the Czochralski method. The as-grown KTiOPO_4 crystals possess a quasi-one-dimensional conductivity along the crystallographic c axis, which is caused by the migration of K^+ cations: σ_║ c = 1.0 × 10^–5 S/cm at 573 K. Wherein the characteristics of the anisotropy of ionic conductivity of the crystals is equal to σ_║ c /σ_║ a = 3 and σ_║ c /σ_║ b = 24. The thermal annealing at 1000 K for 10 h in vacuum increases the magnitude of σ_║ c of KTiOPO_4 by a factor of 28 and leads to an increase in the ratio σ_║ c /σ_║ b = 2.1 × 10^3 at 573 K. A crystal-physical model of ionic transport in KTiOPO_4 crystals has been proposed.

A note on the uniqueness of weak solutions to a class of cross-diffusion systems

The uniqueness of bounded weak solutions to strongly coupled parabolic equations in a bounded domain with no-flux boundary conditions is shown. The equations include cross-diffusion and drift terms and are coupled self-consistently to the Poisson equation. The model class contains special cases of the Maxwell–Stefan equations for gas mixtures, generalized Shigesada–Kawasaki–Teramoto equations for population dynamics, and volume-filling models for ion transport. The uniqueness proof is based on a combination of the H^{-1} technique and the entropy method of Gajewski.

A physics-based model for maintenance of the pH gradient in the gastric mucus layer.

It is generally accepted that the gastric mucus layer provides a protective barrier between the lumen and the mucosa, shielding the mucosa from acid and digestive enzymes and preventing autodigestion of the stomach epithelium. However, the precise mechanisms that contribute to this protective function are still up for debate. In particular, it is not clear what physical processes are responsible for transporting hydrogen protons, secreted within the gastric pits, across the mucus layer to the lumen without acidifying the environment adjacent to the epithelium. One hypothesis is that hydrogen may be bound to the mucin polymers themselves as they are convected away from the mucosal surface and eventually degraded in the stomach lumen. It is also not clear what mechanisms prevent hydrogen from diffusing back toward the mucosal surface, thereby lowering the local pH. In this work we investigate a physics-based model of ion transport within the mucosal layer based on a Nernst-Planck-like equation. Analysis of this model shows that the mechanism of transporting protons bound to the mucus gel is capable of reproducing the trans-mucus pH gradients reported in the literature. Furthermore, when coupled with ion exchange at the epithelial surface, our analysis shows that bicarbonate secretion alone is capable of neutralizing the epithelial pH, even in the face of enormous diffusive gradients of hydrogen. Maintenance of the pH gradient is found to be robust to a wide array of perturbations in both physiological and phenomenological model parameters, suggesting a robust physiological control mechanism.NEW & NOTEWORTHY This work combines modeling techniques based on physical principles, as well as novel numerical simulations to test the plausibility of one hypothesized mechanism for proton transport across the gastric mucus layer. Results show that this mechanism is able to maintain the extreme pH gradient seen in in vivo experiments and suggests a highly robust regulation mechanism to maintain this gradient in the face of dynamic lumen composition.

Benchmark of multi-phase method for the computation of fast ion distributions in a tokamak plasma in the presence of low-amplitude resonant MHD activity

The transport of fast ions in a beam-driven JT-60U tokamak plasma subject to resonant magnetohydrodynamic (MHD) mode activity is simulated using the so-called multi-phase method, where 4 ms intervals of classical Monte-Carlo simulations (without MHD) are interlaced with 1 ms intervals of hybrid simulations (with MHD). The multi-phase simulation results are compared to results obtained with continuous hybrid simulations, which were recently validated against experimental data (Bierwage et al., 2017). It is shown that the multi-phase method, in spite of causing significant overshoots in the MHD fluctuation amplitudes, accurately reproduces the frequencies and positions of the dominant resonant modes, as well as the spatial profile and velocity distribution of the fast ions, while consuming only a fraction of the computation time required by the continuous hybrid simulation. The present paper is limited to low-amplitude fluctuations consisting of a few long-wavelength modes that interact only weakly with each other. The success of this benchmark study paves the way for applying the multi-phase method to the simulation of Abrupt Large-amplitude Events (ALE), which were seen in the same JT-60U experiments but at larger time intervals. Possible implications for the construction of reduced models for fast ion transport are discussed.

