pH Modulated Heterogenous Electron Transfer across Metal/Monolayer Interfaces

Article abstract of DOI:10.1021/jp952057r

Dense monolayers of (2+), where bpy is 2,2'-bipyridyl and p3p is 4,4'-trimethylenedipyridine, have been formed by spontaneous adsorption onto clean platinium microelectrodes.Cyclic voltammetry of these monolayers is nearly ideal, and the area occupied per molecule suggests that only one of the p3p ligands binds to the electrode surface, the other being available for protonation.Chronoamperometry conducted on a microsecond time scale has been used to measure the heterogeneous electron transfer rate constant k for the Os(2+/3+) redox reaction.For electrolyte concentration above 0.1 M, heterogeneous electron transfer is characterized by a single unimolecular rate constant (k/s^-1).Tafel plots of the dependence of ln k on the overpotential η show curvature, and larger cathodic than anodic rate constants are observed for a given absolute value of η.This response is consistent with electron transfer occuring via a through-space tunneling mechanism.Plots of k vs pH are sigmoidal, and the standard heterogeneous rate constant k^o decreases from (6.1 +/- 0.2)E4 to (1.6 +/- 0.1)E4 s^-1 as the pH of the contacting solution is decreased from 5.05 to 1.07.When in contact with pH 5.05 electrolyte, the electrochemical enthalpy ΔH^<*> is 37.5 +/- 2.1 kJ mol^-1 which decreases to 24.6 +/- 1.5 kJ mol^-1 at a pH of 1.07.The reaction entropy ΔS_rc^o is independent of the pH over this range, maintaining a value of 82 +/- 7 J mol^-1 K^-1.In contrast to the behavior expected from the decrease of k with decreasing pH, the free energy of activation ΔG^<*> decreases with decreasing pH.The electronic transmission coefficient k_el, describing the probability of electron transfer once the nuclear transition state has been reached, is considerably less than unity for all pH's investigated. k_el decreases with decreasing solution pH, suggesting an increasingly weaker electronic interaction between the metallic states of the electrode and the orbitals of the redox center as the monolayer becomes protonated.These results suggest that monolayer protonation modulates the heterogeneous electron transfer rate by changing the through-space electron transfer distance.This may be caused either by a change in the tilt angle between the adsorbate and the electrode or by the methylene spacer units within the bridging ligand becoming extended, when the monolayer is protonated.

Full text of DOI:10.1021/jp952057r

J. Phys. Chem. 1996, 100, 3695-3704
3695
pH Modulated Heterogeneous Electron Transfer across Metal/Monolayer Interfaces
Robert J. Forster* and Joseph P. O’Kelly
School of Chemical Sciences, Dublin City UniVersity, Dublin 9, Ireland
ReceiVed: July 21, 1995; In Final Form: October 15, 1995X
Dense monolayers of [Os(bpy)2(p3p)2]2+, where bpy is 2,2′-bipyridyl and p3p is 4,4′-trimethylenedipyridine,
have been formed by spontaneous adsorption onto clean platinum microelectrodes. Cyclic voltammetry of
these monolayers is nearly ideal, and the area occupied per molecule suggests that only one of the p3p ligands
binds to the electrode surface, the other being available for protonation. Chronoamperometry conducted on
a microsecond time scale has been used to measure the heterogeneous electron transfer rate constant k for the
Os2+/3+ redox reaction. For electrolyte concentrations above 0.1 M, heterogeneous electron transfer is
characterized by a single unimolecular rate constant (k/s-1). Tafel plots of the dependence of ln k on the
overpotential η show curvature, and larger cathodic than anodic rate constants are observed for a given absolute
value of η. This response is consistent with electron transfer occurring via a through-space tunneling
mechanism. Plots of k vs pH are sigmoidal, and the standard heterogeneous rate constant k° decreases from
(6.1 ( 0.2) × 104 to (1.6 ( 0.1) × 104 s-1 as the pH of the contacting solution is decreased from 5.05 to
1.07. When in contact with pH 5.05 electrolyte, the electrochemical enthalpy ∆Hq is 37.5 ( 2.1 kJ mol-1,
which decreases to 24.6 ( 1.5 kJ mol-1 at a pH of 1.07. The reaction entropy ∆Src° is independent of the
pH over this range, maintaining a value of 82 ( 7 J mol-1 K-1. In contrast to the behavior expected from
the decrease of k with decreasing pH, the free energy of activation ∆Gq decreases with decreasing pH. The
electronic transmission coefficient κel, describing the probability of electron transfer once the nuclear transition
state has been reached, is considerably less than unity for all pH’s investigated. κel decreases with decreasing
solution pH, suggesting an increasingly weaker electronic interaction between the metallic states of the electrode
and the orbitals of the redox center as the monolayer becomes protonated. These results suggest that monolayer
protonation modulates the heterogeneous electron transfer rate by changing the through-space electron transfer
distance. This may be caused either by a change in the tilt angle between the adsorbate and the electrode or
by the methylene spacer units within the bridging ligand becoming extended, when the monolayer is protonated.
Introduction
CHART 1
The field of molecular electronics ranges from well-defined
and well-understood phenomena such as nonlinear optical
responses to the tantalizing, and conceptually more difficult,
areas of computing and information storage at the molecular
level.1 Supramolecular assemblies, constructed using single
electroactive molecules as building blocks, offer a striking way
to create electrically conducting materials whose organized
architecture makes them suitable for developing molecular
electronic devices.
Progress toward this strategic goal demands not only the
development of new synthetic approaches that yield highly
ordered materials2 but also careful attention to those elementary
processes that dictate the rate of heterogeneous electron transfer
across metal/monolayer interfaces.3 However, it is only recently
that it has been possible to directly probe those factors that
govern the rate of electron transfer processes that are complete
within a few billionths of a second. In fact, coupling recent
advances in the design and fabrication of microelectrodes and
electrochemical instrumentation that operate on a nanosecond
time scale with chemical systems that are organized on a
molecular level, promises to revolutionize investigations into
electron transfer processes.4
bipyridyl and p3p is 4,4′-trimethylenedipyridine, onto clean
platinum microelectrodes. For simplicity, we denote these
monolayers as (p3p)2. These adsorbed monolayers are stable
for long periods at elevated temperatures in aqueous perchlorate
solutions allowing those factors that control the rate and pathway
for electron transfer across metal/monolayer interfaces to be
probed in considerable detail. Moreover, it appears that only
one of the pyridine groups binds to the electrode surface, while
the other is available for protonation, thus allowing chemical
effects on heterogeneous electron transfer to be explored.
We have used chronoamperometry, performed on a micro-
second time scale, to probe the structure of the modified
interface, focusing particularly on the extent to which solvent
and ions permeate the interior of the monolayer. These
investigations are doubly important, since they provide an insight
into the relative perfection of the monolayer and allow one to
Toward the objective of understanding those factors that
influence heterogeneous electron transfer, we have formed
osmium containing monolayers by spontaneously adsorbing
[Os(bpy)2(p3p)2]2+ complexes (Chart 1), where bpy is 2,2′-
* To whom correspondence should be addressed.
X Abstract published in AdVance ACS Abstracts, January 15, 1996.
