J. Phys. Chem. 1991,95. 5225-5233
5225
temperatures for spectra 3-5.
the CO/Cu/Rh( 100) surface and the concurrent increase in the CO-Rh intensity indicate CO diffusion from Cu to Rh sites. This interpretation is corroborated by TPD results that show no measurable CO desorption at a temperature where the IR peak intensity of CO-Cu has been essentially reduced to zero. The experiments also demonstrate that the presence of CO on Cu influences the bonding configuration of CO on Rh. A possible explanation is that the adsorption of CO on Cu may compress the CO on Rh into a more condensed and more highly ordered phase. The unoccupied Rh sites thus created are blocked by the C O on Cu. Upon depopulation of the CO on Cu, the CO on Rh apparently spreads into a more dilute and relatively disordered phase. Another explanation for the observed influence that CO on Cu has on CO-Rh would be the 'intensity sharing" effect, where intensity from the low-frequency mode (CO-Rh) is transferred into the high-frequency mode (CO-Cu), as described in ref 13 and 14. Our results also show that the deposition of Cu onto a CO presaturated Rh(100) surface at 90-100 K causes spillover of the CO from the Rh( 100) surface to the Cu overlayers. A fraction of the C O is screened by the deposited monolayer Cu. The formation of a CO/Cu/Rh(100) structure contrasts with previous studies where the sandwich structures Cu/CO/Ru(O01)2 and Cu/CO/W(110)3 were reported to form a t 85 and 90 K, respectively. The origin of this difference is a t present unclear.
Summary and Conclusions The present work has addressed CO diffusion from Cu sites to Rh sites on the Cu/Rh(100) surface and CO spillover from a Rh( 100) surface to subsequently deposited Cu overlayers. The decrease in the intensity of the CO-Cu peak upon heating
Acknowledgment. We acknowledge with pleasure the support of this work by the Department of Energy, Office of Basic Energy Science, Division of Chemical Sciences, and the Robert A. Welch Foundation. R&stry NO. CO, 630-08-0; CU,7440-50-8; Rh, 7440-16-6.
l " " " " " " " " " ' 1
ecut 1.2 ML
21087
269 K
5
~
4
..
173 K & '
3
1s = 90K -
2
1 2200
2100
2000
1900
1800
WAVENUMBER (CM") Figure 12. IR spectra of CO from Rh(100) surface, first saturated with CO at 100 K (spectrum 1) and then after deposition of 1.2 ML of Cu at 90 K (spectrum 2). The surface then was flashed to the indicated
Electrochemlstry at o-Hydroxy Thiol Coated Electrodes. 2. Measurement of the Density of Electronic States Dlstrlbutlons for Several Outer-Sphere Redox Couples Cary Miller* and Michael Griitzel Institut de Chimie Physique, Ecole Polytechnique Fgdsrale, CH- 1015 Lausanne, Switzerland (Received: August 23, 1990; In Final Form: January 25. 1991)
The use of Au electrodes blocked with w-hydroxy thiols for kinetics measurementsat large electrode overpotentials is discussed. The adsorbed monolayer acts as a tunneling barrier slowing the rate of electron transfer allowing the measurement of redox kinetics at electrode overpotentials over 1 V without mass-transfer limitations. The cathodic heterogeneous electron-transfer kinetics for a series of six outer-sphere transition-metalcomplexes are measured at Au electrodes derivatized by a self-assembled organic monolayer of 16-hydroxy-1-hexadecylmercaptan from aqueous solutions. Plots of the logarithm of the apparent heterogeneous electron-transfer rate constants with electrode overpotential for all complexes studied display strong negative curvature at high electrode overpotentials. These data are analyzed by using the approach of Bennett to obtain the density of electronic states for the oxidized form of these complexes. The density of electronic states are well described by Gaussian distributions and are compared to previous determinations and the predictions of Marcus theory.
Introduction The distribution of electronic states for a redox couple in an electrolyte solution describes the couple's electron-transfer properties.'a2 Experimental determinations of density of states distributions are therefore important tests of current electrontransfer theories.'.' To obtain the density of states distribution from an electrochemical experiment requires the measurements of heterogeneous electron-transfer rate constants over a range of electrode overpotentials extending beyond the reorganization energy of the redox couple. Such measurements are difficult or To whom correspondence should be addressed. Current address: Department of Chemistry and Biochemistry, University of Maryland, College Park, MD 20742.
0022-365419 1/2095-5225$02.50/0
impossible a t bare electrodes due to mass-transfer limitatioms A promising approach for the measurement of fast redox reactions is to use blocked electrodes? A continuous layer of a thin insulating material can slow the rate of electron transfer to such an extent that its rate can be measured by using simple voltammetric techniques on a slow time scale without mass-transfer (1) Gerischer, H.2.Phys. Chem. (Munich) 1960, 26, 325. (2) Vetter, K.J.; Schultze, J. W . Ber. Bunsen-Ges. Phys. Chem. 1973, 77, 945. (3) Marcus, R. A. J. Chem. Phys. 1%5,43, 679. (4) Marcus, R. A.; Sutin, N. Biochim. Biophys. Actu 1985, 811, 265. (5) Greef, P.; Peat, R.; Peter, L. M.; Pletcher, D.; Robinson, J. In fnstrumentol Methods in Electrochemistry; E. Howard Series in Physical Chemistry; Kemp, T. J., Ed.;Wiley: New York, 1985; p 104. (6) Bennett, A. J. J. Elecrroonol. Chem. 1975, 60, 125.
