Numerical modeling of non-steady-state ion transfer in electrochemical systems with allowance for migration (original) (raw)

A unified model for electrochemical electron and ion transfer reactions

Chemical Physics Letters, 1995

Electron and ion transfer reactions on metal electrodes are considered in an extended Anderson model, in which the interactions of the reactant with the metal and with the solvent depend on the separation from the interface. The model allows the construction of effective potential energy surfaces. Explicit calculations are performed for the transfer of an iodide ion and for the electron transfer reaction of the Fe2+/Fe 3+ couple.

Mass-transfer problems in the electrochemical systems

Russian Journal of Electrochemistry, 2012

The problems concerning quantitative analysis of mass transfer processes in the electrochemical systems (ECS) are briefly reviewed. The interrelation between the mass transfer problems in the electro chemical and heat systems is considered. Various approaches to the numerical determination of distributions of concentrations of ions of all types and electrochemical potential in the ECS are considered. The methods of allowance for the migration transfer and choosing the boundary conditions for the transfer equations and other problems are considered. Some actual lines of development of the theory of mass transfer in the ECS are pointed out.

Electroneutrality and ionic interactions in the modeling of mass transport in dilute electrochemical systems

Electrochimica Acta, 2011

We propose a simple, but novel mathematical and numerical approach to describe mass transport in dilute solutions, taking into consideration ionic interactions. Our proposed approach treats fluxes due to ionic interactions as additional unknowns in the transport equation. Through variational arguments, we derive a simple expression for these ionic fluxes in terms of the electroneutrality condition, which allows for a straightforward treatment of the new unknowns. Furthermore, a finite element formulation based on our mathematical model is presented. Finally, using the distribution of the interionic flux density and an energy dissipation function, we show that besides properly capturing flow due to ionic interactions, our model can also describe independent ionic flow as predicted by the conventional Nernst-Planck equation in regions where ionic interactions are weak.

1D Mathematical Modelling of Non-Stationary Ion Transfer in the Diffusion Layer Adjacent to an Ion-Exchange Membrane in Galvanostatic Mode

Membranes, 2018

The use of the Nernst⁻Planck and Poisson (NPP) equations allows computation of the space charge density near solution/electrode or solution/ion-exchange membrane interface. This is important in modelling ion transfer, especially when taking into account electroconvective transport. The most solutions in literature use the condition setting a potential difference in the system (potentiostatic or potentiodynamic mode). However, very often in practice and experiment (such as chronopotentiometry and voltammetry), the galvanostatic/galvanodynamic mode is applied. In this study, a depleted stagnant diffusion layer adjacent to an ion-exchange membrane is considered. In this article, a new boundary condition is proposed, which sets a total current density, , via an equation expressing the potential gradient as an explicit function of . The numerical solution of the problem is compared with an approximate solution, which is obtained by a combination of numerical solution in one part of the d...

Ion Transport Models for Electroanalytical Simulation. 1. Theoretical Comparison

The Journal of Physical Chemistry B, 2009

Ion transport models are compared by computing the limiting current density of an electrodeposition on a rotating disk electrode for various hypothetical electrolytes. The first ion transport model is the pseudoideal solution model, on which many commercial electroanalytical simulation tools are built. The second, more rigorous model consists of the linear phenomenological equations for which the activity coefficients and Onsager coefficients are calculated locally with the mean spherical approximation (MSA).

Study of Ion Transport Models for Electroanalytical Simulation. Part 2: Experimental Comparison †

The Journal of Physical Chemistry A, 2009

Ion transport models are compared by simulating the limiting current density of copper deposition from aqueous CuSO 4 solutions on a rotating disk electrode. The first ion transport model is the pseudoideal solution model, on which many commercial electroanalytical simulation tools are built. The second, more rigorous model consists of the linear phenomenological equations for which the activity coefficients and Onsager coefficients are calculated locally with the mean spherical approximation (MSA). The influence of the formal association constant in the pseudoideal solution model is also investigated.