0022-3654/96/20100-3695$12.00/0 © 1996 American Chemical Society

3696 J. Phys. Chem., Vol. 100, No. 9, 1996
Forster and O’Kelly
probe the interfacial potential distribution.5 High-speed chro-
noamperometry has also been used to investigate the dynamics
of heterogeneous electron transfer across the electrode/mono-
layer interface. When the supporting electrolyte concentration
is greater than about 0.1 M, these chronoamperometric responses
are remarkably well-behaved, with heterogeneous electron
transfer being characterized by a single rate constant over more
than two lifetimes.
Significantly, the solution pH modulates the rate of hetero-
geneous electron transfer, apparently by protonating the pyridine
moiety of the unbound p3p ligand. We have probed the origin
of this pH sensitivity by systematically probing the pH
dependence of the free energy of activation ∆Gq and the degree
of electronic coupling between the remote redox centers and
the electrode. Surprisingly, our investigation suggests that
changes in the pre-exponential factor with pH rather than the
activation barrier cause the heterogeneous electron transfer rate
constant to depend on the extent of monolayer protonation.
Investigations of this type are especially important for
improving our understanding of those processes that limit the
rate of electron transfer within biological systems where subtle
changes in the chemical microenvironment surrounding the
redox site can dramatically alter the electron transfer rates.6
the main compartment by a salt bridge and held at constant
temperature. The nonisothermal salt bridge contained saturated
KCl since it has a low resistance, and the salt remains soluble
at the lowest temperature employed (-5 °C). The high
electrolyte concentration and the design of the bridge minimize
any systematic error in the reported temperature effects on E°′
due to changes in the liquid junction potential with temperature.8
Microelectrodes were fabricated from platinum microwires
(Goodfellow Metals Ltd.) of radii between 5 and 25 µm by
sealing them in soft glass using a procedure described
previously.4b,9 Microdisk electrodes were exposed by removing
excess glass using 600 grit emery paper followed by successive
polishing with 12.5, 5, 1, 0.3, and 0.05 µm alumina. The
polishing material was removed between changes of particle
size by sonicating the electrodes in deionized water for at least
5 min. The polished electrodes were electrochemically cleaned
by cycling in 0.1 M HClO4 between potential limits chosen to
first oxidize and then to reduce the surface of the platinum
electrode. Excessive cycling was avoided in order to minimize
the extent of surface roughening. Finally, the electrode was
cycled between -0.300 and +0.900 V in 0.1 M NaClO4 until
hydrogen desorption was complete.
The real surface area of the electrodes was found by
calculating the charge under the oxide or hydrogen adsorption-
desorption peaks.10 Typically, the surface roughness factor was
between 1.3 and 1.6. Obtaining the real, as opposed to the
projected or geometric, surface area of the electrodes is
important if the area occupied per molecule is to be accurately
measured.
RC cell time constants, measured in blank electrolyte solution,
were between 0.03 and 3 µs, depending on the electrode radius
and the supporting electrolyte concentration. The interfacial
kinetics were measured only at times greater than about 5-10
RC. In chronoamperometry experiments, the initial potential
was either 0.000 or +1.000 V, depending on whether oxidation
or reduction kinetics were being probed.
Experimental Section
Materials. The surface active complex, [Os(bpy)2(p3p)2]2+
,
was prepared by first placing 50 mg (0.09 mmol) of
[Os(bpy)2Cl2] in 40 cm3 of methanol followed by 10 min reflux
to ensure complete dissolution. A solution of 70 mg (0.036
mmol) of 4,4′-trimethylenedipyridine (98%, Aldrich) dissolved
in 5 cm3 of methanol, together with 150 cm3 of milli-Q water
were added, and the resulting solution was refluxed for 15 h.
After approximately 10-12 h the color of the solution changed
from red-brown to dark green. The progress of the reaction
was monitored using HPLC and cyclic voltammetry. After the
reaction was complete, the volume was reduced to 5 cm3 by
rotary evaporation. Ammonium hexafluorophosphate (95+%,
Aldrich) was then added, and the dark green product was
collected by filtration and washed with diethyl ether. The
product was recrystallized from aqueous methanol to give dark
green-black crystals, yield 66 mg, 82%. The complex was
characterized using IR, UV-vis, NMR, and cyclic voltammetry.
Apparatus. Electrochemical cells were of conventional
design and were thermostated within (0.2 °C using a Julabo
F10-HC refrigerated circulating bath. All potentials are quoted
with respect to a BAS Ag/AgCl gel-filled reference electrode,
the potential of which was 35 mV more positive than that of
the saturated calomel electrode (SCE). Cyclic voltammetry was
performed using an EG&G Model 273 potentiostat/galvanostat
and a conventional three-electrode cell. All solutions were
degassed using nitrogen, and a blanket of nitrogen was
maintained over the solution during all experiments. The degree
of monolayer protonation was altered by systematically varying
the pH of the contacting electrolyte solution over the range 5.1
to 1.1 by addition of concentrated HClO4 to LiClO4 solutions.
These solutions were not pH buffered to avoid difficulties with
competitive adsorption effects from buffer ions.
Spontaneously adsorbed monolayers were typically formed
by immersing the electrodes in a methanol/water solution of
the metal complex for 8-12 h. No precautions were taken to
exclude oxygen during monolayer formation. Before electro-
chemical measurements were made, the modified electrodes
were rinsed with the electrochemical solvent to remove unbound
material. Subsequent measurements were performed in blank
electrolyte solutions.
Results and Discussion
General Electrochemical Properties. Figure 1 shows
representative cyclic voltammograms for a spontaneously ad-
sorbed (p3p)2 monolayer, where the supporting electrolyte is
0.1 M LiClO4 (pH ) 4.8) that does not contain any dissolved
[Os(bpy)2(p3p)2]2+. This voltammetric response is consistent
in all respects with that expected for an electrochemically
reversible reaction involving a surface-confined species.11 For
example, the peak shapes are independent of scan rate, at least
over the range of 1-50 V/s, and the peak height scales linearly
with the scan rate υ, unlike the υ1/2 dependence expected for a
freely diffusing species. Therefore, it appears that the osmium
complex adsorbs onto the surface of the platinum microelectrode
to give an electroactive film. Where there are no lateral
interactions between surface confined redox centers and a rapid
equilibrium is established with the electrode, a zero peak-to-
peak splitting (∆Ep) and a fwhm of 90.6 mV are expected for
a reaction involving the transfer of a single electron. As
discussed previously for [Os(bpy)2Cl(pNp)]+ monolayers,7
where pNp is 4,4′-bipyridyl or 1,2-dipyridylethane, we consis-
As described previously,7 a custom built function generator-
potentiostat, with a rise time of less than 10 ns, was used to
apply potential steps of variable pulse width and amplitude
directly to a two-electrode cell. A Pt foil and an Ag/AgCl
reference electrode were combined to form a counter electrode.
The foil lowered the resistance and provided a high-frequency
path.
For the temperature resolved experiments, a nonisothermal
cell was used in which the reference electrode was isolated from

Metal/Monolayer Interface Electron Transfer
J. Phys. Chem., Vol. 100, No. 9, 1996 3697
for adsorbed [Os(bpy)2(pyridine)(p3p)]2+ complexes,14 both of
which contain only one p3p bridging ligand. Molecular
modeling of the [Os(bpy)2(p3p)2]2+ complex suggests that if
both p3p ligands adsorbed onto the electrode surface, then its
area of occupation would be at least 214 Å2, a value that is
approximately 30% larger than that experimentally observed.