0 1991 American Chemical Society
5226 The Journal of Physical Chemistry, Vol. 95, No. 13#1991 limitations. If the effect of the insulator on the electron-transfer rate is known, kinetic parameters for the solution species can be obtained from this voltammetric data. Passive films on metal electrodes such as surface oxide layers and the depletion layer of semiconductors have been used to slow the rate of heterogeneous transfer at metal and semiconductor electrode^.^^'-^^ For these oxide and semiconductor systems, the ability to make reproducible insulating films can be a pr0b1em.I~ In addition, their insulating characteristics can be quite complex due to the presence of "impurity" states, defects and other forms of heterogeneity.Is While the complexity of the oxide films makes for quite interesting studies of their insulating properties, their use for the measurement of solution species kinetics is made difficult by such complexity. A promising approach to the fabrication of insulating films is via the spontaneous self-assembly of amphiphiles into monolayers at electrodes.'b22 In order to use this approach for the measurement of electrode kinetics of fast redox couples at high overpotentials, monolayer films with an exceptional degree of perfection and stability must be produced. We have recently reported that monolayers of o-hydroxy thiols adsorbed onto Au electrodes from aqueous solutions can give rise to extremely stable monolayers displaying very low defect densities.23 For these monolayer coated electrodes, electron tunneling through the ohydroxy thiol monolayer was found to be the dominant mechanism for electron transfer. In this paper we investigate the kinetics of electron transfer to several "outer-sphere" redox couples at a wide range of electrode overpotentials at Au electrodes coated with 16-hydroxyhexadecanethiol. Using the mathematical treatment proposed by Bennett: we extract the density of electronic states distribution for these redox species in solution. Our purpose is to discuss the use of these insulated electrodes for kinetic measurements and compare the density of electronic states functions measured here with previously reported ones obtained using oxide insulator^'^^'^ and those predicted by the Marcus theory.24 Experimental Section The 16-mercaptohexadecanolwas synthesized from 1,16-hexadecanediol and purified by a procedure described p r e v i ~ u s l y . ~ ~ Au electrodes (prepared via the thermal evaporation of Cr and Au onto polished n-type Si wafers) were obtained from the CSEM Neuchttel. Each Au electrode consisted of either a 0.009 94 or a 0.160 cm2 area surrounded by a 8000-A Si02insulating layer. The opposite side of the Si wafer was coated with a Cr/Au layer to afford an electrical contact to the Au electrode. The cleaning of the electrodes in chromic acid and aqueous HF, and their subsequent derivatization in a solution saturated in 16mercaptohexadecanol and containing 50 mM decyltrimethylammonium bromide, were performed as described p r e v i ~ u s l y . ~ ~ (7) Memming, R.; MMlers, R. Ber. Bunsen-Ges. Phys. Chem. 1973, 77, 945. (8) Schultzc, J. W.; Vettcr, K. J. Electrochim. Acta 1973, 18, 889. (9) Kohl, P.; Schultze, J. W. Ber. Bunsen-Ges. Phys. Chem. 1973,77,953. (IO) Kobayashi, K.; Aikawa, Y.; Sukigara,M. BUN.Chem. Soc. Jpn. 1982, 55, 2820. (1 1) Kobayashi, K.; Aikawa, Y.; Sukigara, M.J . Electroanal. Chem. 1982, 134, 11. (12) Morisaki, H.; Ono, H.; Yazawa, K. J . Electrochem. Soc. 1 M . 1 3 5 , 381.
(13) Morisaki, H.; Ono, H.; Yazawa, K. J . Electrochem. Soc. 1989,136, 1710. (14) Schultze, J. W.; Elfenthal, L. J . Electroanol. Chem. 1986. 204, 153. (15) Schmickler, W.; Ulstrup. J. Chem. P h p . 1977, 19, 217. (16) Bigelow. W. C.; Pickett, D. L.; Zisman, W. A. J . ColloidSci. 1946, I , 513. (17) Sagiv, J. J . Am. Chem. Soe. 1980, 92, 102. ( 1 8 ) Allara. D. L.; Nuzzo, R . G . Lungmuir 1985, I , 45. (19) Bain, C. D.; Troughton. E. 9.; Tao, Yu-Tai; Evall, J.; Whitesides, G. M.; Nuzzo. R. G. J. Am. Chem. Soc. 1989, 111. 321. (20) Finklea, H. 0.;Avery, S.; Lynch, M.; Furtsch, T. Lungmuir 1987, 3. 409. (21) Porter, M. D.; Bright, T. B.; Allara. D.L.; Chidsey, C. E. D. J . Am. Chcm. Soc. 1987, 109, 3559. (22) Nuzzo, R.G.; Fusco, F. A.; Allara, D.L.J . Am. Chem. Soc. 1987, 2358. -109. .. __ - .. (23) Miller, C.; Cuendet. P.; Grltzel, M. J. Phys. Chem. 1991, 95, 877.
.
Miller and Griitzel
0
OIMKCI
I
The Journal of Physical Chemistry, Vol. 95, No. 13, 1991 5221
w-Hydroxy Thiol Coated Electrodes
2o
1
10"t
t
c d. A
05
03
.o
-0 1
01
3
.o
5
-0 7
t
%
m
E/
VOItS
*
/versus AgIAgCI, sat KCI)
Figure 2. Cyclic voltammogramsobtained in a solution containing 15
mM Fe(CN)6*, 0.1 M KCI using three different HO(CH2)16SHtreated
Au electrodw. For these voltammograms the scan rate was 0.5 V/s and the area of the electrodes was 0.16 cm2.
