Unusual, Non‐Cottrell Behavior of Ionic Transport in Thin Cells and in Films

Abstract

Transport of a single-salt MX across thin-layer solid/liquid electrolyte cells and corresponding membranes is treated with consideration of the bulk resistance and the resulting bulk voltage drop. The interfaces are reversible ionic or M]M +z character, and X -~ is blocked. The analysis uses floating boundary conditions but linearizes the nonlinear, implicit equations describing current, voltage, and transport parameters. Bulk resistance causes a major distribution of applied voltage between interfacial and bulk components. Modified Cottrell current-time responses appear, in time-region sequence, with ohmic, normal Cottrell, exponential, and steady-state characteristics. Closely related problems are treated approximately, including impedances, e.g., small-amplitude ac responses, of resistive films with simultaneous dc voltage applied and with simultaneous dc current flow; analysis of passive networks with dc-voltage-dependent circuit elements; and distribution of resistivity across small and large levels of concentration-polarized thin-layer films and cells.Reversible-interface-process Cottrell behavior.--The Cottrell equation describes current-time (I-t) responses for one-dimensional, semi-infinite, mass-transport-controlled supply of a reagent reacting reversibly at a uniformly accessible smooth interface in an unstirred medium (1-3). Non-Cottrell responses often imply electron-transfer irreversibility (4), although other kinetic schemes for complex stepwise reactions, especially coupled chemical reaction followed by electron transfer (CE) type, can give non-Cottrell responses as well (5, 6).The Cottrell equation appears when describing I-t responses of a single interfacially permeable species in a static, concentrated, inert supporting electrolyte (1-3). Interfacial permeability, here, includes classical, reversible metal/metal, and ion exchange transport. Bulk ion motions of the permeable species are uncoupled by local electroneutrality conditions, and the applicable diffusion coefficient is that for the single ion moving in a homogeneous medium. Cottrell behavior can also be found in moderately low concentrations of supporting electrolytes, even less concentrated than the electroactive species itself. Then, ion motions are coupled and the Nernst-Planck (dilute solution form) is applied to each ionic species (7-9). The result is a Cottrell equation with a new, coupled diffusion-migration coefficient involving the single-ion values of the reversible ion and all other counterions. In the absence of supporting electrolytes, the coupling is stronger. The Nernst-Planck equation is obeyed, but the diffusion coefficient is the coupled salt value and the transference numbers of cation and anion often appear in the final results (see below). Cottrell behavior, e.g., current proportional to t -~/2 over all time, is not expected for thin cells under voltage step perturbations.Unavoidable bulk resistance.--An internal IR drop is characteristic of thin film and membrane cells, and the internal field cannot be avoided or i...

Transport Properties of H+‐Selective Membranes Containing Amine‐Derivative Ionophores and Mobile Sites

“…where R is the gas constant; T is the temperature; A is the area; F is the faraday; d is the thickness of the membrane; D, is the diffusion coefficient of ion i, and C,(x) is the ionic concentration of either positive ion-complexes or negative sites at x inside the membrane. Whether the membrane resistance is constant or variable depends on the extent of change in ionic concentration profiles, as the potential-step experiment progresses [20] [21]. The absence of change in resistance may be due to several factors pertaining to experimental conditions and membrane properties such as i) small currents in a system where both ionic species (AB' and s-) have large diffusion coefficients, ii) high ionic concentrations, iii) immobility of sites and consequential no change in ionic concentration profiles due to electroneutrality requirements ( e g .…”

Non-Cottrell current–time relationship, caused by reactant adsorption in differential pulse polarography

“…linear dependence of current on t À½ ) belongs to the fundamentals of electrochemistry [16], some processes with different types of current-time relationship are also known [17][18][19]. Such effects could be explained in different ways, but (as far as we know) adsorption was not treated as a possible reason although its influence on current-time relationship could be extracted from the existing results [20,21].…”

Ultrahigh Specific Power Electrochemistry, Exemplified by Al/MnO4- and Cd/AgO Redox Chemistry

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