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The Influence of Migration on Cyclic and Rotating Disk Voltammograms Journal of Electroanalytical Chemistry 538Á/539 (2002) 25Á/33 www.elsevier.com/locate/jelechem The influence of migration on cyclic and rotating disk voltammograms N.P.C. Stevens, Alan M. Bond School of Chemistry, Monash University, PO Box 23, 3800 Clayton, Vic., Australia Received 8 February 2002; received in revised form 15 May 2002; accepted 17 June 2002 Abstract Standard methods of analysis based on the dependence of current magnitudes and waveshapes on scan rate (cyclic voltammetry) Ef ;ks;a and rotation rate (rotating risk electrode voltammetry) are available to interpret processes of the form Az X A(zn) ne when the migration current is negligible. Using analysis of simulated voltammograms, the present study shows that when a migration current is present, it simply acts as a scaling factor with respect to current magnitudes and introduces a small potential shift. The effects are equivalent to altering the diffusion coefficient in the fully supported case. Experimental detection of migration can be confirmed by examining the concentration dependence of a process, but not by dependence on scan rate or rotation rate. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Cyclic voltammetry; Migration; Low support; Low ionic strength; Added supporting electrolyte; Simulation; Finite difference 1. Introduction provides hydrodynamic control of the time domain (rather than the potential scan rate), which also may Recently [1,2], there has been renewed interest in be valuable in mechanistic studies [13]. undertaking voltammetric studies in the absence of In the solution phase, voltammetry is traditionally added supporting electrolyte (ASE) or in dilute electro- undertaken in the presence of a large excess of added lyte media such as ionic liquids, particularly when supporting electrolyte (ASE). For studies on a reversible microelectrodes are employed under near steady state E z f (zn) conditions [1Á/8] (minimum IR drop). However, cyclic A XA ne (1) and rotating disk electrode (RDE) voltammetry also are or a kinetically controlled process: viable [9,10] techniques that offer some advantages E;k ; relative to the microelectrode method. For example, f s a Az X A(zn) ne (2) the inherent simplicity of the interpretation of transient cyclic voltammograms at stationary electrodes with (where E f8 is the formal potential of the couple, ks is the respect to electrochemical and chemical reversibility, heterogeneous rate constant and a is the transfer and mechanistic evaluations of electrode processes is an coefficient for the electrode reaction), the key to obvious advantage. Consequently, this is frequently the theoretical evaluation of such mechanisms is the mass technique preferred by experimentalists for obtaining transport process. In cyclic voltammetry, diffusion, as thermodynamic and kinetic data [11,12], using simulated described by Eq. (3) (Fick’s second law) waves or tabulated data derived from numerical analysis dc @2c of the theory as a reference. Rotation of the electrode D (3) dt @x2 (where D is the diffusion coefficient and c is the Corresponding author. Tel.: /61-3-9905-4507; fax: /61-3-9905- 4597 concentration of the species of interest, t is the time, E-mail addresses: [email protected] (N.P.C. Stevens), and x is the distance from the electrode) is the only form [email protected] (A.M. Bond). of mass transport. When the electrode rotates, the 0022-0728/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 7 2 8 ( 0 2 ) 0 1 0 1 5 - X 26 N.P.C. Stevens, A.M. Bond / Journal of Electroanalytical Chemistry 538Á/539 (2002) 25Á/33 diffusionÁ/convection relationship (Eq. (4)) applies. we focus only on the effects of migration on mass transport. dc @2c @c D u (4) dt @x2 @x (where u is the velocity in the x-direction). 2. Experimental In studies without adequate ASE, a term representing migration has to be added to the equations to give: The simulations of cyclic voltammetry at a stationary macrodisk and the RDE were performed using a dc @2c F @ @f D Dz c (5) previously described finite difference technique [10], dt @x2 RT @x @x allowing the accurate reproduction of voltammograms for solutions where defined levels of supporting electro- (where z is the charge of the species, and f is the lyte are present, and the interfacial kinetics are governed potential, and F, R and T have their usual meanings) or by the ButlerÁ/Volmer equation. The use of an explicit with convection: finite difference method requires the use of very fine dc @2c F @ @f @c time increments to ensure the stability of the simulation, D Dz c u (6) as the time step size is proportional to the square of the dt @x2 RT @x @x @x smallest element of