Reply to comments contained in “Are the reactions of quinones on graphite adiabatic?”, by N.B. Luque, W. Schmickler [Electrochim. Acta xx (2012) yyy]

Accelerated constant-voltage quantum mechanical/molecular mechanical method for molecular systems at electrochemical interfaces

The structure and electronic properties of a molecule at an electrochemical interface are changed by interactions with the electrode surface and the electrolyte solution, which can be significantly modulated by an applied voltage. We present an efficient self-consistent quantum mechanics/molecular mechanics (QM/MM) approach to study a physisorbed molecule at a metal electrode-electrolyte interface under the constant-voltage condition. The approach employs a classical polarizable double electrode model, which enables us to study the QM/MM system in the constant-voltage ensemble. A mean-field embedding approximation is further introduced in order to overcome the difficulties associated with statistical sampling of the electrolyte configurations. The results of applying the method to a test system indicate that the adsorbed molecule is no less or slightly more polarized at the interface than in the bulk electrolyte solution. The geometry of the horizontally adsorbed molecule is modulated by their electrostatic interactions with the polarizable electrode surfaces and also the interactions with cations attracted toward the interface when the adsorbate is reduced. We also demonstrate that the approach can be used to quantitatively evaluate the reorganization energy of a one electron reduction reaction of a molecule in an electrochemical cell.

Effect of a Au underlayer on outer-sphere electron transfer across a Au/graphene/electrolyte interface

The effect of a gold underlayer on the outer-sphere non-adiabatic electron transfer on a graphene surface is investigated theoretically using both periodic and cluster DFT calculations. We propose a model that describes the alignment of energy levels and charge redistribution at the metal/graphene/redox electrolyte interface. Model calculations were performed for the [Fe(CN)₆]^3-/4- and [Ru(NH₃)₆]^3+/2+ redox couples. It is shown that the gold support increases the rate constant of electron transfer. Gold electronic states hybridize with graphene wave functions, which provides an effective overlap with reactant orbitals outside the graphene layer and favors an increasing reaction rate. Although the Fermi level shift relative to the Dirac point in graphene depends significantly on the redox couple, this weakly affects the electron transfer kinetics at the Au(111)/graphene/electrolyte interface due to a small contribution of graphene states to the rate constant as compared to gold ones.

Towards Understanding the Solvent-Dynamic Control of the Transport and Heterogeneous Electron-Transfer Processes in Ionic Liquids

The impact of temperature-induced changes in solvent dynamics on the diffusion coefficient and standard rate constant k⁰ for heterogeneous electron transfer (ET) of ethylferrocene (EFc) in 1-butyl-3-methylimidazolium hexafluorophosphate ([BMIM][PF₆ ]) is investigated. The results are analysed to understand the impact of solvent-dynamic control, solute-solvent interactions and solvent friction on the transport of redox probes and k⁰ . Concentration dependence of the diffusion coefficient of EFc in [BMIM][PF₆ ] is observed. This is attributed to the solute-induced enhancement of the structural organisation of the ionic liquid (IL), which is supported by the concentration-dependent UV/Vis absorption and photoluminescence responses of EFc/[BMIM][PF₆ ] solutions. Similar values of the activation energies for mass transport and ET and a linear relationship between the diffusion coefficient and the heterogeneous ET rate is observed. The ratio between the diffusion coefficient and the heterogeneous rate constant allows a characteristic length L_d , which is temperature-independent, to be introduced. The presented results clearly establish that mass transport and heterogeneous ET of redox probes are strongly correlated in ILs. It is proposed that the apparent kinetics of heterogeneous ET reactions in ILs can be explained in terms of their impact on thermal equilibration, energy dissipation and thermal excitation of redox-active probes.

