Studies of electron transfer through self-assembled monolayers using impedance spectroscopy

Article abstract of DOI:10.1016/S0013-4686(00)00420-5

An investigation of the kinetics of reduction of Ru(NH₃)³⁺₆ has been carried out at single crystal electrodes modified by alkanethiols of varying chain lengths. Careful study of the impedance of the modified electrode system in the absence of the reaction has shown that there is a highly resistive path in parallel to the capacitance due to the self-assembled monolayer. Analysis of the kinetic data and extrapolation of the Tafel plots show that the standard rate constant for the Ru(NH₃^)3+/2+₆ system is 1.7 cm s^-1 at an unmodified Au surface with a transfer coefficient close to 0.5. These parameters are expected for a very fast simple heterogeneous electron transfer reaction. The present results are compared with whose reported previously in the literature.

Full text of DOI:10.1016/S0013-4686(00)00420-5

Electrochimica Acta 45 (2000) 3497–3505
www.elsevier.nl/locate/electacta
Studies of electron transfer through self-assembled
ꢀ
monolayers using impedance spectroscopy
Lesia V. Protsailo, W. Ronald Fawcett *
Department of Chemistry, Uni6ersity of California, Da6is CA, 95616 USA
Received 24 September 1999; received in revised form 24 January 2000
Abstract
An investigation of the kinetics of reduction of Ru(NH3)
3
6
+
has been carried out at single crystal electrodes
modified by alkanethiols of varying chain lengths. Careful study of the impedance of the modified electrode system
in the absence of the reaction has shown that there is a highly resistive path in parallel to the capacitance due to the
self-assembled monolayer. Analysis of the kinetic data and extrapolation of the Tafel plots show that the standard
3
+/2+
−1
rate constant for the Ru(NH3)6
system is 1.7 cm s
at an unmodified Au surface with a transfer coefficient
close to 0.5. These parameters are expected for a very fast simple heterogeneous electron transfer reaction. The
present results are compared with whose reported previously in the literature. © 2000 Elsevier Science Ltd. All rights
reserved.
Keywords: Self-assembled monolayer; Heterogeneous electron transfer; Impedance spectroscopy; Equivalent circuit; Faradaic
impedance; Electron tunneling
chain. Then, if a coherent monolayer is formed on the
electrode, the effects of distance, molecular ordering
and dielectric properties on heterogeneous electron
transfer may be studied [2–5].
The most popular electrochemical technique used to
study redox processes at SAM-modified electrodes has
been cyclic voltammetry [2,6–9]. However, this method
does not provide much information about the electron
transfer process when the SAM is very thick. Other
techniques employed have included potential step
chronoamperometry [10], impedance spectroscopy
1
. Introduction
Self-assembled monolayers (SAMs), have been inten-
sively studied in recent years [1]. Their structural and
chemical properties make them interesting systems for
modifying the electrode/solution interface in a pre-
dictable way. One important application of SAMs is to
study long range electron transfer. When long chain
alkane thiols are used as the molecular unit in the
SAM, the monolayer has a very low dielectric permit-
tivity similar to that in biological systems in which long
range electron transfer takes place. In addition, the
thickness of the monolayer may be increased in a
systematic way by increasing the length of the alkyl
[
[
11,12], and second harmonic generation voltammetry
13]. Each technique has its advantages and disadvan-
tages but impedance spectroscopy has clear advantages
because it allows one to characterize interfacial proper-
ties in the absence of a redox reaction.
Impedance spectroscopy (IS) was used in the present
study to determine the effect of changing the thickness
of the SAM in a systematic way. By measuring the
impedance over a very wide frequency range the kinet-
ꢀ
Based on a presentation made at the 2nd Baltic Confer-
ence on Electrochemistry, 1999.
*
Corresponding author. Fax: +1-530-7528995.
E-mail
address:
fawcett@indigo.ucdavis.edu
(W.R.
Fawcett).
0
013-4686/00/$ - see front matter © 2000 Elsevier Science Ltd. All rights reserved.
