Simulated fractal formation in electrochemical switching of conducting polymer film into an insulating form on the basis of the propagation theory of the conductive zone

The switching described in the title is discussed along the lines of the propagation theory of the conductive zone in a solution of a large excess of dopant ions, and is deduced to occur randomly in the conductive zone. Two- (2D) and three-dimensional (3D) lattice models are proposed for the conducting polymer film. They are initially assigned to the conductive state. When they are switched electrochemically at the electrode, only the conductive sites connected electrically to the electrode are converted into the insulating state. The process is similar to a random percolation problem. Chronoamperometry and linear sweep voltammetry are employed as electrochemical techniques. The potential step response is like a pulse current. A part of the linear sweep voltammogram is the same as the reversible surface wave up to the potential corresponding to a threshold of the percolation, and then suddenly drops to zero. A fraction, 57 (in 2D) or 38% (in 3D), of the conductive sites is excluded from the conversion because the conversion cuts off the electric connection to the electrode. The distribution of the final conductive sites seems random and forms clusters, of which the sizes and radii are evaluated. The cluster size is proportional to the 1.79 (2D) and 2.13 (3D) powers of the radius, indicating fractal formation. Thus, the conductive sites exhibit geometrically self-similar patterns. The local conversion yield is almost uniform throughout the film except close to the electrode.