Steady-State Limiting Currents Determined by Coupled Diffusion, Migration, and Chemical Equilibrium

Abstract

A simple theoretical model is presented for the reduction of a singly charged cation under conditions where migration is important and the cation is coupled to a neutral species through a chemical equilibrium, AB = A(+) + B(-). Only the steady-state transport-limited current, I(l), is considered. Simple algebraic equations describe the ratio of I(l) to the diffusion-limited current, I(d), as it depends on the degree of dissociation, determined by the ratio of equilibrium constant to formal concentration, K(AB)/C*(AB). The ratio I(l)/I(d) is found to depend on the ratio of electrolyte to equilibrium concentration of A(+) in bulk solution just as for the well-known result for the case without the equilibrium (i.e., K(AB) → ∞). The results are in accord with published experimental data for weak acids. Agreement and disagreement with other theoretical treatments of this problem are discussed. The main results are for 1:1 supporting electrolytes; extensions are made to 2:1, 1:2, and 2:2 supporting electrolytes.

Modeling the Effects of Ion Association on Direct-Current Polarization of Solid Polymer Electrolytes

“…In this analysis, all species have distinct diffusion coefficients. Previous analyses 24,25 introduced an apparent diffusion coefficient representing an average of cation and ion-pair diffusivities weighted by the degree of dissociation. Depending on the weighting approach, the apparent diffusion coefficient may be between those of cations and anions 24 or greater than both.…”

“…Depending on the weighting approach, the apparent diffusion coefficient may be between those of cations and anions 24 or greater than both. 25 In this work, we develop a general model for transport in polymer electrolytes which accounts for ion association. Our aim is to provide a rigorous foundation that encompasses previous models [17][18][19] and brings them to completion.…”

“…11 and using the boundary condition Eq. 20 gives [25] Substituting this into Eq. 10 and integrating produce ⌸ I,lim ϵ 1.…”

Switching between voltammetry and potentiometry in order to determine H+ or OH− ion concentration over the entire pH scale by means of tungsten disk electrode

“…As regards to the pH measurements in acidic solutions, several non-potentiometric techniques were reported involving optical detection [12][13][14][15][16][17], chronopotentiometric measurements [1] and voltammetric measurements with internal reference [18]. The voltammetry of proton reduction on suitable type of electrodes, such as platinum microelectrodes [19][20][21][22][23][24] and highly boron-doped diamond (BDD) electrodes [25] was commonly reported as a method for acidity determination.…”

Toward Infinite-Dilution Voltammetry

“…Since the inception of microelectrode voltammetry, it has been recognized that electrodes of very small dimensions allow meaningful measurements to be made in solutions with very little or no intentionally added electrolyte. , The greatest emphasis in studies to date has been upon the measurement of limiting currents, particularly the influence of electromigration of charged reactants and products, though some attention has been paid to the shape and position of the steady-state voltammograms obtained with microelectrodes. ,, An important application that to our knowledge has not yet been reported is the measurement of reversible half-wave potentials from steady-state voltammograms as a function of electrolyte concentration so that extrapolation to infinite dilution can be achieved to obtain potentials unaffected by the ions of the electrolyte (activity and ion pairing effects). This paper presents the first measurements of this kind.…”