Normal Pulse Voltammetry and Steady State Voltammetry of the Square Mechanism at Spherical Microelectrodes

Abstract

[a] Dedicated to Professor R. G. Compton on the Occasion of his 60 th Birthday 1IntroductionThes quare mechanism given in Scheme 1d escribes many experimental systems where electron transfer processes are coupled to structural changes (isomerisation [1][2][3][4], conformation modifications [5,6]), complexation and ligand exchange [7],e ncapsulation [8],( de)protonation and substitution [9][10][11][12],i on pairing [13][14][15],e tc. This is also the case of ion transfer processes across liquid j liquid interfaces where complexation of the ion may take place in the organic and/or aqueous phases [16].M oreover, more simple situations,s uch as the CE, EC and ECE mechanisms,c an be studied as particular cases.T herefore, the theoretical and practical interest of the square scheme is well justified. Thea pproach to the square mechanism is not straightforward given the number of thermodynamic and kinetic variables involved, such that the complete understanding, identification and quantitative analysis are,a tl east, challenging. In this paper we aim to assist the above tasks by reporting as imple (yet accurate) analytical solution for the study of the square mechanism via normal pulse voltammetry (NPV) at microelectrodesa nd also steady state voltammetry.T he diffusive-kinetic steady state (dkss)a pproximation will be employed, which has led to accurate solutions for the CE and EC mechanisms [17][18][19][20] and it enables the derivation of closed-form expressions for the current response and the concentration profiles.A sm entioned above,m any different situations can be considered as particular cases of the square mechanism depending on the values of the formal potentials and the rate and equilibrium constants.I nt his paper we are going to focus on the situations where the two chemical processes take place with similar kinetics as well as on the CE and EC mechanisms.T hese last two mechanisms correspond to the particular cases of the square mechanism where only one of the electron transfers and only one of the chemical reactions occur. Other cases where one of the chemical reactions is significantly slower or even it does not take place (the ECE mechanism) will be tackled in the future.From the analytical solution deduced here,t he effects of the rate and equilibrium constants of the chemical reactions,t he difference between the formal potentials and the electrode radius on the electrochemical response will Abstract:Asimple analytical solution is presented for the study of the square mechanism in normal pulse and steady state voltammetries at spherical (ultra)microelectrodes.T he analytical expression deduced enables the description of ab road range of situations depending on the chemical kinetics and the difference between the halfwave potentials of the electron transfers.R egarding the chemical kinetics,t he electrochemical response is analysed from the limit of slow kinetics,w here the thickness of the reaction layer tends to coincide with that of the diffusion layer, up to the limit of very fast kinetics,w ...

Analytical theoretical approach to the transient and steady state voltammetric response of reaction mechanisms. Linear diffusion and reaction layers at micro- and submicroelectrodes of arbitrary geometry

“…and, in general, for any electrode geometry by: 10 cm s D   ) [21] (and also at macroelectrodes when the chemical kinetics is very fast ( 1   ) [14]). Therefore, the expressions reported in Table 5…”

“…The transient current-potential responseThe dkss assumptions enable the simple resolution of the diffusive-kinetic problems of all the reaction mechanisms (1)-(8) (see references[17,18,[21][22][23][24] and Supporting Information for scheme (d)) and the corresponding analytical solutions has proven to yield accurate results under transient conditions for fast chemical kinetics at electrodes of any shape and size[14].…”