Apparent diffusion coefficient of intercalated species measured with PITT: A simple formulation

Apparent values (Dap) of chemical diffusion coefficients (D) of intercalated species are measured with the potentiostatic intermittent titration technique (PITT) due to the usual approximations of infinitely fast charge-transfer kinetics at the electroactive interface and negligible Ohmic drop effects. A simple expression is derived in this work that enables one to predict the parametric dependence of the diffusion coefficient ratio (Dap/D) on the ‘key-factor’ (Λ) for insertion/extraction processes. The parameter Λ can be either experimentally determined from electrochemical impedance spectra, or predicted from theoretical expressions of insertion/extraction reaction rate. The measurement error of diffusion coefficient is predicted theoretically due to slow charge-transfer kinetics at the interface, Ohmic drop effects and bulk interactions in the host material. The influence of electrode or particle geometry is also analyzed. In most cases, but not in all cases, a minimum value of apparent diffusion coefficient is observed near the standard potential of insertion material. The measurement error of D becomes very important in the presence of attractive interactions in host materials, together with slow charge-transfer kinetics at the electroactive interface. Finally, the superposition between spurious behavior of the chemical diffusion coefficient and its dependence on the guest ions interactions is investigated within the framework of Frumkin insertion isotherm.