Nernstian boundary condition

The simulation of other electrochemical experiments will require different electrode boundary conditions. The simulation of potential-step Nernstian behavior will require that the ratio of reactant and product concentrations at the electrode surface be a fixed function of electrode potential. In the simulation of voltammetry, this ratio is no longer fixed it is a function of time. Chrono-potentiometry may be simulated by fixing the slope of the concentration profile in the vicinity of the electrode surface according to the magnitude of the constant current passed. These other techniques are discussed later a model for diffusion-limited semi-infinite linear diffusion is developed immediately. 

VIII. OTHER NERNSTIAN ELECTRODE BOUNDARY CONDITIONS... 

The boundary condition to introduce is the Nernstian condition at the electrode surface ... 

Instead of the Nernstian boundary condition we have to introduce... 

Nernstian boundary conditions, or those for quasireversible or irreversible systems. All of these cases have been analytically solved. As well, there are two systems involving homogeneous chemical reactions, from flash photolysis experiments, for which there exist solutions to the potential step experiment, and these are also given they are valuable tests of any simulation method, especially the second-order kinetics case. 

In the Cottrell experiment, as described in the last section, we have a step to a very negative potential, so that the concentration at the electrode is kept at zero throughout. It is possible also to step to a less extreme potential. If the system is reversible, and we consider the two species A and B, reacting as in (2.18), then we have the Nernstian boundary condition as in (2.24). Using (2.29) and assigning the symbols CA and Cb, respectively, to the dimensionless concentrations of species A and B, we now have the new boundary conditions for the potential step,... 

As noted in Section 2, when the electron-transfer kinetics are slow relative to mass transport (rate determining), the process is no longer in equilibrium and does not therefore obey the Nernst equation. As a result of the departure from equilibrium, the kinetics of electron transfer at the electrode surface have to be considered when discussing the voltammetry of non-reversible systems. This is achieved by replacement of the Nernstian thermodynamic condition by a kinetic boundary condition (36). 

For an nernstian heterogeneous electron transfer, the boundary conditions at the electrode formulate as in Eqs. (194) and (195) ... 

For the case where adsorbed O is reduced in a totally irreversible one-step, one-electron reaction (32, 33), the langmuirian-nernstian boundary condition (14.3.9) is replaced by a kinetic one, similar to that used for dissolved reactants [e.g., (6.3.1)] ... 

For a simple cyclic voltammetry experiment with Nernstian equilibrium at the electrode surface, this function is given by Eq. (2.7). For other experimental techniques, different potential-dependent boundary conditions may be used. 

The electrode surface boundary conditions are only relevant in the Z-sweep as that sweep considers diffusion perpendicular to the surface. If we suppose Nernstian equilibrium, then the electrode boundary conditions are met by using the following coefficients for the first point, j = 0, of every coliunn... 

When the concentration boundary layer is sufficiently thin the mass transport problem can be solved under the approximation that the solution velocity within the concentration boundary layer varies linearly with distance away from the surface. This is called the L6v que approximation (8, 9] and is satisfactory under conditions where convection is efficient compared with diffusion. More accurate treatments of mass transfer taking account of the full velocity profile can be obtained numerically [10, 11] but the Ldveque approximation has been shown to be valid for most practical electrodes and solution velocities. Using the L vSque approximation, the local value of the concentration boundary layer thickness, 8k, (determined by equating the calculated flux to the flux that would be obtained according to a Nernstian diffusion layer approximation that is with a linear variation of concentration across the boundary layer) is given by equation (10.6) [12]. 

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