Current response for a single redox moiety trapped in a closed generator-collector system: the role of capacitive coupling.

A theoretical model is proposed to describe the steady-state average limiting current associated with a single redox moiety (ox or red) trapped in a closed generator-collector system along with excess supporting electrolyte. By "closed" we mean that neither solvent nor solutes can enter or leave the system. The potential difference, EOE - ERE, between the oxidizing electrode (OE) and the reducing electrode (RE) is maintained constant with the values of EOE and ERE chosen so that the operative faradaic electrode processes are very fast, i.e., red = ox + nETe(-) (kox = ∞) at the OE and ox + nETe(-) = red (kred = ∞) at the RE. Because there is only a single redox moiety the faradaic process occurs at only one electrode at a time while current at the other electrode is purely capacitive (we refer to this as capacitive coupling). We propose that a two-step process is required to transfer nETqe coulombs (qe is the absolute value of the elemental electronic charge). The first step is associated with diffusion (approximated as a random walk) of a single red moiety to the OE where it is oxidized to ox with a concomitant transfer of qstep1 (= nETqe/(1 + AOECOE/ARECRE)) coulombs; the second step is associated with the diffusion (random walk) of the newly formed single ox moiety to the RE with the concomitant transfer of qstep2 (= nETqe/(1 + ARECRE/AOECOE)) coulombs (ARE,AOE andCRE,COEare the areas (cm(2)) and differential capacitances (farads cm(-2)) of the corresponding electrodes). The total charge transferred in the two steps is nETqe(= qstep1 + qstep2). Transport of the redox moiety from one electrode to the other is accomplished by a random walk. The probability density function (pdf) and cumulative density function (CDF) for the duration of a full redox cycle are presented as the analytical solution to a 1-dimensional bounded random-walk problem (confirmed by numerical simulation). These show that tfull, the average time for the full redox cycle (step 1 + step 2), is equal to L(2)/D where L is the intraelectrode distance and D is the diffusion coefficient. The average steady-state limiting current is shown to be described by the familiar expression for a generator-collector system: ilim = (qstep1 + qstep2)/tfull = nETqe/tfull = nETqeD/L(2).

Quantifying the effects of not stirring between repetitive chronoamperometric experiments.

Electroanalytical protocols executed under quiescent conditions generally require that the analyte medium be stirred (or agitated) between repetitions to ensure reestablishment of identical initial conditions in the vicinity of the electrode surface. The present work examines what happens when experimental conditions preclude stirring. We consider two general schemes: Scheme 1 where the potential is stepped from E(start) to E(step) to oxidize the initially present reduced redox moiety, A, to B under diffusion control (i.e., [A](x=0) = 0) for 0 ≤ t ≤ τ(1) followed by a second potential step from E(step) back to E(start) and continuing for τ(1) < t ≤ τ(2) during which time species B is reduced back to the initially present species A under diffusion control (i.e., [B](x=0) = 0) and Scheme 2 where the potential is again stepped from E(start) to E(step) to oxidize A to B under diffusion control for 0 ≤ t ≤ τ(1) followed by a second potential step from E(step) back to E(start) and continuing for τ(1) < t ≤ τ(2) during which there is no electron transfer; i.e., the electrochemical conversion of B to A (or vice versa) does not occur, and the electrode is effectively at open circuit for time τ(1) < t ≤ τ(2). We define a recovery parameter which specifies the concentration of A at distance (D(A)τ(1))(1/2) from the electrode as a function of the recovery-time ratio τ(2)/τ(1) and the operative Scheme (J). We show that for any given level of recovery τ(2)/τ(1) for Scheme 2 is much larger than for Scheme 1.

Electron transfer dynamics of iridium oxide nanoparticles attached to electrodes by self-assembled monolayers.

