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J. Phys. Chem. B 1997, 101, 8286-8291
Long-Range Electronic Coupling between Ferrocene and Gold in Alkanethiolate-based Monolayers on Electrodes Kara Weber,† Lisa Hockett,† and Stephen Creager*,‡ Department of Chemistry, Indiana UniVersity, Bloomington, Indiana 47405, and Department of Chemistry, Clemson UniVersity, Clemson, South Carolina 29634 ReceiVed: May 22, 1997; In Final Form: July 26, 1997X
High-speed cyclic voltammetry was used to measure rates for ferrocene oxidation/reduction in a series of self-assembled monolayers formed by coadsorption of N-(mercaptoalkyl)ferrocenecarboxamide ((C5H5)Fe(C5H4)CONH(CH2)nSH where n ) 7-10, and 15) with mercapto alcohol (HO(CH2)n+1SH where n ) 7-10, and 15) on gold. Standard electron-transfer rate constants were obtained as a function of chain length and from these rate constants, a β value (describing the exponential decay of rate with adsorbate chain length) of 1.1 methylene-1 or 0.85 Å-1 was obtained. The rate data were also used to estimate coupling factors, |VAB|, describing the long-range electronic coupling between the immobilized ferrocene groups and the underlying gold electrode. Electronic coupling factors varied from a low of 0.06 cm-1 for the long-chain monolayer (18 bonds in the pathway linking ferrocene to the electrode) to a high of 6.5 cm-1 for the shortchain monolayer (10 bonds linking ferrocene to the electrode). The latter value is in good agreement with a value of 6.2 cm-1 previously reported by Closs and Miller for an electronic coupling factor in a donoracceptor molecule in which the bridge is a saturated hydrocarbon (a steroid) in which there are also10 bonds linking the donor and acceptor.
Introduction Perhaps the most remarkable aspect of electron-transfer reactions is their capacity for occurring over very long distances. Many examples exist in which single electron transfer occurs rapidly from an electron donor to an acceptor over distances in the 10-20 Å range,1-8 and recent reports have suggested that in certain cases rapid electron transfer may occur in a single step over distances of 50 Å or more.9-11 Electronic coupling between donors and acceptors is critically important in dictating the rate and the pathway for these long-range electron-transfer reactions, and much of the recent research on electron transfer has focused on how molecular bridges linking electron donors to acceptors mediate this long-range electronic coupling.1 These investigations will lend insight into biological systems such as redox proteins12-15 and photosynthetic reaction centers16-18 in which long-range electron transfer plays an important role. This work will also lay the groundwork for the development of a new class of molecular electronic materials in which “circuits” of molecular dimensions may be used to accomplish higherorder functions.19-21 The recent emphasis on bridge-mediated coupling in electrontransfer research is possible in part because of advances in the theories of intramolecular electron transfer.22 In particular, a thorough understanding of the complementary roles of nuclear configuration (Franck-Condon) and electronic coupling factors in controlling electron-transfer rates is required for rate measurements to be interpreted in terms of fundamental parameters including the reorganizational energy and electronic coupling energy.23 The reorganizational energy, λ, is the energy required in an electron-transfer reaction to adjust the nuclear configuration of the reactants to a minimum energy configuration of the products. The electronic coupling factor, VAB, reflects the overall energy of interaction of the two orbitals, one filled and one empty, that participate in the electron-transfer reaction. Many studies have shown that reorganizational energies and X
Abstract published in AdVance ACS Abstracts, September 1, 1997.
