11497
J. Phys. Chem. 1993,97, 11497-1 1500
Relationship between Electronic Tunneling Coefficient and Electrode Potential Investigated Using Self-Assembled Alkanethiol Monolayers on Gold Electrodes Jie Xu, Hu-Lin Li' and Yin Zhangt Department of Chemistry, Lanzhou University, Lanzhou 730000, Gansu, P. R. China Received: May 14, 1993; In Final Form: August 17, 1993'
W e investigated the relationship between the electronic tunneling coefficient and the electrode potential. Monolayers of saturated long-chain alkanethiols, SH(CH2),CH3 (n = 11,13,15,17),were self-assembled from acetonitrile solutions onto gold electrodes. The closely packed and ordered monolayers were insulating and diminished the rate of electron transfer a t the modified gold surface. The rate of electron transfer was the rate-limiting step in the overall electrode reaction pathway. The electronic tunneling coefficient was calculated by varing the thickness of the insulating layer (changing the number of carbon atoms in long-chain thiol) and measuring the change in the heterogeneous electron-transfer rate of the selected redox couple at a given potential. To get a more precise measure of the tunneling coefficient, the observed current was corrected using convolution techniques for diffusional depletion of the surface concentrations of both the oxidized and reduced forms of the redox probe. The electronic tunneling coefficient was determined to be 1.02 f 0.20 per methylene unit in the long-chain alkanethiol with the Fe(CN)63-/Fe(CN)6" redox couple. This same value was obtained when the Fe3+/Fe2+redox couple was used. Least-squares analysis of the data showed that the electronic tunneling coefficient was nearly independent of the electrode potential but may be dependent upon the functional group a t the long-chain alkanethiol terminus.
Introduction The importance and complexity of electron-transfer reactions in nature have led many researchers to look for ways to study the fundamental chemistry of these processes in simplified model systems.' Electrochemical methods have many advantages over homogeneous measurements for the determination of kinetic parameters? The electrode, by virtue of its continuously variable potential, behaves as a universal oxidant or redutant. In a single voltammetric experiment, the electrode current gives a direct measure of the rate of the electron transfer, allowing the reactivity of a given redox molecule to be probed over a continuous range of potentials. However, heterogeneous electron-transferreactions require that the redox molecules must be brought to the electrode surface prior to oxidation or reduction. The rate at which redox species can be transported to the electrode surface sets a limit on the magnitude of heterogeneous electron-transfer rate constants which can be measured. In addition to diffusion limitations, the possible presence of potential drops and specific adsorption sites at the electrode surface complicates the description of the heterogeneous electron-transfer rate. The concentration and structure of the redox center may be different at the electrode surface than those in the bulk s ~ l u t i o n . ~ Self-assembled monolayers of alkanethiol on gold electrodes have been shown to be well-ordered and stable structures that remain intact during electrochemical experiment^.^ They are also well-suited for the study of heterogeneous electron-transfer kinetics. First, electron transfer across the monolayer proceeds via electron tunneling through the insulator, which decreases the absolute electron-transfer rate to a level at which diffusion limitationsare either greatly diminished or eliminated completely. Second, the electron transfer takes place with the redox couple 10-30 A from the metal surface. Thus, complications due to specific adsorption double-layer corrections, and image charge effects are decreased over measurements at a bare electrode. As such, they have been widely used in the measurementof the kinetic parameter of fast heterogeneous electron-transfer reactions.
* To whom correspondence should be addressed.
t Department of Computer Science, Lanzhou University.
Abstract published in Advance ACS Abstracts, October 1, 1993.
