# Exploring the determination of the standard rate constant in electrochemical metal deposition: theory and experiment

## TL;DR

This paper explores how to determine a key rate constant in metal deposition using both simulations and experiments.

## Contribution

New interpolation equations were developed to estimate the standard rate constant while considering transfer coefficient effects.

## Key findings

- Equations were validated using silver, copper, and rhenium ions in different electrolytes.
- Ag+/Ag and Cu+/Cu redox couples are quasi-reversible, while Re6+/Re is irreversible.
- Simulated cyclic voltammetry results matched experimental data closely.

## Abstract

A detailed investigation of the electrochemical metal deposition was carried out using both simulation and experimental cyclic voltammetry (CV). Kinetic curves were developed to relate peak-to-peak potential separation (ΔEp) to the cathodic charge transfer coefficient (α) and the standard rate constant (k0). From these curves, interpolation equations were derived to estimate k0, taking into account the effect of the transfer coefficients sum (α + β), whether equals to or different from 1. The validity of the equations was confirmed through the reduction of silver, copper and rhenium ions in various electrolytes, yielding k0 values of 14.51 × 10−6 m s−1 for Ag+/Ag, 5.98 × 10−7 m s−1 for Cu+/Cu and 10.59 × 10−8 m s−1 for Re6+/Re. According to the Matsuda–Ayabe criteria for assessing electron-transfer reversibility, the Ag+/Ag and Cu+/Cu redox couples are regarded as quasi-reversible, while the Re6+/Re couple is classified as irreversible. The simulated CVs showed strong agreement with experimental results.

Interpolation equations from kinetic curves enable k0 extraction from ΔEp in electrodeposition, accounting for α + β effects and experimental validation.