Diffuse-Charge Dynamics in Electrochemical Systems

The response of a model micro-electrochemical system to a time-dependent applied voltage is analyzed. The article begins with a fresh historical review including electrochemistry, colloidal science, and microfluidics. The model problem consists of a symmetric binary electrolyte between parallel-plate, blocking electrodes which suddenly apply a voltage. Compact Stern layers on the electrodes are also taken into account. The Nernst-Planck-Poisson equations are first linearized and solved by Laplace transforms for small voltages, and numerical solutions are obtained for large voltages. The ``weakly nonlinear'' limit of thin double layers is then analyzed by matched asymptotic expansions in the small parameter $\epsilon = \lambda_D/L$, where $\lambda_D$ is the screening length and $L$ the electrode separation. At leading order, the system initially behaves like an RC circuit with a response time of $\lambda_D L / D$ (not $\lambda_D^2/D$), where $D$ is the ionic diffusivity, but nonlinearity violates this common picture and introduce multiple time scales. The charging process slows down, and neutral-salt adsorption by the diffuse part of the double layer couples to bulk diffusion at the time scale, $L^2/D$. In the ``strongly nonlinear'' regime (controlled by a dimensionless parameter resembling the Dukhin number), this effect produces bulk concentration gradients, and, at very large voltages, transient space charge. The article concludes with an overview of more general situations involving surface conduction, multi-component electrolytes, and Faradaic processes.Comment: 10 figs, 26 pages (double-column), 141 reference

Open-Circuit Photovoltage and Charge Recombination at Semiconductor/Liquid Interfaces

The open-circuit photovoltage (Voc) of semiconductor/ liquid junction solar cells is a critical parameter in determining the energy conversion efficiency. The fundamental process controlling Voc is the recombination of photoexcited electrons and holes. 1' 2 The lower the recombination rate, the larger the Voc. The predominant energy-loss mechanism is determined by competition among the following processes: majority-carrier thermionic emission over the surface barrier, ~ majority-carrier charge transfer across the semiconductor/liquid interface, ~' 4 minority-carrier diffusion/recombination in the bulk of the semiconductor, ~' 8 space-charge recombination, 7 and surface recombination mediated by recombination centers. 8-13 The extent to which each of these processes is understood differs considerably. For example, expressions describing the minority-carrier diffusion/recombination in the bulk semiconductor contacting a redox electrolyte is obtained by direct analogy to formulas developed for solid-state p-n junction devices. ~ When bulk diffusion/recombination is the dominant recombination process, the dependence of Vo~ on the semiconductor bandgap, doping level, and minority-carrier diffusion length can be expressed in simple analytic forms? In contrast, surface recombination has generally been treated in a more complex fashion by numerical simulation. TM In cases in which Voe is limited by surface recombination, no simple analytic expression exists for relating Vo~ and the surface recombination velocity (Sr)-Several groups TM have considered theoretically the effect of surface recombination on the performance of photoelectrochemical (PEC) cells. Although each treatment has achieved some success in describing a certain aspect of the effect of surface recombination, these treatments are generally considered qualitative3 ~ For the most part, it has been difficult to extract quantitative information on surface recombination from * Electrochemical Society Active Member. Visiting professor, on leave of absence from Korea University, Seoul, Korea. experimental results because of the number of adjustable (and often arbitrary) parameters involved in numerical analyses. Up to now, only one study 11 has dealt directly with the dependence of Voc on the surface recombination current; however, because bias-independent surface recombination currents in arbitrary units were used in the numerical calculation, it is difficult to apply the model of this study for interpreting quantitatively experimental measurements. Other studies 8-I~ have focused mainly on the general shape of the photocurrent-voltage (J-V) curves, without addressing the dependence of Voo on Sr. b The absence of a theoretical framework relating Sr to Vo~ impedes the understanding of such processes at the solid/liquid interface. In this article, we derive a simple quantitative expression, based on semiconductor solid-state theory, that directly relates Sr to Voc. The applicability of the expression to account for the PEC behavior of n-St/acetone with FeCp~ j~ (ferrocenium ion/ferrocene) is then investigated. Based on J-Vdata and the dependence of Voe on both the temperature and the concentration of FeCp~, we are able to exclude other possible recombination channels and identify surface recombination as the dominant recombination process in determining Voc. The surface recombination velocity deduced from experimental results compares favorably with reported values. The application of the analytic expression to other PEC systems reported in the literature is also discussed. b The effect of surface recombination is generally discussed in terms of the photoeurrent onset potential. However, unlike the concept of the "open-circuit photovoltage," the "photoeurrent onset potential" is an empirical quantity that cannot be precisely defined. The photocurrent onset potential depends on both Voc and the fill factor. The latter two parameters are more definable quantities and are more relevant in calculating the PEC conversion efficiency