KINETICS OF ELECTRODE REACTION

Now we are discussing the kinetics of reaction at electrodes, whether anode or cathode. The electrode reaction occurs due to the potential difference of electrode surface. In electrochemical reaction, we can manipulate the additional driving force of reaction, i.e the electric potential, beside the conventional parameters such as temperature and catalyst.
Electrode kinetics are governed by the potential difference across the thin layer ( on the order of 10 A) at the electrode surface which is named as the electrical double layer. When we apply a potential to an electrode, the charges accumulate on the electrode surface and attract ions of the opposite charges from the electrolyte. The potential distribution in the double layer is complicated, however for the first approximation we can model the double layer as a simple parallel-plate capacitor (equation 1),

                     (1)



C is capacitance per unit area, D is the dielectric constant (or relative permittivity) and d is the separation between the two layer of charge. The model of double layer proposed by Helmholtz is described in in Figure 1.

Figure 1. Model of double layer proposed by Helmholtz. Two parallel layers of charge are separated by solvent molecules (unmarked cricle) at a distance d, representing the outer Helmholtz plane ( Prentice, 1991)

The ionic distribution at diffuse layer follow Boltzmann distribution,as described in equation (2).

             (2)



Ci is concentration of ion i in the bulk phase, zi is charge of ion and theta is the potential. 
The potential distribution in double layer follow Poisson Distribution as described in equation (3).

                                                            (3)

Charge density is a function of the concentration, Ci and the charge of ions, zi, as described in equation (4)

                  (4)



The combination of (2),(3) and (4) producing equation (5).

         (5)





In cartesian coordinate, equation (5) can be stated as equation (6),

             (6)



THE ELECTRODE KINETICS MODEL
 the reduction reaction of an ion at potential thetha_1 (Q1)is described in equation (7),

    
                     (7)




a more negative potential tends to promote reduction, but as in convension, more negative potential corresponds to a more positive energy. The energy versus reaction coordinate can be drawn as in Figure 2.

Figure 2. Energy along a reaction coordinate for an electrochemical reaction at three different potentials, Q1>Q2>Q3 (Prentice, 1991).

Reference:

Prentice, G., 1991, Electrochemical Engineering Principles, Prentice-Hall International (UK) Limited, London
you may find the ppt file in here

Read my book, click on :

my other papers:
paper 1
paper 2
paper 3
paper 4