0022-365419312097-11497$04.00/0
In our previous work, the formation mechanism was investigated by studying the solvent effects on the formation of n-alkanethiol monolayer.6 We found that the degree of monolayer packing of n-alkanethiols onto gold electrodes varied as a function of the solvent used in the self-assembly step through comparison of the relative dielectric constant of the monolayer. We suggested two possible explanations for this solvent effect. One is that low solubility of alkanethiols in solvents with high relative dielectric constants requires less energy to free alkanethiol molecules from solvent in the formation of monolayers compared to solvents with low relative dielectric constants. Another is that during the monolayer formation solvents with high relative dielectric constants decrease the activation barrier for the oxidative addition of the alkanethiol to the gold surface atoms. Miller has shown that the insulating properties of w-hydroxyalkanethiol monolayers can be measured by comparing electrontransfer rates of solution redox couples at gold electrode derivatized with monolayers of different thickness.* The thickness can be varied by controlling the number of methylene units in the longchain alkanethiol used to form the monolayer. For w-hydroxyalkanethiol monolayer coated gold electrodes, the heterogeneous electron-transfer rate of a redox probe decreased by a factor of ca. 2.9 for each methylene. Assuming a 1.25-A increase in the monolayer thickness with each methylene group, the equivalent height of the tunneling barrier was calculated to be 0.6 eV. The major uncertainty in this work involves the potential dependence of this electron tunneling barrier.* The electron-transfer rate constants can be measured by5 Kapp= i/nFAC
where Kappis apparent rate constant, i is the cathodic faradaic current corrected for the charging current, A is the electrode area, and Cis the bulk concentration of the oxidized electroactive species in the solution. Electron-transfer theories predict that rates of electron-transfer reactions (ket)depend on the distance and driving force between the donor and acceptor sites7 0 1993 American Chemical Society
11498 The Journal of Physical Chemistry, Vol. 97,No. 44, 1993
(3) where HDAZis the electronic interaction between the donor and acceptor sites, and the electronic tunneling coefficient fl is related to the magnitude of this interaction. do is the minimum distance between the redox center and the electrode at which the electron transfer becomes adiabatic. The electron tunneling barrier was assumed to vary linearly with the formal overpotential of the electrode in the early work of Miller.8 If this assumption is correct, the density of electronic states for the redox molecules can be calculated using the mathematical formalism developed by Bennett.9 In a later paper by Miller,2 their assumption was tested and found to be invalid. The value of the electron tunneling coefficient was nearly constant over a range of potentials and independent of redox species in solution. The purpose of our investigation is to test the independence of the electronic tunneling coefficient on potential at monolayers with a differing terminal functional group. We chose long-chain n-alkanethiols which form monolayers on gold electrodes. We found that the value of the electronic tunneling coefficient is nearly identical to Miller's value and conclude that the tunneling coefficient is independent of potential and, possibly, independent of the alkanethiol terminal functional group. If the conclusion of a potential-independent electronic tunneling coefficient is general, then this will simplify analysis of heterogeneous electrontransfer kinetics and will change considerably the interpretation of kinetic data presented previously, particularly in the assignment of the reorganization energies for the redox couple. Experimental Section Synthesis. Long-chain n-alkanethiols, SH(CHz)"CH3 ( n = 11, 13, 15, 17), were synthesized from the corresponding longchain alcohols via the nucleophilic displacement reaction with hydrobromic acid and thiourea followed by NaOH as described previously.6 Final products were purified by column chromatography (silica, HCC13) and their purity verified by comparing boiling points with literature values. Preparation of Electrode. The Au electrode (purchased from PARC Inc.) was cleaned with sulfochromic acid (a saturated solution of K2Cr~07in concentrated H2S04) and 5% HF as described in the paper of Miller.2 Then, the gold disk electrode (diameter ca. 3 mm) was dipped into 1:1 H N 0 3solution, polished using 6-pm diamond polish to get rid of the layer of oxide, and rinsed with redistilled water. Preparationof Self-AssembledMonolayer Films by Adsorption of RAlkanethiol from Solutiononto Gold. According to the results of our previous experiment? a closely-packed monolayer formed in acetonitrile solvent. Therefore, adsorption of the alkanethiols was conducted in ca. 20-mL saturated alkanethiol solution of the acetonitrile. The derivatized Au electrodes were immersed immediately into unstirred solutions of thiols for 1 h before displaying limiting voltammetric behavior. After this time, the electrodes were rinsed with acetonitrile and redistilled water and dried with a stream of air. ElectrochemicalMeasurements. Electrochemical experiments were performed in a conventional three-electrode cell using a Bioanalytical Systems BAS- lOOB electrochemical analyzer. The formal potential of the redox couples was determined from linear sweep voltammograms at bare Au electrodes with a large Pt sheet as counter electrode. All potentials were measured and are reported versus (Ag/AgCl, saturated KC1) reference electrode. Test solutions were 0.01 M in either Fe(CN)6+ or FeS+ and ca. 0.5 M in KN03 electrolyte. Prior toallvoltammetric experiments, all solutions were purged with purified nitrogen. Voltammograms were corrected for diffusional limitations with programs written in Fortran 33.
Xu et al.
