J. Phys. Chem. 1995, 99, 11216-11224
11216
cu-Hydroxythiol Monolayers at Au Electrodes. 5. Insulated Electrode Voltammetric Studies of Cyano/Bipyridyl Iron Complexest Samuel Terrettaz, Anne M. Becka, Michael J. Traub, James C. Fettinger, and Cary J. Miller" Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742 Received: April 17, 1 9 9 p
Au electrodes coated with self-assembled H O ( C H ~ ) I ~ Smonolayers H are used to measure the heterogeneous electron transfer reactivity of a series of structurally related outer-sphere redox complexes. These insulated monolayers act as electron transfer tunneling barriers, decreasing the electronic coupling between the electrode and solution redox molecules and allowing the measurement of electron transfer rates at a wide range of electrode potentials with greatly diminished diffusion limitations and double-layer effects. From electron transfer rate constant versus electrode potential data obtained from simple linear sweep voltammetric experiments, the reorganization energies and inherent adiabaticities of the complexes are determined. As cyano ligands are replaced by bipyridyls in the series Fe(CN)63-, Fe(bpy)(CN)4'-, Fe(bpy)Z(CNz)'+, Fe( b ~ y ) ~the ~ + reorganization , energy decreases monotonically. The measured reorganization energies are in good agreement with Marcus theory estimates. There is an abrupt order of magnitude decrease in the inherent adiabaticity of the complex between the cyano-containing complexes and F e ( b ~ y ) 3 ~ +The . bipyridyl ligand limits the closest approach of the complex when compared to the smaller cyano ligands, decreasing the electronic coupling between the Fe and the electrode surface. These electron transfer characterizations are extended to complexes containing bipyridyl ligands modified by methyl and sulfonate groups and to tris(bipyridyl) complexes of Ru and Os.
Introduction The determination of electron transfer kinetic parameters of simple outer-sphere redox molecules via electrochemical techniques has been a very active and challenging area of research for decades.' The difficulty in characterizing these redox molecules stems from two sources. First, the electron transfer rates can be extremely high, making determination of their electron transfer rates impossible. Most commonly the voltammetric response of these facile electron transfer molecules is determined solely by mass transport processes. The second difficulty stems from the heterogeneous nature of the electrode reaction. The concentration, orientation, and even structure of the redox molecule can be greatly distorted when compared with the bulk solution species due to the double layer at the electrode surface.* Some redox molecules can be preconcentrated at the electrode surface, giving larger apparent electron transfer rates, while others are repelled from the interface, resulting in slower observed electrode kinetics. These double-layer effects can mask the intrinsic reactivity of the redox molecule at a particular electrode. The correction of electrode data for these doublelayer effects is often a difficult and imprecise task.3 The measurement of kinetic properties of redox molecules at electrodes coated with thin insulating films retains much of the information available at bare electrodes4 with greatly diminished diffusion limitations and double-layer effects5 The insulating film decreases the electron transfer rate by increasing the separation between the electrode surface and redox molecules.6 With this increasing separation, the electronic coupling between the electrode surface and the redox molecules decreases rapidly, usually exponentially, allowing one to arbitrarily decrease the absolute rate of the electron transfer. Forming compact low defect density insulating films is the crucial
' This paper is dedicated to the memory of Professor Heinz Genscher.
* To whom correspondence should be addressed. @Abstractpublished in Advance ACS Abstracts, June 15, 1995.
impediment toward implementing this insulated electrode voltammetric method. We have been developing self-assembled o-hydroxyalkylthiol films as monolayer insulators for insulated electrode voltammetric studies.' These w-hydroxythiol monolayers behave as nearly ideal electron-tunnelingbarriers whose insulating properties can be varied simply by controlling the number of methylene units within the thiol molecule.8 By increasing the number of methylene units within the o-hydroxythiol monolayer from 2 to 22, the electronic coupling between the electrode and redox molecules can be decreased by over 9 orders of magnitude. Heterogeneous electron transfer reactions of particularly facile redox molecules which would be too fast to measure at any potential at bare electrodes due to diffusion limitations can be slowed so that they are easily measured at any potential within the voltammetric window of the monolayercoated electrode. The electron transfer rate versus electrode potential data can then be analyzed and compared with current electron transfer theories to obtain kinetic parameters describing the intrinsic electron transfer reactivity of the redox molecule. In this paper we investigate a series of iron-centered complexes with cyano and bipyridyl ligands with the intent of deducing quantitative structurelredox reactivity relationships for this ~ y s t e m .As ~ the cyano ligands are replaced by bipyridyl ligands within the complex, one can monitor how both the activation and adiabaticity of the complex changes. For the extremely facile tris(bipyridy1) complexes, the role of the central metal center is probed for the Fe, Ru, and Os series. More generally, this work is meant to demonstrate the capabilities of this insulated electrode voltammetry method.
Experimental Section 14-Hydroxy-1-tetradecanethiolwas synthesized from 1,14tetradecanediol as described previously.8 The 5-sulfonato-2,2'bipyridine (Sbpy) was prepared using the method of Herrman et al.Io The mixed cyanol2,2'-bipyridyl iron complexes were prepared using the method of Schilt." In the synthesis of the
0022-365419512099-11216$09.00/0 0 1995 American Chemical Society
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J. Phys. Chem., Vol. 99, No. 28, 1995 11217
Cyano/Bipyridyl Iron Complexes Fe(Sb~y)2(CN)2~complex, two isomers were produced which were isolated using column chromatography (C18 silica: H20). Tris(2,2'-bipyridyl)iron(III) perchlorate was synthesized using the method of Brustall and Nyholm.12 Tris(2,2'-bipyridyl)osmium(I1) perchlorate was synthesized by the reductive ligand substitution of &OS(C1)6 (Strem Chemicals) with 2,2'-bipyridine, as described by Dwyer.l3 All other chemicals were purchased from Aldrich and used as received. Au electrodes were fabricated by radio frequency sputtering ca. 3000 8, from a 99.99% Au target onto microscope slides through a special mask. A ca. 500 8, chromium layer was sputtered first to promote adhesion of the gold films. The Au electrodes were cleaned through successive exposures to chromic acid and aqueous HF, rinsed with water, and immediately placed into ethanolic thiol solutions, as described previously.8 The Au electrodes were kept overnight in the ca. 30 mM solution of the 14-hydroxy-1-tetradecanethiol solution prior to their use in the electrochemical studies. The geometrical area of the electrodes was 0.13 cm2. The capacitance of the monolayercoated Au electrodes in 0.25 M CF3COONa was 1.60 f 0.09 pF/cm2. The potential of zero charge of the monolayer-coated electrodes was determined via capacitance measurements in dilute electrolyte to be -0.014 f 0.066 V vs SCE.5 Electrochemical experiments were performed in a conventional three-electrode cell using a BAS lOOA electrochemical analyzer. Some of the redox compounds prepared in the reduced form were oxidized in situ by the addition of ammonium cerium(IV) nitrate. As long as the concentration of Ce(IV) added was less than that of the redox molecule, the electrochemical responses observed were identical to those measured in solutions prepared using the oxidized form of the redox molecule. All kinetic measurements were made in aqueous solutions containing 0.25 M CF3COONa and 0.5-5 mM of the redox molecule. Within this range of redox molecule concentrations, the kinetic parameters were found to be independent of the concentration of the redox molecules. The pH of the CF3COONa electrolyte was measured to be 10.9. All electrochemical solutions were purged with N2 and kept under a blanket of N2 during the electrochemical experiments. The temperature of the electrolyte was maintained at 25.0 "C using a constant-temperature circulator connected to the jacketed electrochemical cell. All potentials were measured and are reported versus a saturated calomel electrode. The single-crystal X-ray structures of Fe(bpy)2(CN)2*(C2HsOH)*(H20)and [Fe(bpy)2(CN)2]*[N03]were determined using an Enraf-Nonius CAD-4 diffractometer. Both complexes display an octahedral coordination environment about the unique Fe atom with two bipyridyls and two cyano groups; the cyano group being cis to one another. Details of the crystal structure determinations and results are collected in the supporting information.