S1089-5647(97)01710-0 CCC: $14.00
electronic coupling factors may be obtained from electrontransfer rate data within structurally related donor-acceptor series. The availability of rate data as a function of reaction driving force is critically important in such work, since one must fit the dependence of rate on driving force to separate the nuclear configuration and electronic coupling contributions to the overall rate. Electrochemical methods are particularly well suited to the study of long-range electron transfer.24 Immobilization of a redox molecule in a rigid layer on an electrode surface creates the electrochemical analogue of a bridged donor-acceptor molecule, and studies of rate as a function of driving force in such “molecules” are straightforward because the reaction driving force can be easily adjusted via the potential applied to the electrode. The electronic coupling factor is more difficult to estimate, since one must account for the nuclear configuration factor in the rate expression and also for the electronic structure of the metal electrode. We report here the use of high-speed cyclic voltammetry25,26 to study redox kinetics in a series of ferrocene-containing monolayers on gold electrodes.27-32 The data analysis accounts explicitly for the electronic structure of gold via a term for the density of electronic states, obtained from published photoelectron spectroscopy data,33,34 variable-temperature electronic heat capacity data,35 and electronic band structure calculations.36 This new approach to the data analysis has enabled us for the first time to make quantitative estimates of electronic coupling factors describing the bridge-mediated long-range electronic coupling between immobilized ferrocene groups and the underlying gold electrode. These factors were found to be in good quantitative agreement with similar factors reported by Closs and Miller in their landmark work on electron transfer in bridged donoracceptor molecules.8,37 Experimental Section Perchloric acid (Mallinkcrodt) and absolute ethanol (AAPER) were used as received. Water for preparing electrolyte solutions © 1997 American Chemical Society
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was purified using a Barnstead-Nanopure system. The ferrocenealkanethiol ((C5H5)Fe(C5H4)CONH(CH2)nSH) and n-mercapto alcohol (HO(CH2)n+1SH where n ) 7-10, 15) coadsorbates were synthesized and characterized as previously described.31,38 Gold disk electrodes were constructed by sealing 1 cm lengths of annealed gold wire (radius ) 25, 62.5, 125, 500 µm) in epoxy (Shell EPON resin 825 from Miller-Stephenson Chemical Co.) cross-linked with 1,3-phenylenediamine (Aldrich).39 Electrodes were polished to smoothness using alumina (5.0, 1.0, 0.3 µm) and were treated by sonication in soapy water twice for10 min followed by sonication in deionized water twice for10 min. The electrodes were then etched in dilute aqua regia (1:3:4 HNO3: HCl:H2O) for 1 min, rinsed with water followed by ethanol, and then immediately immersed in the coating solutions for 1824 h to form monolayers.40 Coating solutions were 1 mM total thiol concentration (0.1 mM (C5H5)Fe(C5H4)CONH(CH2)nSH, 0.9 mM HO(CH2)n+1SH) in ethanol. Electrochemical experiments were performed using a singlecompartment cell (2 mL electrolyte) continuously purged with water-saturated nitrogen. The cell was housed in a Faraday cage to reduce stray electronic noise. Potentials were referenced to a Pd/PdH reference. The auxilliary electrode was a 1 cm2 Pt foil attached to Pt wire at each corner and held approximately parallel to the surface of the working electrode at a distance of approximately 1 mm. Cyclic voltammetry was performed using a low-current, rapidresponse potentiostat (EIS-969, designed and built by the Indiana University Electronic Instrument Services). A microprocessorcontrolled analog function generator (Krohn-Hite Model 5900C) was used to generate potential sweeps, and a digital oscilloscope (Tetronix Model TDS-320) was used to digitize the data. Instrument control was accomplished using a 66 MHZ 80486DX-based PC with programs written in the Lab Windows/CVI (National Instruments) programming environment. Standard electron-transfer rate constants were obtained from fits of peak potential vs log(scan rate) curves from voltammograms acquired over a sweep rate range from 0.1 V s-1 to 10 000 V s-1 using programs written in QuickBasic 4.5.29 Theory The experimental results in the following sections will be best understood in the context of a brief overview of the modern theory of electron transfer at metal electrodes.41-50 Electrochemical electron transfer has long been considered as a special case of molecular electron transfer, and models developed to describe electron transfer between molecules have been modified to describe electron transfer at metal electrodes.
