We develop a theory for outer sphere heterogeneous electron transfer (ET) rate constant (k 0 ) and exchange current density (i 0 ). The model hypothesizes that the transition state is attained by alignment of Fermi and reactant energy levels through exchange of fractional electronic charge (δ ≠ ). This approach accounts the contributions from: (i) work function and Fermi energy of metal, (ii) solvent polarity and size, (iii) electronic nature and size of electroactive species, and (iv) outer Helmholtz plane (OHP) potential-dependent composition. At the outset, we develop a model for the potential ϕ 1 at the inner Helmholtz plane accounting the influence of electronic and inner dipolar layer screening on the metal. The equation for ϕ 1 is used to obtain the potential ϕ 2 at OHP through a modified Gouy−Chapman−Stern approach. The concentration of electroactive species at OHP (c i OHP ) under the influence of the Frumkin effect is obtained by substituting ϕ 2 in Kornyshev's packing density restriction model. Our theory of the Frumkin effect highlights its dependence on metal, ionic strength, and applied potential. Further, free energy of activation (ΔG ≠ ) for the ET reaction is formulated as a product of δ ≠ and the work function of solvated metal. δ ≠ varies linearly with the energy of lowest unoccupied or highest occupied molecular orbitals of electroactive species and the work function of metal. The standard rate constant is obtained in terms of ΔG ≠ , and the exchange current density is expressed in terms of k 0 , c i OHP , and ϕ 2 . The theory unravels that a range of more than 10 orders of magnitude of kinetic reactivity is encompassed through 4−20% variation in δ ≠ . Finally, the theory captures the experimental data for different metals, solvents, supporting electrolytes, and electroactive species.

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We develop the mean-field theory for the step density-induced anomalous variation in electronic capacitance, work function (WF), potential of zero charge (PZC), and interfacial capacitance (IC) of an electrode. The random nanocorrugated step geometry has the functional form as a hyperbolic tangent with a random step edge. The average PZC and IC along with WF expression is obtained as a function of mean-square gradient and mean curvatures. The theoretical result highlights the anomalous non-monotonic lowering of the average PZC and WF with increasing step density. This explains the experimental observation for the stepped platinum electrodes. Further, this theory shows nanocorrugation and the nature of metal-driven large suppression in an average WF of ≈ 0.7 eV, a PZC of ≈ 0.5 eV, and an IC of ≈ 1.4 μF/cm2 from its planar value. Finally, this theory predicts that the step curvature and the step density cause significant variation in electronic WF and PZC, which is consequently the genesis of many anomalies in surface and interfacial phenomena.

We develop a novel theory for nanomorphology dependent outer sphere heterogeneous electron transfer (ET) rate constant ( k0) based on energy level alignment approach. k0 is modeled through the activation...

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