These observations suggest that only one of the p3p ligands is
bound to the electrode surface. This conclusion is supported
by our observation (vide infra) that the heterogeneous electron
transfer rate constant k depends on the pH of the contacting
electrolytic solution. This pH sensitivity of k contrasts with
structurally related [Os(bpy)2(pyridine)(p3p)]2+ monolayers
where the heterogeneous electron transfer dynamics are inde-
pendent of the solution pH.
As described previously,7,15 the ideality of the electrochemical
response can be further probed by using chronocoulometry to
determine the redox composition as a function of the applied
potential.16 The slopes of plots of ln ([Ox]/[Red]) vs potential
are independent of the pH, maintaining a value of 57 ( 3 mV/
decade, as the pH of the contacting electrolyte solution is
changed from 5.05 to 1.07. This slope is indistinguishable from
those predicted for one electron transfer reactions by the Nernst
equation,16 confirming that the thermodynamic aspects of
electron transfer at these metal/monolayer interfaces are nearly
ideal under the experimental conditions employed.
Figure 1. Scan rate dependence of cyclic voltammetry for a spontane-
ously adsorbed (p3p)2 monolayer. The scan rates are (top to bottom)
50, 20, 10, and 5 V/s. The surface coverage is 9.8 × 10-11 mol cm-2
.
The supporting electrolyte is 0.1 M LiClO4 at a pH of 4.8. The radius
of the platinum microelectrode is 25 µm. The cathodic currents are
up, and the anodic currents are down. Each cycle begins at the negative
limit.
tently observe a nonzero ∆Ep, even at low scan rates; e.g., ∆EP
is 12 ( 3 mV at a scan rate of 500 mV/s. Feldberg has
interpreted nonzero peak-to-peak splitting in terms of unusual
quasi-reversibility (UQR).12 In this model, hysteresis is ob-
served in cyclic voltammetry because some rate processes, e.g.,
heterogeneous electron transfer, ion movement, changes in
monolayer structure that accompany redox switching, etc., are
slow compared to the time scale of the experiment. We do not
consider this issue in detail here except to note that neither
heterogeneous electron transfer or double layer assembly (vide
infra) limit the voltammetric response at these scan rates. In
general, the voltammetric response is consistent with that
expected for a rapid, reversible electron transfer to an im-
mobilized redox active species. The peak height and peak area
of the voltammograms do not change by more than 15% when
cycled repeatedly over an 10 h period at temperatures up to
40 °C, indicating that the monolayers are both electrochemically
and thermally stable. We observe only a 20-30 mV difference
between the formal potentials of the solution-phase model
compound, [Os(bpy)3]2+, and the monolayer, suggesting that
the redox centers within the monolayer are solvated.
The total charge introduced or withdrawn to reduce or oxidize
the monolayer can be found from the area under the voltam-
metric peak after correcting for the background charging current.
This charge, together with the real surface area, can then be
used to calculate the surface coverage, or the number of moles
of [Os(bpy)2(p3p)2]2+ per cm2. The surface coverage provides
important information about the packing density of the mono-
layer and may provide a limited insight into the way that the
complex adsorbs onto the electrode surface. This is important
since the cis configuration of the bpy ligands makes it possible
for adsorption to occur through one or both of the p3p ligands.
The surface coverage, Γ, as experimentally determined from
the area under the cyclic voltammetric wave, was found to be
(1.05 ( 0.08) × 10-10 mol cm-2, corresponding to an area
occupied per molecule of 166 ( 12 Å2. When the additional
contributions to the molecular volume are considered, e.g., a
solvent shell or a counterion, this area of occupation is consistent
with that expected for a close packed monolayer in which the
radius of the metal complex (crystallographic data13 indicate
that the radii of osmium and ruthenium polypyridyl complexes
are of the order of 6.7 Å), rather than the length of the bridging
ligands, dictates the surface coverage. This area of occupation
is smaller than that found for adsorbed [Os(bpy)2Cl(p3p)]+
complexes7 (240 Å2) and is indistinguishable from that found
The formal potential for the Os2+/3+ redox reaction shifts from
0.638 to 0.654 V as the pH is systematically varied from 5.05
to 1.07. That E°′ shifts in a positive potential direction indicates
that protonation stabilizes the reduced state of the complex. This
small shift in E°′ is consistent with the methylene spacer groups
preventing effective electronic communication between the two
pyridine rings (vide infra). Moreover, the small shift in E°′
suggests that the electrostatic effects of protonating the unbound
pyridine ring are minor. This behavior probably arises because
the high dielectric constant of water and the high supporting
electrolyte concentration efficiently screen the charge on the
pyridinium ion that is located 9-10 Å away from the osmium
redox center.
Interfacial Capacitance. Probing the double layer capaci-
tance Cdl gives an insight into the change in interfacial charge
distribution that accompanies monolayer formation, the relative
perfection of the monolayer, and perhaps its thickness.5,7,17 Here,
we have used small amplitude potential step chronoamperometry
to measure the interfacial capacitance as the electrolyte con-
centration was systematically varied. The potential step was
centered at 0.100 V where the monolayer is redox inactive, and
a pulse amplitude ∆E of 25 mV was employed. The pulse
amplitude is sufficiently small to allow the measured capacitance
to be regarded as an approximate differential capacitance. This
potential step does not change the redox composition of the
monolayer, and only single exponential decays due to double
layer charging were observed. This capacitive current was
analyzed using a plot of ln ic(t) vs t to obtain the resistance Ru
and double layer capacitance Cdl according to eq 1.18
ic(t) ) (∆E/Ru) exp(-t/RuCdl)
(1)
For an electrochemical double layer, the differential capaci-
tance increases with a decreasing separation between the
electrode surface and the plane of closest approach for ionic
charge and increases with increasing dielectric constant.16 There
are two limiting cases for the potential profile across an adsorbed
monolayer.5 First, the modified interface could be similar to a
bare electrode so that all of the applied potential would be
dropped close to the electrode/monolayer interface. In this case,
the immobilized redox center would not experience a large

3698 J. Phys. Chem., Vol. 100, No. 9, 1996
Forster and O’Kelly
CHART 2
TABLE 1: Electrolyte Concentration Dependence of the
Cell Time Constant RuCdl, Uncompensated Cell Resistance
Ru, and Double Layer Capacitance Cdl as Measured
at +0.100 Va
[LiClO4], M
RuCdl, ns
10-3Ru, Ω
Cdl, pF
0.02
0.05
0.10
0.15
0.21
0.26
0.29
0.35
0.40
0.61
0.80
1.0
266(18)
289(22)
195(8)
177(11)
150(10)
134(12)
114(9)
92(6)
95(7)
58(4)
41(3)
34(2)
25.1(2.0)
18.3(1.8)
9.6(1.1)
7.1(0.6)
5.2(0.4)
4.1(0.4)
3.7(0.2)
3.1(0.3)
2.8(0.2)
1.8(0.1)
1.3(0.2)
1.1(0.1)
0.9(0.1)
10.6(1.0)
15.8(1.2)
20.4(1.8)
24.9(2.2)
28.7(2.4)
32.6(2.9)
30.8(3.0)
29.9(2.5)
34.5(3.2)
32.8(2.9)
31.7(3.1)
30.5(2.8)
32.8(2.5)
Figure 2. Dependence of the total interfacial capacitance for a
spontaneously adsorbed (p3p)2 monolayer on the logarithm of the
supporting electrolyte concentration. The capacitance was determined
using a small amplitude potential step centered on +0.100 V.