Results and Discussion Theoretical Considerations. The implementation of this insulated electrode approach for the characterization of redox molecules requires one to appreciate several differences between the rate data obtained at bare electrodes and those coated with a molecularly thin blocking layer. The presence of the insulating film on the electrode does more than just lower the absolute heterogeneous electron transfer rate. It changes fundamentally the mechanism of electron transfer by radically decreasing the adiabatic it^.^^,'^ For a redox reaction occurring at an electrode polarized at the formal potential of a redox-active molecule, the electron transfer is an activated process requiring the thermal activation of the redox molecules at closest approach to the
r-States -
I I I I
I I
I I I I I I
f i v e r lap (magnified)
States Metal
Monolayer
Solution (reaction layer)
Figure 1. Density of electronic states distribution diagram for a m-hydroxyalkylthiol-coatedAu electrode in contact with a solution containing only the oxidized form of a redox-active molecule. The filled electronic states are shaded.
surface of the electrode. Once a redox molecule achieves this activated or transition state geometry (involving both the atoms of the redox molecule and the surrounding solvent), electron transfer is often assumed to occur adiabatically at a bare electrode, meaning that the probability of electron transfer is unity. The rate of the electron transfer at the bare electrode is then a function of this activation energy and the dynamics of the activation process.15 At the insulated electrode, the same activation of the redox molecule is required, but once the redox molecule achieves the transition state, the probability of electron transfer is extremely small. The rate of electron transfer does not depend on the rate of arrival of the redox molecule to the transition state but rather the fraction of time it remains in the activated state. Because the redox center traverses this activated state many times on average before undergoing electron transfer, dynamic effects involving the motion within the redox molecule or of the solvent are averaged away.16 In this case, the electron transfer rate depends on the long-range electronic coupling between the electronic states within the metal electrode and the redox species. The electron transfer rate at an insulated electrode is most conveniently described using a density of electronics state a p p r o a ~ h . ' ~ ?Figure '~ 1 shows a density of electronic states diagram for an insulated electrode held at the formal potential of a redox couple in contact with a solution containing only the oxidized form of that redox couple. At the surface of the metallic electrode, there is a continuum of electronic states which is filled to the Fermi level as described by the Fermi distribution f~ncti0n.I~ The highest occupied molecular orbitals (HOMOS) and lowest unoccupied molecular orbitals (LUMOs) within the cu-hydroxythiol monolayer insulators are respectively well positive and negative of accessible electrode potentials. These monolayer electronic states mediate the long-range electron tunneling through the monolayer but are not themselves oxidized or reduced during the electron transfer event.20 The electronic states at the monolayer/solution interface correspond to individual redox molecules. The thermal activation of these redox
Terrettaz et al.
11218 J. Phys. Chem., Vol. 99, No. 28, 1995 molecules at the electrode surface causes their instantaneous redox potentials to fluctuate about the potential corresponding to their most stable internal and solvent structure. When viewed at a particular instant in time, the distribution in the instantaneous energy levels of the acceptor orbitals of these redox molecules spans a considerable range, as depicted in Figure 1. In order for electron transfer to occur, the energy levels of the donor states within the metal and the acceptor levels within the solution must be in resonance. The rate of electron transfer is therefore proportional to the overlap between the filled states in the metal and the unfilled states in the solution. Because the filled Au electronic states are nearly rectangular in shape, the heterogeneous electron transfer rate is well approximated as being proportional to the integral of the density of electronic states distribution of the solution species integrated from the bottom of the valence band to the Fermi level.8 Turning this expression around, the potential derivative of the heterogeneous electron transfer rate constant is proportional to the density of electronic states distribution of the redox species in the solution. From these density of electronic states distributions, one can extract reorganization energies and electronic coupling factors which characterize the electron transfer reactivity of the redox molecules. In order to extract kinetic information which is intrinsic to the redox molecule under study, the voltammetric data must be corrected for both double-layer effects and mass transfer. A significant amount of work has been expended developing electrostatic models for the double layer at monolayer-coated electrodes.21 We have shown that double-layer effects for the w-hydroxythiol monolayer coated electrodes are much smaller than are observed at bare Au electrode^.^ In addition, the double layer at these monolayer-coated electrodes follows closely the predictions of the Gouy-Chapman-Stem theory. The hydroxylated monolayer surfaces do not have a strong affinity for hydrophilic or hydrophobic species, so that the double-layer structure is dominated by electrostatic interactions. These electrostatic interactions can be quantitated given the potential difference between the plane of closest approach of the redox species and the bulk electrolyte solution, the diffuse layer potential, 42. For these w-hydroxythiol monolayer coated Au electrodes at electrolyte concentrations typically used for voltammetric investigations, 42 is well approximated by a linear function given by
where Vappis the applied potential versus some reference, V,, is the potential of zero charge measured at the same reference, C, is the monolayer capacitance in pF/cm2, T is the absolute temperature in Kelvin, z is the charge of the z:z electrolyte, and c is its concentration in The potential of zero charge can be easily determined from electrode capacitance measurements made at low electrolyte concentrations or from kinetic data measured at different ionic strengths. This quantitative knowledge of the double-layer structure of the o-hydroxythiol monolayer coated electrodes allows one to correct voltammetric data for the double-layer effect. After corrections are made for diffusion limitations using convolution the electrode currents are scaled using eq 2 below:
where icon is the corrected current at a particular potential, iobs is the measured current at the same potential after diffusion
~10-3
6
5-
4-
4 1
0 -1
1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Potential I V
Figure 2. Voltammogramsfor the bipyridylkyano iron complex series measured at HO(CH2)dH-coated Au electrodes. The measured voltammograms were normalized to unit electrode area ( 1 cm2) and unit concentration (l/nF mol/cm3 or 10.36 mM). The voltammetric currents were obtained at 5.12 V/s in an aqueous solution containing 0.25 M CF3COONa.