Heterogeneous Electron-Transfer Rates for the Reduction of Viologen Derivatives at Platinum and Bismuth Electrodes in Acetonitrile

The standard heterogeneous rate constants for the reduction of a series of viologen derivatives with a range of inter‐ring torsion angles were measured at Bi and Pt electrodes. The electrode potentials for the first one‐electron reduction of the viologens vary from −684 mV to −1070 mV vs. Ag/0.01 m Ag⁺; this enabled a comparison of the behaviour of metallic (Pt) and semi‐metallic (Bi) electrodes over a wide range of applied potentials. The differential capacitance (6.5 μF cm⁻²) of Bi/MeCN,TBAPF₆ interfaces at the potential of zero charge (pzc=−0.60 V) is at least an order of magnitude greater than that calculated on the basis of the bulk Bi carrier density (3×10¹⁷ cm⁻³) and the differential capacitance (9.5 μF cm⁻²) of Pt/MeCN interfaces at their pzc (−0.43 V) is of the same order. The series of viologen derivatives exhibited simple one‐electron redox behaviour and showed similar rate constants at Pt (1.8×10⁻⁴–1.6×10⁻³ cm s⁻¹) and Bi electrodes (1.1×10⁻⁴–1.9×10⁻³ cm s⁻¹) after application of the Frumkin correction. These results demonstrate that the density of states at the Bi surface is much higher than in bulk. Finally, the Frumkin‐corrected standard rate constants were observed to be inversely correlated with the inter‐ring torsion angle of the viologens.

Single graphene nanoplatelets: capacitance, potential of zero charge and diffusion coefficient

Nano-impact chronoamperometric experiments are a powerful technique for simultaneously probing both the potential of zero charge (PZC) and the diffusion coefficient (D0) of graphene nanoplatelets (GNPs). The method provides an efficient general approach to material characterisation. Using nano-impact experiments, capacitative impacts can be seen for graphene nanoplatelets of 15 μm width and 6-8 nm thickness. The current transient features seen allow the determination of the PZC of the graphene nanoplatelet in PBS buffer as -0.14 ± 0.03 V (vs. saturated calomel electrode). The diffusion coefficient in the same aqueous medium, isotonic with many biological conditions, for the graphene nanoplatelets is experimentally found to be 2 ± 0.8 × 10-13 m2 s-1. This quick characterisation technique may significantly assist the application of graphene nanoplatelets, or similar nano-materials, in electronic, sensor, and clinical medicinal technologies.

Electrochemistry at highly oriented pyrolytic graphite (HOPG): lower limit for the kinetics of outer-sphere redox processes and general implications for electron transfer models

Electron transfer kinetics for outer-sphere redox couples is fast on the basal surface of highly oriented pyrolytic graphite (HOPG).

Kinetics of reduction of aqueous hexaammineruthenium(III) ion at Pt and Au microelectrodes: electrolyte, temperature, and pressure effects

Rate constants kel obtained by impedance spectroscopy for the reduction of Ru(NH3)6(3+) at polycrystalline Pt and Au ultramicroelectrodes depend strongly on the identity and concentration of the anion present in the order CF3SO3(-) < Cl(-) < ClO4(-), but not on the cation of the supporting electrolyte (Na(+), K(+), H(+)). For Cl(-) as the sole anion present, kel is directly proportional to the total [Cl(-)], such that kel would be zero if Cl(-) were hypothetically absent, indicating that Cl(-) is directly involved in mediation of the Ru(NH3)6(3+/2+) electron transfer. For CF3SO3(-) as the sole counterion, the dependence of kel on the total [CF3SO3(-)] is not linear, possibly because blocking of the available electrode surface becomes dominant at high triflate concentrations. Volumes of activation ΔVel(⧧) for reduction of Ru(NH3)6(3+) at an electrode in presence of Cl(-) or CF3SO3(-) are much more negative than predictions based on theory (Swaddle, T. W. Chem. Rev.2005, 105, 2573) that has been successful with other electron transfer reactions but which does not take into account the involvement of the anions in the activation process. The strongly negative ΔVel(⧧) values probably reflect solvation increases peculiar to activation processes of Ru(III/II) am(m)ine complexes, possibly together with promotion of desorption of surface-blocking Cl(-) or CF3SO3(-) from electrodes by applied pressure. Frumkin corrections for Ru(NH3)6(3+) within the diffuse double layer would make ΔVel(⧧) even more negative than is observed, although the corrections would be small. The strongly negative ΔVel(⧧) values are inconsistent with reduction of Ru(NH3)6(3+) in direct contact with the metallic electrode surface, which would entail substantial dehydration of both the electrode and Ru(NH3)6(3+). Reduction of Ru(NH3)6(3+) can be regarded as taking place in hard contact with adsorbed water at the outer Helmholtz plane.