hydroxy thiol coated electrodes. 3. Voltage independence of the

J. Phys. Ckem. 1992, 96,2657-2668 Cu(I1) cation. The weak interaction between the cupric cation and ethylene, as indicated by the CU(II)-~Hinteraction distance of 0.37 nm, is evidence of the C2D4 inefficiency to create expedient migration of Cu(I1) cation in SAPO-34. The observation of longer equilibration times with nonpolar adsorbates was also found in CuNaH-ZSM-5 and C ~ H - m o r d e n i t e . ' ~ , ~ ~ The orientation of the ethylene molecule can be determined from the deuterium modulation observed in the ESEM signal. The interaction of Cu(I1) with four equivalent deuterons indicates that C2D4 interacts with the Cu(I1) cation with its molecular plane perpendicular to a line toward the Cu(I1) ion. A similar ethylene orientation is found in Cu(I1)-doped zeolite A.23 In this study we observed the behavior of Cu(I1) cations in H-SAPO-34 when subjected to various treatments to be comparable to the behavior of Cu(I1) ions in zeolites. One similarity between Cu(I1) ions in these materials is the migration of the Cu(I1) cation upon thermal treatment. The appearance of two Cu(I1) species after dehydration indicates the existence of two different site preferences within the molecular sieve. This difference was not observed in dehydrated SAPO-5I0or SAPO-1lZ4 with similar Cu(I1) ion loadings. This site preference suggests that the distribution of silicon atoms varies for each unit cell. A nonhomogeneous distribution of framework atoms has been reported in SAPO-2025and SAPO-47.26 From this study we also observe a change in the ESR parameters of dehydrated samples after the adsorption of various ~~~

~

(22) Sass, C. E.; Kevan, L. J . Phys. Chem. 1989, 93,4669. (23) Ichikawa, T.; Kevan, L. J . Am. Chem. SOC.1981, 103, 5355. (24) Lee, C. W.; Chen, X.; Kevan, L. J. Phys. Chem. 1991, 95, 8626. (25) Hasha, D.; Saldarriaga, L. S. de; Saldarriaga, C.; Hathaway, P. E.; Cox, D. F.; Davis, M. E. J . Am. Chem. SOC.1988, 110, 2127. (26) Pluth, J. J.; Smith, J. V . J . Phys. Chem. 1989, 93, 6516.

2657

molecules. This observation indicates the coordination of the adsorbate to the Cu(I1) cation and hence a migration of one or both of the Cu(I1) species to a position in order to acquire the best coordination. A position near or at site I will allow for the maximum coordination number and is the most accessible location for complexation to occur. We also observed in this work an unusual behavior of the Cu(I1) ion after exposure to methanol. The reason why two species are formed after adsorption of methanol in not clear at this time. Energetically both Cu(I1)-methanol complexes formed should be equally favorable; if not we would expect the migration of the Cu(I1) ion into any one location as was observed with the other adsorbates.

Conclusions In a hydrated sample Cu(I1) is octahedrally coordinated to three zeolitic oxygens and three water molecules. This species most likely resides in site I, which is displaced from the six-membered ring into the ellipsoidal cavity. Dehydration to 400 OC produces two distinct Cu(I1) species. Ammonia adsorption also results in an octahedral complex in which the Cu(I1) is coordinated to three zeolitic oxygens and to three ammonia molecules through the nitrogen. This complex is likely located in site I. Adsorption of methanol results in the formation of two distinct Cu(I1) species. Propanol and ethanol adsorption gives rise to only one Cu(I1) complex. The Cu(I1) complexes with one molecule of ethylene and one molecule of dimethyl sulfoxide. Acknowledgment. This research was supported by the National Science Foundation, the Robert A. Welch Foundation, and the Texas Advanced Research Program.

Electrochemistry at @-Hydroxy Thiol Coated Electrodes. 3. Voltage Independence of the Electron Tunneling Barrier and Measurements of Redox Kinetics at Large Overpotentials Anne M. Becka and Cary J. Miller* Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742 (Received: August 7, 1991)

Self-assembled monolayers of w-hydroxy thiols on Au electrodes are investigated as electron tunneling barriers allowing the measurement of heterogeneous electron kinetics of solution species over a wide range of electrode potentials without mass transport limitations. From the dependence of the electron-transfer rate of a series of redox couples on the thickness of the monolayer film, a more precise tunneling coefficient, 0,of 1.08 0.20 per methylene unit in the w-hydroxy thiol was measured independent of the redox couple and was found to be nearly independent of the electrode potential. The heterogeneous electron-transfer rates for a series of facile redox couples measured at w-hydroxy thiol monolayer coated Au electrodes display a pronounced sigmoidal dependence on the electrode overpotential, which is predicted by the Marcus theory. Reorganization energies and preexponential factors for a series of redox couples are extracted from current/voltage curves. The level of defects within these w-hydroxy thiol monolayers is probed by several electrochemical measurements, which indicate that defects do not significantly perturb the kinetic measurements.

*

Introduction The understanding of redox reactions and the characterization of redox-active molecules are of fundamental importance in chemistry. 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 reductant. 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. The major problem with these heterogeneous electron-transfer reactions is that the redox molecules must be 0022-3654/92/2096-2657$03.00/0

brought to the electrode surface prior to their oxidation or reduction. The rate at which redox species can be transported to the electrode surface sets a limit on the size of heterogeneous electron-transfer rate constants which can be measured. In addition to the problem of 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, structure, and reactivity ( 1 ) Delahay, P. In Double Layer and Electrode Kinetics: Advances in Electrochemistry and Electrochemical Engineering; Delahay, P., Tobias, C. W., Eds.; Wiley Interscience: New York, 1965; Chapter 3.

0 1992 American Chemical Society

2658 The Journal of Physical Chemistry, Vol. 96, No. 6, 1992 of the redox center may be different at the electrode surface than in the bulk solution. Much work has k n directed toward the goal of measuring faster heterogeneous electron-transfer rates.2 The major thrust has been in increasing the rate at which species in solution diffuse to the electrode surface. This is accomplished typically by performing linear sweep voltammetricor potential step experiments at short time scales (millisecond and microsecond time domain^)^ and/or using extremely small electrodes in which the mass-transfer rate is greatly increased by hemispherical diffusi0n.4.~ A more powerful method of eliminating these mass-transfer limitations is to slow the electron-transferrate itself: By coating an electrode with a thin insulating film, one can limit the closest approach of redox species to the electrode surface. Electron transfer in this case proceeds via electron tunneling through the insulator, which decreases the absolute electron-transfer rate to a level at which diffusion limitations are either greatly diminished or eliminated completely. Because the electron transfer takes place with the redox couple 10-30 A from the metal surface, complications due to specific adsorption, double-layer corrections, and image charge effects are decreased over measurements at bare electrodes. Self-assembled monolayers of terminally derivatized thiols on Au electrodes have been shown to be useful tunneling harriers for kinetic measurements. Chidsey has recently reported on the electron-transfer kinetics of a ferrocene derivative covalently linked to a self-asembledthiol monolayer.' In a similar system, Bundig Lee has studied the electron-transfer characteristicsof electroactive viologen centers oovalently bound within self-assembled thiol monolayers.* In the previous papers of this series, w-hydroxyalkanethiol monolayers have been used as tunneling barriers for solution redox species? For electrodes derivatized by a selfassembled monolayer of 16-hydroxy-1-hexadecanethiol,the rate of electron transfer to a series of facile redox couples could be measured over a wide range of overpotentials extending beyond 1 V without mass-transfer limitations.I0 The overpotential dependence of the electron-transfer rates of these redox couples deviated strongly from simple Butler-Volmer kinetics in agreement with Marcus theory predictions." In order to make useful kinetic measurements at insulated electrodes, it is essential to understand the barrier characteristics of the insulating film. For adsorbed thiol monolayers, the insulating properties can be measured by comparing electron-transfer rates to solution redox couples at Au electrodes derivatized with thiol monolayers of different thicknesses. The monolayer thickness can be varied by controlling the number of methylene units in the thiol amphiphile used to form the monolayer. For w-hydroxy thiol monolayer coated Au electrodes, the heterogeneous electrontransfer rate of a redox probe decreased by a factor of ca. 2.5 for each methylene unit. Assuming a 1.25-A increase in the monolayer thickmss with each methylene group, the equivalent height of the tunneling barrier was calculated to be 0.5 eV? A major uncertainty in this previous work with the w-hydroxy thiol coated electrodes was in the potential dependence of this electron tunneling barrier. The electron tunneling barrier was assumed to vary linearly with the formal overpotential of the electrode.I0 This (2) Bindra, P.; Brown, A. P.; Reischmann, M.; Pletcher, D. J . Electroanal. Chem. 1975,58, 3 1. (3) Macdonald, D. D. Transient Techniques in Electrochemistry; Plenum: New York, 1977. (4) (a) Howell, J. 0.; Wightmann, R. M. Anal. Chem. 1984,56,524. (b) Wipf, D. 0.;Kristenscn, E. W.; Dtalrin, M. R.; Wightmann, R. M. Anal. Chem. 1988,60,306. (c) Fitch, A,; Evans, D. H. J . Elecrroanal. Chem. 1986, 202, 83. (5) Penna, R. M.; Heben, M. J.; Longin, T. L.; Lewis, N. S. Science 1990, 250, 1118. (6) (a) Bennett, A. J. J . Elecrrounal. Chem. 1975,60, 125. (b) Mmming, R.; Mdlers, R. Eer. Eunsenges. Phys. Chem. 1973, 77, 945. (c) Kobayashi, K.; Aikawa, Y.; Sukigara, M.J. ElectrounaI. Chem. 1982,134. (d) Morisaki, H.; Ono, H.; Yazawa, K. J. Electrochem. Soc. 1989, 136, 1710. (7) Chidsey, C. E. D. Science 1991, 251, 919. (8) Bunding Lee, K. A. Langmuir 1990, 6, 709. (9) Miller, C.; Cucndet, P.; Gritzel, M. J . Phys. Chem. 1991, 95, 877. (10) Miller, C.; GrHtzcl, M. J. Phys. Chem. 1991, 95, 5225. (1 1) Marcus, R. A. J . Chem. Phys. 1965, 43, 679.