PII: S0013-4686(00)00420-5

3
498
L.V. Protsailo, W.R. Fawcett / Electrochimica Acta 45 (2000) 3497–3505
ics of electron transfer can be measured through thick
films. In previous work in this laboratory, it was shown
that the SAM does not behave as an ideal capacitor but
that it also has a very high resistance, which may be
due to imperfections in the monolayer such as pinholes
Cambridge, UK) with a cylindrical shape. Single-crys-
tals were mechanically polished on the face exposed to
the solution using alumina powder of different grain
sizes (from 3 to 0.05 mm). The electrodes were cleaned
and brought to the same condition before each experi-
ment by electropolishing in 0.01 M HClO4 until the
characteristic oxidation peaks on cyclic voltammograms
were identical. Gold foil of large area was used as an
auxiliary electrode. All potentials are given with respect
to a saturated calomel electrode (SCE).
Cyclic voltammetry (CV) was performed using an
EG&G 283 potentiostat/galvanostat. The a.c.
impedance measurements were carried out with a 1255
frequency response analyzer (SOLATRON) connected
to the potentiostat using a GPIB IEEE-488.2 interface.
The impedance data were automatically acquired using
M398 electrochemical impedance software (EG&G).
Impedance data were collected at 50 frequencies in the
frequency range from 0.1 to 10 kHz. An a.c. potential
amplitude of 10 mV rms was normally added to the d.c.
potential of the working electrode. Both the in-phase
(Z%) and out-of-phase impedance (Z%%) were extracted
from the data at the same time and analyzed with
software based on Macdonald’s algorithm (LEVM 7)
using a complex nonlinear regression technique. The
impedance measurements were performed at various
potentials using the following procedure: the d.c poten-
tial was varied from 0.0 to 0.5 V versus SCE in steps of
50 mV; the electrode was preconditioned at each poten-
tial for about 3 min before impedance data for the
corresponding potential were collected; the potential
was then stepped to a more negative value and the
procedure was repeated.
[
14]. Another aspect of the interface is that it behaves as
a constant phase element rather than an ideal capacitor
due to the properties of the metal substrate. The goals
of this study were also to obtain more information
about these non-ideal aspects of the interface. For this
reason, the study was carried out at two types of single
crystal gold faces, namely, Au (111) and Au (210).
2. Experimental
2
.1. Chemicals
Octadecanethiol (98%), hexadecanethiol (92%), dode-
canethiol (98%) (Aldrich), and nonanethiol (95%)
(
(
Fluka) were used as received. Sodium perchlorate
Fluka) was dried under vacuum at 100°C for 48 h.
[
Ru(NH ) ](ClO ) was prepared from the correspond-
3 6 4 3
ing chloride complex using a synthesis based on their
different solubilities in water.
2
.2. Preparation of the self-assembled monolayer
The n-alkanethiol was dissolved in ethanol to make a
30 mM solution. The Au single-crystal electrode of
cylindrical shape was cleaned in 0.01 M HClO , flame
4
annealed in a natural gas/air flame, and then quenched
with nanopure water. The electrode was then immersed
in the n-alkanethiol solution for a period of 16 h to
form a monolayer. The electrode was removed from the
solution, rinsed with pure ethanol, and then with
nanopure water. After that, it was immediately trans-
ferred into the electrochemical cell containing the work-
ing solution. The electrode was mounted in the cell
using the meniscus contact technique [15], which means
that only the circular end of the gold cylinder touched
the solution.
3. Results and discussion
3.1. Nonlinearity in impedance models
The use of equivalent circuits for electrochemical
systems is common in IS data analysis. However,
difficulties in processing data using electrical analogs
often arise because of non-linearity in the equivalent
circuit proposed. A well-known example is the Randles
circuit [16]; another example is the same circuit in
which the double layer capacity had been substituted by
a constant phase element (CPE) [17]. Wu and cowork-
ers [16,17] distinguished two types of non-linearity: (1)
intrinsic and (2) parametric. Intrinsic non-linearity de-
pends only on the model used in the analysis. Paramet-
ric non-linearity depends not only on the model but
also on the values of the parameters. Thus, this aspect
of the experiment can be greatly reduced by re-parame-
terization [18].