ammograms is characteristic of an ideal capacitor. The value of the capacitance for these derivatized electrodes was previously found to be consistent with a compact hydrocarbon monolayer film.23 For both KCI and NaCH3CO0 electrolytes, the voltammetric window is quite large (ca. + l e to -l.V). At more positive potentials for voltammograms obtained in the NaC104 electrolyte, an increase in the capacitive current is observed. As the electrode is polarized positive of the point of zero charge of the monolayer coated Au electrode (which can be estimated to be that reported for bare Au surfaces at ca. 0.0V vs Ag/AgCl, sat. KCI"), the electric field in the hydroxy thiol monolayer film will increase, favoring the penetration of the hydrocarbon layer by anions in the electrolyte. Because the ions within the apolar hydrocarbon monolayer are expected to be predominantly u n ~ o l v a t e d the ,~~ electric field required to drive the partitioning of the ions into the adsorbed monolayer should be a function of the hydration enthalpy of the ion. For the Clod-which has a lower hydration enthalpy than CI- or CH3COO-, the breakdown field would therefore be expected to be lower than for the more hydrophilic anions.26 In keeping with this assessment, the rise in the anodic background seen in the C1- containing electrolyte occurs slightly smner than is seen in CH3COO-, consistent with the small difference in the hydration enthalpy of these two anions. The result indicates that, at high electrode potentials, ions can penetrate the hydroxy thiol monolayer, especially more hydrophobic ions. The electric field driven partitioning of ions within the monolayer is likely to affect the electron-transfer kinetics measured a t these hydroxy thiol derivatized Au electrodes. For electroinactive ions such as C104-, the partitioning of ions within the monolayer may disrupt the monolayer packing or act as electron-transfer bridge sites accelerating the rate of electron transfer to redox species in solution. If an ionic redox couple being studied partitioned into the monolayer, the rate of electron transfer measured at these derivatized electrodes would almost certainly increase due to the closer approach of the redox sites to the Au electrode surface and possible mediation of redox species at the solution/monolayer interface by the redox centers partitioned in the monolayer. In order to lessen the possibilityof ion penetration into the monolayer, we have studied hydrophilic (multiply charged) redox couples and confined the voltammetric scans to potentials in which the voltammetry indicates p o d blocking of the electrolyte. Figure 2 shows typical cyclic voltammograms for HO(CH2)16SHtreated Au ~ k a o d e in s a Fe(CN)6f solutions. Here three voltammetric experiments performed using three different electrode preparations are presented to show the reproducibility ~
~~
~~
~~~
~~~
(24) Hamelin, A,; Lecoeur. J . Collect. Czech. Chem. Commun. 1971, 36,
714.
(25) Levitt, D . G. In The Chemical fhysfcs ofSoludion, part C ; Dogonadze, R.R.,KtIlmBn, E., Komyshev. A. A.. Ulstrup, J., Eds.;Elsevier: New
York, 1988. (26)
Marcus, Y . Ion Solvation; Wiley: New York, 1985; pp
108-109.
Miller and Grgtzel
5228 The Journal of Physical Chemistry, Vol. 95, No. 13, 1991
A
94
15mM
' 0.01 M KCI
5.1 mM
0
18mM 78mM 220mM
. 8 v1
0.IMKCI 0
I
.
4-51
IMKCI
a
. &
E / Volts (versus Ag/AgCI,
sat.
KCI)
Figure 4. Plots of the apparent heterogeneous electron-transfer rate constant for the reduction of Fe(CN),'- in 0.1 M KCI vs electrode potential. The concentration of the Fe(CN)6* complex used for each experiment are indicated in the figure.
of extrapolating the linear portion of the curves to the standard potential of the redox couple, thereby measuring the standard rate constant. The measurement of the slope of this linear segment gives a measure of the transfer coefficient, CY, for the reaction. Such an analysis using these curves is possible but with several important reservations. The hexadecylhydroxy thiol monolayer decreases the rate of electron transfer by approximately 7 orders of magnitude from that measured at a bare electrode. This has required us to measure the redox kinetics at potentials which are significantly more negative the formal potential of the redox couple. The linear portions of the log (kapp)plots correspond to quite small electron-transfer rates and are therefore subject to increased uncertainty due to the necessity of background (charging) current corrections. This is particularly true for the data for Fe(bpy)$+ in which the background current at potentials more positive than 0.5 V vs Ag/AgCl, sat. KCl displayed some enhancement due to ion penetration into the monolayer. The use of shorter hydroxy thiol monolayers allows one to measure more accurately the standard rate constant and transmission coefficient at the expense of not being able to measure the redox rates at large over potential^.^^ Here we wish to focus on the reduction kinetics at large overpotentials in which significant curvature in the log (kap ) plots is observed. The curvature seen in these plots is pre8icted by the Marcus theory3 and has been experimentally observed at bare metal electrode^.^'-^^ It is our intent to quantitatively analyze the plots in Figure 3 in order to compare them with the predictions of the Marcus theory. Before this can reasonably done, however, the possible influence of double-layer effects must be considered. Double-Layer Effects. The structure of the electrode double layer and the potential distribution within the double layer can have important consequences on the rates of electrode reactiomm If a redox reagent has a special affinity for the electrode surface, it may specifically adsorb so that its local concentration at the electrode surface would be higher than the bulk concentration. The electron transfer to the redox centers specifically adsorbed will cause an increase in the apparent heterogeneous electrontransfer rate constant. As the bulk concentration of the redox couple increases beyond the saturation point of the specific adsorption sites, the component of the measured heterogeneous electron-transfer rate constant due to the adsorbed centers will become constant and therefore of less relative importance to the apparent rate constant. The presence of specific adsorption in this case would be indicated by the apparent heterogeneous ~
~
~~
(27) Marecek, V.;Samec, Z.; Weber, J. J . Electroanul. Chem. 1978,94, 169.
(28) Tyma, P. D.;Weaver, M.J. J. Eltctrounul. Chtm. 1980, I l l . 195. (29) Savtant. J.; Tessier, D.Furuduy Discuss. Chtm. Soc. 1982, 74.57. (30) Delahay, P. Double Luyer und Electrode Kinetics; Advances in
Electrochemistry and Electrochemical Engineering; Delahay, P.,Tobias, C. W., Eds.; Wilcy Interscience: New York. 1965; Chapter 3.
?I I Volts
B
A
0.01MKCI
' O.IM KCI
.
IMKC~ A
. '. ...' '.
alKCI
..
A
.