the grid used. It has been the In the presence of electrolyte, there are well defined experience of the authors that a finer grid is needed relationships that are frequently employed in analysis, for simulations where migration is a factor than for diffusion alone, and so for the simulations presented, a for example the RandlesÁ/Sevcˇik equation which is used 5 in linear sweep voltammetry at a stationary electrode: minimum of 10 time steps were employed. Cyclic voltammograms were simulated at stationary nF 1=2 macrodisk electrodes as a function of scan rate, and at a I 0:4463nFAc n D1=2 (7) P B RT rotating disk electrode (RDE) at a fixed rotation rate. The effects of migration on the shape and position of the (where IP is the peak current, n is the number of resulting waves were determined, relative to the case electrons transferred in the electrode reaction, A is the where migration is negligible (with excess ASE). 2 electrode area, cB is the bulk concentration and n is the An electrode of area 1 cm was assumed. Unless scan rate) and the Levich equation in RDE voltamme- otherwise stated, all species share a common diffusion try. coefficient of 105 cm2 s1. The reversibility of a 1=2 1=6 2=3 voltammogram at a stationary electrode may be gauged ILim 0:62nFAcBv V D (8) using the parameter c, as defined by Nicholson [20]. (where ILim is the limiting current, v is the rotation rate D a=2 nF 1=2 1 2 1 React in rad s and V is the kinematic viscosity in cm s ). c ks pDReact n (9) D RT In the present paper, we wish to examine the influence Prod of migration on cyclic and RDE voltammetry using the (where DReact and DProd are the diffusion coefficients of well defined relationships that apply in the absence of the reactant and the product species, or DOx and DRed, migration as a reference point. It will emerge from the respectively, for a reduction, and vice versa for an analysis that migration acts to perturb the voltammo- oxidation process). grams in a similar manner to a change in diffusion Reversible processes were simulated using large values coefficient. The implications of this conclusion are for ks, the heterogeneous charge transfer rate constant 1 discussed. for the electrode reaction in cm s , such that c ]/20, It is important to distinguish between migration with quasi-reversible behaviour being expected for lower [3,14,15], the mass transport caused by the movement c-values [20]. In all cases presented, a, the charge of ions in response to an electric field, and ohmic drop transfer coefficient, was equal to 0.5. Two cases are [5,11,16Á/18], which enhances the overpotential at the presented in detail, being the one electron oxidation of a electrode surface. Although both effects derive from the species A to A2, and the one electron reduction of presence of the electric field, their actions are different. A2 to A. For each ease, the species A is present as n If a high enough overpotential is applied to any A Xn , at a concentration of 1 mM, along with a solution, a limiting condition may be achieved at the supporting electrolyte species MX. To achieve con- electrode surface, where ohmic drop has no further ditions approximating infinite support, MX concen- discernible effect [19]. The action of migration on mass trations of 10 M were employed in the simulations, and transport depends on the solution composition in the for low support levels where, migration is significant, diffusion layer (and so on the bulk composition), and MX concentrations of 0.02 mM were used (this the exact nature of the electrode reaction. In this paper, being considered more realistic than assuming zero N.P.C. Stevens, A.M. Bond / Journal of Electroanalytical Chemistry 538Á/539 (2002) 25Á/33 27 concentrations of species apart from the analyte). enological sense even when a migration current is However, calculations performed with 0.02 mM ASE present. It follows that if the level of supporting or none are almost indistinguishable, as are results for electrolyte is unknown, as can be the ease with ionic 10 M compared with 1 M ASE. liquids, but is falsely assumed to be adequate to be the purposes of analysis, incorrect conclusions will be arrived at using any method of interpretation based on 3. Results and discussion diffusion-only theory. 3.1. Reversible cyclic voltammetry 3.1.2. Analysis of peak positions Section 3.1.1 concerns linear sweep voltammetry, 3.1.1. Peak current dependence on scan rate whereas in the present section, the influence of migra- In linear sweep voltammetry a linear dependence of IP tion on cyclic voltammetry is considered. Fig. 2(a) shows on n1/2 is generally taken as proof that a process is a cyclic voltammogram for the oxidation of A to A2, diffusion controlled, as in Ref.
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