Mathematical Modeling of Electrode Processes – Potential Dependent Transfer Coefficient in Electrochemical Kinetics

InTech eBooks, 2012

This chapter is dedicated to professor Zbigniew Galus, who consistently applied mathematical approach to electrochemical kinetics and to memory of professor Bogdan Jakuszewski who was succeeded in both theoretical and experimental electrochemistry. In chemical kinetics, elementary (one step) and complex (multi-step) processes are described. Exactly the same situation is observed in electrochemical kinetics where electron transfer steps and chemical steps are often coupled in various sequences. Therefore, electrochemical kinetics uses two kinds of kinetic parameters: elementary describing each single step of kinetic sequence and general (apparent, observed) relating to or describing the complex mechanism as a whole. Consequently, there is a need of showing similarities, dissimilarities and relations between the two approaches to avoid possible confusion. The following significant problems are to be discussed here:  The distinction among apparent and elementary kinetic parameters (Sanecki & Skitał, 2002a; Skitał & Sanecki, 2009).  The accuracy of electrochemical kinetic parameters determination by the estimation method (Sanecki et al., 2003, 2006b).

Simple kinetic models of ion transfer across an interface between two immiscible electrolyte solutions

Electrochimica Acta, 1998

The Nernst±Planck equation is used to examine the kinetic behavior of three simple models of ion transfer, which all assume that the potential of mean force acting on the ion can be obtained as a superposition of the solvation potential and the electrical double layer potential. A comparison is made with the experimental kinetic data for 21 ion transfer reactions at the water/nitrobenzene interface. It is shown that only the models which account in an explicit way for the eect of the electrical double layer can provide a plausible description of experimental behavior. In particular, the absence of a correlation between the apparent standard rate constant or the apparent charge transfer coecient and the standard Gibbs energy of ion transfer across the water/nitrobenzene interface can be due to the mutual compensation of the eect of electrical double layer and the eect of the dierence in solvation energy on the ion transfer rate. It is concluded that a double layer correction is necessary to obtain true kinetic parameters of ion transfer across the interface.

Application of the Convective Diffusion Equation with Potential-Dependent Boundary Conditions to the Charge Transfer Problem in Four-Electrode Electrochemical Cell on the Condition of Small Hydrodynamic Velocity

International Journal of Electrochemical Science, 2016

To describe charge transfer in a four-electrode electrochemical cell for the Iodide-Iodine redox system, the Nernst-Plank equations and the boundary conditions based on the kinetics of the reactions on the electrodes have been modified, assuming the small active component ( 3 I) concentration relative to the background electrolyte concentration (components  I and metal ions  Me). The resulting mathematical model comprises the convective diffusion equation and the Laplace type equation for the potential, while the boundary conditions on the electrodes bond the potential and the concentration of  3 I. The approach was applied for the classical one-dimensional model in case of small hydrodynamic velocity. For realistic parameters of the system, the modelling results are different from the solution of the convective diffusion equation with the fixed concentration on the electrodes and are in good agreement with the experimental data.

Transient Ion Dynamics in Electrolytic Cells - General Approach and Numerical, Nonlinear Analysis

Recent Patents on Catalysis, 2012

The present work reviews the results, obtained by numerical examination of the space and time behavior of ion charges in electrolytic cell when external electric field is applied. The basic governing equations for free ions have been generalized for ion-pairs, the simple boundary conditions for blocking electrodes are generalized taking into account the charge transfer currents at the electrodes, the equilibrium Einstein-Nernst relation between ion mobility and diffusivity is modified to take into account the transient, non-equilibrium processes. All these problems are tackled with the help of a common numerical algorithm applied in both linear and nonlinear approximation. Special attention is attributed to nonlinear processes, to thin cells with nano-scaled inter-electrode gap, to non-equilibrium states and their relaxation to equilibrium, to the enhancement of the interface electrode polarization and capacity by charge pump through a complementary electrode etc. Recent patents concerning electrochemical cells and super-capacitors have also been shortly reviewed.