∫
[
kred(η) ) A exp -
∫
[
kox(η) ) A exp -
]
((F - ) + eη + λ)2 d (1) [f()] 4λkbT kbT
]
((F - ) - eη + λ)2 d (2) [1 - f()] 4λkbT kbT
( )( )
A ) F()|VAB|2
kbT π p λkbT
1/2
(3)
Within a semiclassical framework for describing electrochemical kinetics, rate constants for oxidation/reduction of redox molecules at electrodes are given by eqs 1 and 2,24,45-47,50 where λ is the reorganizational energy, η is the overpotential (equal to the applied potential relative to the formal potential of the redox molecule), F is the Fermi energy (equal to the applied potential), f() is the Fermi function, kb is the Boltzmann constant, T is
Figure 1. Effect of chain length on voltammetry of (C5H5)Fe(C5H4)CONH(CH2)nSH/HO(CH2)n+1SH monolayer at 500 V s-1 in aqueous 1.0 M HClO4 at room temperature. Chain lengths were (A) n ) 7 (electrode radius ) 63.5 µm, ferrocene coverage ) 2.2 × 10-11 mol cm-2), (B) n ) 10 (electrode radius ) 125 µm, ferrocene coverage ) 6.1 × 10-11 mol cm-2), and (C) n ) 15 (electrode radius ) 500 µm, ferrocene coverage ) 3.4 × 10-11 mol cm-2).
absolute temperature, and A is a preexponential factor. The term is an integration variable that corresponds to the energy level in the electrode. The standard electron-transfer rate constant, k0, is obtained from either eq 1 or 2 when the overpotential is zero. In the case of weak coupling between the redox molecule and the electrode (nonadiabatic electron transfer), the preexponential factor A is given by eq 3 where F() is the density of electronic states in the electrode at energy and VAB describes the electronic coupling between the redox molecule and the electrode. The latter two terms are assumed to be constant with respect to the energy level in the electrode. Marcus and co-workers have recently discussed these expressions and the assumptions inherent in them in the specific context of long-range electron transfer in monolayers.50,51 Results and Discussion Figure 1 presents three representative voltammograms that illustrate how cyclic voltammetry may be used to measure electron-transfer rates for ferrocene oxidation/reduction in monolayers.26,52 The voltammograms were acquired at a potential scan rate of 500 V s-1 for three monolayers in which ferrocene groups were linked to a gold electrode by alkane chains of different lengths (i.e., the chain linking the ferrocene group to the electrode contains 7, 10, and 15 methylenes in monolayers A, B, and C, respectively). The clear trend is that as the chains become longer, the voltammetric peak splitting also becomes larger, i.e., the difference between the anodic and cathodic peak potentials increases from 40 mV in A to 184 mV in B to 1008 mV in C. Larger peak splittings indicate slower
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Figure 2. Anodic peak potential (V) versus log(sweep rate) (V s-1) for three chain lengths: (C5H5)Fe(C5H4)CONH(CH2)nSH/HO(CH2)n+1SH: b, n ) 15; 9, n ) 10; 2, n ) 7. The plots shift to the left with decreasing intrinsic rate constant or increasing chain length. The fitting program described in the text was applied to the n ) 15 curve to determine a rate constant, k0 ) 6.6 s-1 and λ ) 0.85 eV (solid line). The dashed curves were calculated by using k0 ) 6.6 s-1 and λ ) 0.65 and 1.05 eV and are included to illustrate the sensitivity of the fit to the value of λ.
