Transition between kinetic and diffusion control during the initial stages of electrochemical growth using numerical modelling

Understanding properly electrochemical nucleation and growth phenomena is crucial for a wide range of highly active research and technological fields. In this paper, we use a Finite Element Method to solve a Time Dependent Multi-ion Transport and Reaction Model (FEM-TD-MITReM) to report on the growth of an isolated nucleus. This approach takes into account the transport driven by diffusion and migration of all species in the electrolyte together with the electrochemical reactions at the electrode boundary. The numerical results show that, a nucleus which is smaller than a critical size, even after the application of a sufficiently large overpotential, always starts to grow under kinetic control. In later stages, a transition from kinetic to mixed and to diffusion control takes place. The corresponding transition times between growth regimes have been identified and are found to be inversely proportional to the concentration of active species and to decrease exponentially with overpotential and linearly with the initial nucleus size. Both effects are more pronounced in the transition from kinetic to mixed control. Interestingly, under the conditions used for the current simulations, typical from experimental nucleation and growth studies, a few seconds are needed to achieve diffusion control. This implies that, although experiments under similar conditions are normally described by growth under diffusion control, such theory is only valid for sufficiently large active surface. As a consequence, kinetic and mixed control regimes cannot be neglected for a proper interpretation of electrochemical nucleation and growth phenomena. These findings provide a significant benchmark for correctly describing, modelling and interpreting the early stages of electrochemical growth without making assumptions on the diffusional or kinetic limitations.