A Systematic Study of M(bpy)₃z+ Complexes in Nafion: Concentration, Activity, and Electron Hopping
Authors: Gellett Wayne L. , Knoche Krysti L. , Rathuwadu Nadeesha , Leddy Johna 
Published: February 2020

Cyclic voltammograms for six tris(2,2'-bipyridyl) complexes, M(bpy)₃z+ at Nafion® modified electrodes are shown [1]. Despite similar concentrations of M(bpy)₃z+ in the films, peak currents measure significant variations in film diffusion coefficients.
Extraction of transition metal complexes such as M(bpy)₃z+ into Nafion from electrolyte solutions is highly favored. The concentration of M(bpy)₃z+ complexes in the hydrated domains of Nafion is sufficiently high that adjacent complexes approach contact distance. Because the distance between metal centers is small, electron hopping can enhance flux measured as current. The concentration of similarly -sized in charge redox probes in Nafion is fixed. The current enhancement due to electron hopping is reflected in the measured diffusion coefficient, Df, which is set as the sum of the physical diffusion coefficient Dp and the electron hopping of diffusion coefficient Det. From models of Dahms and Ruff, the electron hopping diffusion coefficient is related to the self exchange rate k₁₁ for electron transfer between the halves of a redox couple.
M(bpy)₃z+ + M(bpy)₃(z±1)+ ⇌ M(bpy)₃(z±1)+ + M(bpy)₃z+

In the Nafion matrix, the self exchange leads to transposition between M(bpy)₃z+ and M(bpy)₃(z±1)+and this contributes to probe flux characterized by the diffusion coefficient.
Df = Dp + Det = Dp + k₁₁cf
*δ²/6
The concentration of the redox probe in the film is cf
* and the diameter of the redox probe is δ, which for M(bpy)₃z+ is 1.36 nm.
Here, cyclic voltammetry of Nafion films on electrodes for six probes, M(bpy)₃z+ where Mz+is Ru²⁺, Os²⁺, Fe²⁺, Cr³⁺, Co³⁺, and Co²⁺, is presented [1]. Several outcomes are reported.

Df varies linearly with k₁₁H₂0, literature self exchange rates measured in water at or near infinite dilution.

To allow charge compensation for electron transfer events, the matrix must provide sufficient dielectric constant to support ion formation. Electron hopping occurs in the hydrated domains of biphasic Nafion because the fluorocarbon phase does not support ion formation with the dielectric constant of ∼2.

From the density of Ru(bpy)₃²⁺ exchanged Nafion (1.95 g/cm³) [2] and nominal equivalent weight 1100 g/mole of sulfonates, the volume of M(bpy)₃z+ is limited so that the concentration of M(bpy)₃z+ is insufficient to charge balance the available sulfonates.

Electrolyte cations are needed to balance the anionic sulfonates.

Concentration of M(bpy)₃z+ extracted into the film is invariant across electrolyte conditions common to voltammetric measurements.

Measured Df are reported: 2 × 10⁻⁹ cm²/s for Ru(bpy)₃²⁺ and Os(bpy)₃²⁺; 1 × 10⁻¹⁰ cm²/s for Fe(bpy)₃²⁺ and Cr(bpy)₃³⁺; and 1.5 × 10⁻¹² and 5 × 10⁻¹² cm²/s for Co(bpy)₃²⁺ and Co(bpy)₃³⁺. Physical diffusion is estimated as Dp ≲ 10⁻¹² cm²/s.

From the concentration in the film and measured Det, the self exchange rate in Nafion k₁₁Naf is proportional to values in water but lower; k₁₁Naf = 0.010k₁₁H₂O, consistent with higher ion concentration in Nafion.

For Os(bpy)₃2/3, the self exchange rate in water is estimated as k₁₁H₂O≈ 4.5 × 10⁸/Ms.

From these results, a sketch of the hydrated environment in Nafion exchanged with M(bpy)₃z+is presented.
References
[1] Wayne L. Gellett, Krysti L. Knoche, Nadeesha P. W. Rathuwadu, and Johna Leddy, Electron Hopping of Tris (2,2'-bipyridyl) Transition Metal Complexes M(bpy)₃z+ in Nafion, in press, J. Electrochem. Soc. 2016.
[2] K. J. Oberbroekling, D. C. Dunwoody, S. D. Minteer, and J. Leddy, Anal. Chem. 74, 4794 (2002).

Figure 1