redox kinetics, which in turn probably reflect a decrease in the electronic coupling between the ferrocene group and the electrode as the length of the alkane chain linking the ferrocene group to the electrode increases. A more complete picture develops when the voltammetry is performed over a range of scan rates. Figure 2 presents a summary of how increasing the potential scan rate affects the anodic peak potential corresponding to ferrocene oxidation in the three monolayers considered in Figure 1. All three monolayers show reversible behavior (peak splitting near 0 V) at slow scan rates and some peak splitting at faster scan rates. Most important, the shorter-chain monolayer (triangles) requires very fast scan rates to observe any substantial positive shift in the anodic peak potential, whereas the longer-chain monolayers (circles and squares) exhibit positive shifts at relatively slower scan rates. These observations suggest strongly that the differences in peak splitting observed at a fixed scan rate in Figure 1 are caused by differences in electron-transfer rates for the different chain length monolayers. The standard electron-transfer rate constant, k0 (i.e., the rate constant corresponding to electron self-exchange under conditions where the reaction driving force is zero), is a useful indicator of the kinetics of a particular redox reaction. It may be obtained for an immobilized redox agent on an electrode surface by fitting curves such as those in Figure 2 to predictions from theory.27-30 When such fits are achieved using eqs 1 and 2 to describe the dependence of electron-transfer rate on applied potential, one can obtain values for both k0 and also the reorganization energy, λ, for the redox agent immobilized on the electrode, from the fit. When these two parameters are determined, the value for the preexponential factor, A, is also determined, since A is a dependent parameter. Figure 2 presents such a fit to a peak potential vs log(scan rate) data set for the longest-chain monolayer studied in this work. The solid line is a best fit to the points indicated by the circles, corresponding to values of 6.6 s-1 for k0, 0.85 eV for λ, and 9 × 103 s-1 for A. The values for k0 and λ from this work are quite close to those reported in our own earlier work on this system29 and also to values reported by Chidsey for ferrocene oxidation in a slightly different monolayer system studied using chronoamperometry.24 The uncertainty in the best-fit value of λ derived from studies of many independently prepared samples is approximately
Weber et al. (0.05 eV. This uncertainty reflects sample-to-sample variations in the peak potential, primarily at the faster scan rates, as illustrated in Figure 2 via the dashed lines that correspond to calculated peak potential vs log(scan rate) curves using the bestfit value for k0 of 6.6 s-1 and values for λ that are slightly (0.2 eV) higher and lower than the best-fit value of 0.85 eV. The differences among the three calculated curves are most easily discerned at the higher overpotentials, reflecting the fact that the fit is most sensitive to the value of λ in this region.29,30 The differences among the curves are in fact relatively minor, reflecting the fact that the curve shape is in general not strongly sensitive to reorganizational energy. Even so, the best-fit value for λ of 0.85 eV was obtained with acceptable precision from many independent voltammetric studies of the long-chain monolayer. Unfortunately, reliable λ values could not be obtained by similar means for the shorter chain length monolayers. At the fast scan rates required to achieve substantial peak splitting in these monolayers, the peak currents are large and the voltammetric wave shape begins to be affected by uncompensated solution resistance.53 Even a relatively small contribution to the peak splitting from solution resistance would have a large effect on the λ value that would be obtained from a twoparameter fit. For this reason, fits to peak potential vs log(scan rate) data for the shorter-chain monolayers were achieved with λ fixed at 0.85 eV and k0 as the lone adjustable parameter. (The preexponential factor is still a dependent parameter, the value of which is fixed by the values of λ and k0.) This procedure amounts to assuming that λ is independent of chain length. Support for this assumption comes from recent work by Smalley and co-workers in which activation energies for ferrocene oxidation/reduction (obtained from an Arrhenius analysis of standard electron-transfer rate constants obtained at different temperatures) in a slightly different monolayer series were shown to be similar for chains from five to nine carbons in length.54 Standard electron-transfer rate constants and preexponential factors obtained using the fitting procedure described above on the monolayers studied in this work are summarized in Table 1. The obvious and expected trend is that the electron-transfer rate constants increase as chain length decreases. This dependence may be interpreted via a plot of ln(k0) vs chain length, and Figure 3 shows such a plot for the ferrocene monolayers studied in this work. The good linearity of the plot reflects the expectation that electronic coupling (the VAB term in eq 3) in a weakly coupled, nonadiabatic system should depend exponentially on distance and/or the number of bonds in the chain linking the redox molecule to the electrode. The fact that the plot remains linear over 4 orders of magnitude change in rate (corresponding to a decrease in the number of methylenes in the alkane chain from 15 to 7) suggests that the reaction is nonadiabatic over the full range of chain lengths studied. The slope of the plot is indicative of how rapidly the electronic coupling is diminished as the separation between the redox molecule and the electrode is increased. The value of 1.1 per methylene group obtained from Figure 3 is in good agreement with values reported for similar electrochemical systems54-59 and is also consistent with values reported for ground-state and excited-state long-range electron transfer in all-synthetic model systems5-8,37 and in chemically modified redox proteins.12 An examination of the chain length dependence of electrontransfer rates in monolayers on electrodes provides valuable insight into how electron transfer occurs at electrodes. However, it does not provide enough information to enable a direct, quantitative comparison of electronic coupling in molecular donor-acceptor systems with that in electrochemical systems.