Becka and Miller assumption allows one to calculate the density of electronic states for the redox molecules using a mathematical formalism dcvtiopad by Bamett.& In this paper we inwtigate this potential dependence of the electron tunneling rate more closely. Experimental measurements of the dependence of the electron tunneling barrier on electrode potential presented here indicate that our original assumption of a potentialdependent barrier was in error. The near independence of the tunneling barrier with the applied electrode potential simplifies the lrinetic analysis and changes considerably the interpretation of the kinetic data presented previously, particularly in the assignment of the reorganization energies for the redox couples. In addition, we continue the development of the uses of these w-hydroxy thiol monolayer films for kinetic measurements. The effect of defects within these monolayer films on the kinetic measurements is considered and several new electrochemical probes of the monolayer defect structure are described.

Experimental Section The whydroxyalkanethiols, HO(CH,),,SH, n = 6-12, 14, 16, 18,20,22, were synthesized from the hydroxyalkyl bromides by treatment with thiourea followed by NaOH as described previously? Final purification was by column chromatography using silica with a 12:88 (w/w) mixture af ethyl acetate and chloroform. For n = 6-16, the hydroxy bromide was syntheaiztd from either the dibromide or dihydroxy starting compounds, which were purchased from Aldrich. The dibromoalkanes were converted to the hydroxyalkyl bromides upon heating in 15%H20in hexamethy1phasph"nie (HMPA).I2 At 100 OC the optimal reaction time was found to be 2 h. Conversion of the diols to the hydroxy bromides was achieved in a two-phase reaction of the diol with HBr. A 2-g aliquot of the dihydroxyalkane was dissolved in 100 mL of n-octane and heated to 70 OC. A 25-mL aliquot of 48% HBr(aq) was added to the n-octane and the two-phased mixture was stirred rapidly and held at reflux for 30 min. The mixture was allowed to cool and the n-octane fraction was separated. Removal of the n-octane under reduced p u r e afforded the crude hydroxy bromide, which was purified by column chromatography (silica, HCC13). The longer dibromides (n = 18, 20, 22) were synthesized from 10bromodecanoic acid, 11-bromoundecanoicacid, and 12-bromododecanoic acid, respectively, by a Kolbe electrolysis in dry methan01.I~ The 11-bromoundecanoicacid and 12-dodecanoic acid were purchased from Aldrich. The 10-bromodecanoicacid was synthesized from 10-bromo-ldccanoI via a Jones oxidation.I4 Au electrodes were pre red by depositing a 500-A Cr adhesion layer followed by a 5000- layer of Au (each 99.99% purity) onto 2.54 cm by 7.62 cm glass microscope slides by rf sputtering in Ar. A special mask was used to pattern the deposited metal into two circular disks 0.41 cm in diameter connected via a 1.5 cm by 0.06 cm line. One of the disks defiicd the active electrode area while the other served as a contact pad. Each microscope slide contained nine of these electrodes, which were cut into individual electrodesprior to their use. The Au electrodeswere cleaned with exposures to 60 OC sulfochromic acid (a saturated solution of K2Cr207in concentrated H2S04) and 5% H F as described prev i o ~ s l y .Adsorption ~ of the w-hydroxy thiols was conducted in 20-50 m M solutions of the w-hydroxy thiols in 95% ethanol; ca. 3 mg of the w-hydroxy thiol was placed into a small vial with 0.6 mL of 95% ethanol. Due to the water adhering to the electrodes after the final H 2 0 rinse, the finalcomposition of the w-hydroxy thiol solution ranged from 70% to 90% ethanol. As the length of the o-hydroxy thiol increased,its solubility in the ethanol/H20 mixture decreased so that the solutions containing whydroxy thiol longer than 16 methylene units were saturated. The derivatized Au electrodes displayed limiting voltammetric behavior after ea. 30 min in the w-hydroxy thiol solutions. After this time, the

x

~~

(12) Hutchins, R. 0.; Taffer, 1. M. J. Org. Chem. 1983, 48, 1360. (13) Pattison, F. L. M.; Stothers, J. B.; Woolford, R. G. J. Am. Chem. Soc. 1956, 78, 2255. (14) Carey, F. A.; Sundberg, R. J. Advanced Organic Chemistry Part B; Plenum: New York, 1990; p 617.

Electrochemistry at w-Hydroxy Thiol Coated Electrodes

The Journal of Physical Chemistry, Vol. 96, No. 6, 1992 2659

~10.4 electrodes were rinsed with ethanol and H 2 0 and dried with a A 7, I stream of air. The composition of the w-hydroxy thiol solutions I 1 used to derivatize the Au electrodes described here is different from the purely aqueous solutions used previo~sly.~ Both procedures produce monolayer-derivatized electrodes with identical 6 i electrical characteristics. A well-assembled monolayer of the w-hydroxy thiol was found to be completely wetted by water. The extreme hydrophilicity of the monolayer-coated electrode could be judged by watching for interference bands moving across the surface of the electrode upon drying with a stream of air. The observation of these interference fringes requires the contact angle with water to be vanishingly small. Monolayers of the longer w-hydroxy thiols (octadecyl to docosyl) were somewhat less hydrophilic, the water pulling off the electrode in thin beads. These qualitative measurements of the H 2 0 contact angles were made within moments of the withdrawal of the electrode from the thiol solution. After storage of the electrodes for several hours in the laboratory enFormal Overpotential / V vironment, these w-hydroxy thiol derivatized Au surfaces become somewhat more hydrophobic.ls After a voltammetric experiment, the derivatized electrodes were generally stored in the w-hydroxy thiol solution. Alternately, these electrodes could be stored dry in a closed vial for several weeks with little change in their electron-transfer characteristics. K&fo(cN), was synthesized using the method of Van De Poel and Neumann.16 K,W(CN), was a generous gift of Prof. Ezio Pelizzetti, (University of Parma, Italy). K2Fe(2,2'-bipyridine)(CN), was a generous gift of Frangois Rotzinger, (Ecole Polytechnique Faderale Lausanne, Switzerland). R u ( N H ~ ) ~ C ~ ~ was purchased from Strem (Newburyport, MA) and used as received. All other chemicals were reagent grade and used as received. Deionized H 2 0 (MilliQ system from Millipore) was used for all solutions and for rinsing the electrode. Electrochemical experiments were performed in a conventional three-electrode cell using a BAS lOOA electrochemical analyzer. Electrolyte solutions were purged with purified nitrogen and kept under a blanket of nitrogen for all voltammetric measurements. Bulk electrolysis of solutions of W(CN)84- and Mo(CN),,- and Formal Overpotential I V the Fe(b~y)(cN),~were carried out using a large Pt mesh with Figure 1. Voltammograms of 10 mM Fe(CN)63-,0.5 M KCI obtained a Pt counter electrode in a separate solution isolated by a fritted at a bare Au electrode and a series of electrodes derivatized with selfglass disk. Measurements of the formal potentials of the redox assembled monolayers of HO(CH2),,SH(n = 6-1 1 as indicated in the couples were made prior to kinetic measurements via the meafigure). (A) shows the reduction waves plotted versus the formal oversurement of cyclic voltammograms obtained at bare Au electrodes. potential (Eclwtrdc - EO'). (B) shows the reduction waves corrected for the effects of diffusion. (See text.) The scan rate was 0.5 V/s. The average of the half-wave potentials for the oxidation and reduction waves was taken as the formal potential, E O ' , for each from the ratio of the currents obtained using electrodes coated of the couples. All potentials were measured and are reported with monolayers differing in length by 1 or 2 methylene groups. versus a (Ag/AgCl, saturated KC1) reference electrode. In order to use this simple data treatment, the currents must be Results and Discussion purely determined by the kinetics of electron transfer, free from diffusion limitations. The ratio of voltammograms obtained at Tunneling Barrier Determination. The use of insulated elecelectrodes coated with w-hydroxy thiol monolayers of differing trodes in the measurement of redox kinetics requires the characterization of the insulating properties of the tunneling barrier. lengths gives a true measure of @ only in the low overpotential Previous investigations have shown that w-hydroxy thiol monoregion where the reduction currents are less than ca. 5% of the layers could be modeled as simple square well tunneling barriers peak currents. Thus, the voltage ranges over which j3 can be causing an exponential decrease in the electron-transfer rate with measured are extremely narrow. A more accurate method of increasing thickness of the monolayer film.g The current at a determining 0 is to correct the voltammograms for diffusion monolayer-covered electrode, i, is given by limitations. The effect of diffusion on the voltammetric peaks can be i = ioe-Bd (1) corrected through convolution technique^.'^-'^ The concentration of the oxidized redox species a t the electrode surface a t a time, where io is the current measured a t a bare electrode, @ is the t , during the voltammetric experiment, Co(O,t),is given by tunneling barrier coefficient, and d is the thickness of the monolayer film. The tunneling coefficient,B, was measured by varying the thickness of the insulating layer and measuring the change in the heterogeneous electron-transfer rate of a redox couple in solution a t a given potential. For these w-hydroxy thiol monowhere Co* and Do are the bulk concentration and diffusion layers, each methylene unit was found to decrease the electroncoefficient of the oxidized form of the redox couple, n is the transfer rate by a factor of 2.5 f 0.7, which is equivalent to a @ number of electrons transferred in the electron transfer, F is value of 0.9 f 0.3 per methylene unit. This fl value was calculated