corrections, z is the charge of the redox molecule, and kT is the product of the Boltzmann constant and the absolute temperature expressed in eV. It is this corrected current which is normalized for the area of the electrode (1 cm2) and concentration of the redox species (10.36 mM or l/nF mol/cm3, where n is the number of electrons transferred and F is Faraday's constant) to obtain the heterogeneous electron transfer rate constant versus the formal potential of the redox couple, which is used to characterize the electron transfer reactivity of the redox molecule. Cyano/Bipyridyl Complexes of Fe(II1). The Fe(II1) cyano/ bipyridyl series of redox molecules serves as a model system for our more general interest in quantitative insulated electrode studies of the structure/reactivity of redox molecules. As cyano ligands are sequentially replaced by bipyridyl ligands, the reduction kinetics of these iron complexes increase dramatially.'^ For the later complexes in this series, Fe(bpy)2(CN)2'+ and Fe(b~y)3~+, the heterogeneous electron transfer rates increase to a level at which they become difficult to measure at bare electrodes. In comparison, obtaining kinetic data at w-hydroxyhol-insulated electrodes is not only extremely simple but sheds new light on the reactivity of these complexes. Figure 2 shows a series of voltammograms for the cyano/ bipyridyl series obtained at electrodes coated with self-assembled HO(CH2)14SH monolayers. In this series the experimental conditions for each voltammogram were identical, facilitating comparisons between the curves. Correcting the raw data shown in Figure 2 for capacitive background currents, diffusion limitations, and the influences of the electrode double layer yields the plots of heterogeneous rate constants versus electrode potential shown in Figure 3. The potential derivative of the rate constant is proportional to the density of electronic states distribution of the redox molecule and is shown in Figure 4. This density of electronic states distribution corresponds to the distribution of redox molecules within the reaction layer at the electrode surface whose level of thermal activation results in their being reducible (or oxidizable) at a particular potential. The density of electronic states distributions shown in Figure 4 are predicted by the Marcus theory to be Gaussian in shape.25 The solid curves shown in Figure 4 plot the best fit Gaussian to the density of electronic states data. From these density of electronic state distributions, one can determine two parameters which characterize each of these redox
. I Phys. . Chem., Vol. 99, No. 28, 1995
CyanoBipyridyl Iron Complexes I
0.018,
3 0.014
.
x FC(~~Y)(CN)~~.
0.012
+
Fc(bpy)z(CN)zl+
I
:0.01 a 4 0.008
22 0.006
3g
0.004 0.002 0 -1
-0.8
-0.6
6.4
-0.2
0
0.2
0.4
0.6
0.8
Potential I V
Figure 3. Electron transfer rate constants for the bipyridykyano iron
complex series derived from the data shown in Figure 2. The data were corrected for diffusion limitations and the double-layer effect as described in the text.
p.
0.03
:
0.02
0.01
0 -1
TABLE 1: Kinetic Parameters Eo'b
0.016
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Potential I V
Figure 4. Density of electronic states distributions for the bipyridyU
cyano iron complex series. These distributions were obtained as the potential derivative of the rate constant data shown in Figure 3. The length bars mark the potential difference between the peaks of the electronic states distributionsof the redox molecules and their respective formal potentials. The length of each bar is therefore a measure of the reorganization energy for each complex. molecules. The reorganization energy, I , is measured from the peak of these distributions to the formal potential of the redox molecule, as indicated within Figure 4. At the reorganization voltage, electrons at the Fermi level are in resonance with the redox molecules which are in their most stable internal and solvent geometry. Any electron transfer reaction which occurs either positive or negative of this reorganization voltage requires the redox molecule to be activated relative to this most stable configuration. Knowledge of the reorganization energy for a redox molecule allows one to calculate its electron transfer free energy of activation at any electrode potential. The second parameter which one can extract from the kinetic data shown in Figures 3 and 4 is the k,, parameter. This is the maximum heterogeneous electron transfer rate constant which is measurable at a particular electrode at large overpotentials. k,,, is essentially the pre-exponential or frequency factor term in the transition state model for the electron transfer. When the Fermi level in the metal is raised well above the reorganization energy in Figure 1, the entire density of electronic states distribution is in resonance with filled electronic states in the metal electrode. The extents of activation of the redox molecules at the electrode surface become unimportant to their
11219
/Id
km,'
complexe (mV) nc (eV) (CdS) [Fe(CN)d3184 7 1.13 f 0.02 (1.1 i 0.3) x [Fe@py)(CN)41'316 7 0.98 f 0.04 (2.9 & 1.2) x 531 6 0.79 f 0.02 (2.2 f 0.5) x lo-* [Fe(bpy)~(cN)21~+ 803 3 0.56 i 0.01 (2.4 f 0.3) x [Fe(bpyhI3+ [Fe(dMbpy)(CN)4]'267 6 0.95 & 0.06 (3.1 f 0.4) x [Fe(dMbpy)2(CN)211+ 432 6 0.70 f 0.08 (7.0 f 3.4) x [Fe(dMbpy)313+ 640 5 0.50 f 0.02 (1.8 f 0.4) x [Fe(Sbpy)(CN)d2367 6 1.04 i 0.01 (2.6 i 0.6) x [Fe(Sbpy)2(CN)2I1-/Flf 640 4 0.82 f 0.01 (2.0 f 0.3) x [Fe(Sbpy)2(CN)2I1-/F2f 640 10 0.83 f 0.03 (1.1 f 0.5) x low2 [Ru(~PY)~I~+ 1033 5 0.56 f 0.02 (2.7 f 1.1) x [0S(bPY)3l3+ 598 8 0.56 i 0.01 (3.2 i 1.0) x a bpy = 2,2'-bipyridine, dMbpy = 4,4'-dimethyl-2,2'-bipyridine, Sbpy = 5-sulfonato-2,2'-bipyridine. Formal potentials of the redox couple measured at 25 "C in 0.25 M CF3COONa (versus SCE). Number of independent measurements used to calculate the kinetic parameters. Reorganization energy. e Maximum heterogeneous electron transfer rate constant at a gold electrode coated with a HO(CH2)14SH monolayer. f The two stereoisomers of this complex are labeled according to their order of elution in the reverse-phase separation. electron transfer reactivity. Further increases in the electrode overpotential do not increase either the number of reactive redox molecules or their electron transfer rate. The invariability of the electron transfer rate on the electrode potential at high overpotentials is the heterogeneous electron transfer equivalent For bare electrodes, of being in the Marcus inverted the k,,, value is anticipated to be in the range lo3 to lo5 cm/s, which is several orders of magnitude larger than is currently measurable.26 In contrast, the insulated electrodes used in this study dramatically slow the overall rate of the electron transfer, allowing a direct measurement of this k,, parameter. For these insulated electrodes, this kmaxgives a measure of the electrontunneling rate and therefore measures the electronic coupling between the electrode and redox molecule through the insulating monolayer. The k,,, values can be obtained either from the extrapolation of the corrected heterogeneous electron transfer rate constants at high overpotentials shown in Figure 3 or as the area under the density of electronic states distributions shown in Figure 4. The main goal of this research is to quantitatively study how the structure of a redox molecule affects its electron transfer kinetics. Using the insulated electrode voltammetric approach, this goal is synonymous with comparing the reorganization energies and k,,, values as a function of the structure of the redox molecule. Table 1 compiles the kinetic results measured at Au electrodes coated with HO(CH2)14SH monolayers. Focusing first on the Fe(II1) hexacyano to tris(bipyridy1) series, there is a monotonic decrease in the reorganization energy with each bipyridyl substitution. This decrease in the activation energy with increasing bipyridyl substitution accounts for most of the increased kinetic facility within this series2' The qualitative increase in the kinetic facility with increasing bipyridyl substitution is not surprising and has been recognized for a long time.28 The insulated electrode studies performed here allow one to more accurately measure these reorganization energies so that closer comparisons can be made between theoretical expectation and the experimental values. Such a comparison is shown in Table 2. The reorganization energy within the Marcus theory framework is separated into innerand outer-shell component^.^^ The inner-shell reorganization energy measures the energy required to change the most stable internal structure of the product to the reactant's most stable internal structure. The outer-shell reorganization energy measures the energy needed to change the solvent structure around
Terrettaz et al.