A
a
.
m
0 0
m
?I I Volts Figure 5. Plots of the apparent heterogeneous electron-transfer rate constant for the reduction (A) and oxidation (B)of the Fe(CN)6*/C couple. The concentration of the :dox couple was held constant at 15 m M while the concentration of KCI was varied as indicated in the figure.
electron-transfer rate constant decreasing with increasing bulk concentration of the electroactive species. To address the possibility of such a specific adsorption of species near the electrode, the concentration dependence of the Fe(CN)d- reduction rate constant was measured. Figure 4 shows plots of the apparent heterogeneous electron-transfer rate constant, k, , for the reduction of the Fe(CN)63- obtained at a single &(CH2)16sH coated electrode obtained in 0.1 M KCl electrolytes as a function of the electrode potential at different Fe(CN)t- concentrations as indicated in the figure. Below 18 mM, the log (k ) vs E plots are independent of the Fe(CN)63- concentration, inxcating that the specific adsorption of ferricyanide is not strong enough to alter the observed kinetics. At higher Fe(CN)6)- concentrations, the measured rate constant increases significantly. This augmentation in the observed rate constant stems from decreased Coulombic repulsion of the redox active anion from the electrode surface with increasing ionic strength. It is important to note that this effect of ionic strength on the measured rate constant was masked for the low concentrations of Fe(CN)63-by the 0.1 M KCI electrolyte. Only when the concentration of K3Fe(CN)6approached that of the supporting electrolyte was the effect of ionic strength seen in the data. The decrease in Coulombic repulsion stems from two effects. First, the higher ionic strength decreases the potential at the outer Helmholtz plane (OHP), q5*, which at potentials negative of the potential of zero charge would tend to repel anions. Second, the increase in the concentration of the K3Fe(CN)6 increases the K+ association with the Fe(CN)6)- ion reducing its charge." Further demonstration of these effects is shown in Figure 5 in which the apparent rate constant for both the oxidation and reduction of the Fe(CN)63-le couple is plotted as a function of the electrode overpotential for differing concentrations of the KCI electrolyte. (31) Lewis, G.
N.; Sargent. L. W. J . Am. Chem. Soc. 1909, 31, 355.
The Journal of Physical Chemistry, Vol. 95, No. 13, 1991 5229
w-Hydroxy Thiol Coated Electrodes For the oxidation of Fe(CN)6C, increasing the KCI concentration results in a decrease in the apparent rate constant while for the reduction of Fe(CN)t-, the apparent rate constant increases with increasing KCl Concentration. In order to calculate the magnitude of the Coulombic effect on the measured kinetics, the value of 42 (the potential at the OHP), must be calculated. A simple model can be used to calculate this potential. The electrode double layer is considered to be composed of two regions: the hydroxy thiol monolayer which is assumed to be an ideal capacitor, and the diffuse double layer whose capacitance can be calculated by Gouy-Chapman theory. This simple model is identical with the treatment of the double layer by Sterns2except that we replace the capacitance of the compact layer with the much smaller capacitance of the hydroxy thiol monolayer. The electrode capacitance, Ctotsl,is then given by
- 1- - -1 + - 1 Cm Cgc G o b ~
(2)
where C, is the capacitance of the monolayer film and Cgcis the capacitance of diffuse layer calculated from Cgc= 2 2 8 . 5 ~ cosh ~ ~ 1( 1~ 9 . 4 6 ~ 4 ~ )
(3)
where z is the absolute value of the charge of the z:z electrolyte and c is the concentration of the electrolyte in mol/L. The potential applied to the electrode, V (measured relative to the potential of zero charge), will be dropped within the two capacitors. Thus the potential 42 can be calculated from
The value of 42 for a given electrode potential and electrolyte concentration can be found iteratively from this equation if one assumes a value for the potential of zero charge. For 0.1 M KCl and 0.5 V negative of the point of zero charge, the value of 42 is calculated to be -9 mV. While this potential is small, it has a significant effect on the measured rate constants by altering the concentration of the ions at the OHP via the relationship
CoHP= C*e+hlkT) (5) where C is the bulk concentration the ion of charge z and k T is the product of Boltzmann's constant and the absolute temperature expressed in millivolts. The changes in the measured rate constants with KCl concentration shown in Figure 5 agree very well with the magnitude of 42 calculated via eq 4. An important advantage of these "blocked" electrodes over "bare" electrodes is that double-layer effects are greatly diminished because most of the applied potential is dropped within the blocking layer. Because of the small magnitude of the expected double-layer correction and the uncertainty in the point of zero charge for the monolayer derivatized Au electrode, we have not corrected the kinetic data for this double-layer effect. The influence of the double-layer effects on the analysis of kinetic data will be addressed below. Calculation of the Derrsity of Electronic States Distribution. The main focus of this work is to look quantitatively at Tafel data such as those shown in Figure 3 and to compare these experimental results with the prediction of the Marcus theory.3 In particular, we are interested in obtaining the distribution of electronic states for the redox couple at the electrode/electrolyte interface. To do this the effect of the insulating barrier must be considered. Previously we have shown that electron tunneling through the w-hydroxy thiol monolayers is the dominant mechanism for electron transfer.23 For this situation with an insulating film at an electrode, Bennett has proposed a simple mathematical treatment which allows one to calculate the density of electronic states function from the measured redox kinetics and a knowledge of the insulating barriera6 A density of electronic states diagram for a blocked electrode in a solution containing a redox reagent (32) Stern, 0. Z. Elektrochem. 1924, 30, 508.