1

(15) Evans, S. D.; Sharma, R.; Ulman, A. Lungmuir 1991, 7, 156. (16) Van De Pod, J.; Neumann, H. M. In Inorganic Syntheses; Jolly, L.,Ed.;McGraw-Hill: New York, 1968; Vol. 11.

W.

(17) Oldham, K. B. Anal. Chem. 1972,44, 196. (18) Imbeaux, J. C.;SavCnt, J. M. J . EleCtrOaM/. Chem. 1973,44, 1969. (19) Lawson, R. J.; Maloy, J. T. Anal. Chem. 1974,46, 559.

2660 The Journal of Physical Chemistry, Vol. 96, No. 6, 1992

I

Becka and Miller

A

/

xi04

351 11

I

A

31

0.2

I

J

1

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

Electrode potential / V

-1.2

-1

-0.8

Figure 2. Plot of the tunneling coefficient, ,9 (per methylene group), versus the electrode potential. ,9 was calculated from the ratio of the currents (corrected for diffusion) measured at Au electrodes coated with w-hydroxy thiol of differing lengths in solutions containing different electroactive probes as indicated in the figure.

Faraday's constant, A is the electrode area, and i(u) is the electrode current at time u. The kinetically limited current is obtained by multiplying the measured current by Co*/Co(O,t).This corrects the observed current for any diffusional depletion of the surface concentration. This diffusion correction scheme was used for voltammetric data collected at a series of Au electrodes coated with w-hydroxy thiols of differing length. Figure 1A shows the reduction current for a 10 mM solution of Fe(CN)63-in 0.5 M KCl, uncorrected for diffusion, measured at a series of monolayer-coated electrodes. Figure 1B shows the voltammograms corrected for diffusion using the limiting current measured from the convolution of voltammetric data obtained at the bare electrode.*O We have limited the data shown in Figure 1B to potentials at which the corrected current is no more than a factor of 4 times larger than the uncorrected current. The ratio of the corrected currents shown in Figure 1B gives a better measure of the 0 coefficient than the ratio of the uncorrected currents shown in F i e 1A for two reasons. The kinetic currents measured are larger than those obtained directly in the low overpotential region of the voltammograms and are therefore less affected by errors in the background current correction. More importantly, the corrected kinetic currents span a wider range of overpotentials, allowing the comparison of electrodes with monolayer films differing in thickness by 2-5 methylene units. The larger the thickness change between electrodes, the less effect small changes in electrode area and monolayer packing will have on the @ determination. From the data shown in Figure 1 and similar data obtained using three other outer-sphere redox couples, W(CN)&, MO(CN)~~-, and Fe(bpy)(CN)41-,a 0 value of 1.08 f 0.21 per methylene unit was determined. The possible potential dependence of the tunneling barrier is an important concern in the characterization of these hydroxy thiol monolayers and a critical concern if one wishes to probe redox kinetics of solution species with these blocked electrodes. Previously, we had assumed that the barrier to electron transfer at these monolayer-coated electrodes would be modulated by changes in electric field in the hydrocarbon region of the monolayer as the electrode potential is varied.I0 The barrier height under this assumption is expected to decrease by half of the potential drop in the insulator. Because a 6 value of 1.08 corresponds to a barrier height of only 0.6 eV,21 the tunneling barrier would be expected ( 2 0 ) The value of nFAc$0112 used in the diffusion correction was obtained as the value which gave consistent kinetic currents from voltammetric data obtained at two different scan rates. This self-consistent determination of the "limiting current of the convolution" was found to be more accurate than simply calculating the value of nFA6$,t/2 using previously determined constants.

-0.6

-0.4

-0.2

0

0.2

-0 2

0

02

Formal Overpotential / V

'

0 2 11

01 18 -1 2

\\

14 1 16 -1

-0.8

-0 6

-04


Figure 3. Voltammograms of 10 mM Fe(CN)6)-, 0.5 M KC1 obtained at a series of Au electrodes derivatized with self-assembled monolayers of HO(CH2)$H (n = 11, 12, 14, 16, and 18 as indicated in the figure). (A) shows the reduction waves plotted versus the formal overpotential (EeIF - EO'). (B) shows the reduction waves corrected for the effects of diffusion. (See text.) The scan rate was 0.5 V/s.

to decrease dramatically as the potential of the electrode is polarized negative from the point of zero charge. Using the convolution correction for diffusion, one can measure 0 over a wide range of electrode potentials and look for any variation in the tunneling characteristics of the hydroxy thiol monolayers. Figure 2 shows a plot of the 0 value versus the electrode potential measured using four different redox couples. Pairs of electrodes derivatized with monolayers of the longer w-hydroxy thiols [HO(CH,)SH, where n = 12 and 14 or 14 and 161 were used as they allowed the widest range of potentials to be studied. At low overpotentials, the measured 0 values typically curved to lower values due to the difficulties in making accurate background corrections. Over the bulk of the potentials in Figure 2, the 0 value remains nearly constant with a slight decrease with increasing overpotentials. This small dependence of the tunneling barrier height on the electrode potential is contrasted to the solid curve shown in the figure, which shows the anticipated dependence of the tunneling coefficient if the barrier decreases by half the applied potential. Mea"& of H e h q e m a w Kinetics. The characterization of the insulating properties of these w-hydroxy thiol monolayers opens up the possibility of making quantitative kinetic measurements of redox reactivity at potentials unattainable at any bare ( 2 1 ) The relationship between the tunneling coefficient, 6, and the equivalent barrier height, V, is given by 6 = 4 ~ ( 2 m ) ' / * V ' / ~or/ hB = 1.025 VI2, where m is the free electron mass and h is Planck's constant: Hartman, T. E. J. Appl. Phys. 1964, 35, 3283.


