Tafel slope calculation

Some values of the Tafel slopes calculated for these two mechanisms for different values of the size parameter n are shown in Table 2J. 

Determine from this plot the Tafel slopes 6, and 6 by curve fitting using the theoretical curves calculated for various values of 6 and 6,.. Calculate from equation 19.14 using the Rp, value evaluated in Step 1 and the Tafel slopes determined in Step 3. 

The exact calculation of icorr for a given time requires simultaneous measurements of Rp and anodic and cathodic Tafel slopes (/> and be). Computer programs have been developed for the determination of precise values of /corr according to Eqs. (2) and (3). Experimental values of Rp (2p contain a contribution from the uncompensated solution resistance... 

Applications of Rp techniques have been reported by King et al. in a study of the corrosion behavior of iron pipes in environments containing SRB. In a similar study, Kasahara and Kajiyama" used Rp measurements with compensation of the ohmic drop and reported results for active and inactive SRB. Nivens et al. calculated the corrosion current density from experimental Rp data and Tafel slopes for 304 stainless steel exposed to a seawater medium containing the non-SRB Vibrio mtriegens. 

It is known that double-layer effects are the most pronounced in the reaction of multivalent ions in a dilute solution. According to the calculation of Grahame, d°HP A3 potential region far from the pzc. Evaluate the cathodic and anodic Tafel slope values for the reaction... 

Fig. 8.5. In electrochemical reactions involving one or more adsorbed reaction intermediates (sometimes involved in the rate-determining step), the steady-state concentration of the intermediate changes with the potential. However, each intermediate has a time constant to reach the surface coverage corresponding to a given overpotential. The downside of too low a pulse time, or too fast a sweep rate, is that the intermediate concentration does not relax to its appropriate concentration in time. The Tafel slope (sometimes a significant mechanism indicator) may then differ from that calculated for the assumed path and rate-determining step.

The actual current passed / = 2F/4Jt,[H + ]exp[ — J pAE] since two electrons are transferred for every occurrence of reaction I. Equation (1.64) constitutes the fundamental kinetic equation for the hydrogen evolution reaction (her) under the conditions that the first reaction is rate limiting and that the reverse reaction can be neglected. From this equation, we can calculate the two main observables that can be measured in any electrochemical reaction. The first is the Tafel slope, defined for historical reasons as ... 

The transfer coefficients are the ones determining how the electrode potential influences the electrochemical reaction rate or, in other words, the inclination of the relation between log I and the over-potential, also called the Tafel slope, of a multistep reaction. The coefficients are an important aid when unravelling the electrochemical reaction mechanisms, because the experimentally determined Tafel slope should correspond to the value that is calculated for the postulated sub-step sequence and RDS. 

Equation 4.45 cannot explain the experimentally observed influence of the pH and predicts a Tafel slope of 1 and an influence of the oxygen concentration, which was not experimentally observed. The rate equation for a rate-determining fourth stage of the reaction sequence was calculated with Equations 4.41,4.32,4.21,4.22 and 4.24, and, under the additional condition k 3 k4 and/or k 2 k4, the following applies ... 

The use of galvanostatic transients enabled the measurement of the poten-tiodynamic behavior of Li electrodes in a nearly steady state condition of the Li/film/solution system [21,81], It appeared that Li electrodes behave potentio-dynamically, as predicted by Eqs. (5)—(12), Section III.C a linear, Tafel-like, log i versus T dependence was observed [Eq. (8)], and the Tafel slope [Eq. (10)] could be correlated to the thickness of the surface films (calculated from the overall surface film capacitance [21,81]). From measurements at low overpotentials, /o, and thus the average surface film resistivity, could be measured according to Eq. (11), Section m.C [21,81], Another useful approach is the fast measurement of open circuit potentials of Li electrodes prepared fresh in solution versus a normal Li/Li+ reference electrode [90,91,235], While lithium reference electrodes are usually denoted as Li/Li+, the potential of these electrodes at steady state depends on the metal/film and film/solution interfaces, as well as on the Li+ concentration in both film and solution phases [236], However, since Li electrodes in many solutions reach a steady state stability, their potential may be regarded as quite stable within reasonable time tables (hours —> days, depending on the system s surface chemistry and related aging processes). 

The Tafel expressions for both the anodic and the cathodic reaction can be directly incorporated into a mixed potential model. In modeling terms, a Tafel relationship can be defined in terms of the Tafel slope (b), the equilibrium potential for the specific half-reaction ( e), and the exchange current density (70), where the latter can be easily expressed as a rate constant, k. An attempt to illustrate this is shown in Fig. 10 using the corrosion of Cu in neutral aerated chloride solutions as an example. The equilibrium potential is calculated from the Nernst equation e.g., for the 02 reduction reaction,... 

Equipped with the assumption of quasi-equilibrium, we can now proceed to calculate the Tafel slopes and some other kinetic parameters for a few very simple hypothetical cases, to show how such calculations are made. In Section 15 we shall discuss the kinetics of several reactions that either have been important in the development of the theory of electrode kinetics or are of current practical importance. 

We can readily calculate the Tafel slope for this case, if we assign a numerical value to the symmetry factor p. This, as we have said before, is commonly taken to be 0.5. The Tafel slope can then be obtained either from Eq. 5F, namely... 

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