11220 J. Phys. Chem., Vol. 99, No. 28, 1995
TABLE 2: Comparison of Calculated and Experimental Values of the Reorganization Energy radius Lout Icalcc lex: complex
(A)
(ev)
(ev)
(ev)
(eV)
[Fe(CN)613[Fe(bpy)(CN)p]'[Fe(bpy)2(CN)2]]+ [Fe(bpyId3+
4.24 5.33 6.77 7.21
0.06
0.89 0.75 0.59 0.55
0.95 0.80 0.63 0.57
1.13 f 0.02 0.98 f 0.04 0.79 & 0.02 0.56 f 0.01
0.05 0.04 0.02
a Inner-shell reorganization energy (for details see Table 4). Outershell reorganization energy. Calculated total reorganization energy (,Icaic= I,, Lout). Experimentally determined reorganization energy from Table 1.
+
A
TABLE 3: Selected Bond Lengths from the Crystal Structure of [Fe(bpy)z(CN)zl[N031 and
[F~(~PY)z(CN)ZI[CZHSOHI[HZOI
Clll-N11 1 C112-N112 C5-C6 C15-Cl6 c4-c5 C14-Cl5
1.132(6) 1.13l(6) 1.466(6) 1.457(6) 1.379(6) 1.373(6)
1.139(11) 1.152(12) 1.481(13) 1.473(14) 1.384(13) 1.39(2)
a Bonds with significant length changes between the two oxidation states of Fe(bpy)z(CN)? (see text). Values in parentheses are the estimated standard deviations.
TABLE 4: Fe(bpy)z(CN)zParameters Used for the Inner-Shell Reorganization Energy Calculation bond" C111-N111 C112-N112 C5-C6 C15-Cl6 c4-c5 C14-Cl5
02
c4334! B
Figure 5. ORTEP drawings of Fe(bpy)2(CN)?(N03)(A) and Fe(bpyj2(B) derived from single-crystal X-ray deter(CN)~(H~O)(CH~CHZOH) minations. The hydrogen atoms were not determined but were placed at their theoretical locations in part B.
the product from its most stable state to the most stable state of the reactant.30 In order to estimate the inner-shell component of the reorganization energy, it is necessary to know the equilibrium bond distances and angles for both the oxidized and reduced forms of the redox molecule along with the force constants for each displacement. We have determined single-crystal X-ray structures for both the oxidized and reduced Fe(bpy)z(CN)~ complex in order to assess the inner-shell reorganization energy component within this cyano/bpy iron series. The structure of Fe(CN),(bpy)2C104 reported previously by Lu et al. is nearly identical to the Fe(CN)z(bpy)~NO3determined heres3' Figure 5 shows ORTEP drawings of the two structures while Table 3 gives the bond lengths which change significantly between the
force constantb (N m-I)
Alc (A)
1648
0.014
2.0 x
693
0.015
9.7 x
693
0.011
5.2 x 10-3
energyd (eV)
Bonds with significant length changes between the two oxidation states of Fe(bpy)z(CN)Z. Force constants calculated from the reduced mass and the stretching frequency, Y, of each bond. Y = 2080 cm-I (ref 33) and 1400 cm-' (estimated) for the cyano and the carboncarbon bonds within the bipyridyl ligands, respectively. Differences between the average bond lengths of the oxidized and the reduced forms of Fe(bpy)Z(CN)z. Reorganization energy component of each bond type using the harmonic oscillator approximation.
oxidized and reduced complex. Other structural information can be found in the supporting information. The changes in the Fe-C and C E N bonds are in reasonable agreement with those determined from literature X-ray structures of the Fe(CN)63and Fe(CN)64- complexes.32 There are minimal changes in the bond angles between the oxidized and reduced forms of these redox molecules, so only stretches were used to estimate the inner-shell reorganization component. The force constants for each bond also shown in Table 3 were obtained from literature infrared and Raman band assignments using eq 3.33
where klz is the force constant in newtons per meter between atoms 1 and 2, Y is the frequency of the vibration in inverse centimeters, c is the speed of light in centimeters per second, and ml and m2 are the masses of atoms 1 and 2 in kilograms, respectively. The reorganization energy for each bond within the complexes was calculated using eq 4, summing up only those bonds whose changes were larger than the bond length uncertainty in the X-ray structure.