Electrochemistry at w-Hydroxy Thiol Coated Electrodes x10

'

i


Figure 4. A single reduction wave, corrected for diffusion, for a 10 mM Mo(CN)?-, 0.5 M KCI solution measured at an Au electrode derivatized with a 14-hydroxy-I-tetradecanethiol monolayer. The scan rate was 5.12 VIS.

electrode. Varying the thickness of the monolayer from the hexyl to the octadecyl hydroxy thiol allows one to slow the rate of electron transfer by 3-9 orders of magnitude. The voltammetry of simple outer-sphere redox couples measured at a wide range of overpotentials deviates markedly from simple Butler-Volmer kinetics and conforms closely to the expectations of the Marcus theory. This change in kinetic behavior can be seen in Figure 3, which is a continuation of Figure 1 in which the length of the insulating monolayer is increased from 11 to 18 methylene units. The peak of the voltammetric wave broadens and the peak current drops dramatically as the monolayer thickness is increased beyond 12 methylene units. For the longest w-hydroxy thiol monolayers (n = 16-18), the rate of electron transfer is slowed to such an extent that the concentration of ferricyanide at the electrode surface does not vary appreciably from the bulk concentration. For these electrodes, the current is not measurably perturbed by diffusion limitations over the entire voltage range studied and requires no diffusion correction. The transition in the voltammetric behavior noted above stems from a change in the dependence of the electron-transfer rate on the electrode overpotential measured at high overpotentials.22 As the electrode potential is scanned negatively from the formal potential of the redox couple, the electron-transfer rate changes from being exponentially dependent on the electrode overpotential to become linearly dependent and then independent of overpotential. The transition between exponential to a roughly linear dependence can be seen in the corrected currents shown in Figure 3B. Unfortunately, we are limited in how negative we can polarize these w-hydroxy thiol monolayer coated electrodes to roughly 4 . 8 V versus (Ag/AgCl, saturated KCl). At potentials beyond -0.8 V, the background currents rise, distorting the kinetic measurements. Further polarizations beyond roughly -1.0 V cause a rapid rise in the electrode current and result in the destruction of the monolayer, presumably by hydrogen bubble formation. While the w-hydroxy thiol coated electrodes are limited to potentials more positive than -0.8 V (versus Ag/AgCl, saturated KCl), one can make measurements of redox kinetics at higher overpotentials by choosing a redox couple with a more positive formal potential. Figure 4 shows a voltammogram, corrected for diffusion, for a 10 mM solution of Mo(CN)*~-obtained at an electrode coated with a monolayer of 14-hydroxy-1-tetradecanethiol. For the reduction of this redox couple, kinetic measurements can be made over a 1.5-V range. Thevoltammogram for Mo(CNh3. . " has a clear sigmoidal shape. The shape of this voltammogram will be shown below to be in close agieement with that expected from Marcus theory' We Observe qualitatively the Same (22) Tyma, P. D.;Weaver, M. J. J . Electroanol. Chem. 1980, 111, 195.

sigmoidal kinetic current for every facile redox couple we have studied. In addition to the Marcus theory, there is a simpler explanation for the sigmoidal-shaped voltammogram which must be discounted. A sigmoidal voltammogram would be expected if the current observed at these monolayer-coated electrodes was due to an array of widely spaced defect sites.23 The height of the voltammetric wave would depend on the diffusion rate of the Mo(CN)*~-to the defect sites. In this case, the position and shape of the sigmoidal voltammogram would be related to the size, number, and heterogeneous electron-transfer rate constant of the defect sites in addition to any fundamental potential dependence of the electron-transfer rate of the redox couple. The presence of these types of defects would seriously complicate the use of these monolayer-coated electrodes for kinetic measurements. It is extremely unlikely that the sigmoidal voltammograms seen for these blocked electrodes are due to defect sites within the monolayers. The position of the sigmoidal waves and their height vary by less than 20% between different electrodes modified by the same w-hydroxy thiol monolayer. Such a consistency would mandate an incredible reproduction of the defect sites' densities between electrode preparations. More concrete evidence for the absence of these defects can be obtained by measuring the kinetics of electron transfer at a single monolayer treated electrode in two solutions of widely varying viscosity. From the Stokes-Einstein equation, D = kT/6nRh? the diffusion coefficient varies inversely with the solution viscosity, q. Diffusion-limited currents should therefore be strongly dependent on the solution viscosity. Previously, the solution viscosity was changed by varying the temperature of the electrolyte solution? The femcyanide reduction current measured at an 11-hydroxy-1-undecanethiol-derivatized electrode was shown to be independent of temperature as expected for electron tunneling but at odds with electron transfers at defect sites. Another way to alter the diffusion coefficient in aqueous solutions is through the addition of glycerol. Figure 5 shows two sets of voltammetric curves obtained at a bare and a 16hydroxy- 1-hexadecanethiol-derivatizedAu electrode in a 8.0 mM femcyanide, 0.5 M KCl solution made in H20or in a 5050 (w/w) solution of glycerol/H,O. The addition of the glycerol increases the solution viscosity by a factor of 6.2, thereby decreasing the diffusion coefficient of the ferricyanide by the same factor.24 The diffusion-limited current under semi-infinite linear diffusion conditions depends on D1i2,so that one expects the voltammetric current to decrease by 6.21/2or 2.49 times between the two experiments. The ratio of the currents for the bare electrode in H 2 0 versus glycerol/H,O is shown in the inset graph in Figure 5A. The average ratio taken from this graph is 2.46, which is in good agreement with the expected value. The diffusion-limited current to an array of widely spaced microdisk electrodes depends linearly on the diffusion coefficient of the redox-active species so that, for the w-hydroxy thiol derivatized electrode, one would anticipate a 6-fold decrease in the measured current in the glycerol/H20 solution if the current was diffusion limited.4a The current for the voltammogram obtained in H 2 0 is only slightly larger than the one obtained in the glycerol/H,O mixture. The average ratio between the currents is only 1.3. This is far less than the 6-times reduction anticipated if the current was diffusion controlled. The sigmoidal shape of the voltammogram for Mo(CN),3- shown in Figure 4 is therefore not a result of a diffusion limitation. Some of the 1.3-times reduction of the current measured in the presence of glycerol can be traced to defects within the monolayer, but experiments which are described later indicate that a majority of the decrease stems from other effects. Most of the decrease in the measured current is likely a kinetic effect related to a decrease in the solvent relaxation timez5or a change in the solvent (23) Amatore, C.; Savknt, J. M.; Tessier, D. J . Electroanal. Chem. 1983, ! 4 7 , 39. (24) Wolf, A. V.; Brown, M. G.; Prentiss, P. G. Concentrative Properties

of Aqueous Solutions in Handbook of Chemistry and Physics, 55th ed.;Weast, R. C:, Ed.; CRC Press: Cleveland, OH, 1974; p D 206. (25) Nielson, R. M.; McManis, G. E.; Golovin, M. N.; Weaver, M. J. J . Phys. Chem. 1988, 92, 3441.

Becka and Miller


factor, T, is approximated as a constant with respect to E, then the current expression can be greatly simplified to i(Ef) = nFvTNo,

5

box

dE

(4)

So that the derivative of the kinetically limited current with respect to the applied potential is di/dEf = nFvTNo,Do,

.-,..

0

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

Formal Overpotential I V

1

z

0.5

0

..\

1 -1

-0.6

-0.8

-0.4

-0.2

A measure of the density of electronic states is obtained simply as the derivative of the kinetic current with potential. The parameters Y, T, and No, are nearly constant with the electrode potential and therefore serve as only a scaling factor to the electronic density of states. Figure 7 shows a plot of the derivative of the current/voltage data shown in Figure 4. The kinetic data were normalized to unit concentration of the redox molecule ( 1 /nF mol/cm3) and unit electrode area (1 cmz) to convert the currents to heterogeneous electron-transfer rates (in cm/s) prior to taking the derivative. The sigmoidal shape of the current/voltage curve for the Mo(CN)83-complex translates to a peaked density of state distribution. Because the density of electronic state distribution is directly proportional to the rate at which electrons at the Fermi level react with the redox couple, this peaked distribution indicates that there is an optimum driving force for the reduction occurring at ca. 1 eV. Once the Fermi level of the electrode is polarized negative of the peak of the distribution, the reduction rate for the electrons at the Fermi level decreases, as would be predictedfrom the Marcus theory for a reaction in the inverted region. Because the electrode potential can be probed continuously, a detailed picture of the driving force dependenceof the redox reaction can be obtained from a single voltamman’c experiment and conpared to theoretical predictions. The solid curve shown in Figure 7 is the best fit Gaussian of the form di/dEf = e[&+bEt+cl

0

Formal OverpotentialI V

Figure 5. Voltammograms of 8.0 mM Fe(CN)63-, 0.5 M KCl in H20 (solid curves) and 50% glycerol/Hip (dashed curves) obtained at a bare Au electrode (A) and at an Au electrode derivatized with a 16hydroxy- 1-hexadecanethiol monolayer (B). The inset graphs plot the ratio of the currents at each electrode in the two solutions as a function

of the complex). Adyski of VolCImmetric Data. The reduction current of an electroactive species in solution at an insulated electrode can be approximated by the overlap between the density of filled electronic states in the metal and the unfilled states in the solution weighted by the probability of electron tunneling through the insulator:26

where v is a frequency factor, No, is the number of redox centers participating in the electron transfer, El is the energy at the Fermi level, Tis the probability for electron tunneling given by e*, Dox is the normalized density of states for the redox couple, kT is Boltzmann’s constant multiplied by the absolute temperature, and E is the electron energy integration variable. A schematic r e p resentation of q 3 can be obtained by considering the electronic states available in the metal and the solution. Figure 6 shows a set of three density of electronic state diagrams of an insulated electrode in contact with an electrolyte solution containing the oxidized form of a redox couple at three electrode potentials. If the Fermi distribution function (given by the denominator in eq 3) is approximated by a step function at E = Et7and the tunneling (26) Schultze, J. W.; Vetter,

K.J. Electrochim. Actu 1973, 18, 889.