Self-assembled monolayers (SAMs) of carboxylated alkanethiolates (-S(CH(2))(n-1)CO(2)(-)) on flat gold electrode surfaces are used to tether small (ca. 2 nm d.) iridium(IV) oxide nanoparticles (Ir(IV)O(X) NPs) to the electrode. Peak potential separations in cyclic voltammetry (CV) of the nanoparticle Ir(IV/III) wave, in pH 13 aqueous base, increase with n, showing that the Ir(IV/III) apparent electron transfer kinetics of metal oxide sites in the nanoparticles respond to the imposed SAM electron transfer tunneling barrier. Estimated apparent electron transfer rate constants (k(app)(0)) for n = 12 and 16 are 9.8 and 0.12 s(-1). Owing to uncompensated solution resistance, k(app)(0) for n = 8 was too large to measure in the potential sweep experiment. For the cathodic scans, coulometric charges under the Ir(IV/III) voltammetric waves were independent of potential scan rate, suggesting participation of all of the iridium oxide redox sites (ca. 130 per NP) in the NPs. These experiments show that it is possible to control and study electron transfer dynamics of electroactive nanoparticles including, as shown by preliminary experiments, that of the electrocatalysis of water oxidation by iridium oxide nanoparticles.

Surprising effect of uncompensated resistance on the cyclic voltammetric responses for a reversible surface-confined and uniformly accessible redox couple.

A traditional diagnostic for cyclic voltammetric responses is the plot of the peak current i(peak) vs the scan rate |v| or vs |v|(1/2). For a reversible redox couple with redox moieties freely diffusing in bulk solution, a plot of i(peak) vs |v|(1/2) will be linear; for a surface-confined and uniformly accessible reversible couple, a plot of i(peak) vs |v| will be linear; however, if there is significant uncompensated resistance, it is the plot of i(peak) vs |v|(1/2) that will be linear even if the redox species are surface confined. The present work offers a theoretical basis for this result.

Implications of Marcus-Hush theory for steady-state heterogeneous electron transfer at an inlaid disk electrode.

For an outer-sphere heterogeneous electron transfer, Ox + e = Red, between an electrode and a redox couple, the Butler-Volmer formalism predicts that the operative heterogeneous rate constant, k(red) (cm s(-1)) for reduction (or k(ox) for oxidation) increases without limit as an exponential function of -alpha (E - E(0)) for reduction (or (1 - alpha)(E - E(0)) for oxidation), where E is the applied electrode potential, alpha (~1/2) is the transfer coefficient and E(0) is the formal potential. The Marcus-Hush formalism, as exposited by Chidsey (Chidsey, C. E. D. Science 1991, 215, 919), predicts that the value of k(red) or k(ox) limits at sufficiently large values of -(E - E(0)) or (E - E(0)). The steady-state currents at an inlaid disk electrode obtained for a redox species in solution were computed using both formalisms with the Oldham-Zoski approximation (Oldham, K. B.; Zoski, C. G. J. Electroanal. Chem. 1988, 256, 11). Significant differences are noted for the two formalisms. When k(0)r(0)/D is sufficiently small (k(0) is the standard rate constant, r(0) is the radius of the disk electrode, and D is the diffusion coefficient of the redox species), the Marcus-Hush formalism effects a limiting current that can be significantly smaller than the mass transport limited current. This is easily explained in terms of the limiting values of k(red) and k(ox) predicted by the Marcus-Hush formalism. The experimental conditions that must be met to effect significant differences in behavior are discussed; experimental conditions that effect virtually identical behavior are also discussed. As a caveat for experimentalists, applications of the Butler-Volmer formalism to systems that are more properly described using the Marcus-Hush formalism are shown to yield incorrect values of k(0) and meaningless values of alpha, which serves only as a fitting parameter.

The quasicatalytic mechanism: a variation of the catalytic (EC') mechanism.