Ef EO'
E-O
Metal
Barrier
Redox Couple in Solution
Figure 6. A density of electronic states diagram for an insulator coated electrode in contact with a solution containing equal concentrations of the oxidized and reduced form of a redox couple. In this figure, the electrode is biased negatively from the equilibrium potential. The notation is that used by Bennett.('
is shown in Figure 6. Using the notation adopted by Bennett, the current density at an insulated electrode can be approximated by
where a is given by
(7) where m is the mass of the electron and h is Planck's constant, 7 is the standard-state electrode overpotential (i.e., the potential of the electrode measured with respect to the standard potential of the redox couple which is denoted as "V" in Bennett's work), Et is the Fermi level in the metal measured with respect to an arbitrary zero, e is the electronic charge, y is the preexponential frequency factor which is assumed to be a constant with respect to E, d is the thickness of the insulator film, Eo is the height of the barrier, 0, is the density of electronic states function for the oxidized redox species, k is Boltzmann's constant, and T i s the absolute temperature. In this equation the current density is a product of the density of electronic states in the metal electrode and 0, (weighted by the probability of electron tunneling through the insulating barrier) integrated over the entire 0, distribution. The parameter E serves as the integration variable. The density of electronic states in the metal is assumed to be a constant whose occupancy is governed by the Fermi distribution function. From Bennett's derivation, the derivative of the current density with respect to overpotential energy is given by d j / d ( e d = 4 + Dox(Ef - edeyT(ed
(8)
where a(&
a =
+ y2eq)'Iz(Eo- '/ze77)'12 (9)
2elI
T(eV) = exp[-a(Eo
+ t/2er))1/2]
(10)
so that
The density of electronic states for the redox couple can then be calculated by knowing the current density as a function of the electrode overpotential and its derivative. The y factor which is
5230 The Journal of Physical Chemistry, Vol. 95, No. 13, 1991
-0.8
-1.0
6r+4
-0.6
-0.1
0.0
-0.6
-0.2
0.0
-0.4 Electron Energy I eV
Miller and Gratzel
B
>
s2
.
4e+4
2er4
k+O
-1.0
.0.8
-0.4 Electrun Energy I eV
le+4 8e+3 6e+3
&+3 2e+3
-1.0
-0.8
-0.6 -0.4 Electron Energy I eV
-0.2
0.0
Oe+O -1.0
-0.8
-0.6 .0.4 Electron Energy I eV
-0.2
0.0
Figure 7. Plots of yo, distributions vs overpotential energy, q,calculated by using eq 11 from the data shown in Figure 7. The barrier height Y was taken as 0.52 V and the monolayer thickness was set at 21 A. The data points in parts 7A through F correspond to the calculated distributions
of Fe(CN)63-,Fe(bpy),'+, W(CN)*>, Mo(CN),)-, Fe(bpy)(CN),-, and Ru(NH3)()+,respectively. The solid curves correspond to the best fit Gaussian (see text). nominally linked with the nuclear frequency factor is dependent on several other parameters as well. In Bennett's derivation one assumes that in the absence of the tunneling barrier, the electron transfer is adiabatic so that the transmission coefficient, K , is unity. If K is less than 1, this term will appear in the y factor. In the presence of the tunneling barrier, the transmission coefficient is calculated as being identical with the probability of electron tunneling through the barrier, T(e7). In this simplification the average density of electronic states in the metal is not explicitly included in eq 6. Its inclusion would be as a preexponential factor to the T(eg) factor which is included into the constant y. Figure 7 shows the calculated density of electronic states for the redox couples studied here calculated from eq 11. Instead of the current density and its derivative, the apparent heterogeneous electron-transfer rate constant and its derivative with respect to the electrode potential were used in the calculation. The use of the apparent rate constant is identical with scaling the experimental data to unit area of the electrode and unit electrical equivalent concentration of the redox couple (1 cm2 and l / n F mol/cm3, respectively) and was used to allow facile comparison between the data shown in Figure 7. In these calculations, the thickness of the tunneling barrier was taken to be 21 A and the barrier height Eo was set to 0.52 eV as measured p r e v i ~ u s l y . ~ ~ More scatter in yooxon the low-overpotential side of the distributions can be seen due to the low apparent rate constants and hence the low current levels which are difficult to measure. The rate constant data used to calculate these density of states distributions for the redox couples shown in Figure 7 span about 3 orders of magnitude. Because the calculation of the yoox function
depends on the derivative of the current, it is especially sensitive to noise in the kinetic data. Focusing on the data for the Fe(CN)6f reduction, we can see a peaked distribution of the density of electronic states. The maximum of the calculated density of electronic states should occur at the reorganization energy of the redox c ~ u p l e A . ~ reorganization energy for this complex of ca. 0.37 eV can be obtained from this data. Before a discussion of the significance of the density of electronic states distributions shown in Figure 7, several points concerning how the calculated distributions are affected by the experimental parameters used in their calculation must be addressed. The position and shape of the calculated yo,, function depends importantly on the magnitude of the electron tunneling bamer, qq), which is dependent on the insulator thickness and the height of the barrier as seen in eq 10. While this barrier was measured previously by measuring the dependence of the reduction rate constants for Fe(H20)63+and Fe(CN)63- on the length of the hydroxy thiol used to form the insulating barrier, the considerable scatter in the data presented there makes the calculated barrier height only approximate with an uncertainty of as much as f0.2 eV. Figure 8 shows the change in the yD(s) distribution with a change in the barrier height used in its calculation. As the barrier used in the calculation is lowered from 0.72 to 0.32 V, one sees a ca. -0.2-V shift in the peak of the yD,, distribution and a dramatic decrease in the value of the yo,, function. Changing the barrier height used in the calculation from 0.72 to 0.32 V results in a decrease in the yD(s) distribution by a factor of 2000. The shape of the distribution is not nearly as strongly dependent on the barrier height used.
The Journal of Physical Chemistry, Vol. 95, No. 13, 1991 5231
o-Hydroxy Thiol Coated Electrodes TABLE I
complex Fe(bpy)Z+ M0(CN)Bs Fe(bpy)(CN),W(CN)*IFe(CN)63Ru(NH3)6,+
c, ,x
ob
bb
P
-11.44 -16.90 -16.30 -17.34 -15.24 -1 2.77
5.43 12.83 13.33 13.83 11.30 10.88
10.04 7.36 6.17 6.20 6.65 6.99
EO"
+0.884 +OS92 +0.367 +0.324 +0.234 -0.1 14
0.24 0.38 0.40 0.40 0.37 0.43
xwidlhc
integrald
0.85 0.58 0.60 0.56 0.64 0.76
2.3 X 10' 7.7 x 103 5.8 x 103 3.3 x 103 2.9 x 103
5.5 x 103
Ye 2 x IO" 8 X 10" 6 X 10" 3 x IO" 3 x IO" 6 X 10"
Formal potentials of the redox couples versus (Ag/AgCI, sat. KC1). bBest fit coefficients for the quadratic fit of the In (yD,) distribution. (The corresponding Gaussians are shown as the solid curves in Figure 7.) CReorganizationenergies (in volts) calculated from the peak of the rD, distributions, kmk, and from the width of the distributions, Ldlh (see text). dThe integrals of the YD, distributions calculated from the best fit data shown in Figure 7. eEstimates of the y factor assuming that No, = 1 X IO4 C/cm2 for all the complexes (see text).
