Computational and Experimental Study of the Cyclic Voltammetry Response of Partially Blocked Electrodes. Part 1. Nonoverlapping, Uniformly Distributed Blocking Systems Benjamin A. Brookes, ² Trevor J. Davies, ² Adrian C. Fisher, ‡ Russell G. Evans, ² Shelley J. Wilkins, ² Kamran Yunus, ‡ Jay D. Wadhawan, ² and Richard G. Compton* ,² Physical and Theoretical Chemistry Laboratory, Oxford UniVersity, South Parks Road, Oxford OX1 3QZ, United Kingdom, and Department of Chemistry, UniVersity of Bath, ClaVerton Down, Bath BA2 7AY, United Kingdom ReceiVed: August 6, 2002; In Final Form: NoVember 18, 2002 The cyclic voltammetry response of partially blocked electrodes is modeled using finite difference simulations and a method presented for determining currents at electrode surfaces which have a well-defined geometric blocking pattern. Peak current and peak separation data are presented for six decades of scan rates, blocking coverage values between 0.1 and 0.9 and between the limits of reversible and irreversible electrochemistry. The validity of the simulation approach employed is verified by data obtained experimentally from purpose- built partially blocked gold film electrodes, with either a cubic or hexagonal geometric array of electroinactive disks uniformly distributed on the electrode surface. Comparison of theory with experiment suggests that the modeling of hexagonally distributed blocking systems is superior to that of the cubically arranged ones. 1. Introduction Electrochemistry at partially blocked electrodes (PBEs) presents an intriguing problem because the surface blocking of the electrode modifies the absolute and relative rates of diffusive and kinetic flux to the electrode surface. 1-20 Not only can these changes lead to inaccurate electrochemical interpretation but, in some circumstances, the blocked electrode may be mistaken for an unblocked one with the wrong mechanism. 1 Significant research has therefore been undertaken in order to quantify the electrochemistry at PBEs, with the main aim of producing a reliable method for interrogating the characteristics of the surface blocking with existing electrochemical techniques. Since some of the earliest studies carried out by Landsberg, 2-8 results have been published for stationary and rotating disk PBEs with a particular emphasis on impedance techniques. 1-20 Most of the analytical theory accompanying these studies has been derived using underlying simplifications in order to reduce the complexity of the problem. The most unsatisfactory simplifica- tions are highlighted 13,16 as (1) mass transport being formulated under steady-state conditions, (2) the implementation of a Nernst diffusion layer in stationary or rotating conditions, and (3) the omission of radial or axial convection terms. To a large degree, these are circumvented in analytical work by Matsuda 13-15 at stationary partially blocked electrodes, and results were pre- sented for Faradaic impedance, chronoamperometry, chrono- potentiometry, and potential sweep voltammetry. Nevertheless, significant assumptions are introduced in this modeling in order to find a tractable solution. The inaccuracy of such results has been highlighted by data gathered from the numerical solution of the diffusion partial differential equations (PDE), a process which is becoming increasingly favorable with recent advances in computers. 17,18,20 Extensive as the literature is, Amatore 16 has pointed out that the applicability of previous work has been limited to PBEs with macroscopic inhomogeneity, and so all electrochemistry must be considered diffusion limited. Ama- tore’s one-dimensional formulation 16 of the model generates results and allows a method for surface characterization (where electrochemistry is not necessarily reversible) from cyclic voltammogram characteristics. Many authors have performed experimental studies in order to validate theoretically generated results. 13-15 These employ model electrodes fabricated by several methods, including the use of photoresist layers, 13 laser ablation of metal surfaces, 10 and controlled sintering of metal powders followed by applica- tion of Araldite. 10 Where possible, the authors tried to maintain a regular geometry of blocking units in the model PBEs, for example cubic or hexagonal packing. To the authors’ knowl- edge, the dependence of the electrode current on the electrode surface blocking geometry has not been investigated in an experimental context in any depth. This would seem reasonable given that many intrinsically inhomogeneous surfaces that might be experimentally studied would not replicate the geometric regularity of the model electrodes and the theory that ac- companies it. Significant extensions of both theory and experi- mental models are required if the research is to be extended to incorporate such partially blocked electrodes. The aim of this work is to, via a simulation approach, find a general method for characterizing the transient responses of PBEs where both the reversibility of the reaction and the diffusion layer length have a significant effect on the current. In this paper, the effects of blocking geometry on the cyclic voltammetric response are investigated using model gold film partially blocked electrodes in which disk shaped blocks are arranged in a cubic or hexagonally packed geometry. In subsequent work, 21 we will consider the effects of having a * To whom correspondence should be addressed. E-mail: richard.compton@chemistry.oxford.ac.uk. Phone: +44 (0) 1865 275 413. Fax: +44 (0) 1865 275 410. ² Oxford University. ‡ University of Bath. 1616 J. Phys. Chem. B 2003, 107, 1616-1627 10.1021/jp021810v CCC: $25.00 © 2003 American Chemical Society Published on Web 01/29/2003