The classic electrochemical catalytic mechanism, often referred to as the EC' mechanism, is traditionally represented by the two reactions A + e <==> B (E(A/B)(0), k(A/B)(0), alpha(A/B)) and B + P <==> A + Q (K(eq), k(f), k(b)). Implicit in this mechanism is the additional heterogeneous electron transfer P + e <==> Q (E(P/Q)(0), k(P/Q)(0), alpha(P/Q)). To observe EC' behavior, the following conditions must be met (we focus on cyclic voltammetric responses): (1) E(P/Q)(0) > E(A/B)(0) (ensuring that K(eq) > 1), (2) k(P/Q)(0)c(P) exp[-alpha(P/Q)(F/RT)(E - E(P/Q)(0))]/(0.446c(A)(FD(A)|v|/RT)(1/2)) << 1 over the potential range of interest (ensuring that the reaction P + e <==> Q does not occur to any significant extent relative to the peak current for reaction A + e <==> B alone), (3) k(f)c(P)RT/F|v| > 1 (ensuring that the catalytic effect is significant). We offer arguments based on Marcus theory that when condition 2 is met, fulfilling condition 3 will be difficult. This could explain why EC' behavior is rare. In the present work we show that EC'-like cyclic voltammetric responses can be obtained even when P + e <==> Q is facile if D(P,Q) (the diffusion coefficient for the substrate-couple species P and Q) is much smaller than D(A,B) (the diffusion coefficient for the mediator-couple species A and B). When D(P,Q)/D(A,B) is sufficiently small, the system behavior becomes identical to that seen for the classical EC' system. We suggest that this "quasicatalytic" behavior should be considered when EC'-like behavior is observed and when the electrochemical system involves a substrate couple whose diffusion coefficients are much smaller than those of the mediator couple. As has been known for some time, when the diffusion coefficients of species A, B, P, and Q are identical (an assumption commonly made to simplify theoretical analysis) and when both heterogeneous electron transfers are reversible, the homogeneous kinetics have no effect on the cyclic voltammetric response--even though the distribution of species in the diffusion layer is dramatically altered.

Anion-induced adsorption of ferrocenated nanoparticles.

Au nanoparticles fully coated with omega-ferrocenyl hexanethiolate ligands, with average composition Au225(omega-ferrocenyl hexanethiolate)43, exhibit a unique combination of adsorption properties on Pt electrodes. The adsorbed layer is so robust that electrodes bearing submonolayer, monolayer, and multilayer quantities of these nanoparticles can be transferred to fresh electrolyte solutions and there exhibit stable ferrocene voltammetry over long periods of time. The kinetics of forming the robustly adsorbed layer are slow; monolayer and submonolayer deposition can be described by a rate law that is first order in nanoparticle concentration and in available electrode surface. The adsorption mechanism is proposed to involve entropically enhanced (multiple) ion-pair bridges between oxidized (ferrocenium) sites and certain specifically adsorbed electrolyte anions on the electrode. Adsorption is promoted by scanning to positive potentials (through the ferrocene wave) and by high concentrations of Bu4N+ X- electrolyte (X- = ClO4(-), PF6(-)) in the CH2Cl2 solvent; there is no adsorption if X- = p-toluenesulfonate or if the electrode is coated with an alkanethiolate monolayer. The electrode double layer capacity is not appreciably diminished by the adsorbed ferrocenated nanoparticles, which are gradually desorbed by scanning to potentials more negative than the electrode's potential of zero charge. At very slow scan rates, voltammetric current peaks are symmetrical and nearly reversible, but exhibit E(fwhm) considerably narrower (typically 35 mV) than ideally expected (90.6 mV, at 298 K) for a one-electron transfer or for reactions of multiple, independent redox centers with identical formal potentials. The peak narrowing is qualitatively explicable by a surface-activity effect invoking large, attractive lateral interactions between nanoparticles and, or alternatively, by a model in which ferrocene sites react serially at formal potentials that become successively altered as ion-pair bridges are formed. At faster scan rates, both deltaE(peak) and E(fwhm) increase in a manner consistent with a combination of uncompensated ohmic resistance of the electrolyte solution and of the adsorbed film, as distinct from behavior produced by slow electron transfer.

Dimensional analysis of chronoamperometry: proof and verification of Cottrellian behavior of systems with composition-dependent diffusion coefficients.