electrolyte is systematically varied from 0.02 to 1.2 M. Figure
2 shows the approximate differential capacitance, determined
at 0.100 V, as a function of the logarithm of the supporting
electrolyte concentration. The double layer capacitance in-
creases approximately linearly with increasing logarithm of the
electrolyte concentration for LiClO4 concentrations less than
about 0.2 M. This sensitivity clearly indicates that the diffuse
layer capacitance contributes significantly to the total interfacial
capacitance over this concentration range. The limiting value
1.2
29(2)
a Numbers in parentheses represent the standard deviations for at
least three individual monolayers. Supporting electrolyte is lithium
perchlorate. The radius of the platinum microelectrode is 5 µm.
of CT at high electrolyte concentration is at least 28 µF cm-2
,
electric field (Chart 2A). Second, as discussed recently by Smith
and White,5a the existence of an impermeable monolayer that
has a low dielectric constant may cause the potential to decay
linearly across the thickness of the monolayer and then
exponentially in the solution phase (Chart 2B). In this case,
the surface-confined redox centers would experience a large
electric field. An insight into the applicability of either model
to our interfaces can be obtained by measuring the interfacial
capacitance. This objective is doubly important because we
are interested in the electric field effects on heterogeneous
electron transfer, and the interaction of the highly charged
protonated complexes with the interfacial electric field.
For the model illustrated in Chart 2B,19 the reciprocal total
interfacial capacitance, CT, is given by the sum of the reciprocal
capacitances of the film, Cfilm, and the diffuse layer, Cdif
which may represent the film capacitance (Chart 2B), or if
solvent and electrolyte ions freely diffuse into the interior of
the monolayer and the double layer sets up as it would at a
bare electrode (Chart 2A), it may correspond to the capacitance
of the charges held at the outer Helmholtz plane. If this limiting
capacitance is dominated by the film capacitance (Chart 2B),
then, assuming a monolayer thickness of approximately 20 Å,
the relative dielectric constant within the film is estimated from
eq 3 as 63. That the relative dielectric constant within the
monolayer is comparable to that of water (ꢀSOLN ) 78.5) would
suggest that the monolayer is rather permeable to solvent and
counterions.
Alternatively, the double layer may set up within the
monolayer (Chart 2A), in which case the limiting interfacial
capacitance corresponds to the capacitance of the charges held
at the outer Helmholtz plane. Given that the distance of closest
approach is likely to be of the order of 3 Å, the relative dielectric
constant within the double layer would have to decrease from
the value of 78.5 for bulk water to approximately 9 before a
limiting interfacial capacitance of 28 µF cm-2 could be
observed. It is important to note that, as discussed above for
Chart 2B, this model is consistent with a solvated monolayer
interior.
CT-1 ) Cfilm-1 + Cdif
(2)
(3)
(4)
-1
Cfilm ) ꢀ0ꢀfilm/d
Cdif ) ꢀ0ꢀSOLNκ cosh[ze(φPET - φSOLN)/2kBT]
where ꢀ0 is the permittivity of free space, ꢀfilm and ꢀSOLN are
the film and solution dielectric constants, respectively, d is the
monolayer thickness, z is the charge number of the electrolyte
ion, e is the absolute electronic charge, kB is the Boltzmann
constant, T is the absolute temperature, and φPET and φSOLN are
the potentials at the plane of electron transfer and in the bulk
solution, respectively (Chart 2). The quantity κ is given by
(2n°z2e2/ꢀSOLNꢀ0kBT)1/2, where n° is the number concentration
of the ions in solution.16
Therefore, based on these capacitance data, we conclude that
the interior of the monolayer is at least partially solvated. This
conclusion is consistent with the observation that the fwhm in
cyclic voltammetry is close to that theoretically predicted for
noninteracting redox sites, suggesting that solvent and ions
permeate the monolayer and electrostatically insulate adjacent
charges.
Only the diffuse layer capacitance depends on the potential
or the concentration of supporting electrolyte. Therefore, the
relative importance of that component may be probed by
systematically varying the supporting electrolyte concentration
and measuring the total capacitance. Table 1 contains the cell
time constants, uncompensated cell resistances, and double layer
capacitances as the concentration of LiClO4 as supporting
As described recently by Creager and co-workers,5b an insight
into the interfacial potential distribution, and hence monolayer
permeability, can be obtained by probing the kinetics of
heterogeneous electron transfer as the supporting electrolyte
concentration is systematically varied. This is possible since a
significant potential difference between the plane of the im-
mobilized molecules and the bulk solution means that only

Metal/Monolayer Interface Electron Transfer
J. Phys. Chem., Vol. 100, No. 9, 1996 3699
they generate a potential that acts to weaken the applied potential
by an amount iRu, where i is the total current. This ohmic drop
can lead to severe distortions of experimental responses resulting
in inaccurate measurements of the heterogeneous electron
transfer rate. The significance of ohmic effects for these systems
can be assessed using the data presented in Table 1. As
illustrated in Figure 3, the Faradaic currents that flow in these
high-speed chronoamperometric experiments are typically in the
low-microamp range, even for 25 µm electrodes. Therefore,
using the cell resistance data given in Table 1, the calculated
iRu drop is less than 20 mV for supporting electrolyte concen-
trations above 0.1 M. However, not only does the concentration
of the supporting electrolyte play an important role in determin-
ing the magnitude of the uncompensated resistance, so too does
the pH. For example, for the pH 1.05 system illustrated in
Figure 3, the uncompensated resistance is approximately
2500 Ω, making the average ohmic loss approximately 5 mV.
The linearity of the ln iF(t) vs t plot shown in the inset of
Figure 3 indicates that electron transfer is characterized by a
single rate constant over the time required to collect greater
than 95% of the Faradaic charge. At supporting electrolyte
concentrations greater than 0.1 M, the monolayers always gave
linear first order decays over about two lifetimes. Deviations
from linearity would be expected if ohmic drop was present.
Uncompensated resistance causes the applied potential, and
hence the apparent rate, to evolve with time. Therefore, iRu
drop produces negative deviations in the observed current at
short times.7 That such nonidealities are not observed, at least
for high concentrations of supporting electrolyte, is consistent
with negligible ohmic losses. We have further probed the
existence of ohmic effects by reducing the radius of the
microelectrode. This approach is useful since the resistance
increases with decreasing electrode radius, but the current
decreases as the square of the radius leading to reduced ohmic
effects for smaller electrodes. The inset in Figure 3 shows that
the slope of the semilog plot obtained for a 12.5 µm platinum
electrode modified with a spontaneously adsorbed (p3p)2
monolayer is indistinguishable from that obtained at a 25 µm
electrode. This observation is consistent with ohmic losses
being negligible under the experimental conditions employed.
