Independent Quantification of Electron and Ion Diffusion in Metallocene-Doped Metal–Organic Frameworks Thin Films

The chronoamperometric response (I vs t) of three metallocene-doped metal–organic frameworks (MOFs) thin films (M-NU-1000, M = Fe, Ru, Os) in two different electrolytes (tetrabutyl­ammonium hexafluoro­phosphate [TBAPF6] and tetrabutylammonium tetrakis­(pentafluorophenyl)­borate [TBATFAB]) was utilized to elucidate the diffusion coefficients of electrons and ions (D e and D i, respectively) through the structure in response to an oxidizing applied bias. The application of a theoretical model for solid state voltammetry to the experimental data revealed that the diffusion of ions is the rate-determining step at the three different time stages of the electrochemical transformation: an initial stage characterized by rapid electron diffusion along the crystal-solution boundary (stage A), a second stage that represents the diffusion of electrons and ions into the bulk of the MOF crystallite (stage B), and a final period of the conversion dominated only by the diffusion of ions (stage C). Remarkably, electron diffusion (D e) increased in the order of Fe < Ru < Os using PF6 1– as the counteranion in all the stages of the voltammogram, demonstrating the strategy to modulate the rate of electron transport through the incorporation of rapidly self-exchanging molecular moieties into the MOF structure. The D e values obtained with larger TFAB1– counteranion were generally in agreement with the previous trend but were on average lower than those obtained with PF6 1–. Similarly, the ion diffusion coefficient (D i) was generally higher for TFAB1– than for PF6 1– as the ions diffuse into the crystal bulk, due to the high degree of ion-pair association between PF6 1– and the metallocenium ion, resulting in a faster penetration of the weakly associated TFAB1– anion through the MOF pores. These structure–function relationships provide a foundation for the future design, control, and optimization of electron and ion transport properties in MOF thin films.