Chronoamperometry with a Dirichlet boundary condition and semi-infinite linear diffusion exhibits Cottrellian behavior, that is, the product it1/2 is constant as a function of time as long as the system is initially homogeneous, a conclusion that can be reached using only dimensional analysis; no detailed mathematical analysis is required. The generality of this result is known to include purely diffusional systems and systems in which transport also involves migration. In the present work, it is shown that Cottrellian behavior obtains, even when the system diffusion coefficients are a function of system composition, regardless of the exact form of that function. These conclusions are confirmed by simulations of examples for purely diffusional systems as well as for systems with migration. Some experimental examples from the literature are cited.

Systematic approach to the quantitative voltammetric analysis of the FeIII/FeII component of the [alpha2-Fe(OH2)P2W17O61]7-/8- reduction process in buffered and unbuffered aqueous media.

The one-electron reduction of [alpha(2)-Fe(III)(OH(2))P(2)W(17)O(61)](7-) at a glassy carbon electrode was investigated using cyclic and rotating-disk-electrode voltammetry in buffered and unbuffered aqueous solutions over the pH range 3.45-7.50 with an ionic strength of approximately 0.6 M maintained. The behavior is well-described by a square-scheme mechanism P + e(-) <--> Q (E(1)(0/) = -0.275 V, k(1)(0/) = 0.008 cm s(-1), and alpha(1) = 1/2), PH(+) + e(-) <--> QH(+) (E(2)(0/) = -0.036 V, k(2)(0/) = 0.014 cm s(-1), and alpha(2) = 1/2), PH(+) <--> P + H(+) (K(P) = 3.02 x 10(-6) M), and QH(+) <--> Q + H(+) (K(Q) = 2.35 x 10(-10) M), where P, Q, PH(+), and QH(+) correspond to [alpha(2)-Fe(III)(OH)P(2)W(17)O(61)](8-), [alpha(2)-Fe(II)(OH)P(2)W(17)O(61)](9-), [alpha(2)-Fe(III)(OH(2))P(2)W(17)O(61)](7-), and [alpha(2)-Fe(II)(OH(2))P(2)W(17)O(61)](8-), respectively; E(1)(0)' and E(2)(0)' are the formal potentials, k(1)(0)' and k(2)(0)' are the formal (standard) rate constants, and K(P) and K(Q) are the acid dissociation constants for the relevant reactions. The analysis for the buffered media is based on the approach of Laviron who demonstrated that a square scheme with fully reversible protonations, reversible or quasi reversible electron transfers with the assumption that alpha(1) = alpha(2), can be well-described by the behavior of a simple redox couple, ox + e(-) <--> red, whose formal potential, E(app)(0)', and standard rate constant, k(app)(0)', are straightforwardly derived functions of pH, as are the values of E(1)(0)', k(1)(0)', E(2)(0)', k(2)(0)', and K(P) (only three of the four thermodynamic parameters in a square scheme can be specified). It was assumed that alpha(app) = 1/2, and the simulation program DigiSim was used to determine the values of E(app)(0)' and k(app)(0)', which are required to describe the cyclic voltammograms obtained in buffered media in the pH range from 3.45 to 7.52 (buffer-related reactions which effect general acid-base catalysis are included in the simulations). DigiSim simulations of cyclic voltammograms obtained in unbuffered media yielded the values of E(1)(0)' and k(1)(0)'; K(Q) was then directly computed from thermodynamic constraints. These simulations included additional reactions between the redox species and H(2)O. The value of the diffusion coefficient of the [alpha(2)-Fe(III)(OH(2))P(2)W(17)O(61)](7-), 2.92 x 10(-6) cm(2) s(-1), was determined using DigiSim simulations of voltammograms at a rotating disk electrode in buffered and unbuffered media at pH 3.45. The diffusion coefficients of all redox species were assumed to be identical. When the pH is greater than 6, instability of P (i.e., [alpha(2)-Fe(III)(OH)P(2)W(17)O(61)](8-)) led to the loss of the reactant and precluded lengthy experimentation.