Moreover, we find that the heterogeneous electron transfer rate
constant measured at an overpotential of -50 mV is independent
of the supporting electrolyte concentration, maintaining a value
of (2.5 ( 0.2) × 104 s-1 as the LiClO4 concentration was
systematically varied from 0.1 to 1.0 M. On the basis of the
measured cell resistances, and the insensitivity of the apparent
heterogeneous rate constant to changes in electrode size or
supporting electrolyte concentration, we conclude that ohmic
drop and double layer effects on the interfacial kinetics are
negligible for electrolyte concentrations greater than about
0.1 M.
Figure 3. Current response for a 25 µm radius platinum microelectrode
modified with a (p3p)2 monolayer following a potential step where the
overpotential η was -50 mV. The supporting electrolyte is 0.1 M
perchlorate at a pH of 1.05. The inset shows ln iF(t) vs t plots for the
Faradaic reaction for a 25 µm (top) and a 12.5 µm (bottom) radius
platinum microelectrode.
a fraction of the total interfacial drop drives the heterogeneous
electron transfer process. In fact, the driving force would be
governed by an equilibrium electrode potential that is a function
of the electrostatic potential at the site for electron transfer. This
means that the driving force for electron transfer changes as
the redox reaction proceeds, causing the overall dynamics to
deviate from first order kinetics.5b We note that there are many
processes other than interfacial fields that can cause nonexpo-
nential current decays, including multiple site geometries,
surface activity effects,11 the presence of defect sites,20 oxidation
state dependent dipole moments,21 or ion pairing.22 However,
an increased supporting electrolyte decreases the double layer
thickness κ, and if ions permeate into the monolayer, the
situation is approached where all of the applied potential is
dropped close to the electrode/monolayer interface. Therefore,
one can probe the ideality of the chronoamperometric response
without the complication of interfacial electric fields by employ-
ing high concentrations of supporting electrolyte.
Chronoamperometry. For an ideal electrochemical reaction
involving a surface bound species, the Faradaic current following
a potential step that changes the redox composition of the
monolayer exhibits a single exponential decay in time according
to3a,c,7
iF(t) ) kQ exp(-kt)
(5)
where k is the apparent rate constant for the overall reaction
and Q is the total charge passed in the redox transformation.
Figure 3 illustrates a typical example of the chronoampero-
metric response observed for the reduction (Os3+ + e- f Os2+
)
Further evidence suggesting the predominance of a single rate
constant is obtained by examining the intercept of the semilog
plot at zero time. As indicated by eq 5, the intercept for a single
exponential decay is ln(kQ). Nernst plots of the redox composi-
tion as a function of potential (vide supra) confirm that an
absolute overpotential of 50 mV decreases the number of
oxidized species within the monolayer to less than 10% of the
total. Therefore, such a potential step effectively causes
complete reduction of the film, and the full surface coverage,
Γ, can be calculated from the intercept of Figure 3 using the
relation11
of a (p3p)2 monolayer, where the electrolyte is 0.1 M aqueous
LiClO4 at a pH of 1.05. In this experiment the overpotential η
(≡E - E°′) was -0.050 V. This figure shows that on a
microsecond time domain two current decays can be separated.
These responses, which arise from double layer charging and
Faradaic current flow, are time-resolved due to the much shorter
time constant of double layer charging compared to that of the
Faradaic reaction. In our investigations, we have determined
the electron transfer rate constant only when the time constant
of double layer charging is at least five times shorter than the
time constant of the Faradaic reaction.
While fast charging of the electrochemical double layer is
important, the effects of ohmic losses must also be considered.16
When Faradaic and charging currents flow through a solution,
Γ ) Q/nFA
(6)
where n is the number of electrons transferred, F is the Faraday

3700 J. Phys. Chem., Vol. 100, No. 9, 1996
Forster and O’Kelly
Figure 4. Dependence of the heterogeneous electron transfer rate
constant at spontaneously adsorbed (p3p)2 (lower curve) and
[Os(bpy)2(p3p)(pyridine)]2+ (upper line) monolayers on the pH of the
contacting electrolyte. The supporting electrolyte concentration is
approximately 0.1 M perchlorate. The overpotential η is 102 mV.
Figure 5. Effect of various overpotentials η, on the ln iF(t) vs t plots
for a spontaneously adsorbed (p3p)2 monolayer. The supporting
electrolyte is 0.1 M HClO4. Taken on the right-hand side, the
overpotentials are from top to bottom, 0.051, 0.103, 0.200, and
0.349 V, respectively.
constant, and A is the real or microscopic electrode area. This
chronoamperometric determination of the charge passed can then
be compared with the value determined using cyclic voltam-
metry in order to further test the ideality of the chronoampero-
metric response. We find that the charges passed in these two
independent experiments agree within 10%. This agreement
indicates that all of the surface confined molecules are redox
active on a microsecond time scale; i.e., relatively few, if any,
sites are kinetically isolated.
coordination shell of the osmium complex plays a central role
in making k sensitive to the solution pH.
A possible explanation of this pH dependence is that
protonating the free pyridine ring of the p3p ligand alters the
electron density on the redox center. However, the degree of
electronic coupling between the pyridine rings of the p3p ligand
is expected to be weak given that they are separated by three
methylene spacer groups. Our experimental observation that
the formal potential of the Os2+/3+ redox reaction remains
constant to within 23 mV as the pH of the contacting solution
is changed from 5.05 to 1.07 supports this conclusion. More-
over, solution phase absorption spectroscopy of the complex
dissolved in DMF indicates that the position of the metal to
ligand charge transfer band remains constant when the p3p
ligands are protonated. This observation further suggests that
protonation does not significantly affect the electron density on
the osmium redox center.
Effect of Solution pH on Heterogeneous Kinetics. Plots
of ln iF(t) vs t, obtained at an overpotential of 102 mV, remain
linear (R2 > 0.99) as the pH of the contacting electrolyte solution
is systematically varied from 5.05 to 1.07, and heterogeneous
electron transfer rate constants have been evaluated from their
slopes. Figure 4 shows that there is a sigmoidal relationship
between the heterogeneous electron transfer rate constant and
the pH of the electrolyte, with k decreasing from (3.4 ( 0.2) ×
105 to (6.6 ( 0.4) × 104 s-1 when the solution pH is decreased
from 5.05 to 1.07. That k is sensitive to the solution pH, yet
plots of ln iF(t) vs t remain linear over a wide pH range, is
significant. One might imagine that if the system were in two
different states, protonated and nonprotonated, each with
different rate constants, that the corresponding semilog plots
would be nonlinear or, in the extreme case, would exhibit dual
slope behavior. That such nonlinear behavior is not observed
suggests that protonation equilibrium occurs more rapidly than
redox equilibrium.