1
E , , = 6.24 x 10 -kI2Al2 18G
(4)
where El2 is the reorganization energy for the bond between atoms 1 and 2 in electronvolts, 6.24 x 10l8is the conversion factor from joules to electronvolts, and A1 is the change in bond length in meters. A major component of the inner-shell reorganization energies for these complexes is the shortening of the C E N bonds upon oxidation of the Fe(I1) center. As the number of cyano groups decreases in this redox series, the innershell reorganization energy decreases monotonically. There are several caveats about the inner-shell reorganization energy estimates shown in Table 2. First, the bond length
Cyano/Bipyridyl Iron Complexes changes are very near the precision of the single-crystal X-ray measurements. Uncertainties in the bond lengths of 0.01 8, are typical and result in a significant uncertainty in the inner-shell reorganization energy estimate. In choosing which bonds change significantly upon oxidation or reduction, we have compared the bond length variability for several symmetryrelated bonds within the complex. For example, the bond length variability of the bridging C-C bond connecting the pyridyl groups of the two bipyridyl ligands (C5-C6 and C15-Cl6 in Table 3) for the oxidized complex is 0.009 8, while that for the reduced form is 0.008 A. This can be compared to the bond length changes for these bonds between the oxidized and reduced forms A(C5-C6) = 0.015 8, and A(C15-CI6) = 0.016 A. Because the average of the bond length changes upon oxidation is larger than the average differences within the complex, this bond was identified as changing significantly with the oxidation state of the molecule. Second, using the bond length changes for the bipyridyl ligands for the bis(bipyridy1) complex may overestimate the inner-shell reorganization energy for the tris(bipyridy1) complex. This is because the bonding asymmetry introduced by the cyano ligands may cause the bipyridyl bond length changes observed for the bis-complex. However significant changes in the bond lengths of the bipyridyl ligands between different oxidation states have been reported for the tris(bipyridy1) complexes of cobalt and ruthenium.34The main effect is the shortening of the bridge between the two pyridyl moieties of the ligand upon oxidation. This feature is retained in our structure determination of the bis(bipyridy1) Fe complex. We prefer calculating the inner-shell reorganization energy for the tris(bipyridy1) complex using the bis(bipyridy1) complex structures rather than arbitrarily assigning it to zero. The small value for the inner-shell reorganization energy of the tris(bipyridy1) complex demonstrates further that it is the cyano ligand bond changes which dominate the inner-shell reorganization energy of these complexes. The outer-shell or solvent component of the reorganization energy can be calculated using the Marcus theory equation, neglecting the affect of the metal image ~ h a r g e . ~ ~ ~ ~ ~
where Aos is the outer-shell reorganization energy per molecule (in electronvolts), n is the number of electrons transferred (usually l), e is the charge of an electron (in coulombs), E,, is C V-' cm-I), r is the permittivity of a vacuum (8.85 x the effective radius of the reduced complex (in centimeters) and copand cs are the optical and static dielectric constants for the solvent. The effective radii for these nonspherical complexes were determined as the average distance to the first layer of water determined using a 3-D molecular modeling program. In this determination, the density of water around the complexes was held at the bulk density of water. The calculated reorganization energy is the sum of these inner- and outer-shell components and is in reasonable agreement with the measured reorganization energies shown in Table 2. The experimentally determined trend of lower reorganization energies with increasing numbers of bipyridyl ligands is very well reflected in the calculated values. The calculated reorganization energies for the hexacyano and tetracyano complexes are a bit lower than the measured quantities, suggesting an underestimation of the cyano bond length changes upon oxidation, causing a lower inner-shell reorganization energy component or a slight overestimation of the effective radii of these complexes.
J. Phys. Chem., Vol. 99, No. 28, 1995 11221 Perhaps the most interesting kinetic parameter that we can derive from these insulated electrode studies is the k,,, value. The kmm gives a measure of the probability of electron tunneling between the electrode and the redox molecule through the insulating monolayer. Simplistically, one can separate the coupling into three multiplicative terms, the coupling between the Au electronic states and the thiol monolayer, the coupling through the alkyl monolayer, and the electronic coupling from the hydroxylated monolayer to the redox molecule at closest approach. In all the kinetic data displayed in Table 1, the first two components should be identical. Comparing the k,, values between different redox molecules measured at the same w-hydroxythiol monolayer coated electrode should allow one to assess differences in the third component, which is related to the inherent adiabaticity of the redox molecules. In other words, the km, value monitors how strongly a particular redox molecule is coupled to its reaction partner. This inherent adiabaticity is normally an exceedingly hard parameter to Inspection of the k,,, values for the Fe(II1) cyanohipyridyl series listed in Table 1 shows several interesting trends. There is a conspicuous order of magnitude decrease in the kmax value between the Fe(bpy)~(CN)z'+and Fe(bpy)s3+ complexes. The tris(bipyridy1) complex couples to the monolayer less efficiently than any of the cyano-containing complexes. Due to their small size, the cyano ligands allow closer approach of the Fe complex to the monolayer-coated electrode than does the bipyridyl ligand. Each cyano ligand can be viewed as the preferred site for electron transfer. As the number of cyano reactive sites increases from two to four to six, one would then anticipate that the kmax value would increase roughly by 2 or 3 times due to the increasing number of "active sites" on the complex. In fact, while we do see a slightly higher km,x value for the tetracyano complex than for the dicyano complex, the k,, value for ferricyanide is significantly lower than those for the other two complexes. We interpret this as being due to the high charge on the Fe(CN)63- anion.38 In order to come to the cloest approach to the hydroxylated surface, this complex must partially desolvate. For highly charged ions, this desolvation requires many times the thermal energy available and so is not a dominant reduction pathway for this complex.39 The electron transfer in this case proceeds through a partial aqueous solvent shell which lowers the long-range electronic coupling with the electrode. In support of this conclusion, we have reported previously that methyl-terminated monolayer insulator coated electrodes give k,, values for Fe(CN)63- that are over 100 times lower than are measured at electrodes coated with the same length w-hydroxyhol mon~layer.~ The energy required to bring a Fe(CN)63- complex into contact with a hydrophobic methylterminated monolayer will be considerably higher than for the hydroxylated monolayer used in this study. The kinetic parameters collected in Table 1 were obtained from reduction currents and are hence descriptive of the oxidized forms of these molecules. Our focus on the reduction reactions stems from an experimental bias rather than any fundamental limitation of this insulated electrode method. The voltammetric window of these monolayer-coated electrodes is roughly between f 0 . 8 V vs SCE. This means that, for F e ( b ~ y ) 3 ~and + Fe(bpy)z(CN)2'+ complexes which have relatively positive redox potentials, we cannot measure the oxidation rates at a wide enough range of voltages to merit the analysis presented above for the reductions. For the less positive numbers of this series, we can probe independently the kinetic properties of the oxidized and reduced forms of the redox molecules. Table 5 displays reorganization energies and kmaxvalues for both the oxidized
11222 J. Phys. Chem., Vol. 99, No. 28, 1995
Terrettaz et al.