.0.8
-0.4
-0.6
-0.2
0.0
Electron Energy 1 eV
Figure 8. Plots of the yD, distributions for Fe(CN),'
calculated by using two different barrier heights. The distribution on the left was calculated by using a barrier height of 0.72 V while the one on the right was calculated by using a bamer height of 0.32 V. The bamer thickness, d, was held constant at 21 A for both calculations. The shape of the density of electronic states for a redox couple in solution can be calculated from the Marcus theory. The parabolic approximation to the energy of a redox center along the reaction coordinate leads to a Gaussian distribution for the Dox function2
where No, is the number of redox species a t the electrode surface which take part in the heterogeneous electron-transfer reaction per unit area, A is the reorganization parameter for the couple, and E is the energy difference of an electron measured from the standard potential of the redox couple. Taking the logarithm of DOLE)
So the Marcus theory predicts that a plot of the logarithm of the Do, distribution versus (er))should give a parabola
In (Do,) = ax2 + bx
+c
(14)
where (I
-( 1/4AkT)
(15)
b = 1/2kT c = In (Nox(4aAkT)-'I2) -
(16)
x 4kT
(17)
Multiplying the distribution function by y will change only the coefficient so that for In (yDox):
c
c = In (4yN0,(rXkT)-1~2)-
A 4kT
(18)
The best fit a, b, and c parameters calculated from the y D , distributions are collected in Table I. Because the approximation for a given by eq 9 is no longer valid once the overpotential approaches twice the barrier height? the distribution data at very high overpotential energies (>1 eV) were excluded from the
parabolic fits. Similarly, the density of electronic states data a t low electron energies were also excluded from the fits because of the high scatter. The Gaussians derived from these best fits are plotted as the solid lines in Figure 7. While the experimentally generated y o o xdistribution are quite well described by Gaussians (see Figure 7), critical comparison of these distributions to the Marcus theory predictions requires a closer look at the coefficients of the best fit parabolas. This is equivalent to comparing the shape of the distribution with that predicted by eqs 15-18. The reorganization energy of these couples is generally associated with the peak of the y o o xdistribution which occurs at an e l value of (-b/2a). In addition, the width of the distribution (which is dependent solely on the a coefficient) is also a measure of the reorganization energy of the redox species which can be calculated by using eq 15. In Table I are shown the reorganization energies for these complexes calculated by using both these methods. The reorganization energies calculated from the width of the distributions are uniformly higher than those taken from the peaks of the distributions. Thus the widths of the measured distributions are wider than would be predicted from the Marcus theory. At the present time we do not have a satisfactory explanation for the discrepancy in the widths and peak positions of these distributions. There are several possible explanations. For the highly charged cyano complexes, (Fe(CN)63-, W(CN)83-, and Mo(CN),~-), ion pairing of the anions with K+ is well establ i ~ h e d . ~At~ .the ~ ~electrolyte concentration used in this work, significant concentrations of the KM(CN)>- species should be present. The measured density of electronic states in these cases should be the sum of the density of states for the two electroactive species. Because the formal potential of the KM(CN):species is more positive than the unassociated anion, the density of electronic states distributions for the two species will be separated so that their sum should be wider than in the absence of ion pairing. Such an explanation for the other complexes is less tenable especially for the singly charged Fe(bpy)(CN)i complex which would not be expected to ion pair strongly with K+. Double-layer effects, while small for these insulated electrodes, can also have an effect on the calculated ?Do, distribution. For the reduction of anionic redox couples, the increasing Coulombic repulsion as the electrode potential becomes more negative would be expected to narrow the measured distribution. This is because the concentration of the redox active anion at the electrode surface would decrease as the potential of the electrode is scanned negatively resulting in a decrease in the number of electronic states. In contrast for the reduction of a positively charge redox couple, the density of states at the electrode surface would experience an augmentation as the electrode is polarized negatively, broadening the distribution function. We see some evidence for this douvs E plots in Figure 3. The plots ble-layer effect in the log of the anionic redox couples display somewhat more curvature than those for the cationic species. However, because we see equal broadening in the density of electronic states plots shown in Figure 7 for both anionic and cationic species, this double-layer broadening does not appear to be large enough to effect the ?Do, functions. Consistent with this observation, we have calculated the double-layer effect on the distribution function through the (33) Collenberg, 0.Z.Phys. Chcm. 1924, 109, 353.