(6)

where a, b, and c are the best fit coefficients and Et is the Fermi level of the electrode measured relative to the formal potential of the redox couple. The derivative of the kinetic current with mpect to the electrode potential is well fit by this Gaussian, which can be compared to the Marcus theory prediction:28

Do, = No,(4aXkT)-l/Ze-I(”-E1?/4~k~

of the formal overpotential. The scan rate was 0.5 V/s.

structure (affecting the distance of closest approach of the complex with the electrode and possibly changing the reorganization energy

(5)

(7)

where X is the reorganization energy of the couple. The best fit coefficients a, b, and c determined from the fit shown in Figure 7 should be given by

c

a = -(1/4XkT)

(8)

b = 1/2kT

(9)

= In ( n F ~ T N , , ( 4 a X k r ) - ~-/ ~X/4kT )

(IO)

The reorganizationenergy of the redox couple is given by the peak of the distribution shown in Figure 7, which occurs at a potential -b/2a. The peak of the distribution shown in Figure 7 occurs 0.90 eV from the formal potential of the redox couple. The width of the Gaussian, determined by the a parameter, also gives a measure of the reorganization energy, which gives a reorganization value of 1.2 eV. These two measurements of the reorganization energy are in reasanable agreement with each other. Previously, a much larger discrepancy between the reorganization energies of a series of facile redox couples calculated from the peaks and widths of density of electronic state distributions was ~bserved.’~ Much of this discrepancy can now be assigned to an improper assignment of the potential dependence of the tunneling coefficient. In that work, the tunneling barrier (measured in electronvolts) was assumed to decrease by half the overpotential applied to the electrode. The effect of this error is to drastically (27) Schmickler, W. J . Electroanul. Chem. 1986, 204, 31. (28) Gerischer, H. 2. Phys. Chem. NF 1960, 26, 325.



P

E*

Overlap

Figure 6. A series of density of electronic states diagrams for a metal electrode coated with a tunneling barrier in contact with an electrolyte solution containing a reducible electroactive specie. The electrode potential (equivalent to the position of the Fermi level, Ef)in these diagrams is positioned positive of (A), approximately equal to (B), and negative of (C) the reorganization energy of the electroactive species. The overlap between the filled electronic states in the metal and the unfilled Do, distribution in the electrolyte (which is proportional to the rate of electron transfer) is also shown in these diagrams.

0.014 0.012 '

3

. 1 1 0.01

o.w!

0.002

0 -1.8

-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0


Figure 7. Density of electronic states diagram for Mo(CN)*~-calculated as the derivative of the heterogeneous electron-transfer rate constant measured at a 14-hydroxy-1-tetradecanethiol-derivatizedAu electrode in 0.5 M KC1 with respect to the formal overpotential. (See text.) The open points are the experimental values. The solid curve is the best fit Gaussian distribution to the experimental data limited to potentials positive of the peak of the distribution. The dashed curve is the Gaussian distribution predicted by the Marcus theory calculated from eq 7,using the reorganization energy measured from the peak of the solid curve. The dashed curve was normalized to have the same area as the solid curve.

shift the density of electronic states for the redox couples to lower overpotentials, resulting in anomalously low reorganization energies. The widths of the density of states were less strongly effected by the error, giving rise to the large discrepancy between the reorganization energy calculated from the width and the peak of the density of electronic states. Broadening in the Do, Distributions. When the tunneling coefficient is assumed to be potential independent, a small yet significant discrepancy between the reorganization parameter measured from the peak and the width of the distribution remains. This discrepancy can be seen in Figure 7 by comparing the solid and dashed distributions. The dashed curve corresponds to the Do, distribution predicted by the Marcus theory given the reorganization energy taken from the peak of the distribution. The width of the measured density of electronic states for the Mo(CN)83-complex is larger than that predicted by the Marcus theory. While this small broadening of the density of electronic states distribution could be linked to a deficiency in the Marcus theory, there are a large number of experimental factors which

could also explain the additional broadening of the Do, distribution. As mentioned previously, some broadening of the density of states distribution would be expected from ion pairing of the Mo(CN);with K+.l0 In this case, the density of electronic states would be the sum of the two major species in solution, the unassociated complex, Mo(CN),~-, and the ion-paired complex, KMo(CN)t-. The broadening stems from a difference in the redox potentials of these two species. Several assumptions made in order to extract the density of electronic states distribution from the current/voltage curves may also cause broadening. The filled electronic states distribution in the metal is not a perfect step function at room temperature as was assumed but is somewhat rounded by the Fermi distribution function. This rounding will cause the Do, distribution to appear broader by approximately kT or 0.03 eV. The density of electronic states in the metal was also assumed to be constant at a value characteristic of the Fermi level. As the electrode potential is increased beyond the reorganization energy of the redox couple, a significant fraction of the reduction current is a result of electron transfer from electronicstates below the Fermi level. Any change in the density of electronic states in the Au from the Fermi level value will cause a distortion in the Do, distribution. The Fermi level in Au lies above the d states of the metal in a particularly constant portion of the density of electronic states distribution. calculation^^^ and measurements30indicate that there is a small increase in the density of states below the Fermi level which could add some small broadening to the Do, distributions. The presence of a sloping density of electronic states in the metal would also result in the sigmoidal voltammograms not achieving a constant current at high overpotentials. The current of the high overpotential plateau would increase in this case due to the increasing overlap between the Do, distribution and the sloping density of electronic states in the metal. We typically observe this sort of increased current in the plateau region of the current/voltage curves. A potentially larger source of broadening of the Doxdistribution could come from the contribution of inelastic tunneling through the monolayer film.31 Electrons tunneling through the w-hydroxy thiol monolayer may excite vibrational transitions in the hydrocarbon monolayer. The current from inelastic tunneling will have the same characteristic sigmoidal shape predicted by the Marcus ~~

~~

(29) Papaconstantopoulos, D. A. Handbook of The Band Structure of Elemental Solids; Plenum: New York, 1986; p 202. (30) Fadley, C. S.;Shirley, D. A. In Electronic Density of States; Bennett, L. H., Ed.; NBS Spec. Publ. (U.S.)1971, 323.

(31) Hansma, P. K. In Tunneling Spectroscopy; Hansma, P. K., Ed.; Plenum: New York, 1982.


