Theory for electrode kinetics of surface-immobilized monolayers in cyclic voltammetry is developed based on the Marcus free energy-rate relation. Numerical calculations show that when the applied overpotential exceeds ~30% of the reorganizational energy of the electrode reaction, voltammetry predicted from Marcus theory differs from that based on classical Butler-Volmer kinetics with regard to wave shape, peak currents and their dependence on potential sweep rate, and variation of peak potential with potential sweep rate. Estimates of the standard rate constant, A®, can be made from Epak data without exact knowledge of reorganizational energies.Examples are given of evaluating A® for monolayers of ferrocene alkanethiols chemisorbed on Au(lll) electrodes, when the monolayers are highly ordered, and kinetically monodisperse, and when they are somewhat disordered, and kinetically disperse on bulk gold electrodes at room and 150 K temperatures.Theory enabling measurement of heterogeneous electrontransfer rates from cyclic voltammetric oxidation-reduction peak potential separations, AEpeak, was presented some time ago by Nicholson and Shain1 for diffusing and by Laviron2 for diffusionless (i.e., surface bound) electrochemical systems. This methodology is appealing by its ease of application; standard electron-transfer rate constants (A°) result from analysis of the dependence of AE^v alues on potential sweep rate using numerically generated working curves1 or explicit expressions.2 These theoretical formulations are based on the Butler-Volmer3 free energy-rate relation, which in the context of modern electron-transfer theory due to Marcus,4 assumes that the applied potential (free energy, overpotential, = E -E°') is much smaller than the electrode reaction's reorganizational energy barrier ( ). This paper will describe the theoretical and experimental behavior of cyclic voltammetry of nondiffusing (immobilized) electrode reactants when is not negligible in comparison to , i.e., in or approaching what is commonly referred to as the Marcus inverted region.4•5 This contribution is made in the context of recent potential step experiments6•7 with electroactive, self-assembled monolayers in which the ratio / is not small. Cochemisorption of a mixture of the alkanethiols CH3(CH2)i5SH and CpFeCpC02(CH2),6SH

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Mixed monolayers of (ferrocenylcarboxy)-alkanethiol/n-alkanethiol have been investigated electrochemically in 2:1 (v:v) chloroethane:butyronitrile solvent in the temperature range of 120K to 150K. Cyclic voltammetry of these monolayers shows large oxidation-reduction peak potential separations indicative of electron transfer rate control.The voltammetric waveshapes are also broadened; this and curved log[i] vs. time transients observed in potential step experiments are interpreted as a dispersion in the reaction rates of the ferrocene sites. This paper considers origins and three models for such kinetic dispersion: (i) Using simulations, the observed kinetic dispersion effects can be successfully represented by a Gaussian distribution among the formal potentials E 0 ' of the surface redox sites. While only an apparent kinetic dispersion (having a thermodynamic origin), we show by simulations that its presence affects potential step log[k APP ,] vs. tj plots, depressing the apparent reorganizational barrier energies (X) and elevating the apparent rate constants (k°), consistent with previous experimental observations. Similarly, cyclic voltammetric simulations with a Gaussian E 0 ' distribution give excellent fits to experimental 2 voltammograms with mid-point average rates (that with voltammograms can be simulated to fit both the experimental waveshape and AE PEAK ) that are roughly 6-fold smaller than the average rate (determined from a fit to the experimental AE PEAK assuming a homogeneous population). The temperature and chain length dependence of simulations are also consistent with experimental observations and indicate that the dispersion has little effect on accurate determination of X (from an activation analysis) or ß (from a plot of log(k°) vs. chain length), (ii) A Gaussian distribution of reorganizational energies, which is a real kinetic dispersion, has consequences on the appearance and the analysis of data quantitatively equivalent to those of a distribution of formal potentials, (iii) A kinetic dispersion model based on a Gaussian distribution of tunneling distances (or equivalently electronic coupling parameter) from the electrode surface is also evaluated. This model predicts curved potential step log[i] vs. time plots, and in analysis of log[k A p Pl) ] vs. rj plots, undistorted results for X but alteration of the apparent k°.

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