TABLE 5: Comparison of the Kinetic Parameters between Oxidized and Reduced Form@ oxidized form.
reduced formb
complex 1 (ev) kmu ( c ~ s ) 1 (eV) kmu ( c ~ s ) [Fe(CN)6]3-’41.13 f 0.02 (1.1 f 0.3) x 0.89 i 0.07 (1.8 f 0.6) x lov3 (2.9 f 1.2) x 0.96 f 0.08 (3.0 f 1.8) x [Fe(bpy)(CN)4I1-’*0.98 f 0.04 Symbols are the same as in Table 1. The presented data are the average and standard deviations of eight and seven independent measurements for Fe(CN),j4-and Fe(bpy)(CNd2-,respectively. and reduced forms of Fe(CN)6 and Fe(bpy)(CN)4. A lower overpotential range was used for the oxidation kinetic measurements, requiring a greater extrapolation to obtain the reorganization energies and k,,, values for the Fe(cN)64- and Fe(bpy)(CN)d2- complexes. In spite of the greater uncertainty in the reorganization energy and kmax values for the reduced forms of these complexes when compared to the oxidized forms, several comparisons can be made. The reorganization energies of the oxidized and reduced redox forms of the Fe(bpy)(CN)4I-l2- complex are approximately equal, as would be expected from the Marcus theory.40 The same argument would suggest that the reorganization energy for the Fe(CN)64- complex should be the same as that for the Fe(CN)63- complex. We observe a small decrease in the reorganization energy for the ferrocyanide, which could be a result of the ion pairing with the Na+ electrolyte!1 The ion pairing would increase the size of the complex somewhat, decreasing the outer-shell reorganization energy component. The kmaxvalue for the Fe(bpy)(CN)4*- complex is roughly identical to that for the oxidized form whereas there is a significant decrease in the k, value for the Fe(CN)64- complex compared with its oxidized form. The decreased electronic coupling for the F ~ ( C N ) Gcomplex ~stems most likely from its increased electrical charge and the concomitant increase in its solvation energy. As with the Fe(CN)63- complex, we postulate that the electron transfer reaction for the Fe(CN)64- complex occurs with a significant portion of its aqueous solvation shell intact. The electron transfer reaction for this complex occurs at a greater distance than for the lower charged Fe(CN)63complex. Reactivity of Functionalized Bipyridyl Complexes. The electron transfer properties of these bipyridylkyano complexes can be further controlled by introducing substituents on the bipyridyl rings. Table 1 includes several examples of complexes containing methylated and sulfonated bipyridyl ligands. The affect of these substituents on the electron transfer reactivity of the complex depends on several factors. The sulfonate group is strongly electron withdrawing, which tends to destabilize the oxidized form of the complexes relative to the reduced form. This is evident from the positive shift in the redox potential of the complexes containing the sulfonated ligand relative to the unmodified bipyridyl ligands.42 For the Fe(CN),j3-I4- and Fe(b~y)2(CN)2’+’~ complexes, the X-ray crystal structures show that the oxidized forms of these complexes have longer FeCN bond lengths, resulting in a shortening of the CEN bonds, which gives rise to significant inner-shell reorganization components. Further destabilization of the oxidized complex by the sulfonate ligands would be expected to augment this effect and increase the inner-shell reorganization energy. This increase in the inner-shell should be partially offset by the increase in the size of the sulfonated complex, which decreases the outershell component of the reorganization energy. The balancing of these two affects results in the measured reorganization energies for the sulfonated complexes being only slightly larger than those of their nonsulfonated analogs.43 When the bipyridyl ligands are dimethylated, both the innerand outer-shell components of the reorganization energies are
expected to decrease. The two methyl groups stabilize the oxidized form of the redox molecule relative to the reduced form, as seen from the negative shifts in the formal potentials of the methylated complexes. In addition, the size of the redox molecules is increased, reducing the outer-shell component of the reorganization energy. The decreases in the measured reorganization energies for the methylated complexes seen in Table 1 are in good agreement with the theoretical expectations. It is interesting to note that the k,, values for the methylated bipyridyl complexes display the same drop with the replacement of the last two cyano ligands. The k,,, value for the Fe(dMb~y)3~+ complex is about an order of magnitude smaller than that for the Fe(dMbpy)2(CN)2If complex and is smaller than that for the Fe(b~y)3~+ complex. A final variation in the composition of the tris(bipyridy1) complexes is to change the central metal atom. The tris(bipyridyl) complexes of Fe, Ru, and Os are extremely facile, making kinetic comparisons, particularly electrochemical comparisons, extremely difficult. Using the insulated electrode method, the electron transfer properties of each complex can be measured quite simply. We find that these complexes have identical reorganization energies. This is not surprising given their near identical size and lack of an appreciable inner-shell component of the reorganization energy. The kmax values are also identical, indicating that the change of the metal does not change the amount of ligand character in the redox site. One might expect that strong ligand character within the redox molecule would allow stronger electronic coupling of the redoxactive orbital to the periphery of the molecule.44 Although possessing identical kinetic properties, these redox complexes span a reasonably wide range of formal potentials. They would be ideal candidates for probing the driving force dependence of homogeneous electron transfer reactions. Literature Comparisons. While the k,, values are generally unique to these insulated electrode studies, the reorganization energies for several of the redox molecules listed in Table 1 have been determined using other experimental techniques. Comparing those earlier determinations with these insulated electrode derived reorganization energies is not completely straightforward. There are often very large differences in the reported reorganization energies for the same redox molecule. For the Fe(CN)64-’3- couple, reorganization energies from approximately 0.5 to 1.6 eV have been reported using electrochemical45 and stop flow measurement^.^^ The historically large deviations between reported reorganization energies can be traced to both experimental and definitional reasons. Experimentally, the determination of reorganization energies using different techniques often requires extensive extrapolation from the measured data. Small deviations in the measured data can result in very large changes in the reorganization energy. Reorganization energies are sometimes calculated from self-exchange rates.3s Extracting the reorganization energy using an electron transfer rate determined at a single driving force assumes knowledge of the redox reaction’s adiabaticity and the frequency of nuclear motions. In addition, the reorganization energies measured via a homogeneous and heterogeneous measurement need not be the same.47 For
CyanoBipyridyl Iron Complexes
J. Phys. Chem., Vol. 99, No. 28, 1995 11223
TABLE 6: Comparison of Reorganization Energies with Literature Values complex
IEV"
PES 1
PEST
[Fe(b0)6l3+ [Fe(CN)6I3[Fe(bpy)d3+ [FddMbpy Id3+
2.0 & 0.2 1.13 f 0.02 0.56 f 0.01 0.50 0.02
1.84 0.74
2.05 1.36
*
0.57 0.72
a Insulated electrode voltammetric determination from this work. Photoelectron emission spectroscopic determination from Watanabe et al.48b Photoelectron emission spectroscopic determination from Delahay et a1?8a
molecules with a significant inner-shell reorganizational barrier, the homogeneous methods should give higher reorganization energies. The closest comparisons between measured reorganization energies can be made between these insulated electrode values and those obtained through photoemission threshold measurements. Table 6 shows a comparison between our insulated electrode results and those determined using photoelectron emission measurements from two separate groups.48 We find good agreement in the measured reorganization energies for Fe(H20)63+ and Fe(b~y)3~+. For the other complexes listed in the table, the insulated electrode measurements differ significantly from the photoelectron emission results. In each case the insulated electrode values are in closer agreement with theoretical estimates.49
Acknowledgment. The authors would like to thank Marshall Newton for providing preprints of his work and W. Ronald Fawcett for pointing out an error in our earlier analysis. S.T. gratefully acknowledges the support of the Fonds National Suisse de la Recherche Scientifique. This work was supported in part by grants from the Petroleum Research Fund, the National Association of Corrosion Engineers, the National Science Foundation (CHE 9417357), and the State of Maryland.
