Voltage-step transient on circular electrodes

Abstract

Using the well-known Cottrell asymptote, voltage-step transient (VST) experiments in a two-electrode cell may provide data on the bulk concentration and diffusion coefficient of a working depolarizer, essential for interpretation of liming-diffusion-current (LDC) experiments. However, the Cottrell asymptote is never applicable in the early stages of the voltage-step transient process.There are three additional transport resistances to the basic diffusion transport that cannot be neglected at extremely high initial currents: Faradaic resistance at the working electrode surface, overall Ohmic losses in the electrochemical cell, and a possible galvanometric constraint in the outer circuit, involving the galvanometer, current follower, potentiostat, etc. The effect of these additional transport resistances on the transient current at higher polarization voltage is non-linear. In the present analysis, a 1D approximation is used, assuming tacitly uniform accessibility of the working electrode and negligible transport resistances at the counter electrode. The Faradaic resistance of a redox couple O ? ne -= R according to ButlerVolmer electrode kinetics is considered. The results of 1D theory are corrected for edge effects using the Oldham asymptote. The effect of convection at longer times is included using the recent model of a transient process for circular working electrodes in the LDC regime. List of symbols Variables AEffective area of working electrode, m 2 A ? area of ideally smooth working electrode, m 2 B:c B;W O;R Molar concentration of depolarizers and their boundary values (mol m -2 s -1 ) D, D O,R Coefficient of diffusion; values for the components (m 2 s -1 ) d À1=2 T Semi-integral operator E = Exp[P] f = (E -1)/(E?B), Nernst-Petersen factor G = k G /k S , normalized galvanometric constraint I Current (A) J O,R Diffusion fluxes of depolarizers at surface (mol m -2 s -1Rate constant factor in Butler-Volmer kinetics (m s -1 ) k C = U/(nFAR C c B work ), Ohmic limit for k(t) (m s -1 ) k G = I G /(nFA c B work ), galvanometric constraint (m s -1 ) k S = lk C , starting (upper) limit for k(t) (m s -1 ) L C Equivalent resistor length (m) M: K/k C nFThe charge transfer per 1 mol of the working depolarizer (C mol -1 ) N = N(T) : k/k S , normalized flux O. Wein (&) Á

Estimate of mass-transfer rate via Nernst model with Ohmic losses

“…For detecting a remarkable effect of a fast electrode reaction on the electrochemically driven convective dif fusion, the mass transfer coefficient should be larger (and diffusion thickness lesser) by two decimal orders. Such experimental conditions can be realized in the early stage of the voltage step experiment [6].…”

“…The quantities w O,R , characterizing the concentra tion profiles of the both depolarizers, are related by the constraint (6) which follows from the mass balance and reaction sto ichiometry.…”

“…(4), (6), and (8) results in a sin gle equation, interrelating the current density, expressed through w = k/k* = i/i* and the voltage, expressed through Р. In particular, for the Oxy form as a working depolarizer, w = w O etc., the Nernst model provides the equation…”

“…Parameters Р and β are always constant, В is con stant for the steady laminar high Peclet cases [2,7], p = 2/3, or the early stage asymptote of the voltage step experiment [6], p = 1/2:…”

“…The electrochemical testing and calibrations of the ED cells is based on two standard electrochemical techniques-quasi steady voltammetry and voltage step transient. Recently published theory [6] of the voltage step transient under simultaneous effect of Faradaic and Ohmic resistances is based on a suitably extended Nernst model. An analogous theory of the voltammetric experiment is presented here.…”