Symmetry coefficient

The symmetry coefficient = —P d nk/dAE is usually close to j, in agreement with the Marcus formula. Turning to the quantum limit, one observes that the barrier transparency increases with increasing AE as a result of barrier lowering, as well as of a decrease of its width. Therefore, k grows faster than the Arrhenius rate constant. At 7 = 0... 

This relationship is the analogue of the BPS rule for tunneling reactions. The quantum symmetry coefficient a, = — d nk /dAE is greater than and it may exceed 1. 

The symmetry coefficient a is important in electrode kinetics, but less important for the operation of electrochemical sensors. The discussion of its meaning can be found in standard electrochemical textbooks (e.g. Koryta et al., 1993). Its value typically lies between 0.3 and 0.7. 

Charge transfer coefficient— (also called transfer coefficient or electrochemical transfer coefficient or symmetry coefficient (factor)) [i-vi]. 

In Eqs. (42)-(44), i g is the steady-state current density at potential V, / the charge-transfer symmetry coefficient, io the exchange current density, I the integration constant for Eq. (41), and r (0) the initial overpotential at time t = 0. 

Eq. (41) factorizes the coefficient to the semiempirical parameter as a first factor, , tabulated in Table 6, and depending only on the symmetry of the system. This factor, the symmetry coefficient, may be calculated using Table 7 and Eq. (98). The second factor, the geometry coefficient ]/A/ + (2). depends on the coordinates of the... 

For convenience we use the terms symmetry coefficient and geometry coefficient. However, it should be noted that the geometry coefficient is sometimes also symmetry-determined. This is the case in our cubic example of p. 94 and in all of Table 8. 

The factor a is the charge transfer coefficient described above. The charge transfer coefficient characterizes the symmetry of the activation energy barrier and therefore is also sometimes called symmetry coefficient. This is made clear in Fig. 3, where a is seen to be the fractional length along the reaction coordinate from the metallic state at which the activated state is located. The value of a is typically close to 0.5 when a = 0.5, the activated state is exactly midway between the two end... 

Equation (1.2.40) is very frequently used to determine the formal potential of a redox system with the help of cyclic voltammetry however, one should never forget that it holds true only for reversible systems, and provided that the symmetry coefficient a = 0.5 (see Chap. 1.3). To be cautious, it is better to refer to the value determined by Eq. (1.2.40) as the mid-peak potential determined by cyclic voltammetry. The formal potential E has the same meaning as discussed above for direct current polarography. Hence Eqs. (1.2.32) and (1.2.34) can be applied accordingly. 

The third index of the symmetry coefficients results from the possible values of and Ki,Kj, respectively, under the restrictions included in the Kronecker delta. It can be seen from these equations that the main contribution to the electron-electron interaction potentials at the origin is given by the (R ) expectation value, which by far dominates the above expressions. Additional contributions can be written in terms of (r ") matrix elements. These small corrections, which cause the shell dependence of the electron-electron interaction potentials, result from the local self-interaction term and the non-local... 

Figure 1.4 Example of a cell of a charging accumulator or an electrolyzer for which all the symmetry coefficients are equal to 0.5, the exchange current densities 10 mA/cm and T = 330 K. [TUR 08]...

C7 is a symmetry coefficient which depends on the complexity of the molecule, and whose value is, at most, a few units. 

P is the charge transfer barrier (symmetry coefficient) for the anodic or cathodic reaction, usually close to 0.5 n is the number of participating electrons R is the gas constant, that is, 8.314 J mol" K ... 

The symmetry coefficient d nk/dAE is usually close to in agreement with the... 

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