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Transition-metal ions regularly undergo charge transfer (CT) by directly interacting with electrodes, and this CT governs the performance of devices for numerous applications like energy storage and catalysis. These CT reactions are deemed inner sphere because they involve direct formation of a chemical bond between the electrode and the metal ion. Predicting inner-sphere CT kinetics on electrodes using simple physicochemical descriptors would aid the design of electrochemical systems with improved kinetics. Herein, we report that the average energy of the d electrons (i.e., d-band center) of a transition-metal electrode rationalizes the kinetic trends of inner-sphere CT of transition-metal ions. We demonstrate that V2+/V3+, an important redox reaction for flow batteries, is an inner-sphere reaction and that the kinetic parameters correlate with the adsorption strength of the vanadium intermediate on Au, Ag, Cu, Bi, and W electrodes, with W being the most active electrode reported to date. We show that the adsorption strength of the vanadium intermediate linearly correlates with the d-band center such that the d-band center serves as a simple descriptor for the V2+/V3+ kinetics. We extract kinetic data from the literature for four other inner-sphere CT reactions of metal ions involving Cr-, Fe-, and Co-based complexes to show that the d-band center also linearly correlates with kinetic trends for these systems. The d-band center of the electrode is a general descriptor for heterogeneous inner-sphere CT because it correlates with the adsorption strength of the metal-ion intermediate. The d-band center descriptor is analogous to the d-electron configuration of metal ions serving as a descriptor for homogeneous inner-sphere CT because the d-electron configuration controls bond strengths of intermediate metal-ion complexes. 

Phenol is an important model compound to understand the thermocatalytic (TCH) and electrocatalytic hydrogenation (ECH) of biomass to biofuels. Although Pt and Rh are among the most studied catalysts for aqueous-phase phenol hydrogenation, the reason why certain facets are active for ECH and TCH is not fully understood. Herein, we identify the active facet of Pt and Rh catalysts for aqueous-phase hydrogenation of phenol and explain the origin of the size-dependent activity trends of Pt and Rh nanoparticles. Phenol adsorption energies extracted on the active sites of Pt and Rh nanoparticles on carbon by fitting kinetic data show that the active sites adsorb phenol weakly. We predict that the turnover frequencies (TOFs) for the hydrogenation of phenol to cyclohexanone on Pt(111) and Rh(111) terraces are higher than those on (221) stepped facets based on density functional theory modeling and mean-field microkinetic simulations. The higher activities of the (111) terraces are due to lower activation energies and weaker phenol adsorption, preventing high coverages of phenol from inhibiting hydrogen adsorption. We measure that the TOF for ECH of phenol increases as the Rh nanoparticle diameter increases from 2 to 10 nm at 298 K and −0.1 V vs the reversible hydrogen electrode, qualitatively matching prior reports for Pt nanoparticles. The increase in experimental TOFs as Pt and Rh nanoparticle diameters increase is due to a larger fraction of terraces on larger particles. These findings clarify the structure sensitivity and active site of Pt and Rh for the hydrogenation of phenol and will inform the catalyst design for the hydrogenation of bio-oils.