The heterogeneous electron transfer rate is considered to
depend on a frequency factor and a Franck-Condon barrier
and can be expressed as24
k ) Γnκelυn exp(-∆Gq/RT)
(7)
where Γn is the nuclear tunneling factor, κel is the electronic
transmission coefficient, υn is the nuclear frequency factor, and
∆Gq is the free energy of activation.25,26 Since the experimental
frequency factors are always less than kBT/h (h is the Planck
constant), the nuclear tunneling factor is unity.24 From eq 7, it
is evident that the sensitivity of the heterogeneous electron
transfer rate to the solution pH could be caused by changes in
the free energy of activation or the pre-exponential factor. Since
the free energy of activation equals λ/4, where λ is the total
reorganization energy associated with switching the oxidation
state of the monolayer, one strategy for estimating ∆Gq is to fit
the dependence of the logarithm of the rate constant on the
overpotential.2c,3a,c,27
It is important to note that the cell resistance decreases as
the pH of the electrolytic solution decreases. Therefore, one
would expect ohmic effects to be more significant at high, rather
than low, pH, which would cause the heterogeneous electron
transfer rate constant to be underestimated at high pH. That
the opposite trend is experimentally observed, i.e., k increases
with increasing pH, supports our conclusion that ohmic effects
do not adversely affect the chronoamperometric determination
of k.
The inflection point of Figure 4 is located at a pH of
approximately 2.9, which is consistent with the pKa of the
unbound p3p ligand.23 These data suggest that protonating the
unbound p3p ligand alters the rate of heterogeneous electron
transfer across the electrode/monolayer interface. Figure 4 also
shows that the rate of heterogeneous electron transfer to
spontaneously adsorbed [Os(bpy)2(pyridine)(p3p)]2+ monolay-
ers, which do not contain groups capable of becoming proto-
nated, is independent of solution pH in this range. This
observation suggests that the second p3p ligand within the
pH Effects on the Potential Dependence of k. Figure 5
illustrates the effect of various overpotentials on the ln iF(t) vs
t plots, where the supporting electrolyte is 0.1 M HClO4. This
figure shows that linear responses are observed at each of the
overpotentials investigated. These linear responses are consis-
tent with negligible ohmic effects despite the higher Faradaic
currents that flow when a larger overpotential is applied. These
data highlight another advantage of high-speed electrochemistry.
As illustrated in Figure 1, the background current in cyclic
voltammetry tends to rise as the positive potential limit is

Metal/Monolayer Interface Electron Transfer
J. Phys. Chem., Vol. 100, No. 9, 1996 3701
electron transfer predicts these nonlinear Tafel plots, because
it includes a term that is quadratic in η in the rate equation.28
Simplified models incorporating the basic concepts of the
Marcus theory have been developed to model heterogeneous
electron transfer across electrode/monolayer interfaces.3a,c
Chidsey has developed a model describing through-bond
electron tunneling across metal/monolayer interfaces.3a How-
ever, this model predicts that Tafel plots will be symmetric with
respect to overpotential. That we experimentally observe larger
cathodic than anodic heterogeneous electron transfer rate
constants for a given absolute value of the overpotential suggests
that through-bond electron tunneling is not an appropriate model
for our system. Finklea and Hanshew3c have assembled a model
describing through-space electron tunneling that predicts our
experimental observation of asymmetric Tafel plots. In
Finklea’s model, the heterogeneous electron transfer rate
constant is given by the integral over energy of three functions,
namely, the Fermi function of the metal, the distribution of
energy levels for acceptor or donor states in the monolayer
(assumed to be Gaussian), and a rate parameter for electron
tunneling at a given energy. In order to fit this model to the
experimental data shown in Figure 6, estimates are required for
the average barrier height to heterogeneous electron transfer,
the total reorganization energy associated with switching the
redox state of the monolayer, and the preintegral factor.
The average barrier height for electron tunneling at
[Os(bpy)2Cl(pNp)]+ monolayers, where pNp is 4,4′-bipyridyl,
1,2-di(4-pyridyl)ethane or 4,4′-trimethylenedipyridine, has pre-
viously been estimated from the distance dependence of k°.27a
Given that the same bridging ligand is used here, we employ
the same value of the average barrier height, 200 kJ mol-1, in
the present analysis. The total reorganization energy λ, dictates
the degree of curvature in the Tafel plots. Therefore, λ was
chosen so that there was satisfactory agreement between shapes
of the theoretical Tafel plots and the experimental data. Finally,
the preintegral factor was adjusted to give the experimental value
of k°.
Figure 6. Tafel plots for (p3p)2 monolayers as a function of the
supporting electrolyte pH. The data (top to bottom, right hand side)
represent electrolyte pH’s of 5.05, 3.10, and 1.07, respectively. The
solid lines denote theoretical fits obtained from a through-space
tunneling model where λ ) 100, 68, and 56 kJ mol-1 from top to
bottom, respectively. The errors are approximately equal to the size of
the symbols.
TABLE 2: Effect of Electrolyte pH on Standard
Heterogeneous Rate Constants, Activation Parameters, and
Pre-exponential Factorsa
electrolyte
pH
λ,
10-4k°,b s-1 kJ mol-1 kJ mol-1 kJ mol-1 10-6Aet,d s-1
∆Hq,
∆Gcq,c
5.05
3.95
3.10
2.08
1.07
6.1(0.2)
6.0(0.2)
4.3(0.1)
2.0(0.1)
1.6(0.1)
100
93
68
54
56
37.5(2.1) 25.1(2.2) 1547(345)
34.6(1.8) 22.1(1.7) 451(78)
30.3(1.3) 17.0(0.9) 41(6)
26.1(2.2) 13.8(1.4) 5.3(0.6)
24.6(1.5) 14.3(1.1) 5.2(0.4)
a Numbers in parentheses represent the standard deviations for at
least three individual monolayers. Supporting electrolyte is 0.1 M
perchlorate. b All standard rate constants were determined at 298 K.
c Free energy of activation determined from the cathodic ideal
electrochemical enthalpies using ∆Src°. d Pre-exponential factor ex-
tracted from the standard heterogeneous electron transfer rate constant
using ∆Gq.
Figure 6 shows the experimental dependence of ln k on
overpotential for solution pH’s of 5.05, 3.10, and 1.07. This
figure indicates that the degree of curvature of these Tafel plots
depends on pH, suggesting that the reorganization energy
depends on the extent of monolayer protonation. Figure 6 shows
that satisfactory agreement between Finklea and Hanshew’s
model and the experimental data is obtained when λ is 100, 68,
and 56 kJ mol-1 for solution pH’s of 5.05, 3.10, and 1.07,
respectively. However, we note that the electron transfer
dynamics can only be probed over a restricted range of
overpotentials because of the rapid nature of the process. This
restriction means that only limited confidence can be placed in
these fitted values of the reorganization energy.
The Marcus theory can provide a theoretical estimate of the
reorganization energy.28 In the Marcus model, λ is considered
to be the sum of an inner sphere and outer sphere component.
The inner sphere component describes the distortion of bond
angles and lengths accompanying electron transfer, while the
outer sphere component reflects solvent reorganization effects.
Crystallographic data demonstrate that switching the oxidation
state of osmium and ruthenium polypyridyl complexes does not
significantly change either the bond lengths or angles. This
observation suggests that the inner sphere reorganization energy
for this system is negligible, at least in the solid state. The
outer sphere solvent reorganization energy λOS is given by
approached. This increasing background current arises from
the initial electrochemical cleaning of the platinum surface and
is caused by incomplete removal of adsorbed oxygen or platinum
oxide. However, the processes responsible for these background
currents appear to be slow and take place on a millisecond time
scale. By probing the electron transfer dynamics on a micro-
second time scale, these background currents can be effectively
eliminated so that the chronoamperometric data are not affected
even at overpotentials where the background in cyclic voltam-
metry may be rising.