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TABLE 1: Rate Constants, Preexponential Factors, and Electronic Coupling Factors for Ferrocene-Containing Monolayers on Gold
no. bonds k0, s-1 A,a s-1 V,b cm-1
18 6.6 9 × 103 0.06
13 1.2 × 103 1.6 × 106 0.9
12 6.0 × 103 8 × 106 2
11 1.5 × 104 2 × 107 3
10 6.6 × 104 9 × 107 6.5
a Calculated from experiemntal k values assuming a reorganizational energy of 0.85 eV. b Calculated from A values assuming an electrode 0 density-of-states of 0.3 eV-1.
near the Fermi energy. Another approach involves measurement of the temperature coefficient of the electronic heat capacity, also known as the Sommerfield parameter.35 In a free-electron gas model of electronic structure in metals, this parameter is proportional to the electronic state density at the Fermi energy according to eq 4, where γ is the Sommerfield parameter and F(F) is the electronic state density at the Fermi energy. Using the experimentally determined value of 0.728 mJ mol-1 K-2 for the Sommerfield parameter for gold, one can readily calculate that the electronic state density of gold at the Fermi energy is 0.31 states eV-1 atom-1. Figure 3. Plot of ln(k0) versus number of methylene units (n) in the monolayer component containing the electroactive ferrocene, (C5H5)Fe(C5H4)CONH(CH2)nSH. From the slope of the plot the β value is 1.1 per methylene unit or 0.85/Å.
This important comparison would provide insight into the question of whether the electronic coupling between two electronic orbitals each localized on a discrete molecule is fundamentally similar to or different from the coupling between an orbital localized on a molecule and an extended electronic orbital, such as that in a metal. Electronic structure in redox molecules is moderately well understood. However, any attempt at a more detailed analysis of electronic coupling in an electrochemical system must consider the electronic structure of both the molecule and the metal. This metal electronic structure is accounted for in eqs 1-3 via the term for the electronic state density of the metal as one element of the preexponential factor. To proceed further, we must evaluate this term explicitly. Electronic state densities have been estimated for gold (and other metals) by both experimental and theoretical means. For example, estimates of the electronic state density of gold as a function of energy were obtained by Krolikowski and Spicer,33 and later by Eastman,34 from measurements of photoelectron yields as a function of energy in soft X-ray photoemission spectroscopy experiments. Both groups evaluated their data in terms of an optical density of (occupied) electronic states as a function of energy relative to the Fermi energy, and both groups report values near 0.3 states eV-1 atom-1 for gold at energies
π2F(F)kb2 γ) 3 F(F) )
3N 2F
(4) (5)
One can also estimate the electronic state density of a metal from the free-electron gas theory using eq 5, which gives the density of electronic states at the Fermi energy as a function of the Fermi energy and the number of conduction electrons contributed to the electron gas per metal atom.35 In the case of gold, each atom contributes one electron to the electron gas, and the Fermi energy is 5.51 eV. Thus, the electronic state density of gold at the Fermi energy is estimated to be 0.27 states eV-1 atom-1. Finally, one can describe the electronic structure of gold using much more sophisticated models than the freeelectron gas model, and band structure calculations based on such models have been performed. Not surprisingly, these advanced models predict a more complex band structure than does the simple free-electron gas model, particularly for energies deep in the valence band where d- and f-electrons make a significant contribution to the overall state density. Even so, a relativistic electronic band structure calculation carried out by Kupratakuln for gold predicts an electronic state density near 0.3 states eV-1atom-1 at energies near the Fermi energy, in good agreement with the other estimates presented above.36 This agreement indicates (among other things) that the free-electron gas model is a good approximation of the electronic structure of gold at energies near the Fermi energy.
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Weber et al.
