Comparison between potentiostatic and galvanostatic intermittent titration techniques for determination of chemical diffusion coefficients in ion-insertion electrodes

Using well-cycled, thin composite graphite electrodes we analyze carefully the limitations of potentiostatic and galvanostatic intermittent titration techniques (PITT and GITT, respectively) for determination of the differential (incremental) intercalation capacitance, C_dif, and the chemical diffusion coefficient, D, of Li ions in these ion-insertion electrodes (IIEs). We demonstrate the superiority of the GITT over PITT to determine these quantities as the former technique allows for a more accurate determination of C_dif and hence D which closely approach to the spinodal domain related to the first-order phase transition during ion-insertion. We show that GITT is also more effective in eliminating the parasitic contributions of background currents to the total measured response. A pronounced difference in the initial, intrinsic kinetics of formation of a new phase in the bulk of the old one has been observed depending on the direction of titration (phases less saturated with Li are formed faster during deintercalation than the Li-rich phases in the course of intercalation).     

The application of electroanalytical methods to the analysis of phase transitions during intercalation of ions into electrodes

Mechanisms of first-order phase transition induced by electrochemical intercalation of Li ions into composite graphite electrode are studied both theoretically, in the framework of lattice gas models, and experimentally, by a combination of electroanalytical techniques, such as cyclic voltammetry, potentiostatic intermittent titration (PITT), galvanostatic intermittent titration (GITT), and electrochemical impedance spectroscopy (EIS). From the analysis of the mismatch between the accessible phase-transition rate constants and the characteristic time windows for various electroanalytical methods, we conclude that only a combined application of these techniques provides sufficient, self-consistent information on the mechanisms of phase transitions in graphite electrodes. The advantages and disadvantages in using these techniques are discussed. PITT with a small potential step is the most appropriate tool for measuring the entire sequence of rate-determining steps of phase transitions as a function of time. The latter technique can be conveniently used for quantitative analysis of slow nucleation and the growth of new phases in the bulk of the old one, followed by the coalescence of nuclei and the formation of phase boundaries between the coexisting phases. The movement of this boundary into the electrode’s bulk has been properly modeled in terms of two alternative models. “Contribution to the International Workshop on Electrochemistry of Electroactive Materials (WEEM-2006), Repino, Russia, 24–29 June 2006.”     

Understanding the effects of diffusion coefficient and exchange current density on the electrochemical model of lithium-ion batteries

The diffusion coefficient and exchange current density are the two dominant parameters that determine the electrochemical characteristics of the electrochemical battery model. Nevertheless, both parameter values are generally adopted from well-known literature or experimental data measured under limited conditions and are sometimes overfitted to match actual electrochemical behaviors without full consideration. Herein, the diffusion coefficients and exchange current densities of a LiNi_0·4Mn_0·3Co_0·3O₂/Li cell are measured and applied to the electrochemical model (based on Newman's model) using four different electrochemical methods: galvanostatic intermittent titration technique (GITT), potentiostatic intermittent titration technique (PITT), electrochemical impedance spectroscopy (EIS), and cyclic voltammetry (CV). Without any fitting, the model adopting the diffusion coefficient and exchange current density measured from PITT and EIS, respectively, simulates the actual voltage–capacity profiles well. Thus, this case study provides a valuable opportunity to understand the advantages and disadvantages of each measurement method in obtaining key experimental parameters for electrochemical battery models.     

Estimation of concentration-dependent diffusion coefficient in pressure-decay experiment of heavy oils and bitumen

Molecular diffusion has been considered to be an underlying mechanism for many of oil recovery processes like miscible and immiscible gas injection projects. Reliable estimation of the molecular diffusion coefficient as a transport property is therefore important in studying the performance of such systems. Interpretation of pressure-decay data has been traditionally used to estimate the molecular diffusion coefficient and usually to simplify the interpretation, its concentration dependency has been neglected. A pressure-decay model with concentration-dependent diffusion coefficient leads to a non-linear problem in which an analytical solution is difficult if not impossible to obtain. In this study, we used the Heat Integral Method (HIM) to solve the non-linear diffusion problem as a forward model. Using that forward model, we have developed a simple methodology for estimating the diffusion coefficient regardless of the form of function used for the concentration dependency of the molecular diffusion. Three different forms of functions for diffusion coefficient were considered. In its simplest form, the diffusion coefficient is set to be a constant value. In the two other forms, the diffusion coefficient was evaluated as a concentration-dependent two parameter equation using exponential and power-law functions, respectively. The proposed methodology is verified and tested using direct numerical solutions of the non-linear diffusion problem. Many numerical examples with a wide range of input parameters demonstrate the effectiveness of the proposed approach.     

Mass transport and effective diffusion coefficient in the reduction of hydrogen ions from aqueous sulfuric acid solutions: Numerical modeling

This work presents results of the numerical solution to a system of equations of material balance and the movement of particles in solution under the influence of the forces of diffusion, migration, and convection, which describe the process of mass transport during the reduction of hydrogen ions at a rotating disk electrode from aqueous sulfuric acid solutions with and without excess supporting electrolyte. Results of the calculations show that the diffusion kinetics of hydrogen ion reduction can be observed only with measurements in dilute (≤10^?3 M) sulfuric acid solutions with an excess of indifferent supporting electrolyte. For more acidic solutions it is necessary to take into account the simultaneous diffusion of hydrogen and bisulfate ions. In the study of the regularities of hydrogen ion reduction in sulfuric acid solutions with a sulfate supporting electrolyte, it is necessary to take into account that with excess supporting electrolyte, the limiting current of hydrogen reduction is caused solely by the diffusion of bisulfate ions, but for small concentration ratios of the supporting electrolyte to acid, the influence of migration effects is significant.     