5232 The Journal of Physical Chemistry, Vol. 95, No. 13, 199‘1 calculation of the potential at the OHP, &, described above. The magnitude of the double-layer effect is not sufficient to explain the broadening over the Marcus theory prediction seen in Figure 7. Finally, the increased width of the distribution may stem from an incorrect estimation of the electron tunneling barrier and particularly its potential dependence. Using Bennett’s analysis, we assume that the w-hydroxy thiol monolayer behaves as a symmetric square barrier. The height of this barrier decreases by half the overpotential applied to the electrode. To the extent that the true barrier at these monolayer derivatized electrodes may deviate from this simple assumption, deviations in the shape of the yoox distribution functions obtained by Bennett’s analysis may be expected. From Figure 8 one can see that the measurement of the barrier to electron transfer is essential to obtaining accurate reorganization energies and density of electronic states distributions. The barrier measurement consists in the measurement of the T ( q )factor used in eq IO. While the peak position of the distribution function and hence the reorganization energy depend importantly on the T ( q ) factor used, the width of the distribution also increases with increasing T(e7)so that the discrepancy between the peak of the distribution and its width remains nearly constant. So, small uncertainties in the barrier height will not explain the increased width in the distribution functions. A final important point about these yo,, distributions is that they have definite units (number of states/(eV s)). Because of the y factor which is generally not known, densities of electronic states of redox species in solution are often given in arbitrary or normalized ~nits.’Z’~ This practice obviates the need and possible benefit of making an assessment of the y factor. The number of unfilled electronic states in the solution corresponds to the number of oxidized redox centers participating in the electrontransfer reaction. If the electron-transfer kinetics are uniform over the entire surface of the electrode, the number of unfilled electronic states would correspond to the number of oxidized redox centers within a certain reaction layer thickness of the electrodeVM This reaction layer thickness is of the order of 1 A.35 In addition, one must take into consideration any specific adsorption or electrostatic preconcentration within this reaction volume. With these estimates in hand, one can compare the theoretical number of states, Nox,with the integral of the yoo,function and obtain an estimate of the y proportionality constant. The added uncertainty in the value of the y factor obtained will be dependent on the accuracy of the reaction layer thickness and double-layer correction which could be estimated to within a factor of 2 or 3 without difficulty. This added uncertainty in the y factor is likely to be less than the uncertainty in the measurement of the yoox distributions. In Table I are shown the integrals of the yoox distributions and the estimates of the y factor. For all six redox couples, the measured y factors are within an order of magnitude of each other. The average value of ca. 7 X 10” s-’ is within the range of literature estimates of transition metal complex nuclear frequency factors (1011-1013 s-’).~~Because there are no adjustable parameters in the calculation of these frequency factors, this agreement adds credibility to our analysis of the kinetic data from these hydroxy thiol derivatized Au electrodes. It would be tempting to compare more closely the frequency factors measured here with theoretical estimates calculated from the ligand and solvent vibrational frequencies involved in the activation of the electron-transfer reaction. The ratio of the measured frequency factor to the calculated value would give a measure of the transmission coefficient K and thus measure the adiabaticity of the electron-transfer reaction on the bare electrode. However, it is important to note that the frequency factors measured from the density of electronic states distributions are sensitive functions of the barrier parameters used in their calculations. An uncertainty in the electron tunneling barrier of 0.06 eV would cause (34) Hupp, J. T.; Weaver, M. J. J . Phys. Chem. 1984, 88, 1463. (35) Hupp, J. T.; Weaver, M. J. J . Eledroanal. Chem. 1983, 152, 1. (36) Sutin, N . Prog. Inorg. Chem. 1983, 30, 441.
Miller and Grgtzel an uncertainty in both the value of density of electronic states distribution and the nuclear frequency factor by a factor of 10. Thus the transmission coefficient for the electron transfer on the bare metal electrode, K , would have to be at least 0.01 before it would become noticeable in the frequency factors measured here. The uncertainties discussed above would cause a systematic error in the estimation of the y factor. Therefore, comparisons between y factors calculated by using different redox couples should be much more useful. That all the calculated y factors lie within an order of magnitude of each other is significant. Because the vibrational frequencies for these transition-metal complexes should be quite similar?’ one would anticipate that the y factors for all these complexes should be close to each other. Calculating the y factor assuming a constant barrier height, we observe that the y factors are indeed quite close to each other. Because a deviation of only 0.12 V in the barrier height would result in a change of the integral of the yo,, distribution by a factor of 10, it appears that the barrier height of the self-assembled hydroxy thiol monolayer is the same for each of these redox couples. This consistency in the barrier height may be a bit surprising given that the formal potentials of the couples span approximately 1 V. This same independence in the apparent barrier height with the potential of the redox couple was noted previou~ly.~~ If the barrier to electron tunneling corresponded to a specific redox state or “conduction”band of the hydroxy thiol monolayer, one would have predicted that the barrier height would have scaled with the formal potential of the solution redox couple. That the barrier height appears constant for each of the redox couples studied here suggests that the coupling between the electronic wave functions in the metal electrode and the redox molecules is better explained by a coupling through the hydrocarbon network rather than through a definite redox state of the hydroxy thiol monolayer. Indeed, the barrier height measured for these hydroxy thiol monolayers is in close agreement with other measurements of intramolecular electron transfer through rigid hydrocarbon spacer groups.3842 In these studies the rate of electron transfer from a donor to an acceptor was found to decay exponentiallywith the number of methylene groups in the spacer. The proportionality constant 0 was measured to be in the range 0.98-1.15 per methylene group. For the hydroxy thiol monolayers a j3 of ca. 0.9 was found.23 One of the attractive features about measuring redox kinetics by using electrodes blocked with electron tunneling barriers is that, once the tunneling barrier is characterized, the measured kinetic parameter should be independent of the blocking layer. The density of electronic states data for the reduction of ferricyanide obtained here can be directly compared with that obtained using SiOz insulated PtSi electrodes by Morisaki et aL13 In this work, the density of states was normalized so as to render it with indeterminate units. However, the magnitude of their yooxfunction can be estimated from the Tafel data given in this paper. The current densities at +0.045 and -0,455 V (vs Ag/AgCI, sat. KCI) (corresponding to 0 and 4 . 5 V vs SCE) were compared to those observed for the hydroxy thiol coated electrodes studied here. The difference in concentration of the ferricyanide used in these two works is small (0.12 M versus 0.10 M) and has been corrected in this comparison. The current density at the HO(CH2),6SH derivatized electrode is approximately 16 times smaller than for the oxidized Ptsi electrode at both electrode potentials. However, the barrier to electron transfer used by these authors (oxide thickness = 18 A, barrier height = 3.1 eV) is over 7 orders of magnitude higher than the one measured for the hydroxy thiol (37) Hupp, J. T.; Weaver, M. J. J . Phys. Chem. 1985.89, 2795. (38) Closs, G.L.; Calcaterra, L. T.; Green,N. J.; Penfield, K. W.; Miller, J. R.J . Phys. Chem. 1986, 90, 3673. (39) Beratan, D. N. J . Am. Chem. SOC.1986, 108, 4321. (40) Ocvering. H.; Paddon-Row, M. N.; Heppener, M.; Oliver, A. M.; Cotsaris, E.; Verhoeven, J. W.; Hush, N. S. J . Am. Chem. Soc. 1987, 109, 3258. (41) Paddon-Row, M. N.; Oliver, A. M.; Warman, J. M.; Smit, K. J.; de Haas, M. P.; Oevering, H.; Verhoeven, J. W. J . Phys. Chem. 1988,92,6958. (42) Van der Auweraer, M.; Verschuere, B.; Biesmans, G.;De Schryver, F. C.; Willig, F. Lungmuir 1987, 3, 992.
