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.

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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 Chemistry 561, 2004 pp. 191–202.
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