Kinetics of Concentration Polarization

Abstract

The concentration of a specie j is lower at the electrode surface than in the bulk Cb CoThe kinetics of concentration polarization is a rate-controlling electrochemical process since the electrode is cathodically polarized. The mass transfer may be by diffusion, migration, convection or a combination of these modes. Thus, the Nernst-Plank equation can give reasonable results. However, if diffusion is the solely mechanism, Fick’s first law states that the diffusion molar flux depends on the concentration gradient at a steady-state since the concentration rate is dC/dt=0. On the other hand, Fick’s second law of diffusion requires that dC/dt≠0, but it strongly depends on the concentration gradient ∂2C/∂x2 and time. The solution of Fick’s second law depends on the type of diffusion problem and related boundary conditions, but the presented solution given in Appendix A is based on the error function of the Bell-Shaped Function y=exp(−x2), and it predicts that the concentration of a specie j the concentration gradient, and current density decay with time t−1/2 at the electrode surface. Despite that the current density is a time-dependent parameter, it is influenced by the flux of specie j and it is restrictive to the limiting current density (iL) as its maximum value. Therefore, the overpotential needed for concentration polarization depends on the current density ratio ic/iLas described by the Nernst equation as ηc= f(ic/iL).