Reaction Orders in Electrode Kinetics

The reaction order is defined in chemical kinetics by the partial derivative 

In electrode kinetics, the reaction order is defined in a similar manner, but, in addition to keeping the temperature and the pressure constant, a constant potential is maintained. As a result, there are two reaction orders in electrode kinetics, one taken at constant potential 

It is important to distinguish between these two parameters, since the reversible potential changes as we change the concentration of the reactant, and the overpotential can thus change while the applied potential remains constant. 

the potential , which we keep constant, is that measured with respect to a fixed reference electrode. It does not matter which reference electrode is used, as long as it is the same throughout the experiment. Actually, we would like to obtain the reaction order while keeping the metal-solution potential difference, constant. This would seem to be impossible, since cannot be measured, as 

Which of the two reaction-order parameters should one prefer When measurement is made with a constant reference electrode (e.g., calomel), the reaction order at constant potential, p, is obtained. If, however, an indicator-type reference electrode is employed (e.g., a reversible hydrogen electrode, often used in the study of the hydrogen-evolution reaction), the overpotential can be kept constant and the parameter P2 is the one directly obtained. In either case, both parameters can be calculated 

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Extensive work on reaction orders in electrode kinetics, and their interpretation, have been made by Vetter (140), Yokoyama and Enyo for the Clj evolution and other reactions (141, 142, 144), and by Conway and Salomon for the HER (143). In the extensive treatment of the kinetics of O2 evolution by Bockris (145), reaction orders were derived for various possible reaction mechanisms and provide, among other factors, diagnostic criteria for the mechanisms in relation to the experimentally determined behavior, for example, pH effects in the kinetics and Tafel slope values (145). 

In electrode kinetics, however, the charge transfer rate coefficient can be externally varied over many orders of magnitude through the electrode potential and kd can be controlled by means of hydrodynamic electrodes so separation of /eapp and kd can be achieved. Experiments under high mass transport rate at electrodes are the analogous to relaxation methods such as the stop flow method for the study of reactions in solution. 

In electrode kinetics, the reaction order with respect to the species k can be defined by... 

A distinguishing aspect in electrode kinetics is that the heterogeneous rate constants, kred and kox, can be controlled externally by the difference between the inner potential in the metal electrode (V/>M) and in solution (7/>so1) that is, through the interfacial potential difference E = electrode setup (typically, a three-electrode arrangement and a potentiostat), the E-value can be varied in order to distort the electrochemical equilibrium and favor the electro-oxidation or electro-reduction reactions. Thus, the molar electrochemical Gibbs energy of reaction Scheme (l.IV), as derived from the electrochemical potentials of the reactant and product species, can be written as (see Eqs. 1.32 and 1.33 with n = 1)... 

Considering first the direct kinetic methods for the study of electrode processes, the mechanistic criterion of most consequence is Ra/b, the reaction order in substrate and primary intermediate as defined by (55) (Parker, 1981e). Using DCV as an example of a direct kinetic technique we can write... 

We recall that the current is a very sensitive measure of the rate of an electrochemical reaction. It is therefore quite easy to determine the current-potential relationship without causing a significant change in the concentration of either reactants or products. Thus, measurements in electrode kinetics are conducted effectively under quasi-zero-order kinetic conditions. It would be wrong to infer from this that electrode reactions are independent of concentration. To determine the concentration dependence (i.e., the reaction order), one must obtain a series of HE or //ri plots and derive from them plots of log i versus logC. at different potentials, as shown in Fig. IF. The slopes in Fig. lF(b) yield the parameter p since p = (alog i/alogC.) is measured at constant potential E. Here, and in all further equations, we shall assume that T, P, and the concentration of all other species in solution are kept constant, to permit us to write the equations in a more concise form. 

The Tafel slope for this mechanism is 2.3RT/PF, and this is one of the few cases offering good evidence that P = a, namely, that the experimentally measured transfer coefficient is equal to the symmetry factor. A plot of log i versus E for the hydrogen evolution reaction (h.e.r.), obtained on a dropping mercury electrode in a dilute acid solution is shown in Fig. 4F. The accuracy shown here is not common in electrode kinetics measurements, even when a DME is employed. On solid electrodes, one must accept an even lower level of accuracy and reproducibility. The best values of the symmetry factor obtained in this kind of experiment are close to, but not exactly equal to, 0.500. It should be noted, however, that the Tafel line is very straight that is, P is strictly independent of potential over 0.6-0.7 V, corresponding to five to six orders of magnitude of current density. 

In contrast to the above results, Davitt and Albright (555) reported kinetically controlled reduction of acetylene and ethylene-acetylene mixtures at positive potentials. Surface reaction of hydrogen atoms with associatively adsorbed acetylene was postulated, based on the negative reaction order in acetylene and on the experimental Tafel slope of about 120 mV. However, possible diffusion in the porous electrode structure was not considered. Pore diffusion could alter the order and the Tafel slope as shown later. 

