Temperature dependence of electrode reaction

According to Eq. (14.2), the activation energy can be determined from the temperature dependence of the reaction rate constant. Since the overall rate constant of an electrochemical reaction also depends on potential, it must bemeasured at constant values of the electrode s Galvani potential. However, as shown in Section 3.6, the temperature coefficients of Galvani potentials cannot be determined. Hence, the conditions under which such a potential can be kept constant while the temperature is varied are not known, and the true activation energies of electrochemical reactions, and also the true values of factor cannot be measured. 

Before proceeding to direct attention to the real temperature dependence of Tafel slopes as found experimentally for a number of systems, it will be necessary to review the conventional behavior usually assumed and describe its theoretical and historical origins. The remarkable contrast of the behavior actually observed, to be described in Section III, to that conventionally assumed will then be apparent and thus the present major gap in our understanding of the fundamental aspect of potential dependence of electrode reaction rates will be better perceived. 

The rate of an electrode process directly depends on magnitude, of the potential drop at the electrode-solution interface. Therefore, while determining the activation energy from the temperature dependence of the reaction rate, we would have to maintain constant not only such common independent variables as pressure P and concentration m, but also ... 

The type of electrode reaction that will occur depends on the electrode and electrolyte and also on external conditions the temperature, impurities that may be present, and so on. Possible reactants and products in these reactions are (1) the electrode material, (2) components of the electrolyte, and (3) other substances (gases, liquids, or solids) which are not themselves component parts of an electrode or the electrolyte but can reach or leave the electrode surface. Therefore, when discussing the properties or behavior of any electrode, we must indicate not merely the electrode material but the full electrode system comprising electrode and electrolyte as well as additional substances that may be involved in the reaction for example, ZnCl2, ag I (Clj), graphite [the right-hand electrode in (1.19)]. 

Uchida H, Izumi K, Watanabe M. 2006. Temperature dependence of CO-tolerant hydrogen oxidation reaction activity at Pt, Pt-Co, and Pt-Ru electrodes. J Phys Chem B 110 21924-21930. 

Agar had suggested in 1947 that there might be a temperature dependence of p, the electrode kinetic parameter, and Conway took this up in 1982 and showed experimentally that in certain reactions this was the case. 

In either group of electrode reactions, the energy level of reacting particles (electrons or ions) in the electrode depends linearly on the electrode potential. Hence, the reaction afiinily (A = — AG) can be varied over a wide range by simply controlling the electrode potential. This is one of the characteristics of electrode reactions, in contrast with ordinary chemical reactions whose affinity can be varied in a relatively narrow range by controlling the temperature and the concentration of reaction particles. 

The latter authors used anode and cathode symmetrical cells in EIS analysis in order to simplify the complication that often arises from asymmetrical half-cells so that the contributions from anode/ electrolyte and cathode/electrolyte interfaces could be isolated, and consequently, the temperature-dependences of these components could be established. This is an extension of their earlier work, in which the overall impedances of full lithium ion cells were studied and Ret was identified as the controlling factor. As Figure 68 shows, for each of the two interfaces, Ra dominates the overall impedance in the symmetrical cells as in a full lithium ion cell, indicating that, even at room temperature, the electrodic reaction kinetics at both the cathode and anode surfaces dictate the overall lithium ion chemistry. At lower temperature, this determining role of Ra becomes more pronounced, as Figure 69c shows, in which relative resistance , defined as the ratio of a certain resistance at a specific temperature to that at 20 °C, is used to compare the temperature-dependences of bulk resistance (i b), surface layer resistance Rsi), and i ct- For the convenience of comparison, the temperature-dependence of the ion conductivity measured for the bulk electrolyte is also included in Figure 69 as a benchmark. Apparently, both and Rsi vary with temperature at a similar pace to what ion conductivity adopts, as expected, but a significant deviation was observed in the temperature dependence of R below —10 °C. Thus, one... 

The double-layer effect in the electrode kinetics of the amalgam formation reactions was discussed [67]. The dependences on the potential of two reduction (EE) mechanisms of divalent cations at mercury electrode, and ion transfer-adsorption (lA) were compared. It was suggested that a study of temperature dependence of the course of these reactions would be helpful to differentiate these two mechanisms. 

In previous sections, apparent rate coefficients of electrode reactions have been described as a function of the electrode—electrolyte potential difference. As in other chemical processes, their dependence on temperature can be expressed by the Arrhenius equation... 

