Role of film history and observational timescale in redox switching kinetics of electroactive films. Part 2. - Visualizing electrochemical redox switching pathways involving four or more distinct relaxation times

The classic 'scheme-of-squares' (two-dimensional) representation is a powerful way of visualizing the various mechanistic possibilities when a reacting system can be described in terms of two parallel mechanisms involving two processes with distinguishable timescales. The kinetics of multi-step chemical interconversions involve many parallel paths. The 'scheme-of-cubes' (three-dimensional) representation extends the classical approach to reacting systems involving three processes with distinguishable timescales. Here we generalize the approach to a 'scheme-of-hypercubes' (q-dimensional) description that permits illustrating an arbitrary number of competing parallel pathways involving q (where q > 3) elementary steps with distinguishable characteristic time-scales. The strategy involves (i) assigning a dimension to each elementary step with a distinguishable characteristic; (ii) defining a hypergeometric figure in terms of these dimensions and (iii) applying a step-wise procedure to reduce the dimensionality of the hyperfigure. The approach permits visualizing the problem in terms of a family of simple geometric objects (cubes, squares and lines) and is generally applicable to any physicochemical process. We discuss the model in terms of the redox switching and reconfiguration kinetics of electroactive polyvinylferrocene films under non-permselective conditions.