2
.3. Procedure and data analysis
All the electrochemical experiments were performed
in a three-electrode cell made of Pyrex glass with a
water jacket for temperature control and a Teflon cap.
The cell was enclosed in a grounded Faraday cage. All
the experiments were carried out at 2590.1°C. Elec-
trolyte solutions were prepared with nanopure water
with a resistivity of 17.9–18.1 MV cm, purged with
nitrogen gas (99.997% pure) before electrochemical
measurements, and kept under an nitrogen atmosphere
during the course of the experiment. The working elec-
trodes were single-crystals (Metal Crystal and Oxides,
An additional method of improving the fit and reduc-
ing the errors caused by parametric non-linearity is

L.V. Protsailo, W.R. Fawcett / Electrochimica Acta 45 (2000) 3497–3505
3499
s and € is related
−
1
−2 €
presented here. It is well known that obtaining the best
fit to data and establishing an absolute minimum for
deviations depends on three factors: selection of an
appropriate model; good initial estimates of the
parameter values; and a good algorithm. In our opinion
one of the ways to reduce the parametric non-linearity
is by setting initial estimates of some parameters deter-
mined during the fit. This can be performed with
parameters, which remain constant throughout the ex-
periment. In the present study, parameters such as the
solution resistance and the constant phase element
should remain almost constant for measurements per-
formed in the absence and in the presence of a faradaic
process. Determination of these parameters in the ab-
sence of a reaction and using them as initial estimates
in the presence of the reaction helps to reduce the error
in the fit.
At this point, it is useful to introduce some of the
elements of the equivalent circuit used for the data
interpretation. The impedance of an ideally polarizable
electrode/solution interface may be represented as a
series combination of a solution resistance and a dou-
ble-layer capacitance. Such a circuit gives a straight
line, perpendicular to the axis corresponding to the
in-phase impedance, in the plot of out-of-phase
impedance against in-phase impedance. However, at
solid electrodes, a straight line with an angle lower than
where Q is a constant in V
cm
to the angle of rotation of a purely capacitive line on
the complex plane plots: a=90°(1−€). Only when
€=1, is purely capacitive behavior obtained (Q=Cdl)
[19].
The presence of a CPE has been found for every
system studied in the absence of the redox reaction. The
values of € in our experiments performed in solutions
containing only the supporting electrolyte were approx-
imately 0.98. Even though this can be considered as
close to ideal behavior, the CPE was used instead of the
ideal capacitor in every fit in order to improve the final
fit and minimize error. The value of Q decreases with
increase in the thickness of the SAM. Since Q is ap-
proximately equal to the specific capacity of the inter-
face, this result is easily understood in terms of the
properties of an adlayer of constant permittivity but
increasing thickness.
RSAM represents the resistance of the monolayer to a
species moving through the film. Values of this parame-
ter obtained from the CNLS fit are given in Table 1 for
the Au (210) electrode. There is no obvious trend in
RSAM with length of the hydrocarbon chain. The neces-
sity of using of this element becomes obvious after one
examines the improvement of the fit of the simulated
model to the experimental data. For example, in the
case of the dodecanethiol-based SAM on Au (111), the
correlation between the fit and experimental points is
90° is often observed. In order to account for this
behavior a model of distributed time constants was
suggested [19]. Such a distribution may arise from
microscopic roughness on the solid electrode caused by
scratches, pits, and other defects, which are always
present on solid surfaces. In this case, the double-layer
capacitance may be expressed in terms of a so-called
constant phase element, CPE. Its impedance is then
given by:
characterized by a weighted sum of squares (WSS)
2
equal to 0.608 and  equal to 0.020. Introducing R
SAM
in the circuit improves the correlation by a factor of
2
two with WSS and  equal to 0.360 and 0.012, respec-
tively (Fig. 1). RSAM is attributed to collapsed sites and
pinholes within the film structure. Finklea [9] has pro-
posed that there are sites at which the redox couple can
approach the electrode surface more closely but not
come into direct contact with it. At some localities the
monolayer may be collapsed (see Scheme 1). These sites
are associated with grain boundaries in the substrate
gold, and with the effect these sites have on monolayer
structure. They lead to the presence of RSAM in the
equivalent circuit model proposed here. The highest
value of RSAM and thus, the best quality film, is found
for the C12 system which is known to form the best
SAM [1]. The smaller value for the C18 system is
attributed to a higher degree of bending and tilting of
the long hydrocarbon chains.
