Limiting current, electrochemical reactions

Ohmic Control The overall electrochemical reactor cell voltage may be dependent on the kinetic and mass-transfer aspects of the electrochemical reactions however, a third factor is the potential lost within the electrolyte as current is passing through this phase. The potential drops may become dominant and limit the electrochemical reactions requiring an external potential to be applied to drive the reactions or significantly lower the delivered electrical potential in power generation applications such as batteries and fuel cells. 

In the previous section we saw how voltammetry can be used to determine the concentration of an analyte. Voltammetry also can be used to obtain additional information, including verifying electrochemical reversibility, determining the number of electrons transferred in a redox reaction, and determining equilibrium constants for coupled chemical reactions. Our discussion of these applications is limited to the use of voltammetric techniques that give limiting currents, although other voltammetric techniques also can be used to obtain the same information. 

An electrochemical reaction is said to be polarized or retarded when it is limited by various physical and chemical factors. In other words, the reduction in potential difference in volts due to net current flow between the two electrodes of the corrosion cell is termed polarization. Thus, the corrosion cell is in a state of nonequilibrium due to this polarization. Figure 4-415 is a schematic illustration of a Daniel cell. The potential difference (emf) between zinc and copper electrodes is about one volt. Upon allowing current to flow through the external resistance, the potential difference falls below one volt. As the current is increased, the voltage continues to drop and upon completely short circuiting (R = 0, therefore maximum flow of current) the potential difference falls toward about zero. This phenomenon can be plotted as a polarization diagram shown in Figure 4-416. 

The first study on the oxidation of arylmethanes used this reaction as a model to show the general advantages of electrochemical micro processing and to prove the feasibility of an at this time newly developed reactor concept [69]. Several limits of current electrochemical process technology hindered its widespread use in synthetic chemistry [69]. As one major drawback, electrochemical cells stiU suffer from inhomogeneities of the electric field. In addition, heat is released and large contents of electrolyte are needed that have to be separated from the product. 

Key Components Most electrochemical reactions involve several reactants and/or products. The surface concentrations of all of them change. As the current density is raised, the limiting concentration for one of them will be attained before it is attained for the others. This substance can be called the key component for this reaction. The actual limiting current attained in the system corresponds to the limiting current of this key component (i.e., is determined by its parameters, in particular by its concentration). 

The basic theory of mass transfer to a RHSE is similar to that of a RDE. In laminar flow, the limiting current densities on both electrodes are proportional to the square-root of rotational speed they differ only in the numerical values of a proportional constant in the mass transfer equations. Thus, the methods of application of a RHSE for electrochemical studies are identical to those of the RDE. The basic procedure involves a potential sweep measurement to determine a series of current density vs. electrode potential curves at various rotational speeds. The portion of the curves in the limiting current regime where the current is independent of the potential, may be used to determine the diffusivity or concentration of a diffusing ion in the electrolyte. The current-potential curves below the limiting current potentials are used for evaluating kinetic information of the electrode reaction. 

This value represents the upper limit of a first order reaction rate constant, k, which may be determined by the RHSE. This limit is approximately one order of magnitude smaller that of a rotating electrode. One way to extend the upper limit is to combine the RHSE with an AC electrochemical technique, such as the AC impedance and faradaic rectification metods. Since the AC current distribution is uniform on a RHSE, accurate kinetic data may be obtained for the fast electrochemical reactions with a RHSE. 

B. Electrochemical Reactions Used in Limiting-Current Measurements. 219... 

From an analysis of the electrochemical mass-transfer process in well-supported solutions (N8a), it becomes evident that the use of the molecular diffusivity, for example, of CuS04, is not appropriate in investigations of mass transfer by the limiting-current method if use is made of the copper deposition reaction in acidified solution. To correlate the results in terms of the dimensionless numbers, Sc, Gr, and Sh, the diffusivity of the reacting ion must be used. 

The exchange current density, /0- From equations (1.28) and (1,29) it is clear that /Q is a direct measure of the kinetics of the reaction at the equilibrium potential Er. A high exchange current density indicates a facile electrochemical reaction that will rapidly become limited by transport at potentials away from E°. 

Since transport and electrochemical reactions are in series, the slower process determines the overall current. Hence we can obtain the rate constants of the reaction only, if the reversible current jrev is not much slower than the kinetic current. This limits the magnitude of the reaction rates that can be measured with any given method. 

There are, however, obvious limitations. It is not possible to make a very small spherical electrode, because the leads that connect it to the circuit must be even much smaller lest they disturb the spherical geometry. Small disc or ring electrodes are more practicable, and have similar properties, but the mathematics becomes involved. Still, numerical and approximate explicit solutions for the current due to an electrochemical reaction at such electrodes have been obtained, and can be used for the evaluation of experimental data. In practice, ring electrodes with a radius of the order of 1 fxm can be fabricated, and rate constants of the order of a few cm s 1 be measured by recording currents in the steady state. The rate constants are obtained numerically by comparing the actual current with the diffusion-limited current. 

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