Thus, the reaction order in the reactant itself is useful to evaluate. If the reactant is likely to be adsorbed significantly, then the reaction order must be interpreted, as in other types of heterogeneous reactions, with due attention to the type of adsorption isotherm and the extent of coverage. Since the kinetics of electrode reactions depend in a primary way on the potential (see Section 4), the reaction order must be specified and evaluated with respect to a constant electrode potential. Usually a supporting (electrochemically inactive) electrolyte is used so that effects of ion distribution and potential in the double layer remain approximately constant as other quantities are varied in the experimental analysis, viz., pH, reactant concentration. 

This is an example of a reversible reaction the standard electrode potential of the 2PS/PSSP + 2c couple is zero at pH 7. The oxidation kinetics are simple second-order and the presence of a radical intermediate (presumably PS-) was detected. Reaction occurs in the pH range 5 to 13 with a maximum rate at pH 6.2, and the activation energy above 22 °C is zero. The ionic strength dependence of 2 afforded a value for z Zg of 9 from the Bronsted relation... 

Thus, worldwide efforts have focused on the elucidation of the reaction mechanism. For this purpose, knowledge about the following items is vital (1) identification of reaction products and the electrode kinetics of the reactions involved, (2) identification of adsorbed intermediate species and their distribution on the electrode surface, and (3) dependence of the electrode kinetics of the intermediate steps in the overall and parasitic reactions on the structure and composition of the electrocatalyst. It is only after a better knowledge of the reaction mechanisms is obtained that it will be possible to propose modifications of the composition and/or structure of the electrocatalyst in order to significantly increase the rate of the reaction. 

Consider the case when the equilibrium concentration of substance Red, and hence its limiting CD due to diffusion from the bulk solution, is low. In this case the reactant species Red can be supplied to the reaction zone only as a result of the chemical step. When the electrochemical step is sufficiently fast and activation polarization is low, the overall behavior of the reaction will be determined precisely by the special features of the chemical step concentration polarization will be observed for the reaction at the electrode, not because of slow diffusion of the substance but because of a slow chemical step. We shall assume that the concentrations of substance A and of the reaction components are high enough so that they will remain practically unchanged when the chemical reaction proceeds. We shall assume, moreover, that reaction (13.37) follows first-order kinetics with respect to Red and A. We shall write Cg for the equilibrium (bulk) concentration of substance Red, and we shall write Cg and c for the surface concentration and the instantaneous concentration (to simplify the equations, we shall not use the subscript red ). 

Early studies of ET dynamics at externally biased interfaces were based on conventional cyclic voltammetry employing four-electrode potentiostats [62,67 70,79]. The formal pseudo-first-order electron-transfer rate constants [ket(cms )] were measured on the basis of the Nicholson method [99] and convolution potential sweep voltammetry [79,100] in the presence of an excess of one of the reactant species. The constant composition approximation allows expression of the ET rate constant with the same units as in heterogeneous reaction on solid electrodes. However, any comparison with the expression described in Section II.B requires the transformation to bimolecular units, i.e., M cms . Values of of the order of 1-2 x lO cms (0.05 to O.IM cms ) were reported for Fe(CN)g in the aqueous phase and the redox species Lu(PC)2, Sn(PC)2, TCNQ, and RuTPP(Py)2 in DCE [62,70]. Despite the fact that large potential perturbations across the interface introduce interferences in kinetic analysis [101], these early estimations allowed some preliminary comparisons to established ET models in heterogeneous media. 

In Chapter 7 general kinetics of electrode reactions is presented with kinetic parameters such as stoichiometric number, reaction order, and activation energy. In most cases the affinity of reactions is distributed in multiple steps rather than in a single particular rate step. Chapter 8 discusses the kinetics of electron transfer reactions across the electrode interfaces. Electron transfer proceeds through a quantum mechanical tunneling from an occupied electron level to a vacant electron level. Complexation and adsorption of redox particles influence the rate of electron transfer by shifting the electron level of redox particles. Chapter 9 discusses the kinetics of ion transfer reactions which are based upon activation processes of Boltzmann particles. 

The kinetics of MeOH oxidation of a 1 1 PfRu in an MEA has been well established by Vidakovic, Christov, and Sundmacher. At low overpotentials, the MeOH oxidation reaction was found to be zero order in MeOH concentration, indicating that CO oxidation is the rate-determining step. A Tafel slope of 50-60 mV dec was found at 60°C. At higher overpotentials, positive reaction orders were found, suggesting that MeOH adsorption becomes rate determining. An activation energy of 55 kj moP was found this agrees well with the values found for similar bulk PtRu electrodes. 

Equations 2.26 and 2.27 carmot be solved analytically except for a series of limiting cases considered by Bartlett and Pratt [147,192]. Since fine control of film thickness and organization can be achieved with LbL self-assembled enzyme polyelectrolyte multilayers, these different cases of the kinetic case-diagram for amperometric enzyme electrodes could be tested [147]. For the enzyme multilayer with entrapped mediator in the mediator-limited kinetics (enzyme-mediator reaction rate-determining step), two kinetic cases deserve consideration in this system in both cases I and II, there is no substrate dependence since the kinetics are mediator limited and the current is potential dependent, since the mediator concentration is potential dependent. Since diffusion is fast as compared to enzyme kinetics, mediator and substrate are both approximately at their bulk concentrations throughout the film in case I. The current is first order in both mediator and enzyme concentration and k, the enzyme reoxidation rate. It increases linearly with film thickness since there is no... 

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