On the determination of the diffusion coefficients of electrons and of potassium ions in copper(II) hexacyanoferrate(II) composite electrodes

Composite electrodes of graphite, paraffin, and copper(II) hexacyanoferrate(II) (Cu hcf) were studied by cyclic voltammetry (0.05-1000 mV s(-1)) and electrochemical impedance spectroscopy(10 Hz to 1 MHz). Cyclic voltammetric measurements were also performed with copper(II)) hexacyanoferrate(II) which was mechanically immobilized on a paraffin impregnated graphite electrode (PIGE). The Nyquist plots which were obtained from impedance measurements could be modeled with an adsorption process in series to the charge transfer of K+ ions between the electrolyte solution and the Cu hcf, the diffusion of K+ ions in the Cu hcf, and the conduction of electrons in the Cu hcf. The charge transfer and the diffusion of K+ ions obeys the Randles mechanism. The charge transfer resistance as well as the Warburg coefficient exhibit a minimum at the formal potential. Both effects could be explained theoretically on the basis of the potential dependence of the oxidized and reduced forms of Cu hcf. The electron transfer from the graphite to the Cu hcf is so fast that even at 1 MHz it was impossible to determine its rate constant. The conduction of electrons in the Cu hcf exhibits the feature of a diffusion process with a transmissive boundary. The experiments proved that a surface oxidation of the graphite has no influence on the electrode kinetics. However, for the first time it has been possible to separately determine the diffusion coefficients of ions and electrons by impedance spectroscopy. With other techniques, e.g., cyclic voltammetry only an effective diffusion coefficient for a coupled transport of cations and electrons is accessible. With cyclic voltammetry a diffusion coefficient of Kf ions ((1.49 +/- 0.04) x 10(-9) cm(2) s(-1)) and a rate constant of ion transfer ((1.42 +/- 0.05) x 10(-7) m s(-1)) were determined. Impedance spectroscopy at low frequencies yields the same diffusion coefficient for Kf ions ((1.4 +/- 0.2) x 10(-9) cm(2) s(-1)). The rate constant for potassium ion transfer between the electrolyte solution and the Cu hcf was found to be (3.0 +/- 0.2) x 10(-6) m s(-1). In the high-frequency range it was possible to determine the diffusion coefficient of electrons as (0.10 +/- 0.01) cm(2) s(-1). In the case of mechanically immobilized particles, the rate constant for the ion transfer was determined with the help of cyclic voltammetry as (2.0 +/- 0.2) x 10(-7) m s(-1).