Contributions of fractional differentiation to the modelling of electric double layer capacitance

The electric double layer phenomenon is sometimes described by means of a specific element called “constant phase element”, instead of the usual electric double layer capacitance. This article deals with such an element, often associated with rough surfaces. It is first shown, using a lithium–ion battery and a PEM fuel cell, that this element can obviously improve accuracy in the modelling of electrochemical device harmonic spectrum. The article then focuses on an approximation method, which enables easy use of constant phase element in time domain. This method, which comes from fractional differentiation theory, is based on some properties of recursive transfer functions. The approximation procedure is explained, and comparisons between exact and approximated results are carried out.