Results and Discussion The spontaneous self-assembly of alkanethiols onto Au electrodes produced monolayers with exceptional insulating properties. It was shown2 that if electronic tunneling across the monolayer is implicated in the electron transfer, then the redox a t any potential should decrease exponentially with the monolayer thickness according to the expression (4) where io is the current measured a t a bare electrode, 0 is the electronic tunneling coefficient, and d is the thickness of the monolayer film. @wasmeasured by varying the thickness of the insulating layer and measuring the change in the heterogeneous electron-transfer rate of a redox couple in solution at a given potential. To use this simple data treatment, the currents must be determined purely by the kinetics of electron transfer, free from diffusion limitations. The ratio of voltammograms obtained a t electrodes coated with an alkanethiol monolayer of differing lengths gives a true measure of 0 only in the low overpotential. A more accurate method of determining 0 is to correct the voltammograms for diffusion limitations. Convolution techniques were employed to eliminate the diffusion limitations.'O The concentration of the redox species at the electrode surface at any time t during the voltammetric experiment is given by C(0,t) = C* - (nFAC*D1i2)-1~o'i(u)/(t - u ) l i 2du ( 5 )
where C* is the bulkconcentration, D 1 / 2is thediffusioncoefficient of the redox couple, n is the number of electrons transfered, F is Faraday's constant, A is the electrode area, and i(u) is the electrode current at time u. The process to obtain the value of C(0,t)is as follows. First, the i ( u ) function was computed from the changes in the experimentally determined currents with time. Because electrode potential changed with time, we can substitute potential with time. Then, c(0,r)values were computed (eq 5 ) by a convolution integral. The kinetically limited current is obtained by multiplying the measured current by C/C(O,t).This corrects the observed current for any diffusional depletion of the surface concentrations. The value of nFACD112used in the diffusion correction was obtained as the value which gave consistent kinetic currents from voltammetric data obtained at twodifferent scan rates (500 and 200 mV/s). This self-consistent determination of the "limiting current of the convolution" was found to be more accurate than simply calculating the value of nFAC*D112using previously determined constants. The reason is not clear. Figures 1 and 2 are linear sweep voltammograms of 0.01 M Fe(CN)& and 0.01 M Fe3+ in 0.5 M KNO3, respectively, uncorrected for diffusion limitations. Figures 3 and 4 are the voltammograms of Figures 1 and 2 corrected for diffusion using the limit current measured from the convolution techniques. From Figures 1 and 2, it can be seen that with dodecylthiol-coated electrodes mass diffusion is still the limiting rate step. With tetradecylthiol-coated electrodes, electron-transfer rates have apparently decreased. The uncorrected and corrected currents for the tetradecylthiol-, hexadecylthiol-, and wtadecylthiol-coated electrodes were nearly identical. This suggests that at these modified electrodes the electron-transfer step is rate-limiting. According to eq 4, we can obtain the value of 0 simply a t -0.234 V for Fe(CN)& and -0.552 V for Fe3+ by ratioing the current a t bare Auelectrodewith thecurrent a t thelong-chainalkanethiolmodified electrode. This method was used for the diffusion limitation-free electrode reaction. Average 0 values of 0.98 (for hexadecylthiol) and 1.05 (for octadecylthiol) per methylene unit were obtained where the monolayer thickness, d, is 1.25 X 16 and 1.25 X 18 A, respectively. These values were close to the value obtained by the ratio of two different alkanethiol-derived electrode
Electronic Tunneling Coefficient and Electrode Potential
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The Journal of Physical Chemistry, Vol. 97, No. 44, 1993 11499
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Potential (V vs. Ag/AgCI)
Potential (V vs. AgIAgCI) Figure 4. Plot of the corrected current (from Figure 2) versus electrode potential.
Figure 1. Linear sweep voltammograms of 0.01 M Fe(CN)& in 0.5 M KNO, at gold electrodes modified with a series of alkanethiols (HS(CHz).CHs where n = 11, 13, 15, 17): (1) bare electrode, (2) n = 11, (3) n = 13, (4), n = 15, (5) n = 17. Scan rate: 500 mV/s.
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Figure 2. Linear sweep voltammograms of 0.01 M Fe3+ in 0.5 M KNOl at gold electrodesmodified with a series of alkanethiols (SH(CHz).CH3 n 11, 13, 15, 17): (1) bare electrode, (2) n = 11, (3) n = 13, (4) n = 15, (5) n = 17. Scan rate: 500 mV/s.
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Potential (V vs. AglAgCI) Figure 3. Plot of the corrected current (from Figure 1) versus electrode potential. reaction currents (1.02 for hexadecylthiol and octadecylthiol). Thus, the ratio provides a convenient method for evaluating when an electrode reaction is controlled by heterogeneous kinetics. We can substitute the values of (3 and d to calculate current and compare with measured current. When the two current values are close, the electrode reaction will not be affected by diffusion limitation.