1
ZCPE
=
(1)
€
Q( jꢀ)
Table 1
CNLS regression analysis for the Au (210) modified electrode
a
for the SAM systems in the absence of a Faradaic process
−
1
cm−2
€
2
SAM
Q /mV
s
€
RSAM/kV cm d/nm
Data, averaged for at least three newly prepared
SAMs formed from a given thiol, were used to obtain
initial estimates of RSAM, Q, € and RS in the fits for
systems complicated by a faradaic process. For these
calculations, the solution resistance was reduced slightly
C9
1.32 (0.03)
1.07 (0.05)
0.72 (0.03)
0.65 (0.03)
0.993 0.33 (0.02)
0.988 1.91 (0.03)
0.994 1.09 (0.02)
0.995 0.60 (0.01)
1.1
1.4
1.8
2.0
–
C12
C16
C18
Bare Au 22.7 (0.8)
0.972 –
(
ꢀ30 V) to account for the presence of the reactant (1
a
mM [Ru(NH ) ](ClO ) ). The parameters for the SAM
The standard deviation of the estimated parameter is
3 6
4 3
shown next to the best value of the parameter. These values
were also used as initial estimates for Au (111).
obtained for systems in the absence of the redox active
species and which were used as initial estimates for the

3
500
L.V. Protsailo, W.R. Fawcett / Electrochimica Acta 45 (2000) 3497–3505
Fig. 1. Complex plane plots of the impedance of Au (111) modified with n-dodecanethiol in 0.1 M NaClO . The frequency range
4
was 0.1 Hz–10 kHz, and the applied potential was −0.17 V versus SCE. Circles represent experimental data and line represents the
fit of simulated model. (A) Fit is performed using R and CPE in series as a model; (B) fit is performed using model A from Scheme
s
2
.
fitting of data in the presence of the reaction are given
in the Table 1. The equivalent circuit model used to
describe the behavior of the system with a SAM but in
the absence of a reaction is shown in Scheme 2A.
of the current strongly depends on the thickness of film,
the greatest decrease in the current occurring for the
n-octadecanethiol-modified Au electrodes.
3.3. Analysis of impedance spectra using CNLS fitting
3
.2. Cyclic 6oltammetry
The experimentally obtained impedance data for a
given electrode interface may be analyzed using an
exact mathematical model that predicts the theoretical
impedance Z(ꢀ), or by a relatively empirical equivalent
circuit consisting of ideal and non-ideal electrical
analogs to the real physical and chemical processes [20].
The latter approach was used in the present work.
Impedance data were fitted to an equivalent circuit
using a complex nonlinear least squares (CNLS) fitting
The main requirement of studying the kinetics of
electron tunneling through a SAM is that it forms a
compact nearly perfect blocking film on the electrode.
Since the redox system used in the present study is not
attached to the SAM, mass transfer is involved in the
electron transfer reaction at the SAM/solution interface
[
1]. In the case of fast electron transfer reactions, mass
transport is the rate limiting process in the absence of
the SAM. As can be seen from Fig. 2A, for an un-
modified Au (210) electrode, Ru(III) reduction is a
diffusion limited reaction in the potential range of
interest. In contrast, cyclic voltammograms at
a
modified electrode (Fig. 2B and C) do not show the
characteristic peak currents at low overpotentials. The
situation for Au (111), whose cyclic voltammograms
are not shown here, is analogous to that at the Au (210)
modified electrode. The cyclic voltammograms allow
one to conclude that the SAMs are of high quality, and
relatively free of pinholes so that the kinetics of elec-
tron tunneling through the SAM may be studied. It is
obvious from the voltammograms that the suppression
Scheme 1.