theory but shifted to higher overpotential values by the energy last to the monolayer. The large& feature in an inelastic tunneling spectrum of a hydrocarbon is the carbon-hydrogen stretches, which occur at ca. 3000 cm-’ or 0.37 eV.32 Because the width of the sigmoidal current function is larger than the expected separation between the elastic and inelastic sigmoids, the presence of an inelastic tunneling contribution to the measured current would be manifested in a broadening of the Do, distribution by some amount approaching 0.37 eV if the inelastic current is equal to the elastic current. In metal/metal oxide/adsorbed monolayer/metal capacitor junctions used in inelastic tunneling spectroscopy, the inelastic tunneling is obscrved to be much less efficient than elastic tunneling, accounting for only ca. 1% of the measured current in the tunneling junction.33 If the contribution of inelastic tunneling processes is only about 1% of the elastic tunneling, the Do, distribution would not be expected to be broadened significantly. A final distortion in the Do, distribution shown in Figure 7 arises from the possible slight potential dependence of the tunneling coefficient suggested by the data shown in Figure 2. Any decrease in the tunneling coefficient, 8, with the electrode potential would result in a broadening of the density of electronic states. Such a potentialdepndent 8 would also cause an increase in the current in the plateau region of the voltammograms. Frequency Factor Determination. The data shown in Figure 4 indicate that the electron-transfer rate at high driving forces becomes nearly independent of the electrode potential. This potential independence stems from the nearly complete overlap between the filled and unfilled electronic states at the electrode/electrolyte interface (Figure 6C). At these high overpotentials, nearly all the Mo(CN)*~-molecules at the eleetrode surface will be in resonance with electrons in the metal. The reduction rate in this case depends only on the total number of Mo(CN)*> centers at the electrode surface rather than the shape or position of the Dm distribution. Mathematically, eq 4 can be simplified to give the plateau current, i,,,,,, by noting that the integral of the D, distribution approaches 1 at high electrode overpotentials so that i,,, = nFvTN,, For the data shown in Figure 4, an i,, of 1 mA can be extracted. This value can be corrected for the area of the electrode and the solution concentration of the redox couple to give a maximum rate constant of 8.9 X cm/s. By use of a 8 value of 1.08 per methylene unit, this i,, is attenuated by the 14 hydroxy-l-tetradecanethiol monolayer by a factor 3.7 X lo6. Multiplying the i,, by this tunneling factor, one obtains a limiting rate constant of 3.3 X lo4 cm/s, which would be approximately the limiting rate constant at the bare Au electrode.34 This limiting rate constant, nFvNo,, is close in magnitude to theoretical estimates of the preexponential factor for heterogeneous electron transfers.3s The value nFNo, is the total number of electrical equivalents of the oxidized redox couple which participates in the electrontransfer reaction. It can be estimated if one assumes a reasonable value for the reaction layer thickness (the distance, on average, a redox couple must approach the electrode surface before it participates in the electron-transfer reaction) of 1 A3’ and neglects (32) Walmsley. D. G.; Nelson, W. J. In Tunneling Specrroscopy; Hansma, P. K., Ed.; Plenum: New York, 1982. (33) Kirtley, J. In TunnrlingSpecrroscopy; Hansma, P. K., Ed.; Plenum: - . New York, 1982. (34) The current measured at a w-hydroxy thiol derivatized electrode multiplied by the tunneling probability ( Y T ) would be the current anticipated at a bare electrode only for an electron transfer which was diabatic at the bare electrode. The expression i,/T would be an overestimation of the current at the bare electrode for an adiabatic electrode transfer. The magnitude of this overestimation would depend on the minimum number of methylene units which would be required to make the electron transfer at the monolayer-aated electrode diabatic. Another complication with this analysis is that the frequency factor determinedat these insulated electrodes may be different from that characteristicof a bare electrode: Hupp, J. T.; Weaver, M. J. J . Phys. Chem. 1984,88, 1463. (35) Hupp, J. T.; Weaver, M. J. J . Elecrroonal. Chem. 1983, 52, I . (36) Sutin, N . Prog. Inorg. Chem. 1983, 30, 441.

B e c k and Miller

TABLE I complex Fe(CN)? Mo(CNjs3W(CN)B)Fe(CN),(bpy)-

Ru(NH,)t+f Ce4+f Fe’+f

E,’” : ,A 0.26 0.99 0.61 0.90 0.38 0.87 0.38 0.96 -0.15 1.3 1.20 2.1 0.46 2.1

1.3 1.2 1.0 1.4 1.6 2.6 2.4

kWd 8.5 X 10’ 3.2 X lo‘ 4.9 X lo‘ 6.5 X lo‘ 1.1 X lo5 6.3 X lo4 1.8 X lo5

%Pp’

8X 3X 5X 6X 1X

6X 2X

10” 10I2 10l2 10” IO1’

lo1* lo1)

“The formal potentials of the complex v c m Ag/AgCI, saturated KCI. *The reorganization energy measured from the peak of the dk/dE distribution. CThereorganization e u l a t e d from the width of the dk/dE distribution. dThe maximum rate constant (in cm/s) corrected for the-tunneling probability by assumieg fl = 1.08 per methylene unit of the w-hydroxy thiol. ‘The vibrational frequency factor (in s-I), assuming a reaction layer thickness of 1 A (see text). ’The dk/dE data used for these complexes did not extend to the reorganization energy so these entries are subject to greater error.

any doublelayer effects on the concentration of the redox couple s-’ is at the electrode surface. A frequency factor of 3.3 X then obtained from the data. Again this is close to theoretical estimates for the frequency A similar analysis was performed for the reductions of other outer-sphere redox couples measured at Au electrodes derivatized with a self-assembled monolayer of 14hydroxy-1-tetradeanethiol. As seen in Figure 8, each of the dk/dE plots can be closely modeled with a Gaussian distribution. The solid curves in Figure 8 are the best fit Gaussians to the dk/dE data limited to the peak of the distribution. The dashed curves show the distribution predicted by the Marcus theory, given the reorganization energy determined by the peak of the best fit Gaussian. The kinetic parameters derived from these data are collected in Table I. For all of these complexes, we observe that the widths of the distributions are somewhat larger than that predicted by the Marcus theory. This can be seen by comparing the solid to dashed curves in Figure 8 or by noting that the reorganization energies calculated from the widths of the best fit Gawians are uniformly larger than those obtained from the peak of the distributions. For the redox couples whose dk/dE distributions can be measured at overpotentials approaching their reorganizationenergies, the precision of the measured reorganization energies is typically within 0.05 eV. The measured frequency factors for these complexes vary typically within a factor of 2 for different electrode preparations. For the redox couples with large reorganization energies (Ce4+ and Fe3+)or negative formal potentials ( R U ( N H ~ ) ~ ~the + )kinetic , data could not be collected at the reorganization energy of the complex. The calculation of best fit Gaussians for these data required a much larger extrapolation from the data and therefore is subject to greater uncertainties. This was especially noted for the kinetic data for Ru(NH3)d+,where the reorganization energies measured at different electrodes were obscrvd to vary by several hundred millielectronvolts. When the dk/dE distributions span only the initial portion of the Do, distribution, large variations in the calculated reorganization energies required only small changes in the current/voltage curves between different electrode preparations. The reorganization energies for the kinetically facile complexes are all quite similar in value and can be approximated t o be 1.O eV. In contrast, the reorganization energies for Ce4+and Fe3+ are considerably larger, which is consistent with the slow heterogeneous electron-transferrates observed for these complexes at bare R electr~des.~’The frequency factors for all the redox couples studied here are also close in value and approximately equal to 5 X 10l2PI. Because no doublelayec corrections were made, some differences between the cation and anionic complexes would be expected. As the electrode is swept to more negative potentials, one would expect a small negative diffua layer potential to develop at the monolayer/electrolyte interface. This negative potential will preconcentrate cations at the electrode surface while repelling anionic redox couples. The true value of No, therefore (37) Galus, Z.; Adams, R. N . J . Phys. Chem. 1%3,67, 866.


A

The Journal of Physical Chemistry, Vol. 96, No. 6,1992 2665

xi03 4.5

i

,...

4

I~

0.04 -

>

.

-1.5

-2


-0.5

-1

0


E

1

xi03 ':

0.9 0.8

",

007,

-

Fe+3

0.05

*

0.7 -

0.6

. Y

2

5

-

z

003

0.5 0.4 -

0.2 0.1

-1.8

-1.6

-1 4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0 -1.2

-1

-0.8

-0.6

-0.4

-0.2

Formal Overpotential I V

c

0.03

1


Formal Overpotential

Figure 8. Density of electronic states diagrams for Fe(CN),S-, Fe(bpy)(CN),-, W(CN)83-,Ru(NH3)2+,Fe3+,and Ce4+(A-F, respectively). Symbols and curves are the same as in Figure 7. The voltammetric data used to calculate these dk/dE distributions for Fe(CN),S-, Fe(bpy)(CN),-, and Ru(NH3):+ were obtained in 0.5 M KCI at 22 OC. The Fe3+and Ce4+distributions were measured in 0.5 M H2S04at 22 OC. The data used to measure the dk/dE distribution for W(CN)83-was measured in 0.5 M Na2HP04at 0.0 OC in order to extend the voltammetric window to -1.0 V.

will be dependent on the charge of the redox couple. We have sought to minimize this effect by using a fairly high ionic strength and anticipate that this double-layer effect will cause only a factor of 2 difference in the frequency factors listed in Table I.I0 The frequency factor governing the rate of electron transfer at a w-hydroxy thiol coated electrode could be very different from the frequency factor appropriate for a bare electrode. Electrontransfer reactions of facile outer-sphere redox couples are generally assumed to proceed adiabati~ally,~' the probability of electron transfer being unity for activated redox molecules at the electrode

surface. The electron-transfer rate in the adiabatic limit depends solely on the rate a t which the redox centers achieve a transition-state geometry of internal nuclear coordinates and solvent structure. The pre-exponential frequency factor in this case is determined by the frequency of motion of the redox couple along the reaction coordinate and so is determined by internal ligand vibrational and solvent polarization freq~encies.'~In contrast, (38) Bmnschwig, G. S.;Logan, J.; Newton, M.D.; Sutin, N. J . Am. Chem. SOC.1980, 102, 5798.