A Comprehensive Biophysical Model of Ion and Water Transport in Plant Roots. I. Clarifying the Roles of Endodermal Barriers in the Salt Stress Response.

In this paper, we present a detailed and comprehensive mathematical model of active and passive ion and water transport in plant roots. Two key features are the explicit consideration of the separate, but interconnected, apoplastic, and symplastic transport pathways for ions and water, and the inclusion of both active and passive ion transport mechanisms. The model is used to investigate the respective roles of the endodermal Casparian strip and suberin lamellae in the salt stress response of plant roots. While it is thought that these barriers influence different transport pathways, it has proven difficult to distinguish their separate functions experimentally. In particular, the specific role of the suberin lamellae has been unclear. A key finding based on our simulations was that the Casparian strip is essential in preventing excessive uptake of Na+ into the plant via apoplastic bypass, with a barrier efficiency that is reflected by a sharp gradient in the steady-state radial distribution of apoplastic Na+ across the barrier. Even more significantly, this function cannot be replaced by the action of membrane transporters. The simulations also demonstrated that the positive effect of the Casparian strip of controlling Na+ uptake, was somewhat offset by its contribution to the osmotic stress component: a more effective barrier increased the detrimental osmotic stress effect. In contrast, the suberin lamellae were found to play a relatively minor, even non-essential, role in the overall response to salt stress, with the presence of the suberin lamellae resulting in only a slight reduction in Na+ uptake. However, perhaps more significantly, the simulations identified a possible role of suberin lamellae in reducing plant energy requirements by acting as a physical barrier to preventing the passive leakage of Na+ into endodermal cells. The model results suggest that more and particular experimental attention should be paid to the properties of the Casparian strip when assessing the salt tolerance of different plant varieties and species. Indeed, the Casparian strip appears to be a more promising target for plant breeding and plant genetic engineering efforts than the suberin lamellae for the goal of improving salt tolerance.

Computation of Alfvèn eigenmode stability and saturation through a reduced fast ion transport model in the TRANSP tokamak transport code

Alfvénic instabilities (AEs) are well known as a potential cause of enhanced fast ion transport in fusion devices. Given a specific plasma scenario, quantitative predictions of (i) expected unstable AE spectrum and (ii) resulting fast ion transport are required to prevent or mitigate the AE-induced degradation in fusion performance. Reduced models are becoming an attractive tool to analyze existing scenarios as well as for scenario prediction in time-dependent simulations. In this work, a neutral beam heated NSTX discharge is used as reference to illustrate the potential of a reduced fast ion transport model, known as kick model, that has been recently implemented for interpretive and predictive analysis within the framework of the time-dependent tokamak transport code TRANSP. Predictive capabilities for AE stability and saturation amplitude are first assessed, based on given thermal plasma profiles only. Predictions are then compared to experimental results, and the interpretive capabilities of the model further discussed. Overall, the reduced model captures the main properties of the instabilities and associated effects on the fast ion population. Additional information from the actual experiment enables further tuning of the model’s parameters to achieve a close match with measurements.

Resistive switching in memristive electrochemical metallization devices

We report on resistive switching of memristive electrochemical metallization devices using 3D kinetic Monte Carlo simulations describing the transport of ions through a solid state electrolyte of an Ag/TiOx/Pt thin layer system. The ion transport model is consistently coupled with solvers for the electric field and thermal diffusion. We show that the model is able to describe not only the formation of conducting filaments but also its dissolution. Furthermore, we calculate realistic current-voltage characteristics and resistive switching kinetics. Finally, we discuss in detail the influence of both the electric field and the local heat on the switching processes of the device.