TABLE 2: Rate Constants and Electronic Coupling Factors for Electron Transfer in Bridged Naphthyl-Biphenyl Compounds (from Refs 8 and 37)
no. bonds k,a s-1 V, cm-1 a
10 1.5 × 106 6.2
7 5.0 × 107 30
6 2.9 × 108 54
5 1.9 × 109 128
4 4.2 × 109 168
Electron transfer from biphenyl to naphthyl. ∆Grxn ) -50 mV.
We are now able to analyze the preexponential factors in Table 1 more completely. For example, for the long-chain monolayer, a preexponential factor of 9 × 103 s-1 was obtained from the fit to the peak potential vs log(scan rate) data in Figure 2. Using the best-fit value of 0.85 eV for the reorganizational energy and the value of 0.3 states eV-1 atom-1 estimated above for the electronic state density of gold, we readily calculate a value of 8 × 10-6 eV or 0.06 cm-1 for the electronic coupling factor (VAB) for this monolayer. Similar calculations were carried out for the other monolayers, and the resulting electronic coupling factors are also reported in Table 1. As expected, the maximum electronic coupling factor of 6.5 cm-1 corresponds to the shortest monolayer studied. In this case, there are10 individual bonds in the bridge linking the ferrocene group to the electrode (including the alkane chain, the amide group linking the ferrocene group to the alkane chain, and the carbonsulfur bond at the gold surface). All of the electronic coupling parameters obtained are less than the 50 cm-1 value suggested as the upper limit for an electron-transfer reaction to be considered nonadiabatic.60 This is significant, since weak coupling and a nonadiabatic reaction are assumed in the derivation of eqs 1-3. It is instructive to compare the electronic coupling factors in Table 1 with parameters describing electronic coupling in bridged donor-acceptor molecules. Table 2 presents a summary of selected rate constants and electronic coupling factors reported in Closs and Miller’s work on electron transfer in bridged donor-acceptor molecules with saturated hydrocarbon bridges.8,37 The particular compounds shown in Table 2 are derivatives of cyclohexane, Decalin, and 5-R-androstane (a steroid) in which a biphenyl electron donor is located at one position on the bridge and a naphthalene electron acceptor at another position across the bridge. Within each series the naphthalene moiety was systematically replaced by other electron acceptors with progressively less negative redox potentials. Thus, a study of an entire series gives rate data as a function of reaction driving force. The rate constants in Table 2 correspond to electron transfer from biphenyl to naphthyl, which is energetically favorable by about 50 mV. These rate constants cannot be compared with the rate constants in Table 1, which correspond to the zero driving force condition for electrochemical ferrocene oxidation/reduction. Also, the reor-
ganization energies and overall activation barriers are likely to be very different in the two cases. Despite these differences, if activation energy and driving force effects have been properly accounted for in the data treatment, the electronic coupling factors for the two systems may be compared even when the rate constants cannot. Electronic coupling in Closs and Miller’s donor-acceptor molecules is generally stronger than in the ferrocene-containing monolayers. This is expected, since the overall length of the bridges in the donor-acceptor molecules (as indicated by the number of bonds in the shortest pathway between donor and acceptor) is less than in the monolayers. The comparison between the shortest bridge in the ferrocene monolayer series and the longest bridge in the molecular donor-acceptor series is especially significant, since in both cases the shortest throughbond pathway linking the two partners in the electron-transfer reaction contains10 bonds. The electronic coupling factors in these two cases are nearly identical (6.5 cm-1 in the ferrocene monolayer vs 6.2 cm-1 in the bridged naphthalene/biphenyl compound). This good quantitative agreement of the electronic coupling factors is obtained despite the fact that the two systems are physically quite different and indicates that the long-range electronic coupling between an electronic orbital in a molecule and one in a metal is not greatly different from that between two electronic orbitals both localized on discrete molecules. Several points should be considered regarding the interpretation of this result. First, the very close agreement between the two electronic coupling factors (less than 5% difference) should not be overinterpreted. For example, a 0.1 eV error in the estimation of