The Journal of Physical Chemistry, Vol. 95. No. 13, 1991 5233
w-Hydroxy Thiol Coated Electrodes monolayers used in this work. This discrepancy would have to be due the y factor varying by 108-109 between the two systems for both works to be mutually consistent. It is doubtful that the y factor in such closely related systems would be different by such a large factor. Another discrepancy between this work and the work presented here is in the measurement of the reorganization parameter and the width of the distribution function. Morisaki et al. report a reorganization energy of 0.6 eV compared to 0.37 for this work. Both these reorganization energies are within the wide range reported for the Fe(CN)63-/4-couple in the literature (0.31-0.83 eV)F7 In addition, the widths of distribution function in their work were consistent with the reorganization energy obtained from the peak of the distribution in spite of the ion pairing with K+ which was not considered. The most likely explanation for these discrepanciesis that there is an error in the measurement of the barrier height for the electron transfer in this work or that of Morisaki et al. An external check of the barrier height determination is possible. One can extrapolate the heterogeneous electron-transfer rate at a bare electrode by dividing the apparent rate constant by the tunneling factor T ( q ) given in eq 10. This requires one to extrapolate the linear region of the log (/cam) curves in Figure 3 to the formal potential of the redox couple. As mentioned earlier, the linear regions of these plots are subject to some uncertainty due to the low current levels, but for this discussion all we require is an order of magnitude assessment. In the case of the ferricyanide reduction at HO(CHJI6SH treated Au electrodes, this gives a value of 0.06 cm/s which is in remarkably good agreement with that reported under similar conditions at a Au electrode (0.03 cm/s).*' In contrast, the apparent electron-transfer rate constant obtained by using the data of Morisaki et al. yields a value of ca. 106 cm/s. A similar check of the barrier height of the hydroxy thiol monolayer was made by extrapolating the linear region of the Tafel plots shown in Figure 3 to the formal potentials of the Ru(NH,)t+, Fe(bpy)J+, Mo(CN)*~-,and F e ( b ~ y ) ( c N ) ~complexes. The extrapolated rate constants divided by the T(e7) for each of these couples is within the range (2-0.3 cm/s) and are in good agreement with those reported in the literature measured at bare electrodes (1-0.4 C ~ / S ) ' ~ ~ In the work of Morisaki et al.,', the insulator barrier was measured by a photoemission experiment in which the photocurrent was analyzed as a function of the energy of the incident photons. Due to the limited sensitivity in the measurement of the quantum yield of the photoinduced electron transfer, this determination of the barrier height will be only an upper bound to the electrochemically relevant barrier. In the photoemission exper~
(43) Saji, T.; Yamada. T.; Aoyagui, S. J . Electroanal. Chem. 1975, 61, 147. (44)Saji, T.; Maruyama, Y.; Aoyagui, S.J. Electrwnal. Chem. 1978,86, 219.
(45) Endicott, J. F.; Schroedcr, R. R.; Chidcstcr, D. H.;Fcrrier, D. R. J . Phys. Chem. 1973, 77, 2579.
iment, electron transfer across the oxide insulator must compete with electron-hole recombination in the F't silicide. Therefore, a large number of states in the conduction band of the insulator are required to obtain a measurable current. For electron transfers in the dark, there is no such competition so fewer electronic states in the insulator are required to define the effective barrier height. For amorphous oxide insulators,the conduction bands are expected to be diffuse with many states within the band gap.46 The effective tunneling barrier height, therefore, may be different between the photoemission and dark current measurements. The measurement of the electrode kinetics dependence on the thickness of the insulator therefore seems a more accurate method for determining the electrochemically relevant barrier. Unfortunately, this alternate measurement of the tunneling barrier may be difficult, or impossible for the oxide coated films because of the difficulty in controlling and measuring their thicknesses. Except for the assignment of the tunneling barrier, these works are in quite good agreement. The i / u curves for the reduction of ferricyanidedisplay the same important curvature with overpotential, and the derived densities of electronic states from Bennett's method are reasonably well described by a Gaussian distribution.
Conclusions Important contributions to the study of electron-transferkinetics can be made via the measurement of redox kinetics at these hydroxy thiol coated electrodes. This is because kinetic measurements can be made over a wide range of electrode overpotentials even for very facile redox couples. The low current densities observed at these blocked electrodes eliminate masstransfer effects and lower the problem of uncompensated resistance. Indeed, blocked electrodes may find use in the same highly resistive solutions which are currently the sole domain of the ~ltramicroeIectrode.4~In addition to the low current densities, the doublelayer corrections required at the blocked interfaces are much smaller and more quantitatively applied than with "bare" electrodes. The one difficulty in analyzing the kinetic data obtained at blocked electrodes is that one must measure and understand the characteristics of the blocking barrier. This requirement has until recently limited the applicability of the approach. With the continued development of both organic monolayer barriers such as the ones studied here and thin inorganic films, one can expect much more definitive measurements of electron-transferparameters such as the density of electronic states and ever more stringent tests of current electron-transfer theories. Acknowledgment. We thank Dr.Guido Rothenberger (Ecole Polytechnique FEdCrale, Lausanne) for discussions concerning the calculation of the density of electronic states. This research was funded by a grant from the Swiss National Science Foundation (Programme Nationale 24). (46) Newmark, A. R.; Stimming, U. J. E/ectmna/. Chem. 1986,201,197. (47) Wightman, M. AMI. Chem. 1981, 53, 1125A.
