Critical Nucleus Size and Activation Energy of Ag Nucleation by Electrochemical Observation of Isolated Nucleation Events

The induction times for electrodeposition of individual Ag nanoparticles on Pt nanodisk electrodes in acetonitrile were used to determine the critical nucleus size and activation energy barrier associated with the formation of Ag nuclei. Induction times for the nucleation and growth of a single Ag nanoparticle were determined following the application of a potential step to reduce Ag⁺ at overpotentials, η, ranging from -130 to -70 mV. Sufficiently small Pt electrodes (5.1 × 10^-10-2.6 × 10^-11 cm²) were used to ensure that the detection of a single Ag nucleation event occurred during the experimental observation time (150 ms-1000 s). Multiple measurements of Ag nucleation induction times were recorded to determine nucleation rates as a function of η using cumulative probability theory. Both classical nucleation theory (CNT) and the atomistic theory of electrochemical nucleation were employed to analyze experimental nucleation rates, without a requisite knowledge of the nucleus geometry or surface free energy. Using the CNT, the number of atoms comprising the critical size nucleus, N_c, was estimated to be 1-9 atoms for η ranging from -130 to -70 mV, in good agreement with 1-5 atoms obtained using atomistic theory. The experimental nucleation rates were also used to determine the activation energy barriers for nucleation from the CNT, which varied from 3.31 ± 0.05 to 13 ± 1 kT over the same range of η.