the reorganization energy for either the immobilized ferrocene or the donor-acceptor molecule translates into a factor of 3 error in the preexponential factor and a factor of 31/2 or 1.7 error in the electronic coupling factor. The important point is not that the two electronic coupling factors are so close but rather that they are not greatly different from one another, as might have been the case if the extended nature of the electronic orbital in the metal had a dramatic effect on the coupling. Second, in using eqs 1-3 to fit our data, we have assumed that the electronic coupling factor and the density of electronic states in the metal electrode are both constant. This is not a fundamental assumption in eqs 1-3, and if one knew the functional dependence of these factors on energy, the
Coupling between Ferrocene and Gold expressions could easily be modified to incorporate this dependence. Unfortunately, it will probably not be possible to work in reverse and extract the functional dependence of these parameters on energy from voltammetric data, since there are many other factors besides a slow variation with energy of the electronic coupling or the electronic state density of the electrode that could affect the voltammetric wave shape. Other relevant issues include the possible role of multiple pathways for electronic coupling, either via bridges with multiple through-bond pathways (as in most bridged donor-acceptor molecules) or via pathways that include one or more nonbonded jumps (as in electrochemical systems in which the redox agent is not covalently bound to the monolayer surface), and the possible contribution of the gold-thiol bond to the overall electronic coupling between the ferrocene and the gold electrode. Recent calculations by Hsu and Marcus and experiments by Slowinski and co-workers suggest that the contribution from multiple chains will be low.50,61 The latter issue is particularly important in light of recent suggestions that in certain cases, molecule-mediated electronic coupling between two metals or between a metal substrate and an STM tip may be dominated by the binding interaction between the molecule and the metal, with the molecular bridge playing only a secondary role.62,63 The present data do not directly address either of these points, but we believe that they do suggest experiments and research directions, which should lend further insight into these important questions. Conclusions Fast-scan cyclic voltammetry was used to measure heterogeneous electron-transfer rate constants for ferrocene oxidation/ reduction in monolayers on gold electrodes. Rate constants were analyzed in such a way that a factor describing the strength of electronic coupling between the immobilized ferrocene group and the gold electrode could be obtained. Such factors were found to be in good agreement with electronic coupling factors previously reported by Closs and Miller in their work on electron transfer in donor-acceptor molecules, albeit only for the specific case where the number of bonds in the pathway linking the ferrocene to the electrode in the monolayer is the same as the number of bonds in the pathway linking the donor to the acceptor in the donor-acceptor molecule. This good quantitative agreement suggests that, at least from the viewpoint of longrange electronic coupling, a molecular electron donor-acceptor and a metal electrode are not greatly different. Acknowledgment. The authors gratefully acknowledge the National Science Foundation for financial support of this work and also Mr. Robert Ensman and the Indiana University Electronic Instrument Services group for their skilled technical assistance in the design and construction of fast potentiostat instrumentation. References and Notes (1) Barbara, P. F.; Meyer, T. J.; Ratner, M. A. J. Phys. Chem. 1996, 100, 13148. (2) Forbes, M. D. E. J. Phys. Chem. 1993, 97, 13029. (3) Fox, M. A. Chem. ReV. (Washington, D.C.) 1992, 92, 365. (4) Gust, D.; Moore, T. A. Tetrahedron 1989, 45, 4669. (5) Paddon-Row, M. N. Acc. Chem. Res 1994, 27, 18. (6) Gust, D.; Moore, T. A.; Moore, A. L. Acc. Chem. Res 1993, 26, 198. (7) Bowler, B. E.; Raphael, A. L.; Gray, H. B. Long-Range Electron Transfer in Donor (Spacer) Acceptor Molecules and Proteins; John Wiley & Sons: New York, 1990; Vol. 38. (8) Closs, G. L.; Miller, J. R. Science 1988, 240, 440. (9) Wilson, E. K. Chem. Eng. News 1997, February 24, 33. (10) Arkin, M. R.; Stemp, E. D. A.; Holmlin, R. E.; Barton, J. K.; Hormann, A.; Olson, E. J. C.; Barbara, P. F. Science 1996, 273, 475.
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