Electrochemical Measurements of Single H2 Nanobubble Nucleation and Stability at Pt Nanoelectrodes.

Single H2 nanobubble nucleation is studied at Pt nanodisk electrodes of radii less than 50 nm, where H2 is produced through electrochemical reduction of protons in a strong acid solution. The critical concentration of dissolved H2 required for nanobubble nucleation is measured to be ∼0.25 M. This value is ∼310 times larger than the saturation concentration at room temperature and pressure and was found to be independent of acid type (e.g., H2SO4, HCl, and H3PO4) and nanoelectrode size. The effects of different surfactants on H2 nanobubble nucleation are consistent with the classic nucleation theory. As the surfactant concentration in H2SO4 solution increases, the solution surface tension decreases, resulting in a lower nucleation energy barrier and consequently a lower supersaturation concentration required for H2 nanobubble nucleation. Furthermore, amphiphilic surfactant molecules accumulate at the H2/solution interface, hindering interfacial H2 transfer from the nanobubble into the solution; consequently, the residual current decreases with increasing surfactant concentration.

Metal-mediated electrochemical oxidation of DNA-wrapped carbon nanotubes.

As part of the ongoing effort to describe electron transfer reactions of carbon nanotubes (CNTs), we studied the mediated electrochemical oxidation of CNTs solubilized by wrapping with a T(60) deoxyribooligonucleotide. Cyclic voltammetry revealed that the oxidation of this CNT-DNA material by electrogenerated ML(3)(3+) mediators completes a catalytic cycle that increases the oxidative current compared to that obtained by voltammetry of the mediator alone (M = Fe(III), Ru(III), or Os(III); L = 2,2'-bipyridine or 4,4'-dimethyl-2,2'-bipyridine). We observed a greater increase in current at higher nanotube concentration, slower experimental scan rate, and higher mediator redox potential (E(0)'). Using computer simulation, these observations were shown to be consistent with CNT oxidation involving the removal of multiple electrons from each CNT-DNA moiety (the T(60) oligonucleotide was chosen because it is not oxidized by any of the mediators). The data are well-described by a simulation model based on the classical catalytic mechanism (EC') with the following embellishment: three populations of CNT-DNA redox-active sites with different E(0)' and therefore different oxidation rates are employed to represent the varying redox potentials of different valence band electrons within one CNT chiral type and within the distribution of CNT types present in our sample. This modeling suggests the number of CNT-DNA sites available for oxidation increases with the E(0)' of the mediator. This result can be qualitatively interpreted in terms of CNT band theory.

Simulations of cyclic voltammetric and chronoamperometric electrode responses at a disk electrode using combinations of spherical and cylindrical electrode geometries.

Using geometric models based on one-dimensional transport at spheres and cylinders, three methods for improving the simulation of voltammetric behavior of a disk electrode have been explored. One method is based on the common assumption of equivalency between the limiting currents for a disk and a hemisphere under steady-state diffusion conditions. The second method involves the use of a partial-sphere geometry which is a better approximation that is suitable at the extreme diffusional limits achievable at a disk electrode of fully planar and steady-state transport. The third method, which is generally applicable, is a further refinement that uses a combination of appropriate one-dimensional spherical and cylindrical geometries. The results demonstrate that reasonably accurate approximations of disk behavior for several reaction mechanisms can be achieved in a fraction of the time required to compute the more rigorous two-dimensional model. We propose that the approximation serve primarily as a fast way to explore system behavior and establish approximate values of the relevant parameters. More accurate computations can then be performed using the two-dimensional model.

pH-dependence of the aqueous electrochemistry of the two-electron reduced alpha-[Mo18O54(SO3)] sulfite Dawson-like polyoxometalate anion derived from its triethanolammonium salt.

