Linear Sweep Voltammetry: Infinite Series Approximation

The solution of a current-potential curve in linear sweep voltammetry (LSV) can be expressed as an infinite series. Linear sweep voltammetry is a method in which the current at a working electrode is measured while the potential between the working electrode and a reference electrode is swept linearly in time.

At the working electrode, a catalytic reaction with reversible charge transfer occurs:

,

(rate constant ).

When , there is no catalytic reaction and this case becomes a simple reversible electrochemical reaction: .

The current-potential relation is solved from the Butler–Volmer equation and diffusion equation. The analytical solution in infinite series [1] was calculated using Mathematica's LerchPhi function.

[1] J. Mocak and A. M. Bond, "Use of Mathematica software for Theoretical Analysis of Linear Sweep Voltammograms," Journal of Electroanalytical Chemistry561, 2004 pp. 191–202.