L.V. Protsailo, W.R. Fawcett / Electrochimica Acta 45 (2000) 3497–3505
3501
A general equivalent circuit that is capable of de-
scribing the impedance data in the presence of a slow
electron transfer process is shown in Scheme 2C. The
Scheme 2.
algorithm which has demonstrated high resolving
power and accuracy compared to other methods. One
of the objectives of the present study was to define and
discuss the analogies between circuit elements and elec-
trochemical processes, so that the result of data fitting
can be more easily interpreted in terms of its physical
relevance.
Fig. 2. Cyclic voltammograms at Au(210). Scan rate 50 mV
−1
3+
s
. The solutions are 1 mM [Ru(NH ) ]
in 0.1 M NaClO4.
3
6
Fig. 3 shows the impedance spectrum in a Nyquist
presentation obtained at bare Au (111) in the presence
(A) Bare Au (210); (B) Au (210)/n-nonanethiol; (C) Au (210)/
n-hexadecanethiol.
3
+
of 1 mM [Ru(NH ) ]
with 0.1 M NaClO4 as the
supporting electrolyte. The data were collected at −
.17 V versus SCE, that is, at the formal potential for
3
6
0
the Ru(III/II) reaction. The electrode process is mass
transport limited over the whole chosen frequency
range (0.1 Hz to 10 kHz). A wider range of frequencies
obviously would not provide interfacial kinetic data at
this interface. The equivalent circuit, which describes
this behavior is given in Scheme 2B and, does not
include parameters related to interfacial charge transfer.
The additional parameter ZW accounts for the Warburg
impedance due to mass transfer from the bulk of the
solution to the reaction site. There is no RSAM element
in this case because there is no SAM present.
Fig. 4 shows the results of impedance spectroscopy at
Au (210) modified with n-octadecanethiol (A), n-hex-
adecanethiol (B), n-dodecanethiol (C), and n-
nonanethiol (D) collected at the same conditions
described above for unmodified Au (111). A dramatic
difference in the data compared to those at the un-
modified electrode is observed.
Fig. 3. Complex–plane plot of the impedance of Au (111) in
3+
the presence of 1 mM [Ru(NH ) ]
with 0.1 M NaClO4 as
3
6
the supporting electrolyte. The frequency range was 0.1 Hz–10
kHz, and the electrode potential was −0.17 V versus SCE.

3
502
L.V. Protsailo, W.R. Fawcett / Electrochimica Acta 45 (2000) 3497–3505
3
+
Fig. 4. Complex–plane plots of the impedance of Au (210) modified with SAMs in 1 mM [Ru(NH ) ]
and 0.1 M NaClO . The
4
3
6
frequency range was 0.1 Hz to 10 kHz, and the applied potential was −0.17 V versus SCE. (A) n-octadecanethiol; (B)
n-hexadecanethiol; (C) n-dodecanethiol; (D) n-nonanethiol.
Table 2
a
Dielectric constants and tunneling parameters for electron transfer through SAMS on gold electrodes
m
i
V/eV
Au (111)
Au (210)
Published
Data
2
2.9
0.83
0.87
0.9 [6]
–
0.66
0.72
Au
Hg
3.0 [6], 2.6 [2]
2.0 [8]
0.5 [6], 1.15–0.98 [26]
–
a
m is a dielectric constant of the SAM; i, the electron tunneling coefficient; and V, the barrier height.
additional parameter Rct is used to determine the rate
constant for electron transfer. In order to keep the
value of the solution resistance RS constant in each
experiment (ꢀ270910 V) the position of the reference
electrode was carefully maintained constant. Analysis
of the double-layer capacity provides a means of exam-
ining the structure of the monolayer assemblies. As the
deviation of the CPE from ideal behavior is very small
1). The slope of the linear plot gives the relative dielec-
tric permittivity for the hydrocarbon region of mono-
layer. The value obtained for Au (111) was 2.0, and
that for Au (210), 2.9; these data compare favorably to
the values reported by other authors [2,6]. The results
are shown in Table 2. The value of the permittivity for
the Au (210) modified electrode is probably slightly
overestimated. This may be due to the assumption that
the real area of the electrode is equal to its geometrical
area. Since the structure of the Au (210) surface is
rougher than that of Au (111), this assumption is less
valid for Au (210).
