Effects Due to Uncompensated Resistance and Capacitance

Electrochemists are aware of the annoying residual uncompensated solution resistance Ru between the Luggin probe and the working electrode, see, for example, [1], Although it is possible in principle to compensate fully for the iR error thus introduced [2,3], this is rarely done, as it introduces, in practice, undesirable instrumental oscillations or, in the case of damped feedback [3], sluggish potentiostat response. 

The other often annoying fact electrochemists must live with is the double layer capacitance Cdi. This produces capacitive currents whenever the appUed potential changes (see again [1]). The two effects work together, as capacitive currents also give rise to further iR errors. 

With potential step methods, the capacitive current is a transient, decaying with a time constant equal to RuCdi- The usual procedure is to wait several of these time constants before making the current measurement, by which time the capacitive current has declined to a negligible value. It is therefore not a serious problem with potential step experiments. 

Bowyer et al. [5] and Strutwolf [6] show examples of such distorted potentialtime relations and also distorted LSV curves, see also below. 

The simulation literature deals with this problem sporadically, although it is often simply ignored. The iR effect introduces nonlinear boundary conditions (see below), and these have been dealt with in various ways. Gosser [7] advocates simple subtraction, using known measured currents of the experiment one is simulating in order to fit some parameter. Deng et al. [8] use a stepwise procedure that 

Dieter Britz Digital Simulation in Electrochemistry, Lect. Notes Phys. 666, 193—199 (2005) www.springerlink.com c Springer-Verlag Berlin Heidelberg 2005 

Simulations must thus handle the nonlinear boundary conditions. Some have taken the easy way out and used explicit methods [123,429]. Bieniasz [105] used the Rosenbrock method (see Chap. 9), which makes sense because it effectively deals with nonlinearities without iterations at a given time step. 

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In Fig. II. 1.12, cyclic voltammograms incorporating both IR drop and capacitance effects are shown. Effects for the ideal case of a potential independent working electrode capacitance give rise to an additional non-Faradaic current (Fig. II. 1.12b) that has the effect of adding a current, /capacitance = Cw x v, to both the forward and backward Faradaic current responses. Tbe capacitance, Cw, is composed of several components, e.g. double layer, diffuse layer, and stray capacitance, with the latter becoming relatively more important for small electrodes [61]. On the other hand, the presence of uncompensated resistance causes a deviation of the applied potential from the ideal value by the term R x /, where R denotes the uncompensated resistance and I the current. In Fig. II. 1.12, the shift of the peak potential, and indeed the entire curve due to the resistance, can clearly be seen. If the value of Ru is known (or can be estimated from the shape of the electrochemically reversible... 

The effect of too high a scan rate is due to the existence of the interfacial capacitance, whereas the effect of uncompensated ohmic resistance is the result of the solution resistance between the working electrode surface and the point in solution at which the reference electrode senses this potential. These effects are explained in more detail below. 

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