Improvement of MCDI operation and design through experiment and modelling: Regeneration with brine and optimum residence time

Membrane Capacitive Deionization (MCDI) is an energy efficient, electrochemical desalination technology, in which ions are removed from a salty stream upon applying a constant voltage or current. The ions are stored in carbon electrodes and then released back into the stream by reversing the polarity. In this work, we aimed to assess the feasibility of using a brine stream to regenerate the MCDI unit in order to improve water recovery. We further aimed to determine the optimum residence time in the MCDI unit. To achieve these objectives, we first enhanced the ion transport model previously developed for MCDI by independently measuring the counter-ion and co-ion diffusion coefficients in the ion-exchange membranes. These experiments allowed for an asymmetric model of the MCDI unit where the voltage drop across the cation exchange membrane was greater than that across the anion exchange membrane. Using this revised model, we found that in batch operation, a brine to feed water concentration ratio of around two was optimum. In continuous operation, over 40% enhancement in water recovery could be achieved when the regeneration brine was partially recycled, but water productivity dropped. We further showed that the maximum desalination capacity did not increase beyond a critical residence time in the MCDI cell, while the water recovery decreased.

A model for time-dependent grain boundary diffusion of ions and electrons through a film or scale, with an application to alumina

A model for ionic and electronic grain boundary transport through thin films, scales or membranes with columnar grain structure is introduced. The grain structure is idealized as a lattice of identical hexagonal cells – a honeycomb pattern. Reactions with the environment constitute the boundary conditions and drive the transport between the surfaces. Time-dependent simulations solving the Poisson equation self-consistently with the Nernst-Planck flux equations for the mobile species are performed. In the resulting Poisson-Nernst-Planck system of equations, the electrostatic potential is obtained from the Poisson equation in its integral form by summation. The model is used to interpret alumina membrane oxygen permeation experiments, in which different oxygen gas pressures are applied at opposite membrane surfaces and the resulting flux of oxygen molecules through the membrane is measured. Simulation results involving four mobile species, charged aluminum and oxygen vacancies, electrons, and holes, provide a complete description of the measurements and insight into the microscopic processes underpinning the oxygen permeation of the membrane. Most notably, the hypothesized transition between p-type and n-type ionic conductivity of the alumina grain boundaries as a function of the applied oxygen gas pressure is observed in the simulations. The range of validity of a simple analytic model for the oxygen permeation rate, similar to the Wagner theory of metal oxidation, is quantified by comparison to the numeric simulations. The three-dimensional model we develop here is readily adaptable to problems such as transport in a solid state electrode, or corrosion scale growth.

Insights into the Ultra-Fast Li Storage Properties of Organic Polymers

Organic materials have long been recognized as resource-abundant, sustainable, and potentially low-cost electrode materials that will handily satisfy the ever-growing demand for batteries. Although once had the reputation as being less stable and kinetically slow compared with their traditional inorganic counterparts, organic materials have been steadily improving on performance to be competent electrode candidates in recent years. We have recently reported a π-conjugated redox polymer with high cycling stability, high capacity utilization, and ultra-fast Li storage kinetics. The polymer delivers 80% of its theoretical capacity at a rate of 50C even with a high active mass ratio of 80 wt.% at practical mass loading, which is unusual for organic electrode materials. There is no established theory as for how such performance can be achieved and optimized via molecular design and microstructure engineering. We set out to scrutinize the charge storage mechanism of polymer electrodes and investigate the influence of molecular electronic structure and electrode microstructure on electrochemical performance. We have designed and synthesized a series of polymers with similar molecular structure but varying degree of conjugation in the backbone. The polymers are evaluated as Li storage electrode materials. The morphology and its evolution, charge transfer process, and state-of-charge-dependent electron and ion transport of the polymer electrodes are monitored and correlated to the cell performance. We found that regardless of the degree of conjugation, the redox reaction and the bulk ionic diffusion in the polymers proceed at comparable rates. We developed a procedure to directly measure the electrical conductivity of electrochemically lithiated polymers. This conductivity increases by 100-fold as the π-conjugation degree of the polymers increases. The structural order and morphology of the polymers differ widely with the conjugation length, leading to significantly different microstructure. The electrochemical surface area of the polymer electrode is continuously altered by the π-conjugation degree, which in turn impacts the ion transport model in the electrode. Overall, our study establishes general analysis tools that elucidate the underlying charge storage mechanism of polymer electrode materials. The results shown here provide guidance for further advancing high-energy/power energy battery based on organic materials.