(
€:0.98°), and does not depend on the length of the
alkanethiol which forms the SAM, Q can be assumed
to be approximately equal to Cdl and used as a capaci-
tance in further data analysis. For an electrochemical
double-layer, the differential capacitance increases with
decreasing separation between the electrode surface and
the distance of the closest approach for the ionic coun-
ter charge. Our measurements show that a plot of the
inverse of Q versus the length of hydrocarbon chain of
the monolayer is linear. The monolayer thickness for
the alkyl mercaptans on gold obtained by Finklea using
ellipsometry [9] was used in our calculations (see Table
The voltage dependence of the double-layer capaci-
tance (on the basis of the CPE) is similar to that at a
metal electrode covered by
a strongly adsorbed
molecule. The capacitance of the modified electrode is
almost independent of the applied potential, indicating
that the double-layer properties approach the
Helmholtz model, with a constant contribution from
the diffuse layer.

L.V. Protsailo, W.R. Fawcett / Electrochimica Acta 45 (2000) 3497–3505
3503
Fig. 5. Complex–plane plots of the impedance of Au (210) modified with n-hexadecanethiol. The frequency range was 0.1 Hz–10
kHz. (A) −0.17 V versus SCE (standard potential); (B) −0.25 V versus SCE; (C) −0.35 V versus SCE; (D) −0.45 V versus SCE.
3
.4. Tafel plots
The kinetic results obtained at modified Au (111) and
Au (210) are shown as plots of ln k against overpoten-
f
Kinetic data for a simple electron transfer reaction
tial in Figs. 6 and 7, respectively. Excellent linear plots
were obtained from which the values of the standard
rate constant ks and transfer coefficient h were ex-
tracted. The results are summarized in Table 3. The
transfer coefficient is close to 0.5 as one would expect
for a simple electron transfer reaction in the absence of
the double layer effects. The second feature of the
present results is that the standard rate constant is
independent of the nature of the metal within experi-
mental error. This is also expected for systems in which
double layer effects are absent.
can be easily obtained from the IS data (Fig. 5). The
faradaic impedance was obtained by subtracting the RS,
CPE and RSAM contributions to the total impedance of
the system. Then the in- and out-of-phase components
−
1/2
of the faradaic impedance were plotted against ꢀ
according Randles [20] where ꢀ=2yf and f is the
frequency of the ac signal in Hz. This analysis served to
demonstrate that the reaction is indeed simple and that
the chosen equivalent circuit is correct.
For the simple electron transfer process
Some comment about double layer effects at SAMs is
necessary in view of the above results. Since the capac-
A+e“B
(2)
the in- and out-of-phase components of the faradaic
impedance can be used to calculate the quantity b
given by [21–23]
Z¦
kf
kb
b=
=
1/2+
(3)
1/2
Z%−Z¦ (2ꢀDA)
(2ꢀDB)
where k and kb are the forward and backward rate
f
constants for reactions (2), respectively, D , the diffu-
A
sion coefficient for the reactant, and D , that for the
B
product. Using the relationship
k =k exp( fp)
(4)
(5)
f
b
Eq. (3) may be rearranged to obtain the expression
1/2
ꢀ
Z¦
n
(2ꢀD )
A
1/2
kf=
Z%−Z¦ 1+(D /D ) exp( fp)
A
B
Fig. 6. Plot of the logarithm of the rate constant for reduction
Thus, values of k are easily extracted from the experi-
mental data given the overpotential p and the diffusion
coefficients DA and DB.