The electrochemistry of the Dawson-like sulfite polyoxometalate anion alpha-[Mo18O54(SO3)2]6-, derived from the TEAH6{alpha-[Mo18O54(SO3)2]} salt (TEAH+ is the triethanolammonium cation; pKa=7.8), has been investigated in aqueous media using cyclic and rotated disk voltammetry at glassy carbon electrodes and bulk electrolysis, with a focus on the pH-dependence for oxidation to alpha-[Mo18O54(SO3)2]4-. In buffered media at pH>or=4, the cyclic voltammetric response for alpha-[Mo18O54(SO3)2]6- reveals two partially resolved one-electron oxidation processes corresponding to the sequential generation of alpha-[Mo18O54(SO3)2]5- and alpha-[Mo18O54(SO3)2]4-. At lower pH, using electrolytes containing sulfuric acid, the two waves coalesce but the individual apparent E0' reversible formal potential values for the two processes can be extracted down to pH 2 by assuming that reversible protonation accompanies fast electron transfer. The results for 2

Identification of the radical anions of C2N4S2 and P2N4S2 rings by in situ EPR spectroelectrochemistry and DFT calculations.

The previously unknown radical anions of unsaturated E2N4S2 ring systems (E=RC, R2NC, R2P) can be generated voltammetrically by the one-electron reduction of the neutral species and, despite half-lives on the order of a few seconds, have been unambiguously characterized by electron paramagnetic resonance (EPR) spectroelectrochemistry using a highly sensitive in situ electrolysis cell. Cyclic voltammetric studies using a glassy-carbon working electrode in CH3CN and CH2Cl2 with [nBu4N][PF6] as the supporting electrolyte gave reversible formal potentials for the [E2N4S2]0/- process in the range of -1.25 to -1.77 V and irreversible peak potentials for oxidation in the range of 0.66 to 1.60 V (vs the Fc+/0 couple; Fc=ferrocene). Reduction of the neutral compound undergoes an electrochemically reversible one-electron transfer, followed by the decay of the anion to an unknown species via a first-order (chemical) reaction pathway. The values of the first-order rate constant, kf, for the decay of all the radical anions in CH2Cl2 have been estimated from the decay of the EPR signals for (X-C6H4CN2S)2*-, where X=4-OCH3 (kf=0.04 s(-1)), 4-CH3 (kf=0.02 s(-1)), 4-H (kf=0.08 s(-1)), 4-Cl (kf=0.05 s(-1)), 4-CF3 (kf=0.05 s(-1)), or 3-CF3 (kf=0.07 s(-1)), and for [(CH3)3CCN2S]2*- (kf=0.02 s(-1)), [(CH3)2NCN2S]2*- (kf=0.05 s(-1)), and [(C6H5)2PN2S]2*- (kf=0.7 s(-1)). Values of kf for X=4-H and for [(CH3)2NCN2S]2*- were also determined from the cyclic voltammetric responses (in CH2Cl2) and were both found to be 0.05 s(-1). Possible pathways for the first-order anion decomposition that are consistent with the experimental observations are discussed. Density functional theory calculations at the UB3LYP/6-31G(d) level of theory predict the structures of the radical anions as either planar (D2h) or folded (C2v) species; the calculated hyperfine coupling constants are in excellent agreement with experimental results. Linear correlations were observed between the voltammetrically determined potentials and both the orbital energies and Hammett coefficients for the neutral aryl-substituted rings.

Supporting electrolyte and solvent effects on single-electron double layer capacitance charging of hexanethiolate-coated Au140 nanoparticles.