Becka and Miller complex derived from current/voltage curves obtained at electrodes coated with w-hydroxy thiol monolayers of differing lengths. The

r

-r?

B .

e

103

3 10‘

‘

10’ -1

-09

-0 8

-07

-0 6

-0.5

-04

I

-0 3


Figure 9. Density of electronic states curves for Fe(CN)& calculated as in Figure 7 using voltammetric data obtained at Au electrodes derivatized by whydroxy thiols differing in length as indicated in the figure. (Note: Gaussian distributions are parabolic in shape in a logarithmic plot.)

the electron transfers at w-hydroxy thiol coated electrodes are extremely nonadiabatic. The frequency factor in this case should not depend on the motion of the redox couple along the reaction coordinate but rather on the electronic parameters of the metal. The average density of electronic states in the metal at the Fermi level energy enters into the electron-transferrate as a multiplicative factor to the vibrational frequency factor. Parameters for the motion of the electrons in the metal may also contribute to the frequency factor. Currently, we do not have a clear sense as to what these frequency factors measure. Nevertheless, these frequency factors are measured quantities which are essential in describing the electron-transfer rate at these insulated electrodes. The Inverted Region. As the electrode potential is polarized beyond the reorganization energy of the oxidized redox center, the rate at which electrons at the Fermi level are transferred to the redox couple is reduced. We are interested in characterizing this “inverted” free energy region39to probe the effects of solvent structure and to assess the possible reduction of the complexes to electronic excited states. For redox couples with sufficiently positive formal potentials such as M O ( C N ) ~ ~W(CN)g3-, -, and Fe(bpy)(CN),-, one can begin to probe the electron-transfer characteristia of the inverted region. Some deviation in the dk/dE distributions from the best fit Gaussian is observed, which could be explained by some breakdcwn in the Marcus theory. Calef and Wolynes have published an extension of the Marcus theory in which the solvent is treated molecularly rather than as a dielectric continuum.40 The inclusion of solvent molecular orientations results in the broadening of the Do, distribution in the inverted region relative to that in the “normal” region. Ulstrup and Jortner have proposed that the presence of high-frequency “quantum modes” of the solvated redox center would result in the same broadening of the Do, distribution in the inverted region.41 Just this sort of broadening at overpotentials beyond the peak of the Do, distributions is observed to differing extents in the distributions shown in Figures 7 and 8. No second Gaussian distribution at higher potentials is observed, indicating that for these complexes reduction to an excited efectronic state d a s not occur within the potentials accessible to these w-hydroxy thiol coated electrodes. Effect of 0-Hydtoxy TMd Lesgsh on the Dttsrsrlcprtioa of -tic Pam”.The roorganihtion energies and frequency factors calculated from these kinetic data are not dependent on the length of the w-hydroxy thiol monolayer. Even so, there is an optimal length for the kinetic measurement. Figure 9 shows a series of electronic states distribution plots for the Fe(CN),3(39) Marcus, R. A.; Siders. P. J. Phys. Chcm. 1982, 86, 622. (40)Calef, D. F.;Wolynes, P. G. J . Cliem. Phys. 1983, 78. 470. (41) Ulstrup, J.; Jortner, J. J . Chem. Phys. 1975, 63, 4358.

distribution functions have a similar shape but span about 3 orders of magnitude owing to the change in the electron tunneling rate with the length of monolayer fh. For whydroxy thiol monolayers less than 11 methylene units in length, diffusion corrections cannot be made over the entire voltage range so that only the low overpotential side of the distribution is measurable. The best fit parameters of a Gaussian fit to these limited data give generally poor estimates of the peak and width of the distribution. The w-hydroxy thiol monolayer must be thick enough to allow the measurement of kinetic data at overpotentials approaching the reorganization energy. As the number of methylene units in the w-hydroxy thiol monolayer is increased from this point, the electron-transfer rates become smaller and smaller until, at n = 20 or 22, the currents become difficult to measure over the charging and background currents. For an Au electrode coated with a 22-hydroxy-1-docosanethiol monolayer, one can calculate that the maximum current density anticipated at -0.8 V (versus Ag/AgCl, saturated KCl) for a 10 mM solution of Fe(CN),’would be less than 2 bA/cmZ while the capacitive current at 1 V/s would be approximately 1 pA/cm2. The precision at which one can measure such low currents makes extracting kinetic data very difficult. This is especially true because the kinetic parameters are obtained from the derivative of the measured current/voltage curves, which makes the data analysis more sensitive to noise. Between the errors from the diffusion correction and the background correction, 12-16 methylene units appear to be the optimal lengths for the w-hydroxy thiol monolayera4* Effect of Monolryer Defects. While the insensitivity of the reduction current of Fe(CN)63-to changes in the solution viscosity indicates that the current measured at these whydroxy thiol coated electrodes is not due to widely spaced defect sites, it does not preclude the presence of defects within these monolayers. Defects within these self-assembled monolayers should be extremely common given the structure of the monolayer and the underlying Au substrate. Vacuum-depositedAu electrodes on glass substrates are polycrystalline and rough at the ato@c le~e1.4~Defects in the underlying Au surfaces such as atomic steps, grain boundaries between crystallites, and impurities on the Au surface should introduce imperfections in the adsorbed monolayer. Even on a perfect Au single crystal, defects could arise from the packing faults within the thiol monolayer itself. In order to discuss the influence of defect sites on the rate of electron transfer through the monolayer film, one must present some model for the possible defect sites. This is necessarily a speculativeexercise between we have no direct means of assaying the number or molecular structure of the defects within these monolayers. The voltammetric curves for redox couples such as those shown in Figures 1,3, and 4 do give some insight as to the structure of the defect sites. In particular it is apparent that the defect sites which expose bare Au surface are not in measurable concentration within these monolayer-coated electrodes. Penner et al. have reported the voltammetric response for facile outersphere redox couples measured at extremely small electrodes approaching atomic dimension^.^ Cyclic voltammetry at these ‘nanodes” gives diffusion waves very near the formal potential of the redox couple. The kinetically limited reduction currents observed at these w-hydroxy thiol coated electrodes are shifted d r a m a t i d y negative of the fonnal potentials of the redox couples studied. Any defect site which contributes measurably to the observed currents must be characterized by a slower heterogeneous electron-transfer rate than that at a h e electrode. In other words, the defects must be covered to some extent by the alkyl chains of the w-hydroxy thiols. (42) The optimal length also depeds on the Scan rate uscd to collect the cunent/voltage curvvcs. The faster the scnn rate, the lea difhsion limitations interfere with the kinetic measurements and the shorter the o-hydroxy thiol can be. We generally use 5 V/s and find that monolayersof 14-hydroxy-ltetradecanethiol give the most accurate data. (43) Nuzzo, R. G.; Fusco, F.A.; Allara, D. L. J . Am. Chcm. Soc. 1987, 109, 2358.



A

Monolayer collapse site

Au

B

Monolayer grain boundary

Au

C

Au substrate grain boundary

Au Figure 10. Cartoons of possible defect site types at the w-hydroxy thiol

monolayer coated Au electrodes.