There has been keen interest in determination of activation parameters for electrode reactions. The enthalpy of activation for a heterogeneous electron transfer reaction, AH X, is the quantity usually sought [3,4]. It is determined by measuring the temperature dependence of the rate constant for electron transfer at the formal potential, that is, the standard heterogeneous electron transfer rate constant, ks. The activation enthalpy is then computed by Equation 16.7 ... 

The cuprous-cupric electron transfer reaction is believed to be the rate-limiting step in the process of stress corrosion cracking in some engineering environments [60], Experimental studies of the temperature dependence of this rate at a copper electrode were carried out at Argonne. Two remarkable conclusions arise from the study reviewed here [69] (1) Unlike our previous study of the ferrous-ferric reaction [44], we find the cuprous-cupric electron transfer reaction to be adiabatic, and (2) the free energy barrier to the cuprous cupric reaction is dominated in our interpretation by the energy required to approach the electrode and not, as in the ferrous-ferric case, by solvent rearrangement. 

Decomposition potential (voltage) — The onset voltage for electrochemical decomposition of the electrolytic solution or the electrodes. The decomposition can take place due to either oxidation or reduction, or both. The decomposition potentials define the electrochemical window of the system. Its value depends on the salt, solvent, electrode material, temperature, and the existence of materials that can catalyze decomposition reactions, such as Lewis acids. Exact decomposition voltages are hard to reproduce as the onset current of the process is very sensitive to the experimental conditions (e.g., scan rate, temperature, type of electrode, etc.). Decomposi-... 

A voltmeter is an electronic instrument that measures the voltage between its two leads. The student in Figure 14 is using the meter to measure the difference in potentials between the electrodes in a Daniell cell. With such a meter, measuring the voltage of a cell is easy. However, the voltage of a cell depends on such factors as temperature and concentration. And because there are so many combinations of electrode reactions, it would be very difficult to measure the voltage for each combination. 

While the form of the Tafel equation with regard to the potential dependence of i is of major general interest and has been discussed previously both in terms of the role of linear and quadratic terms in 77 " and the dependence of the form of the Tafel equation on reaction mechanisms/ the temperature dependence of Tafel slopes for various processes is of equal, if not greater general, significance, as this is a critical matter for the whole basis of ideas of activation and reorganization processes " in the kinetics of electrode reactions. 

Following the first indication in the work of Stout" that b can be independent of temperature, Bockris and Parsons, and Bockris et showed that a similar effect arose in the h.e.r. at Hg in methanolic HCl between 276 and 303 K below these temperatures, b apparently varied in the conventional way with T. However, the derived a values showed a considerable spread. Variations of the temperature effect in b were discussed in terms of the possible influence of impurities but an overall assessment of all other, more recent, observations of the dependence of 6 on T for various types of reactions leads to the conclusion that the unconventional dependence is not due to some incidental effect of impurities. In fact, in another paper, Bockris and Parsons" suggested that the temperature dependence of p for the h.e.r. at Hg arose because of expansion of the inner region of the double layer with temperature. They also noted that, formally, for b to be independent of T, the entropy of activation should be a function of electrode potential. 

Factors (1) to (5) above are known in one way or another to affect the kinetics of an electrode reaction including, in most cases, the Tafel slope. Since the anion adsorption is normally temperature dependent owing to the usually finite enthalpy of adsorption (most chemisorptions are energy as well as entropy controlled in their thermodynamics), it follows that anion effects could give rise to unconventional temperature dependence of a. 

Further measurements need to be made on the temperature and potential dependence of the rates of simple ionic redox reactions at electrodes with proper corrections for double-layer effects at various temperatures, so that the temperature dependence of (3 for an elementary electron transfer reaction, without chemisorption and coupled atom transfer, would become better known. This is an essential requirement for progress in understanding the true significance of the temperature effects on electrode-kinetic behavior reliable experiments will not, however, be easy to accomplish and will require parallel double-layer studies over a range of temperatures. 

Chapter 2, by B. E. Conway, deals with a curious fundamental but hitherto little-examined problem in electrode kinetics the real form of the Tafel equation with regard to the temperature dependence of the Tafel-slope parameter 6, conventionally written as fe = RT/ aF where a is a transfer coefficient. He shows, extending his 1970 paper and earlier works of others, that this form of the relation for b rarely represents the experimental behavior for a variety of reactions over any appreciable temperature range. Rather, b is of the form RT/(aH + ctsT)F or RT/a F + X, where and as are enthalpy and entropy components of the transfer coefficient (or symmetry factor for a one-step electron transfer reaction), and X is a temperature-independent parameter, the apparent limiting... 

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