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

TLDR

The study examines impedance of electron diffusion and recombination in spatially restricted systems, identifying four canonical cases (finite diffusion with reflecting or absorbing boundaries, Gerischer impedance, and a Warburg–reaction arc combination), and discusses the generality of the approach via electrochemical potential distributions and transmission line representations, linking to other electrochemical transport frameworks. The paper analyzes the small‑signal AC impedance of electron diffusion and recombination in spatially restricted situations, relevant to porous TiO₂ nanostructured photoelectrodes and intrinsically conducting polymers. The authors extend the diffusion–recombination model to lithium‑intercalation electrodes coupled to a homogeneous solid‑state reaction. The model predicts a finite set of distinct frequency‑domain behaviors classified by physical parameters, depending on the boundary conditions.

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 TiO2 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.