The defects in the w-hydroxy thiol monolayers are likely to be extremely small in dimension, perhaps 1-10 nm in diameter.# This assumption is based on the molecular nature of the selfassembly of the whydroxy thiol on the Au surface. The adsorption of the whydroxy thiols is performed under conditions which favor the complete saturation of the Au surface. Once the Au surface is saturated with the thiol, the size of underivatized patches on the Au surface should be of the order of the size of the thiol amphiphile. With these observations and assumptions in mind, several different types of defect sites can be proposed, which are depicted schematically in Figure 10. These defect types have been proposed and studied by Finklea et al. for alkanethiol When the packing of the thiols on the Au surface is incomplete within a localized spot, a “collapse site” could form where the long alkyl chains fold over the defect. w-Hydroxy thiols within self-assembled monolayer films on Au surfaces have been observed to tilt relative to the surface The grain boundary between two monolayer domains with differing orientation of this surface tilt angle would be a second type of defect within these w-hydroxy thiol monolayers. A third type of defect would arise as the monolayer attempts to conform to grain boundaries or steps in the underlying Au substrate. Even though monolayer defects of the types depicted in Figure 10 may be common within these w-hydroxy thiol monolayers, many of the defects need not influence significantly the insulating characteristics of the monolayer. For the collapsed sites in which the surface is completely covered with the hydrocarbon chains, ~

~~

~

(44) Bain, C . D.; Evall, J.; Whitesides, G. M. J . Am. Chem. SOC.1989, 111,7155. (45) Finklea, H. 0.;Avery, S.; Lynch, M.; Furtsch, T. Longmuir 1987, 3. 409. (46) Finklea, H.0.;Snider, D. A,; Fedyk, J. Longmuir 1990, 6, 371. (47) Nuzzo, R.G.; Dubois, L. H.; Allara, D. L. J . Am. Chem. SOC.1990, 112, 558.

the rate of electron transfer through the defect may be identical to that observed at a close-packed region of the monolayer. Even though the thickness of the monolayer could be significantly smaller at the collapse site, the length of the hydrocarbons which are responsible for the long-range coupling between the metal and the redox couple would still be the same in the two regions. In order for the electron-transfer rate to increase at the collapse site, a significant electronic coupling between adjacent hydrocarbon chains would be necessary. Such a strong electronic coupling would not be expected given the weak dispersive bonding between the hydrocarbon chains. Grain boundaries between different monolayer domains would generate small hydrophobic fissures within the monolayer film. The rate of electron transfer at these grain boundary defects would depend on the extent the electroactive molecule partitions into these hydrophobic defects. The large hydrophilic redox couples studied here would not be expected to penetrate these defects. For defect sites at which the rate of electron tunneling is significantly larger than at the complete monolayer, the distortion to the voltammetric data collected at the blocked electrode will depend on the competition between the electron-transfer and mass-transfer rates at the defect sites. If the electron-transfer rate at the defect site remains much lower than the diffusion rate during the voltammetric experiments, the electrode current would be shifted to higher current values relative to an electrode coated with a perfect monolayer but its shape would be unaffected by the presence of the defects. This is because the potential dependence of the redox kinetics would be the same at the defect site and at regions with a complete monolayer. The presence of such defects will increase the measured dk/dt distribution but not affect its position. The result of this distortion of the Do, distribution will be to increase the apparent frequency factor but leave the reorganization energy unaffected. We do see some variability in the barrier characteristics between a series of electrodes derivatized by the same w-hydroxy thiol, especially in the longer w-hydroxy thiols (n = 18-22). However, the differences in the electron-transfer rate measured with different electrode preparations are remarkably small. For HO(CH,),,SH monolayers where n < 18, we observe typically less than 20% deviations in the electron-transfer rates between replicate monolayer preparations. Defect sites at which the concentration of the redox couple decreases below that at the bulk of the electrode surface during the voltammetric experiment should be in much lower density than the defects mentioned above. This is because they would require a greater disruption of the monolayer structure. The extent of the disruption required for a defect to alter the kinetic results presented here can be estimated given some estimates of the defects’ sizes. For defect sites 1-10 nm in diameter, the rate of mass transfer would be 3-4 orders of magnitude greater than the diffusion rate to a semi-infinite planar electrode under the voltammetric conditions used to collect the data shown in Figure 4.48 This means that the apparent rate constant at the defect site would have to be greater than 3-4 orders of magnitude faster than that at a defect-free monolayer-coated electrode in order for diffusion effects at the defect to influence the voltammetric shape. An increase in the rate constants by 3-4 orders of magnitude would be equivalent, given a tunneling coefficient equal to 1.08 per methylene unit, to a decrease in the effective thickness of the w-hydroxy thiol monolayer at the defect site of 6-9 methylene units. Presumably, the redox complex would have to approach the hydrocarbon chain 6-9 methylene units from the terminal hydroxy group to achieve this increase in the electron-transfer rate constant. Such a penetration of the electroactive species would require a particularly large disruption of the monolayer film. The purpose of this calculation is to show that minor packing faults in the monolayer will not affect the kinetic data collected at these (48) This increase in the rate of mass transfer for the defect sites was calculated by taking the ratio of the diffusion-limited current density at an ultramicroelectrode disk ( i l i m= 4nFDrC/A) to the peak current density observed at a bare electrode: Saito, Y. Rev. Polarogr. 1968, I S , 178.


monolayer would mimic the hydroxylated surface of the whydroxy thiol monolayers. The current measured at the 16-hydroxy-lhexadecanethiol-derivatized electrode is only slightly decreased by the addition of octanol in the electrolyte. The electrode derivatized with the longer 18-hydroxy-l-octadecanethiolshows a greater effect of octanol. We infer from this that the current at defect sites accounts for a greater proportion of the measured current for the monolayer with 18 methylene groups as opposed to the one with 16. We see a continuation of this trend for electrodes derivatized with still longer w-hydroxy thiols. The reproducibility of voltammograms obtained using electrodes coated with the 20-hydroxy-1-eicosanethioland 22-hydroxy-1-docosanethiol was much poorer than for the shorter w-hydroxy thiols. Instead of deviations of &20% between different electrode prep arations, we typically observe deviations of &200%for electrodes derivatizad with the eicosanyl and docusany1 whydroxy thiol. The electron-transfer rates measured at electrodes derivatized with these longer w-hydroxy thiols were consistently higher than would be predicted from eq 1, Also consistent with the larger defect density of the longer whydroxy thiol monolayers is the observation that these monolayers are noticeably less hydrophilic than monolayers formed by the shorter w-hydroxy thiols. To the extent that defects in the monolayer should expose the hydrocarbon portion of the amphiphile to the electrolyte solution,49one might expect that the contact angle may scale with the defect density of the monolayer. Quantitative measurements of contact angle within the range of &loo are not easily made. We are continuing our investigations of the defects in these w-hydroxy thiol monolayers in order to measure their number, size, and electron-transfer characteristics.

0 4

. I

1

-

0

-1.2

-1

-0.8

-0.6

-0 4

-0.2

Formal Overporential / V

\ " ,

0.61

I

... -.___ -1

-0.8

-0.6

-0.4

-0.2

Becka and Miller

0

Formal Overpotenttal/ V

Figure 11. Plots of the heterogeneous electron-transfer rate constant for Fe(CN)&-, 0.5 M KC1 with (solid curves) and without (dashed curves) 1.0 mM I-octanol measured at an Au electrode derivatized with a 16-

hydroxy-1-hexadecanethiol monolayer (A) or a 18-hydroxy-I-octadecanethiol monolayer (B). The inset graphs plot the ratio of the rate constants at each electrode in the two solutions as a function of the formal overpotential. The scan rate was 0.5 V/s.

w-hydroxy thiol monolayer coated electrodes. One can probe the defect density in these w-hydroxy thiol monolayers by introducing an amphiphile in the solution of the redox couple. Adsorption of the amphiphile on the monolayercoated electrode will occur preferentially at the defect sites, resulting in a decrease in the electron-transfer rate at the defect site. Figure 11 shows voltammograms of Fe(CN)63-in 0.5 M KCl with and without 1 mM 1-octanol obtained at two electrodes, one coated with a monolayer of 16-hydroxy-1-hexadecanethioland the other with 18-hydroxy-1-octadecanethiol. Octanol was chosen as the amphiphile in these experiments because it has an appreciable solubility in water and once adsorbed at defect sites in the

Conclusions Decreasing the rate of heterogeneous electron transfer by derivatizing electrodes with self-assembled monolayers of whydroxy thiols is a powerful means by which electron-transfer kinetics of even facile redox species can be studied over a wide range of electrode overpotentials. The analysis of current/voltage data obtained at these w-hydroxy thiol derivatized Au electrodes is simplified by the observation that the electron tunneling rate is nearly independent of the voltage of the electrode. Reorganization energies and frequency factors describing the kinetic facility of an eiectroactive species are easily measured at these insulated electrodea ushg cyclic voltammetry. The reduction kinetics of a series of redox-active species were in very good agreement with Marcus theory predictiops and demonstrated clearly the presence of the Yinverted" region. Some small deviation between the theoretical and m e a s d Dm distributionsfor several redox couples were noted. The origin of this deviation from the Marcus theory prediction could stem from experimental uncertainties as well as from a failure of the Marcus theory. Further compafisoIls of these data to contemporaryelectron-transfertheories will require a more accurate understanding of the tunneling barrier and the electronic structure of the Au electrode surface. Acknowledgment. This work was funded in part by the General Research Board of the University of Maryland. (49) Bain, C. D.; Whitesides, G. M. J . Am. Chem. SOC.1988, 110,3665.

hydroxy thiol coated electrodes. 3. Voltage independence of the

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