Butler-Volmer equation dimensionless

Pi partial pressure of species i, atmosphere Butler-Volmer equation, dimensionless... 

For the quasireversible case, the procedure is as follows. At a given stage in the simulation, assume that the two concentration profiles, C, i and CB,i, with i = 1,2,..., N, have been calculated and that the potential is p. The dimensionless form of the Butler-Volmer equation applies (2.30) and provides the concentration gradient G A, proportional to the current ... 

For the reversible case, the Nernst equation applies instead of the Butler-Volmer equation, that is, in dimensionless terms as in (2.32), rewritten as... 

A quasireversible system is characterised by the Butler-Volmer equation, here in dimensionless form,... 

Lastly, the system described by Reaction (5) might be quasireversible or even irreversible, in which case the boundary condition is given by the Butler-Volmer equation. It is preferable to express it in dimensionless form, using potential p, and the heterogeneous rate constant ko... 

Here n is the nnmber of moles of electrons involved in the reaction the rate constants have been assumed to be thermally activated and kj and kl are potential-independent rate constant parameters. The potential-dependent concentrations CRed and Cox are evaluated at their points of closest approach to the electrode, taken here as the outer Helmholtz plane. Further, a is here a dimensionless symmetry factor often assumed to be 0.5 (the symmetrical barrier case), and is the charge transfer overvoltage effective in driving the reaction away from eqnilibrium (for Rmh = 0, J = 0). The Butler-Volmer equation is usually a good approximation for both biased and unbiased conditions. 

For the quasireversible case, two species A and B must again be considered and the two boundary conditions are the flux condition (2.49) and the dimensionless form of the Butler-Volmer equation. The forward and backward heterogeneous rate constants kf and kb are normalised ... 

In above two equations, rrij is an integer constant which takes values of -1, +1, and 0 for species R(z-i) Os and inert electrolyte species respectively if the reduction current is considered positive p refers to the thickness of the compact EDL Fq refers to the radius of electrode y is the ratio between the standard rate constant of ET reaction and the mass transport coefficient of the electroactive species. It can be seen that the current density, which is given in a dimensionless form through normalization with the limiting diffusion current density (i, and the electrostatic potential distribution appear simultaneously in the two equations. Equation 2.2 could be approximated to the PB equation at low current density, while Equation 2.3 would reduce to Eq. 2.4, which is the diffusion-corrected Butler-Volmer equation and has been used to perform voltammetric analysis in conventional electrochemistry, as exp(-Zj/ rcp/F)=1, that is, electrostatic potentials in CDL are close to zero. These conditions are approximately satisfied in large electrode systems, suggesting that the voltammetric behaviour and the EDL structure can be treated separately at large electrode interface ... 

The dimensionless time (t), potential ( ), and current (i/0 are all as defined in equations (1.4). The exact characteristics of the voltammograms depend on the rate law. In the case of Butler-Volmer kinetics,... 

The two successive electron transfer reactions are assumed to obey the Butler-Volmer law with the values of standard potentials, transfer coefficient, and standard rate constants indicated in Scheme 6.1. It is also assumed, matching the examples dealt with in Sections 2.5.2 and 2.6.1, that the reduction product, D, of the intermediate C, is converted rapidly into other products at such a rate that the reduction of B is irreversible. With the same dimensionless variables and parameters as in Section 6.2.4, the following system of partial derivative equations, and initial and boundary conditions, is obtained ... 

Introduction of r, p = [P]/C , = nF/RT(E - E), and in the Volmer-Butler rate law [Eq. (143)] readily yields Eq. (168). The latter shows that a convenient dimensionless rate of electron transfer is A = k (5/D, since it compares the intrinsic value of the rate constant to that of the mass transfer process. Thus Eq. (168) reformulates as Eq. (169). Let us now examine the time- and space-dependent partial derivative equation of the kind demonstrated by Eq. (158), which describes variations in the concentration profiles in the stagnant layer adjacent to the electrode. For any species S, introducing t, y, and s leads to reformulation of Eq. (158) as in Eq. (170) ... 

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