Figure 5. Plot of the tunneling coefficient fl (per methylene unit) versus the electrode potential. j3 was calculated from the ratio of the currents (corrected for diffusion) measured at Au electrodescoated with alkanethiol of differing lengths in solutions containing (open circles,dotted line) 0.01 M Fe(CN)& and (filled circles, solid line) 0.01 M Fe3+. For the thinner alkanethiol monolayers, the ratio of the corrected currents shown in Figures 3 and 4 gives a better measure of /3 than the ratio of the uncorrected currents shown in Figures 1 and 2 for two reasons. As Miller has noted, the kinetic currents measured are larger than those directly obtained in the lowoverpotential region of the voltammograms and are therefore less affected by errors in the background current correction. Second, the corrected kinetic currents span a wider range of overpotential, allowing the comparison of electrodes with monolayer films differing in thickness by two to five methylene units. The larger the difference in insulating monolayer thickness between electrodes, the less effect small changes in electrode area and monolayer packing will have on the (3 determination. The value of the electronic tunneling coefficient can be obtained from the current data determined for each of several alkanethiolmodified gold electrodes in which the monolayer thickness is systemmatically varied. Figure 5 is the plot of calculated (3 versus the electrode potential. Linear least-squares fits to the data gave the following relationships: @(u) = 0.00365B+ 1.02 (Fe(CN)&) and @(u)= 0.00574E 1.03 (for Fe3+), where E is the electrode potential. The correlation coefficients for these fits were 0.971 and 0.983, respectively. The slope terms from both of the above two equations are essentially zero. Thus, we conclude that the electronic tunneling barrier is independent of the electrode potential. The intercept terms (our (3 value) from these equations are 1.02 & 0.2. Our value for the electronic tunneling coefficient of n-alkanethiol monolayers is smaller than the value of w-hydroxyalkanethiol
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11500 The Journal of Physical Chemistry, Vol. 97, No. 44, 1993
Xu et al.
monolayers (1.08 f 0.21). Wesuggest that thedifferencereflects additional steric hindrance provided by the alkanethiol terminating functional group. For a rectangular barrier," /3 gives a measure of the barrier height through the equation
functional group at the monolayer-solution interface on the electronic tunneling barrier is not clear. Measurements of the electronic tunneling coefficient a t gold electrodes modified with alkanethiols possessing a wider range of terminating functional groups are currently under way.
0 = 4?r(2m)'f2'V'f2/h where m is the free electron mass, h is Planck's constant, and V is the height of the barrier in electron volts. Substituting the values of the constants in eq 6, one obtains
Acknowledgment. This work was supported by a grant from the National Science Foundation of China. The authors are grateful to Mr. Zhang Jinfor his help withcomputer programming and acknowledge Prof. L. A. Bottomley of Georgia Tech for helpful discussions concerning this work.
= 1.O25'V'l2 (7) where the barrier thickness is in angstroms and the barrier height is in electron volts. Thus, a /3 value of 1.02 corresponds to a barrier height of only 0.6 eV. These data were consistent with the previously determined barrier height value of ca. 0.4-0.7 eV. 1 2 ~ 3 Conclusion Decreasing the rate of heterogeneous electron transfer by derivatizing electrodes with self-assembled monolayers of alkanethiols is a powerful means by which electron-transfer kinetics of a redox species can be tuned. In this paper, we verified Miller's conclusion of a potential-independent electronic tunneling coefficient. A smaller p value was obtained for n-alkanethiolmodified electrodes compared to that obtained at o-hydroxyalkanethiol-modified gold electrodes. The role of the terminal
References and Notes (1) Wasielewski, H. R. Chem. Rev. 1992, 92, 435. (2) Becka, A. M.; Miller, C. J. J . Phys. Chem. 1992, 96, 2657-2668. (3) Delahay, P. In Double Layer and Electrode Kinetics: Advances in Electrochemistry and Engineering, Delahay, P., Tobias, C. W., Eds.; Wiley Interscience: New York, 1965; Chapter 3. (4) Finklea, H. 0.;Hanshew,D. D. J. Am. Chem.Soc. 1992,114,31733181. (5) Miller, C. J.; Gratzel, M. J. Phys. Chem. 1991, 95, 5225-5233. (6) Xu,J.; Li, H.-L., submitted for publication in J . Elecrroanal. Chem. (7) Marcus, R. A. J. Chem. Phys. 1956, 24,966. (8) Miller, C. J.; Cuendet, P.; Gratzel, M. J. Phys. Chem. 1991, 95, 811-886. (9) Bennett, A. J. J. Electroanal. Chem. 1975, 60, 125. (10) Oldham, K. B. Anal. Chem. 1972, 44, 196. (11) Hartman, T. E. J. Appl. Phys. 1964,35, 3283. (12) Morisaki, H.; Ono, H.; Yazawa, K. Proc.-Electrochem. Soc. (Photoelectrochem. Electrosynth, Semicond. Mater.) 1988, 88, 436. (13) Marecek, V.; Samec, Z.; Weber, J. J . Electroanal. Chem. 1978,94, 169.