Transport Limitations in Binary Electrolytes: The Temperature Dependence of the Electrolyte Transport Parameters

The ion-transport model for concentrated electrolyte solutions introduced by Newman and Thomas-Alyea1is frequently used for numerical simulations of battery systems and depends on three ion transport parameters: the conductivity, the transference number and the binary diffusion coefficient. In addition, the thermodynamic factor, which is derived from the mean molar activity coefficient, is required for the correct description of the thermodynamic behavior of a binary electrolyte solution. The resistive ion transport of the binary electrolyte in a lithium ion battery causes the formation of temperature gradients, especially in large format cells. To understand the influence of local temperature inhomogeneity on, e.g., the aging of the cell, it is necessary to have a profound understanding of the temperature dependence of the ion transport parameters. While a vast spectrum of physico-chemical parameters can be found in the literature only few publications study their temperature dependence, e.g., Valoen and Reimers2. In addition, some of the parameters are often fitted to match experimental performance data and may thus be fitting parameters rather than intrinsic physico-chemical parameters with predictive capability. We present the results of our temperature dependent study of the ionic transport parameters from commonly used lithium electrolytes by using a new method to determine the thermodynamic factor3and combining it with concentration cell experiments to determine transference numbers. Using common polarization cell experiments, we additionally determine diffusion coefficients while conductivities are measured using turn-key equipment. We chose common battery electrolytes, e.g., LiPF6 in EC:EMC (3:7 w:w) and LiPF6 in EC:DMC (1:1 w:w) for our analysis. Exemplarily shown in Figure 1. is the relative temperature dependence of the transference number, thermodynamic factor and the diffusion coefficient for a 0.1 M, 1 M and a 2 M LiClO4in EC:DEC (1:1 w:w) electrolyte. Our results allow us to use numerical experiments to study the temperature dependent transport limitations in binary electrolyte and their influence on the cell performance. Adaption of our transport parameters in Newman type battery models will enhance numerical predictions. The study of temperature variations in large format cells might help to understand the observed, spatially dependent aging in, e.g., cylindrical cells and thereby enables the design and improvement of better lithium ion batteries in the future. Figure 1. Relative change of transference number, binary diffusion coefficient and thermodynamic factor versus their 20°C value a LiClO4in EC:DEC (1:1 w:w) electrolyte at 0.1, 1 and 2 M concentrations.

Transport Limitations in Binary Electrolytes: EC-Free Solvents and NaPF6 Vs. LiPF6 Salts

For numerical simulations of battery systems, the ion-transport model for concentrated electrolyte solutions introduced by Newman and Thomas-Alyea1is frequently used and depends on three ion transport parameters: the conductivity, the transference number and the binary diffusion coefficient. In addition, the thermodynamic factor which is derived from the mean molar activity coefficient is required for the correct description of the thermodynamic behavior of a binary electrolyte solution. A vast spectrum of physico-chemical parameters can be found in the literature (e.g., Valoen and Reimers2), but since the investigated electrolytes and the experimental techniques differ from study to study, it is difficult to find a consistent parameter set for a given electrolyte. In addition, some of the parameters are often fitted to match experimental performance data and may thus be fitting parameters rather than intrinsic physico-chemical parameters with predictive capability. In our work, a new method to determine the thermodynamic factor3is combined with con-centration cell experiments to determine trans-ference numbers. Using common polarization cell experiments, we additionally determine diffusion coefficients while conductivities are measured using turn-key equipment. Our main objective is to analyze the limitations of new, emerging battery chemistries, e.g., EC-free electrolytes4 for lithium ion batteries or electrolytes for sodium batteries,5 and compare their electro-chemical transport properties to a common solution, e.g., LiPF6 in EC:EMC (3:7 w:w). Exemplarily shown is the comparison of the ionic conductivity for a NaPF6 and a LiPF6electrolyte in the same solvent, EC:DEC (1:1 v:v). To compare the obtained transport parameters and to depict their impact on the cell performance, we incorporate the obtained functional descriptions in an arbitrarily chosen graphite-NMC cell model. We will show which fraction of the cell overpotential is caused by the electrolyte and analyze its effect on the rate performance of the cell. Our research will help to understand the limitation caused by concentration overpotentials in current lithium ion battery systems. Adaption of our transport parameters in Newman type battery models will enhance numerical predictions. Analysis of the type of solvent and salt will help to understand the sources for ionic transport limitations and thereby helps improving future battery electrolyte solutions. Figure 1: Conductivity of NaPF6 and LiPF6 from 0.1 M to 2 M in EC:DEC (1:1 vol.) at 25°C.

