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 TFAB^1- 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 TFAB^1- 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 TFAB^1- 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.