Figure 6 illustrates Tafel plots of ln k vs overpotential, η, for
monolayers in contact with perchlorate electrolytes at different
pHs. For overpotentials less than about 200 mV, ln k depends
approximately linearly on η. The standard heterogeneous
electron transfer rate constant k° has been determined by linearly
extrapolating ln k to zero overpotential, and Table 2 contains
these data. However, at large overpotentials the response is
clearly nonlinear, and the slopes decrease in magnitude with
increasing overpotential in both the anodic and cathodic
directions. In the conventional Butler-Volmer formulation of
electrode kinetics,16 these slopes represent (1 - Ra)F/RT and
-RcF/RT for the oxidation and reduction reactions, respectively,
where Ra is the anodic, and Rc the cathodic, transfer coefficient.
Therefore, in contrast with the expectations of the Butler-
Volmer formulation, Figure 6 suggests that the transfer coef-
ficients are potential dependent. Furthermore, as reported
previously for [Os(bpy)2Cl(p3p)]+ monolayers,27a Ra tends
toward zero more rapidly than Rc. The Marcus theory of
-1
λOS ) (e2/2)(r-1 - Re-1)(ꢀop-1 - ꢀSOLN
)
(8)
where e is the absolute electronic charge, r is the radius of the

3702 J. Phys. Chem., Vol. 100, No. 9, 1996
Forster and O’Kelly
metal complex (6.7 Å), Re is the reactant-image distance, ꢀop is
the optical dielectric constant of water (5.5), and ꢀSOLN is the
static dielectric constant (78.5). As discussed previously,27a we
have neglected imaging effects, i.e., Re f ∞, in calculating the
theoretical solvent reorganization energy. Equation 8 yields a
solvent reorganization energy of 56.9 kJ mol-1, which agrees
with the value of 56 kJ mol-1 obtained from fitting the data in
Figure 6 when the monolayer is fully protonated. This
observation suggests that the activation energy barrier to
heterogeneous electron transfer at a protonated monolayer is
dictated by solvent reorganization. In contrast, the experimental
reorganization energy for nonprotonated monolayers
(100 kJ mol-1) is significantly larger than that predicted by eq
8 for solvent reorganization. There are a number of factors that
may cause the activation barrier to heterogeneous electron to
depend on the monolayer’s state of protonation. For example,
the interfacial potential distribution may be different with the
higher ionic strength of the low-pH solutions causing the
potential to drop more sharply at the electrode/monolayer
interface. These differences in electric field strength may
change the solvent or ion content of the film. It is important to
note that the experimental semilog current vs time responses
remain linear over the pH range investigated. The linearity of
these responses suggests that diffusional processes; e.g., the
motion of charge compensating counterions does not influence
the rate of, or the barrier to, heterogeneous electron transfer.
Alternatively, redox induced changes in the film structure, e.g.,
a change in the tilt angle θ (Chart 1), may accompany oxidation
of the monolayer. This reorientation of the adsorbate could act
as an “inner sphere” reorganization energy, making the experi-
mental λ larger for nonprotonated monolayers.
Figure 7. Effect of the pH of the contacting electrolyte solution on
the temperature dependence of the formal potential for (p3p)2 mono-
layers spontaneously adsorbed on platinum microelectrodes. The data
represent (top to bottom) electrolyte pH’s of 1.5, 5.2, and 3.6,
respectively.
positive potential direction with increasing temperature indicat-
ing positive reaction entropies and a higher degree of local
ordering in the oxidized than in the reduced state. Figure 7
shows that plots of E°′ vs T are linear over the pH range 5.2 to
1.5, and reaction entropies have been calculated from the slopes
according to eq 9. The slopes of these lines do not depend on
the pH of the contacting solution, and ∆Src° remains constant
at 82 ( 7 J mol-1 K-1 over the pH range 5.2 to 1.5. This
observation clearly demonstrates that changes in the activation
entropy are not responsible for the pH dependence of the free
energy of activation suggested by Figure 6.
Temperature Dependence of k. Weaver and co-workers31
have established that a temperature independent Galvani po-
tential difference, φm, across the metal/solution interface can
be achieved using a nonisothermal cell. The electrochemical
activation enthalpy determined from an Arrhenius plot of ln k
vs T-1, where φm is held constant, has been termed “ideal”,32
and we label it here as ∆HIq. For a reduction or cathodic
reaction, this electrochemical activation enthalpy can be sepa-
rated into “chemical”, ∆Hq, and “electrical”, RcFφm, contribu-
tions according to
In the Marcus theory, the free energy of activation ∆Gq is
equal to λ/4. Therefore, while the largest heterogeneous electron
transfer rate is observed for nonprotonated monolayers (Figure
4), this process is associated with the largest free energy of
activation (Figure 6). If the pre-exponential factor of eq 7 did
not change as the monolayer became protonated, then a higher
free energy of activation would give a lower, not a higher,
heterogeneous electron transfer rate. This is an important
observation and suggests that changes in the pre-exponential
factor with monolayer protonation cause the heterogeneous
electron transfer to be pH sensitive.
To avoid the inherent inaccuracy of fitting Tafel plots over
a limited potential range to estimate ∆Gq, and to obtain a more
quantitative insight into the origin of the pH sensitivity of k,
we have performed temperature-resolved measurements of the
formal potential and heterogeneous electron transfer rate to
independently probe the pH dependence of the activation entropy
and enthalpy, respectively.
Reaction Entropies. One might anticipate that since pro-
tonating the monolayer changes its charge, the reaction entropy
∆Src°, quantifying the difference in entropy between the reduced
and oxidized forms of the redox couple, would depend on the
pH of the contacting electrolytic solution.29 If ∆Src° was pH
dependent, then it could explain the pH dependence of the free
energy of activation suggested by Figure 6.
The reaction entropy has been determined using a noniso-
thermal cell by measuring the temperature dependence of the
formal potential obtained from cyclic voltammetry as the pH
of the contacting solution was systematically varied. As
discussed by Weaver and co-workers, the temperature depen-
dence of the formal potential can be expressed as29,30
∂ ln k
∂(1/T)
∆HI,cq ) -R
) ∆Hq - RcFφm
(10)
|
φm
We have investigated the temperature dependence of the
heterogeneous electron transfer rate using temperature-resolved
chronoamperometry over the temperature range -5 to +40 °C.
An overpotential of -50 mV, as determined at 298 K, was used
throughout these experiments, and the resulting current-time
transients were similar to those illustrated in Figure 3. The
corresponding semilog plots were linear over approximately two
lifetimes, and the heterogeneous electron transfer rate was
evaluated from the slopes. In a typical set of experiments, the
temperature was systematically varied over a range and then
returned to the initial temperature. The same slope, -k, and
intercept, ln(kQ), were observed within experimental error for
the initial and final transients. This consistency indicates that
cycling the temperature does not change the heterogeneous
kinetics or the quantity of material immobilized on the electrode
surface. The heterogeneous electron transfer rate constant
increases with increasing temperature as anticipated for a
thermally activated process. Arrhenius plots of ln k vs T-1 are
linear (R2 > 0.995) over the temperature range -5 to +40 °C.