Electrochemical Techniques for Intercalation Electrode Materials in Rechargeable Batteries.

Understanding of the thermodynamic and kinetic properties of electrode materials is of great importance to develop new materials for high performance rechargeable batteries. Compared with computational understanding of physical and chemical properties of electrode materials, experimental methods provide direct and convenient evaluation of these properties. Often, the information gained from experimental work can not only offer feedback for the computational methods but also provide useful insights for improving the performance of materials. However, accurate experimental quantification of some properties can still be challenging. Among them, chemical diffusion coefficient is one representative example. It is one of the most crucial parameters determining the kinetics of intercalation compounds, which are by far the dominant electrode type used in rechargeable batteries. Therefore, it is of significance to quantitatively evaluate this parameter. For this purpose, various electrochemical techniques have been invented, for example, galvanostatic intermittent titration technique (GITT), potentiostatic intermittent titration technique (PITT), electrochemical impedance spectroscopy (EIS), and cyclic voltammetry (CV). One salient advantage of these electrochemical techniques over other characterization techniques is that some implicit thermodynamic and kinetic quantities can be linked with the readily measurable electrical signals, current, and voltage, with very high precision. Nevertheless, proper application of these techniques requires not just an understanding of the structure and chemistry of the studied materials but sufficient knowledge of the physical model for ion transport within solid host materials and the analysis method to solve for chemical diffusion coefficient. Our group has been focusing on using various electrochemical techniques to investigate battery materials, as well as developing models for studying some emerging materials. In this Account, the principles of the aforementioned four electrochemical techniques and the corresponding analytical equations for calculating the chemical diffusion coefficients are first briefly summarized, followed by a discussion of the hidden assumptions for deriving these analytical equations and the resulting limitations in their implementation. To address these limitations, various corrections have been made in the literature. Nevertheless, the phase transition behavior, which is the typical feature for many intercalation materials, is barely considered. Here we retrospect our previous work on developing a two-phase model for describing the phase transition behavior of some intercalation compounds and discuss how to obtain the chemical diffusion coefficients based on the model, using LiFePO4 as an example material. After that, we have a discussion on the methodology for using electrochemical techniques to investigate new material features. It is our hope that this Account can serve as a call for more endeavors into the development of novel electrochemical tools for battery research.

A Rayleighian approach for modeling kinetics of ionic transport in polymeric media.

We report a theoretical approach for analyzing impedance of ionic liquids (ILs) and charged polymers such as polymerized ionic liquids (PolyILs) within linear response. The approach is based on the Rayleigh dissipation function formalism, which provides a computational framework for a systematic study of various factors, including polymer dynamics, in affecting the impedance. We present an analytical expression for the impedance within linear response by constructing a one-dimensional model for ionic transport in ILs/PolyILs. This expression is used to extract mutual diffusion constants, the length scale of mutual diffusion, and thicknesses of a low-dielectric layer on the electrodes from the broadband dielectric spectroscopy measurements done for an IL and three PolyILs. Also, static dielectric permittivities of the IL and the PolyILs are determined. The extracted mutual diffusion constants are compared with the self-diffusion constants of ions measured using pulse field gradient (PFG) fluorine nuclear magnetic resonance (NMR). For the first time, excellent agreement between the diffusivities extracted from the Electrode Polarization spectra (EPS) of IL/PolyILs and those measured using the PFG-NMR are found, which allows the use of the EPS and the PFG-NMR techniques in a complimentary manner for a general understanding of the ionic transport.