Modelling enzyme electrodes - What do we learn and how is it useful?

There has been an enormous increase in the computational power readily available since the first numerical treatments of electrochemical problems in the early 1960s. This development has been accompanied by the development of powerful, widely available, commercial software modelling tools. Despite this, approximate analytical treatments remain extremely useful in the modelling of coupled diffusion/reaction problems in electrochemistry because of the insights they provide into the different possible behaviours of the system. In this paper we discuss the modelling of amperometric enzyme electrodes, taking as our exemplar redox hydrogel-based enzyme electrodes in which the enzyme is immobilized in a redox active polymer which wires the enzyme to the electrode. In this system the measured current is related to many different experimental variables including substrate concentration and diffusion coefficient, reaction rate constants, and film properties and thickness. The interplay of these factors is described and the role of Case diagrams in understanding coupled diffusion/reaction problems of this type is discussed.