Supporting Information Available: Text defining crystal data and structural refinement methods and tables of crystal data, structural refinement parameters, atomic coordinates, bond lengths and angles, and anisotropic displacement parameters for Fe(bpy)z(CN)z and Fe(bpy)2(CN)2(N03) (16 pages); tables of structure factors for Fe(bpy)z(CN)z and Fe(bpy)2(CN)2(N03)(16 pages). Ordering information is given on any current masthead page. References and Notes (1) (a) Weaver, M. J. J . Phys. Chem. 1980, 84, 568. (b) Weaver, M. J. Chem. Rev. 1992, 92,463. (c) Ryan, M. D.; Bowden, E. F.; Chambers, J. Q. Anal. Chem. 1994, 66, 360R. (d) Saji, T.; Maruyama, Y.; Aoyagui, S. J . Electroanal. Chem. 1978, 86, 568. (e) Fawcett, W. R.; Opallo, M. Angew. Chem., Int. Ed. Engl. 1994, 33, 2131. (2) 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. (3) (a) Samec, Z.; Weber, J. J . Electroanal. Chem. 1977, 77, 163. (b) Weaver, M. J.; Anson, F. C. J . Phys. Chem. 1976, 80, 1861. (4) (a) Bennet, A. J. J . Electroanal. Chem. 1975, 60, 125. (b) Memming, R.; Mollers, R. Ber. Bunsen-Ges. Phys. Chem. 1972, 76, 475. (c) Vetter, K. J.; Schultze, J. W. Ber. Bunsen-Ges. Phys. Chem. 1973, 77, 945. (d) Kohl, V. P.; Schultze, J. W. Ber. Bunsen-Ges. Phys. Chem. 1973, 77,953. (e) Kobayashi, K.; Aikawa, Y.; Sukigara, M. J . Electroanal. Chem. 1982,134, 11. (0 Morisaki, H.; Ono, H.; Yazawa, K. J . Elecrrochem. SOC. 1989, 136, 1710. (g) Xu, J.; Li, H.-L.; Zhang, Y. J . Phys. Chem. 1993,97, 11497. (h) Hupp, J. T.; Zhang, X. L. J . Phys. Chem. 1995, 99, 853. ( 5 ) Becka, A.; Miller, C. J. J . Phys. Chem. 1993, 97, 6233. (6) (a) Li, T. T.-T.; Liu, H. Y.; Weaver, M. J. J . Am. Chem. Soc. 1984, 106, 1233. (b) Li, T. T.-T.; Weaver, M. J. J . Am. Chem. Soc. 1984, 106, 6107. (c) Chidsey, C. E. D. Science 1991, 251, 919. (d) Finklea, H. 0.; Hanshew, D. D. J . Am. Chem. Soc. 1992, 114, 3173. (7) Miller, C. J.; Cuendet, P.; Gratzel, M. J . Phys. Chem. 1991, 95, 877.
(8) (a) Becka, A.; Miller, C. J. J . Phys. Chem. 1992, 96, 2657. (b) Becka, A. M.S. Thesis, University of Maryland, College Park, MD, 1993. (9) The goals and scope of this paper are similar to those of Brown and Sutin, who measured the reactivity of Ru(bpy),,(NH3)6-2, complexes using homogeneous methods. Brown, G. M.; Sutin, N. J . Am. Chem. Soc. 1979, 101, 883. (10) Herman, W. A.; Thiel, W. R.; Kuchler, J. G.Chem. Ber. 1990, 123, 1953. (11) Schilt, A. A. J. Am. Chem. SOC.1960, 82, 3000. (12) Burstall, F. H.; Nyholm, R. S. J. Chem. Soc. 1952, 3570. (13) Dwyer, F. P.; Gibson, N. A,; Gyarfas, E. C. J . P roc. R. Soc. N . S. W. 1952, 84, 80. (14) (a) Logan, J.; Newton, M. D. J . Chem. Phys. 1983, 78,4086. (b) Hupp, J. T.; Weaver, M. J. J . Phys. Chem. 1984, 88, 1463. (15) Marcus, R. A. J . Chem. Phvs. 1965, 43, 679. (16) McManis, G. E.; Mishra, K. A.; Weaver, M. J. J . Chem. Phys. 1987, 86, 5550. (17) (a) Gerischer, H. Z. Phys. Chem. (Munich) 1960, 26, 223. (b) Gerischer, H. Z. Phys. Chem. (Munich) 1960, 26, 325. (18) The analysis presented below is in many respects equivalent to those developed by Chidsey's and Finklea's groups for the redox kinetics of molecules tethered to the surface of the The description below is optimized for the determination of kinetic parameters of solution redox species. (19) Kittel, C. Introduction to Solid State Physics 3rd ed.; Wiley: New York, 1966; p 228. (20) (a) McConnell, H. M. J . Chem. Phys. 1961, 35, 508. (b) Liang, C.; Newton, M. D. J . Phys. Chem. 1992, 96, 2855. (c) Curtiss, L. A,; Naleway, C. A.; Miller, J. R. J . Phys. Chem. 1993, 97, 4050. (d) Curtiss. L. A.; Naleway, C. A.; Miller, J. R. J . P hys. Chem. 1995, 99, 1182. (21) (a) Smith, C. P.; White, H. S. Anal. Chem. 1992, 64, 2398. (b) Creager, S. E.; Weber, K. hngmuir 1993, 9, 844. (22) This linear function is valid for monolayers composed of hexyl or longer o-hydroxythiols at z:z electrolyte concentrations above 0.1 M. At lower concentrations, a somewhat more complicated function described previously is needed. In the previous work,5 we mistakenly used the differential capacitance rather than the integral capacitance of the monolayercoated electrode. For the high electrolyte concentration range, this error has no effect on the calculated potential dependence of the $2 parameter. (23) (a) Oldham, K. B. Anal. Chem. 1972,44, 196. (b) Imbeaux, J. C.; Savbant, J. M. J . Electroanal. Chem. 1973, 44, 1969. (c) Lawson, R. J.; Maloy, J. T. Anal. Chem. 1974, 46, 559. (24) Saji, T.; Yamada, T.; Aoyagui, S. J. Elecrroanal. Chem. 1975, 61, 147. (25) Schultze, J. W.; Vetter, K. J. Electrochim. Acta 1973, 18, 889. (26) (a) Hupp, J. T.; Weaver, M. J. J . Electroanal. Chem. 1983,152, 1. (b) Forster, R. J. Chem. Soc. Rev. 1994, 23, 289. (27) The reorganization energies and k,,, parameters reported here for the Fe(CN)63- and Fe(bpy)(CN)4'- complexes are somewhat different from those reported previously.* The data used to obtain the previously reported values were not corrected for the double-layer effect. When that data is corrected for the influence of the electrode double layer, the parameters between the two studies come into agreement. (28) Stasiw, R.; Wilkins, R. G.Inorg. Chem. 1969, 8, 156. (29) (a) Marcus, R. A. J . Chem. Phys. 1956, 24, 966. (b) Marcus, R. A. J . Chem. Phys. 1965, 43, 58. (c) Marcus, R. A. In Special Topics in Electrochemistry; Rock, P. A,, Ed.; Elsevier: New York, 1970; p 180. (30) This description of the reorganization energy of the reactant which focuses on changing the product's internal structure and solvation may seem backward from conventional wisdom. When the electrode is held at the reorganization voltage of the reactant, the electron transfer reaction between the Fermi level and the reactant occurs without activation. The free energy required to activate the reactant