Cation Identity Matters: Thermodynamics of Sodium- vs. Proton-Coupled Electron Transfer Reactions on Ti-oxo Nodes of the Metal–Organic Framework, Ti-MIL-125

Charge transfer reactions like Na-coupled electron transfer (Na-CET) at solid-liquid interfaces are fundamental to energy storage devices and beyond. Yet, thermodynamic parameters of charge transfer reactions beyond proton-coupled electron transfer (PCET) reactions are rare in the literature. Here, we report the successful derivation of Na-CET thermodynamics by employing redox-active and colloidally stable Ti-based metal–organic framework (MOF), Ti-MIL-125. We and others have previously demonstrated that the Ti8(μ2-O)8(μ2-OH)4 nodes of this MOF undergo reversible Na-CET and PCET reactions with equimolar amounts of electrons and the charge-balancing cations (H+’s or Na+’s). UV-Vis spectra of the colloidal Ti-MIL-125 with sequential titrations of reductants and Na+ revealed that 6-7 Na+/e- pairs are added per Ti8 nodes of the MOF. Furthermore, the apparent ‘adsorption-desorption’ thermodynamics of these Na+/e- pairs follow what is expected for the Frumkin isotherm with a net repulsive interaction. The strength of this repulsive interaction was quantified and was observed to exhibit an empirical linear trend with respect to the reducing strength of the reductants. The derivation of these Frumkin isotherms yielded the reaction free energy of Na-CET. Combining this free energy with the reduction free energy of Na+ resulted in the free energy to add Na atoms to the Ti8 nodes that are averaged over the number of transferred electrons, ΔGNa/n. Notably, this thermochemical value is closely related to bond dissociation free energies (BDFEs), which are readily employed to predict the reaction free energies of covalent bond formation/breakage. Similarly, this parameter is intrinsically correlated to the chemical properties of Ti-MIL-125 in Na-CET and fundamentally describes its viability as, for example, a candidate electrode in Na-ion batteries. Thus, we advocate that ΔGNa/n should become the cornerstone for designing energy storage devices. Implications of the presented findings are contrasted to PCET reactions of the same MOF, as well as TiO2 and other metal oxides that undergo charge-transfer reactions.