Simple technique for the simultaneous determination of solvent diffusion coefficient in polymer by Quantum Resistive Sensors and FT‐IR spectroscopy

A simple, quick and novel method for the determination of diffusion properties through polymer films, based on Quantum Resistive Sensors made of Conductive Polymer nanoComposites is presented. The integral time lag method is employed for the calculation of diffusion coefficient, and the results are compared simultaneously with that of Fourier transform infrared spectroscopy and sorption method. Two model polymers, a semi‐crystalline poly(lactic acid) and an amorphous poly(isobutylene‐co‐isoprene), are used to validate the study. A good correlation is established between the diffusion coefficient values derived from all techniques demonstrating the interest of such reliable, simple and cheap nanosensors for the quick determination (several minutes) of diffusion properties in polymer films. Our first results suggest that this technique is meaningful for the determination of barrier properties in nanocomposite membranes filled with platelets of graphene or clay. Copyright © 2013 John Wiley & Sons, Ltd.     

A parallel pore and surface diffusion model for predicting the adsorption and elution profiles of lispro insulin and two impurities in gradient-elution reversed phase chromatography

Lispro insulin (LPI), a widely used insulin analog, is produced on tons per year scale. Linear gradient reversed phase chromatography (RPC) is used in the production to separate LPI from two impurities, which differ from LPI by a single amino acid residue. A chromatography model for the ternary separation in this RPC process is unavailable from the literature. In this study, a parallel pore and surface diffusion model is developed and verified for LPI and the two impurities. The LPI can be recovered with high yield (≥95%) and high purity (>99.5%). A new method, which requires a small amount of materials and an order of magnitude fewer experiments, has been developed to estimate the solvent-modulated isotherm parameters. A modified reversed phase modulator model is developed to correlate the adsorption isotherms of LPI and impurities. A strategy has been developed for estimating the intrinsic pore diffusivity and surface diffusivity. Since the adsorption affinities decrease by more than three orders of magnitude as organic fraction (φ) increases from 0.19 to 0.40, the apparent diffusivities based on a pore diffusion model or a surface diffusion model can also vary by several orders of magnitude. For this reason, a pore diffusion model or a surface diffusion model with a constant apparent diffusivity cannot predict closely the chromatograms over the same range of organic fractions, concentrations, and loadings. The parallel pore and surface diffusion model with constant diffusivities can predict closely the frontal and elution profiles over a wide range of organic fractions (0.19-0.40), LPI concentrations (0.05-18 g/L), linear velocities (<10 cm/min), and loading volume (0.0004-13 CV). For large loading stepwise and linear gradient elution, the peaks of LPI and the impurities are strongly focused by self-sharpening and gradient focusing effects as a result of the steep decrease of adsorption affinity from the loading φ (0.19) to elution φ (≥0.27). When the ratio of diffusion rate to convection rate is greater than 10, spreading due to diffusion is largely compensated by the focusing effects. As a result, a pore diffusion model with a constant pore diffusivity can predict closely the elution profiles in stepwise and linear gradient elution. The experimental yield values (≥95%) can be predicted to within ±1% by the model.     

Active layer of the oxygen cathode in a fuel cell with Nafion and platinum: The role played by the diffusion and ohmic restrictions and the selection of the working thickness of the active layer

The basic parameters that characterize the operation of the active layer of a cathode with Nafion are the effective coefficient of the diffusion of oxygen, the effective ionic conductance, and the thickness of the active layer. One of the deficiencies intrinsic to the fuel cells containing Nafion is their extreme sensitivity to the heat and moisture exchange. Nafion demands an optimum degree of humidification. Upon thoroughly draining the active layer of a cathode with Nafion, its effective ionic conductance substantially lowers, and large diffusion restrictions arise following the flooding of pores in the active layer. The goal of this work is to perform a comparison of values of some dimensional characteristics pertaining to the flooded and thoroughly drained active layers of a cathode with similar indicators of an active layer in its optimum (normal) state. It is demonstrated how one should perform the selection of the working thickness of an active layer that would provide for the efficiency of its functioning.     

Temperature and Concentration Dependence of the Electrical Conductance,Diffusion, and Kinetics Parameters of the Ions in Aqueous Solutions of Sulfuric Acid,Selenic Acid,and Potassium Tellurate

The temperature and concentration dependences of the electrical conductance of aqueous solutions of sulfuric acid, selenic acid, and potassium tellurate were studied. The coefficients of the corresponding empirical equations were determined, and the values of equivalent conductances of the anions were evaluated at infinite dilution at the experimental temperatures. The values of the coefficients in the Fuoss and Onsager equation were evaluated for the three electrolytes at 298 K. The values of the molecular and ionic coefficients of self-diffusion at infinite dilution were calculated in the temperature range 288–318 K. The change of the translational energy Δ E∘_tr. of water molecules in the ionic hydration sphere was determined. The number of water molecules participating in the ionic hydration sphere at 298 K and the changes of Gibbs free energy, enthalpy, and entropy of activation of ionic conductance were calculated. The results obtained were interpreted according to the Samoylov’s theory of positive and negative hydration of ions. The differences observed in the temperature dependences of the mentioned parameters were explained in terms of the different radii and hydration numbers of the ions.