Sequential injections of single electrons (or holes) into the cores of Au(140) hexanethiolate monolayer-protected clusters (MPCs) occur at measurably different electrochemical potentials owing to the extremely small (subattofarad) values of the single MPC capacitance (C(MPC)) of the nanoparticle. The potential increment for each sequential injection is DeltaV = e/C(MPC). The dependence of DeltaV on the concentration of supporting electrolyte (from 1 to 100 mM), measured using square wave voltammetry, is shown to be caused, primarily, by changes in the diffuse double layer component (C(DIFFUSE)) of C(MPC). The dependence of C(DIFFUSE) on r(core), the radius of the nanoparticle, is considered. Additionally, significant changes in the magnitude of the compact double layer component (C(COMPACT), equivalent to the Stern layer) of C(MPC) were induced by adding hydrophobic solvent components such as hexane or dodecane or by introducing hydrophobic electrolyte ions (tetrabutyl-, tetrahexyl-, and tetraoctylammonium, perchlorate, and tetraphenylborate). These changes are interpreted as specific solvation and ion penetration of the hexanethiolate monolayer. For brevity we will refer to these phenomena as solvation/penetration phenomena.

Ion atmosphere relaxation and percolative electron transfer in Co bipyridine DNA molten salts.

Polypyridyl complexes of Co decorated with 350-Da polyether chains (Co(350)(2+)) form molten phases of nucleic acids when paired with DNA counterions (Co(350)DNA) or 25-mer oligonucleotides. Analysis of voltammetry and chronoamperometry of mixtures of these phases with complexes having ClO(4)(-) counterions (Co(350)(ClO(4))(2)) and no other diluent provides charge transport rates from the oxidation and reduction currents for the complexes. As the mole fraction of the Co(350)(ClO(4))(2) complex in the mixture is varied from ca. 0.25 to 1, the physical diffusion constants derived from the Co(III/II) wave increase from 1 x 10(-11) cm(2)/s to 5 x 10(-10) cm(2)/s, and apparent diffusion constants dominated by the Co(II/I) electron self-exchange increase from 1 x 10(-10) cm(2)/s to 2 x 10(-8) cm(2)/s. Pure Co(350)DNA melts, containing no Co(350)(ClO(4))(2) complex, do not exhibit recognizable voltammetric waves; DNA suppresses the Co(II/I) electron transfer reactions of Co complexes for which it is the counterion. There are therefore two microscopically distinct kinds of Co(350) complexes, those with DNA and those with ClO(4)(-) counterions, with respect to their Co(II/I) electron-transfer dynamics, leading to percolative behavior in their mixtures. The electron-transfer rates of the Co(II/I) couple are controlled by the diffusive relaxation of the ionic atmosphere around the reaction pair, and the inactivity of the bound Co complexes can be attributed to the very low mobility of the anionic phosphate groups in the DNA counterion. Substitution of sulfonated polystyrene for DNA produced similar results, suggesting that this phenomenon is general to other polymer counterions of low mobility. We conclude that the measured Co(II/I) charge transport and electron-transfer rate constants reflect more the diffusive mobility of the perchlorate counterion than the intrinsic Co(II/I) electron hopping rate.

Resistance, capacitance, and electrode kinetic effects in Fourier-transformed large-amplitude sinusoidal voltammetry: emergence of powerful and intuitively obvious tools for recognition of patterns of behavior.

Large-amplitude sinusoidal ac voltammetric techniques, when analyzed in the frequency domain using the Fourier transform-inverse Fourier transform sequence, produce the expected dc and fundamental harmonic ac responses in addition to very substantial second, third, and higher ac harmonics that arise from the presence of significant nonlinearity. A full numerical simulation of the process, Red right arrow over left arrow Ox + e(-), incorporates terms for the uncompensated resistance (R(u)), capacitance of the double layer (C(dl)), and slow electron transfer kinetics (in particular, the reversible potential (E degrees ), rate constant (k(0)), and charge transfer coefficient (alpha) from the Butler-Volmer model). Identification of intuitively obvious patterns of behavior (with characteristically different sensitivity regimes) in dc, fundamental, and higher harmonic terms enables simple protocols to be developed to estimate R(u), C(dl), E degrees , k(0), and alpha. Thus, if large-amplitude sinusoidal cyclic voltammograms are obtained for two concentrations of the reduced species, data obtained from analysis of the recovered signals provide initial estimates of parameters as follows: (a) the dc cyclic component provides an estimate of E degrees (because the R(u) and k(0) effects are minimized); (b) the fundamental harmonic provides an estimate of C(dl) (because it has a high capacitance-to-faradaic current ratio); and (c) the second harmonic provides an estimate of R(u), k(0), and alpha (because the C(dl) effect is minimized). Methods of refining the initial estimates are then implemented. As a check on the fidelity of the parameters (estimated on the basis of an essentially heuristic approach that solely utilizes the dc, fundamental, and second harmonic voltammograms), comparison of the predicted simulated and experimental third (or higher) harmonic voltammograms can be made to verify that agreement between theory and experiment has been achieved at a predetermined level. The use of the heuristic pattern recognition approach to evaluate the oxidation of ferrocene at a platinum electrode (a reversible process) in the very high resistance solvent dichloromethane (0.1 M Bu(4)NPF(6)) and the reduction of [Fe(CN(6))](3)(-) at a glassy carbon electrode (a quasi-reversible process) in much lower resistance but higher capacitance conditions found in aqueous (0.5 M KCl) media is described and verifies the inherent advantages of employing large-amplitude sinusoidal techniques in quantitative studies of electrode processes.