by a given amount is not of direct concern. Once the electron transfer occurs, the product relaxes along its free energy versus reaction coordinate curve toward its most stable internal and solvent structure. The free energy lost in the deactivation of the product is identical to the reorganization energy of the reactant. The reason for the entanglement between the reorganization energy of the reactant and the properties of the product is due to the use of the formal potential as the reference potential. The formal potential of the redox couple depends on the activation characteristics of both the oxidized and reduced species. The reorganization energies calculated for oxidized and reduced forms of the redox species studied here are identical within the uncertainty of the input parameters, so that this subtlety in the meaning of the reorganization energy is rather academic. (31) Lu, T.-H.; Kao, H.-Y.; Wu, D. I.; Kong, K. C.; Cheng, C. H.Actu Crystullogr. 1988, C44, 1184. (32) (a) Vannerberg, N.-G. Acra Chem. Scand. 1972, 26, 2863. (b) Tullberg, A,; Vannerberg, N.-G. Acta Chem. Scand. 1971, 25, 343. (33) (a) Nakamoto K. Infrared and Raman Spectra of Inorganic and Coordination Compounds, 4th ed.; Wiley: New York, 1986. (b) Nakagawa, I.; Shimanouchi, T. Specrrochim. Acra 1962, 18, 101. (34) Biner, M.; Burgi, H.-B.; Ludi, A,; Rohr, C. J . Am. Chem. Soc. 1992, 114, 5197.
Terrettaz et al.
11224 J. Phys. Chem., Vol. 99, No. 28, 1995 (35) In a recent paper Liu and Newton describe a three-layer electrostatic model of an insulated electrode. Using their equations, one can calculate only a small dependence of the reorganization energy on the monolayer thickness for the range of thicknesses which allows a determination of the reorganization energy. The deviation is on the order of 0.1 eV for Fe(CN)63-. Our observations are in agreement in that we do not observe a significant difference in the reorganization energy when the thickness of the HO(CH2),SH monolayer is increased from n = 10 to 16. Liu, Y.-P.; Newton, M. D. J. Phys. Chem. 1994, 98, 7162. (36) Hupp, J. T.; Weaver, M. J. J . Phys. Chem. 1985, 89, 2795. (37) For redox reactions occurring at bare electrode surfaces, molecules are often assumed to react adiabatically. As the redox molecule achieves the transition state geometry, the electronic coupling is assumed to be strong enough to allow electron transfer with unit efficiency. This assumption of adiabaticity is most commonly made for convenience rather than with a specific knowledge of the electronic coupling. In contrast, at these insulated electrodes, all redox molecules react nonadiabatically, so that the difference in the molecules’ inherent adiabaticity can be assessed even when the two molecules react adiabatically at a bare electrode. (38) This interpretation requires that there are not specific interactions between the complexes and the hydrophilic monolayer surface. Such interactions could preferentially preconcentrate or predeplete the redox molecules from the reaction layer, affecting the k,,, values. Although we have shown that the double-layer effect of these w-hydroxythiol monolayer coated electrodes can be accurately accounted for using a Gouy-ChapmanStem model, the small deviations between the k,,, values for the cyanocontaining complexes could be due to residual specific interactions of the complexes with the monolayer surface. (39) Marcus, Y. Ion Solvation; Wiley: New York, 1985; p 108. (40) Because the redox molecular radii do not change appreciably upon oxidation or reduction, the Marcus theory estimate of the outer-shell component of the reorganization energy is predicted to be constant. The force constants for the C=N bonds do not change much with the oxidation state of the complex, so that the inner-shell component of the reorganization energy should also be constant.
(41) (a) Lewis, G. N.; Sargent, L. W. J. Am. Chem. Soc. 1909,31,355. (b) Blackwood, D. J.; Pons, S. J. Elecrroanal. Chem. 1988, 244, 301. (c) Beriet, C.; Pletcher, D. J. Electroanal. Chem. 1993, 361, 93. (42) For the tris Fe(Sbpy)3’-’O complex, the destabilization of the Fe(111) state leads to the decomposition of Fe(Sbpy)3’- upon oxidation. This instability of the oxidized form of the tris-complex made its characterization impractical. (43) Two isomers of the Fe(Sbpy)2(CN)Z2- complex were separated. These are designated as “Fl” and “F2” from their elution order in the reverse-phase chromatographic separation. Most likely both isomers have the two cyano ligands oriented cis to each other. The difference between the two isomers would then be the orientation of the sulfonate groups with respect to each other. Attempts to crystallize either of the isomers have not resulted in large enough crystals for X-ray analysis. The electrochemical properties of the two complexes are nearly indistinguishable. (44) Nielson, R. M.; McManis, G. E.; Safford, L. K.; Weaver, M. J. J. Phys. Chem. 1989, 93, 2152. (45) Marecek, V.; Samec, 2.; Weber, J. J . Electroanal. Chem. 1978, 94, 169. (46) Eberson, L. In Electron Transfer Reactions in Organic Chemistry; Springer-Verlag: Berlin, 1987; p 53. (47) For a good description of the differences between reorganization energies measured by various techniques, see: (a) Delahay, P. Chem. Phys. Len. 1982, 87, 607. (b) Hupp, J. T.; Weaver, M. J. J . Phys. Chem. 1984, 88, 6128. (48) (a) Delahay, P.; Dziedic, A. J. Chem. Phys. 1984, 80, 5793. (b) Watanabe, I.; Ono, K.; Ikeda, S. Bull. Chem. SOC.Jpn. 1991, 64, 352. (49) The Marcus theory estimates of the reorganization energies for the complexes calculated here and in the previous photoemission studies are in very good agreement. This is in spite of several differences in the underlying molecular parameters used in the calculation. Jp95 10781
