Theory of the Impedance of Electron Diffusion and Recombination in a Thin Layer

Abstract

This paper analyzes the small signal ac impedance of electron diffusion and recombination in a spatially restricted situation with application in systems such as porous TiO 2 nanostructured photoelectrodes and intrinsically conducting polymers. It is shown that the diffusion−recombination model with the main types of boundary conditions assumes a finite set of possible behaviors in the frequency domain, which are classified according to relevant physical parameters. There are four possible cases: (i) the impedance of finite diffusion with reflecting boundary, (ii) the impedance of finite diffusion with absorbing boundary, (iii) the impedance of diffusion-reaction in semiinfinite space or Gerischer impedance, and (iv) the impedance that combines Warburg response at high frequency and a reaction arc at low frequency. The generality of the approach is discussed in terms of the spatial distribution of the electrochemical potential or quasi-Fermi level and also in terms of the transmission line representation. An extension is considered to the diffusion in lithium intercalation electrodes coupled to a homogeneous solid-state reaction. The connection is established with other frameworks for the description of transport and reaction in electrochemical systems.