Interfacial electron-transfer kinetics of ferrocene through oligophenyleneethynylene bridges attached to gold electrodes as constituents of self-assembled monolayers: observation of a nonmonotonic distance dependence.

The standard heterogeneous electron-transfer rate constants (k(n)0) between substrate gold electrodes and the ferrocene redox couple attached to the electrode surface by variable lengths of substituted or unsubstituted oligophenyleneethynylene (OPE) bridges as constituents of mixed self-assembled monolayers were measured as a function of temperature. The distance dependences of the unsubstituted OPE standard rate constants and of the preexponential factors (An) obtained from an Arrhenius analysis of the unsubstituted OPE k(n)0 versus temperature data are not monotonic. This surprising result, together with the distance dependence of the substituted OPE preexponential factors, may be assessed in terms of the likely conformational variability of the OPE bridges (as a result of the low intrinsic barrier to rotation of the phenylene rings in these bridges) and the associated sensitivity of the rate of electron transfer (and, hence, the single-molecule conductance which may be estimated using An) through these bridges to the conformation of the bridge. Additionally, the measured standard rate constants were independent of the identity of the diluent component of the mixed monolayer, and using an unsaturated OPE diluent has no effect on the rate of electron transfer through a long-chain alkanethiol bridge. These observations indicate that the diluent does not participate in the electron-transfer event.

Heterogeneous electron-transfer kinetics for ruthenium and ferrocene redox moieties through alkanethiol monolayers on gold.

The standard heterogeneous electron-transfer rate constants between substrate gold electrodes and either ferrocene or pentaaminepyridine ruthenium redox couples attached to the electrode surface by various lengths of an alkanethiol bridge as a constituent of a mixed self-assembled monolayer were measured as a function of temperature. The ferrocene was either directly attached to the alkanethiol bridge or attached through an ester (CO(2)) linkage. For long bridge lengths (containing more than 11 methylene groups) the rate constants were measured using either chronoamperometry or cyclic voltammetry; for the shorter bridges, the indirect laser induced temperature jump technique was employed to measure the rate constants. Analysis of the distance (bridge length) dependence of the preexponential factors obtained from an Arrhenius analysis of the rate constant versus temperature data demonstrates a clear limiting behavior at a surprisingly small value of this preexponential factor (much lower than would be expected on the basis of aqueous solvent dynamics). This limit is independent of both the identity of the redox couple and the nature of the linkage of the couple to the bridge, and it is definitely different (smaller) from the limit derived from an equivalent analysis of the rate constant (versus temperature) data for the interfacial electron-transfer reaction through oligophenylenevinylene bridges between gold electrodes and ferrocene. There are a number of possible explanations for this behavior including, for example, the possible effects of bridge conformational flexibility upon the electron-transfer kinetics. Nevertheless, conventional ideas regarding electronic coupling through alkane bridges and solvent dynamics are insufficient to explain the results reported here.