Table 2 contains the activation enthalpies, ∆Hq, obtained from
the slopes of these plots after using the experimental transfer
coefficient to correct for the electrical driving force (-50 mV)
∆Src° ) F(∂E°′/∂T)
(9)
For all situations investigated, the formal potential shifts in a

Metal/Monolayer Interface Electron Transfer
J. Phys. Chem., Vol. 100, No. 9, 1996 3703
the electrode and the redox site. There are several possible
causes of the observed dependence of the electronic transmission
coefficient, and hence the heterogeneous electron transfer rate,
on the pH of the contacting solution. For example, it is possible
that at high pH immobilization occurs through both uncom-
plexed pyridine nitrogens and that lowering the solution pH
causes desorption of one of the pyridine rings which then
becomes protonated. We note however, that the experimental
area of occupation as measured at high pH is considerably
smaller than that predicted for the situation in which both
uncomplexed pyridine groups bind to the electrode surface.
Moreover, the pKa’s of both uncomplexed pyridines are identi-
cal, making selective desorption of one of them from the
electrode surface unlikely. Alternatively, protonating the mono-
layer may either cause the tilt angle (Chart 1) between the
bridging ligand and the electrode surface to increase, or the
methylene spacer groups to adopt a more extended configura-
tion. It is possible that this proton induced restructuring of the
monolayer arises because the formal potential of the adsorbed
complex is positive of the potential of zero charge. This
situation is expected to cause repulsive interactions between the
positively charged electrode and the highly charged protonated
(4+) complexes, causing the redox centers to move away from
the electrode and thus increasing the through-space tunneling
distance.
If this model is appropriate, then the change in the through-
space tunneling distance between the protonated and nonpro-
tonated forms of the monolayer can be estimated from the data
illustrated in Figure 8 by assuming that the tunneling parameter
â° is identical to that found previously27a for [Os(bpy)2Cl(p3p)]+
monolayers (1.5 Å-1). Using this value of â°, an increase in
the through-space electron transfer distance of approximately
3.5 Å would be required to cause κel to decrease from (9.1 (
2.4) × 10-4 to (4.4 ( 2.0) × 10-6 as the monolayer goes from
a nonprotonated to a fully protonated state. When any
directional component in the electronic coupling between the
metallic states of the electrode and the orbitals of the adsorbed
complex is ignored, this difference in through-space electron
transfer distance could be accounted for by a change in the tilt
angle from approximately 40° in the nonprotonated state to 90°
in the protonated state.
Figure 8. Dependence of the logarithm of the electronic transmission
coefficient κel for heterogeneous electron transfer across platinum/(p3p)2
monolayer interfaces on the pH of the supporting electrolyte.
according to eq 10. These data confirm that the activation
enthalpy changes as the monolayer becomes protonated, de-
creasing from 37.5 ( 2.1 to 24.6 ( 1.5 kJ mol-1 as the pH is
reduced from 5.05 to 1.07.
In principle, it is possible to use the experimental enthalpies
and entropies to calculate free energies of activation. Comparing
these values with the value of the reorganization energy provided
by Finklea and Hanshew’s model is an important test of
consistency between these two independent experiments. We
have calculated the cathodic free energy of activation according
to eq 11,27a,32 and Table 2 contains the data. These data show
that, at the five pH’s investigated, ∆Gcq and λ/4 agree to within
5%.
∆Gcq ) ∆HI,cq - TRc∆Src°
(11)
Pre-exponential Factor. That both ∆Gcq and k decrease with
decreasing electrolyte pH suggests that the pre-exponential factor
of eq 7 decreases as the monolayer becomes protonated. Table
2 contains values of Aet (≡κelυn) that have been determined using
our experimental free energies of activation and the standard
heterogeneous electron transfer rate constant. To isolate the
effects of the electronic transmission coefficient, we have
calculated the nuclear frequency factor, υn, using the dielectric
continuum model,33
Conclusions
The adsorbed monolayers considered here exhibit nearly ideal
cyclic voltammetry and chronoamperometry as the pH, tem-
perature, and experimental time scale are varied over a wide
range. Chronoamperometry has been used to probe the rate of
heterogeneous electron transfer across the monolayer/micro-
electrode interface. This process can be characterized by a
single rate constant at high electrolyte concentrations, suggesting
that heterogeneous electron transfer across these metal/mono-
layer interfaces is mechanistically uncomplicated. This unusual
ideality has allowed us to probe the nature of the activation
barrier to electron transfer, and the degree of electronic coupling
between the remote redox centers and the microelectrode, in
considerable detail. Measurements of the potential dependence
of the heterogeneous electron transfer rate constant, k, suggest
that electron transfer occurs via a through-space rather than a
through-bond tunneling mechanism and that it depends on the
pH of the contacting solution. By determining the free energy
of activation using two independent methods, we have shown
that changes in the pre-exponential factor rather than ∆Gq cause
this pH sensitivity. It appears that the interaction of the highly
positively charged protonated complexes with the interfacial
electric field causes the through-space electron transfer distance
to increase, perhaps by altering the tilt angle between the
υn ) τl-1(∆Gcq/4πkBT)1/2
(12)
where τl-1 is the inverse longitudinal relaxation time for water
(1.9 ps-1). These values have then been used to estimate κel
from the experimental pre-exponential factor. Figure 8 shows
that for all pH’s investigated the electronic transmission
coefficient is considerably less than unity. This observation
indicates that there is a low probability of electron transfer once
the nuclear transition state has been attained, suggesting a
nonadiabatic reaction involving weak coupling between the
metallic states of the electrode and the localized orbitals of the
redox center. The pH dependency of log κel is illustrated in
Figure 8. Significantly, κel increases dramatically from (4.4 (
2.0) × 10-6 to (9.1 ( 2.4) × 10-4 on going from a protonated
to a nonprotonated monolayer.
As discussed above, our observation of larger cathodic than
anodic heterogeneous electron transfer rate constants for a given
absolute value of the overpotential is consistent with through-
space rather than through-bond electron tunneling. This is an
important point since, unlike a through-space tunneling mech-
anism, the electron transfer distance for a through-bond tun-
neling process is not sensitive to the tilt angle (Chart 1) between

3704 J. Phys. Chem., Vol. 100, No. 9, 1996
Forster and O’Kelly
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adsorbate and the electrode surface or by causing the methylene
spacer groups to become extended.
Although the change in heterogeneous electron transfer rate
constant on going from nonprotonated to fully protonated
monolayers is less than an order of magnitude, this pH induced
“conformational gating” of the electron transfer rate offers the
possibility of developing pH triggered electrical switches. We
expect that fundamental investigations focusing specifically on
the role that the local medium, particularly the bridging structure
linking the reactants, plays in dictating the rate and pathway
for electron transfer, will make it possible to design molecular
systems that maximize electron transfer efficiency and their
sensitivity to specific chemical triggers.
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Acknowledgment. R.J.F. gratefully acknowledges Professor
Larry R. Faulkner of the University of Illinois at Urbana-
Champaign for the generous loan of the high-speed potentiostat
used in this work. Financial support from Forbairt, the Irish
Science and Technology Agency, under Basic Research Grant
SC/95/209 is gratefully acknowledged.
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