3+
f
of [Ru(NH ) ]
at Au (111) modified by a SAM consisting of
3
6
an alkanethiol with chain length corresponding to C (ꢁ), C
9
12
(ꢂ), C16 (ꢃ), and C18 (").

3
504
L.V. Protsailo, W.R. Fawcett / Electrochimica Acta 45 (2000) 3497–3505
Fig. 7. Plot of the logarithm of the rate constant for reduction
Fig. 8. Plots of the logarithm of the standard rate constant for
3
+
of [Ru(NH ) ]
at Au (210) modified by a SAM consisting of
3+/2+
3
6
the [Ru(NH ) ]
system against the thickness of the SAM
3
6
an alkanethiol with chain length corresponding to C (ꢁ), C
9
12
for Au (111) (ꢁ) and Au (210) ("). The data for Au (210)
have been shifted vertically by four units for the sake of
clarity.
(ꢂ), C16 (ꢃ), and C18 (").
ity of the SAM is very low, it is almost certain that the
average potential experienced by the reactant at its
reaction site outside of the SAM is different from the
average potential in the bulk of the solution. However,
since the charge on the electrode changes very little in
the potential region where data were obtained, the
potential at the reaction site changes negligibly. For
this reason double layer effects are not seen.
k =k exp(−id)
(7)
s
0
k0 is the value of the standard rate constant at an
uncovered electrode.
Plots of ln k against film thickness for the Au (111)
s
and Au (210) systems are shown in Fig. 8. These plots
are linear within experimental error and yield values of
−
1
i equal to 8.3 and 8.7 nm , respectively. The values
−
1
−1
of k are 0.4 cm s
(
at Au (111) and 6.9 cm s
210). Considering the long extrapolation involved, the
values of k agree quite well. In addition, the estimate
at Au
0
3
.5. Electron tunneling parameters
0
If there are no pinhole defects at the Au/SAM inter-
−
1
obtained from the average value of ln k (1.7 cm s ) is
s
3
face, the mechanism for electron transfer is tunneling
across the film. In this case the redox current at any
overpotential should decrease exponentially with the
barrier thickness according to the expression:
+/2+
consistent with the fact that Ru(NH3)6
known to be very fast reaction at bare electrodes
24,25].The tunneling parameter i is related to the
system is
[
barrier height V by the equation
i=i exp(−id)
(6)
1/2
0
i=4y(2m V) /h
(8)
e
where i is the current measured at a bare electrode, i
is the potential independent electron tunneling coeffi-
cient, and d is the thickness of the monolayer film. It
0
where m is the electron mass and h, Planck’s constant.
Substituting in the values of the fundamental constants,
the relationship between V and i is
e
follows that the standard rate constant k should also
s
−
V=9.525×10 3i2 eV nm
−2
be an experimental function of monolayer thickness:
(9)
Table 3
3
+/2+
Kinetic parameters for the [Ru(NH ) ]
electron transfer reaction through SAM modified Au single crystal electrodes
3
6
Au(111)
Au(210)
Hg
−
1
ks/cm s−1
9.35v10−5
ks/cm s−1
SAM
ks/cm s
h
h
h
−
5
C9
C12
C16
C18
9.21×10
0.48
0.57
0.51
0.49
0.49
0.55
0.55
0.52
–
–
–
–
–
–
–
–
1.08×10-
6
2.13×10
2.75×10
3.58×10
–
−6
−
7
8
−7
−8
1.44×10
3.28×10
−
−13
3×10 [8]
a
Bare polycr. Au
1.0 [24], 1.8 [25]
0.51 [24]
0.35 (2.0) [27]
0.65 [27]
a
Corrected for double layer effects.

L.V. Protsailo, W.R. Fawcett / Electrochimica Acta 45 (2000) 3497–3505
3505
Thus, the electron tunneling barrier height determined
from the present data is 0.66 and 0.72 eV for the Au
111) and Au (210) systems, respectively. These results
agree very well with those reported by other workers
see Table 2).
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