The electrochemical behavior of a system with a limited number of molecules

In this paper, based on Einstein relationship between diffusion and random walk, the electrochemical behavior of a system with a limited number of molecules was simulated and explored theoretically. The transition of the current vs time responses from discrete to continuous was clearly obtained as the number of redox molecules increased from 10 to 10⁶. By correlation analysis between the simulation results and the results of analytical expressions, a quantized extent parameter was proposed to investigate the underlying rules of these discrete signals, which looked stochastic. The results revealed that this parameter would be useful to describe such systems.