Cyclic staircase voltammetry and cyclic voltammetry in current and charge modes for the analysis of the responses of fast redox probes under finite diffusion

• Analytical model for CSCV and CV responses under finite diffusion (FD) is given. • Two FD modes are analyzed for the charge-potential and current-potential curves. • Thickness of the FD field can be obtained from the analysis of the responses. • Unbounded diffusion leads to an enhanced sensitivity for the current and charge. Finite diffusion (FD) cells, that is, those involving experimental configurations with spatial restrictions that affect the overall mass transport, are becoming a very attractive way for carrying out electrochemical measurements. This experimental set-up presents numerous advantages in terms of sensitivity and simplicity in characterizing charge transfer processes. In this context, one of the most widely used tools is Cyclic Voltammetry (CV) and, although the theoretical analysis of its response under FD conditions has been previously reported (especially for the thin-layer, TL, limiting behaviour), there were some gaps that hindered its application to numerous cases of interest. The treatment presented here extend the existing CV analysis to Cyclic Staircase Voltammetry (CSCV), which is indeed the real technique applied in many digital potentiostats. Moreover, the expression for the charge-potential responses under FD conditions is reported for the first time. Thus, the converted charge is directly related with the concentration of electroactive species, and it can be measured with high reliability by following adequate experimental protocols. Two different diffusive modes are considered: bounded diffusion, corresponding to absence of mass renovation at a finite distance from the electrode, and unbounded diffusion, for which a fast mass renovation at such finite distance takes place. The general analytical expressions of the current-potential and charge-potential responses are simplified under TL conditions, leading to very simple ways for determining key parameters of the systems under study. The application of this formalism to the oxidation of a metallic complex under both configurations is presented, and practical values for the operating parameters are also discussed.