Electrochimica Acta 56 (2011) 6812–6823 Contents lists available at ScienceDirect Electrochimica Acta j ourna l ho me pag e: www.elsevier.com/locate/electacta Transient solutions of potential steps at the rotating disc electrode with steady state initial concentration profiles for one electron transfer reactions Sönke Schmachtel ∗,1 , Kyösti Kontturi ∗∗,1 Laboratory of Physical Chemistry and Electrochemistry, School of Chemical technology, Aalto University, Kemistintie 1, PO Box 16100, 00076 Aalto, Finland a r t i c l e i n f o Article history: Received 5 April 2011 Received in revised form 18 May 2011 Accepted 21 May 2011 Available online 27 May 2011 Keywords: Rotating disc electrode Potential step Transient solution Closed form solution Background current rejection a b s t r a c t In this paper the transient solution of a potential step at a rotating disc electrode (RDE) for irreversible and quasireversible one electron transfer reactions is derived by Nernst diffusion layer approximation and separation of variables. This is then compared to finite element simulation results. For the initial conditions steady state concentrations are chosen, such that with this theory it is possible to fit and simulate quasi steady-state linear sweep RDE measurements or other quasi steady-state sequences of potential steps. It was found that it is possible to derive accurate closed form solutions for the initial parts of the transient response. However, the Nernst diffusion layer approximation leads to inaccuracies in the inter- mediate times with relative errors of up to 10%. By fitting the initial transient to the closed form solution it is possible to extract steady state background currents. Additionally, we use the potential step theory to derive an expression for kinetically controlled transition times and show that these can exceed the mass transport controlled transition time. © 2011 Elsevier Ltd. All rights reserved. 1. Introduction A common way to deal with background currents at the rotating disc electrode (RDE) would be to use hydrodynamic modulation at an RDE (HMRDE [1,2]), a technique that usually requires lock-in amplifiers and comes with a theory required to correct for nonlin- earity [3–6]. As an alternative to that, we will derive a theory for potential steps, which can be used for background current rejection with systems affected by electrochemical solid state reactions. The other key interest is to derive a theory for kinetic transients at the RDE to evaluate standard one electron transfer parameters with a special focus on kinetic parameters, such as the charge trans- fer coefficient ˛ and the standard rate constant k 0 . Mathematically more advanced and presumably more accurate is to solve the convection diffusion equation on a semi-infinite interval [7–11]. The easiest approach, when solving such transients, however, bases on transformation of the convection diffusion equation to a finite interval diffusion equation (Nernst diffuse layer model). Transient solutions are then derived using Laplace transformation ∗ Corresponding author. Tel.: +358 44020 3377. ∗∗ Corresponding author. Tel.: +358 50 505 2575; fax: +358 9 47022580. E-mail addresses: sonke.schmachtel@aalto.fi (S. Schmachtel), kyosti.kontturi@aalto.fi (K. Kontturi). 1 ISE member. methods [12–17], although this is not as trivial as for systems with a semi-infinite extension. Arising sinh and cosh terms have to be approximated by series to be able to do the back transformation to time domain [18]. We use the Nernst diffuse layer model approach in connection with the method of separation of variables, because it is a standard technique to solve transients in the heat/diffusion equation on a finite interval. Most of the transient models for the RDE use constant initial concentrations (flat bulk concentration profiles) and fast/reversible electrode reactions with constant concentration (Dirichlet) bound- ary conditions at the electrode [7,11,12,15]. Some systems have been solved for constant current or constant gradient (Neumann) boundary conditions [7,11,14]. With these models it is impossible to determine kinetic parameters, because a constant concentra- tion boundary condition assumes in practice very fast/reversible or actually infinite reaction rates. For the potential step experiment without convection it is known that it is only a matter of time until a quasireversible system behaves like a reversible one [2]. Due to the absence of convection near the surface of an RDE it can be suspected that its short time response will be similar to the potential step at a stationary electrode and reach a steady state surface con- centration after an initial kinetic transient. On the basis of the above assumptions it is possible to determine the length of the transients to be expected for RDE measurements as presented by [2,19]. 0013-4686/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2011.05.087