Do molecular conductances correlate with electrochemical rate constants? Experimental insights

Article abstract of DOI:10.1021/ja201042h

We measured single-molecule conductances for three different redox systems self-assembled onto gold by the STMBJ method and compared them with electrochemical heterogeneous rate constants determined by ultrafast voltammetry. It was observed that fast systems indeed give higher conductance. Monotonous dependency of conductance on potential reveals that large molecular fluctuations prevent the molecular redox levels to lie in between the Fermi levels of the electrodes in the nanogap configuration. Electronic coupling factors for both experimental approaches were therefore evaluated based on the superexchange mechanism theory. The results suggest that coupling is surprisingly on the same order of magnitude or even larger in conductance measurements whereas electron transfer occurs on larger distances than in transient electrochemistry.

Full text of DOI:10.1021/ja201042h

ARTICLE
pubs.acs.org/JACS
Do Molecular Conductances Correlate with Electrochemical Rate
Constants? Experimental Insights
Xiao-Shun Zhou,3,†,‡,§ Ling Liu,3,‡ Philippe Fortgang,§ Anne-Sophie Lefevre,§ Anna Serra-Muns,§
Noureddine Raouafi,§,^ Christian Amatore,*,§ Bing-Wei Mao,*,‡ Emmanuel Maisonhaute,*,§,z and
Bernd Sch€ollhorn*,§,#
†Zhejiang Key Laboratory for Reactive Chemistry on Solid Surfaces, Institute of Physical Chemistry, Zhejiang Normal University, Jinhua,
Zhejiang 321004, China
‡Chemistry Department and State Key Laboratory for Physical Chemistry of Solid Surfaces, College of Chemistry and Chemical
Engineering, Xiamen University, Xiamen 361005, China
§UMR CNRS 8640 Pasteur, Ecole Normale Supꢀerieure, Universitꢀe Pierre et Marie Curie ꢀ Paris 06, 24 rue Lhomond,
75231 Paris Cedex 05, France
^Laboratoire de Chimie Analytique et d’Electrochimie, Dꢀepartement de Chimie, Facultꢀe des Sciences de Tunis, Universitꢀe El-Manar,
2092 Tunis El-Manar, Tunisia
zLISE-Laboratoire Interfaces et Systꢁemes Electrochimiques, UPR 15 du CNRS, Universitꢀe Pierre et Marie Curie ꢀ Paris 06,
Case Courrier no. 133, 4 place Jussieu, 75252 Paris Cedex 05, France
#Laboratoire d’Electrochimie Molꢀeculaire, Universitꢀe Paris Diderot ꢀ Paris 07, CNRS UMR 7591, 15 rue Jean-Antoine de Baïf, Bat.
Lavoisier, 75013 Paris, France
S Supporting Information
b
ABSTRACT: We measured single-molecule conductances for three different
redox systems self-assembled onto gold by the STMBJ method and compared
them with electrochemical heterogeneous rate constants determined by ultra-
fast voltammetry. It was observed that fast systems indeed give higher
conductance. Monotonous dependency of conductance on potential reveals
that large molecular fluctuations prevent the molecular redox levels to lie in
between the Fermi levels of the electrodes in the nanogap configuration.
Electronic coupling factors for both experimental approaches were therefore
evaluated based on the superexchange mechanism theory. The results suggest
that coupling is surprisingly on the same order of magnitude or even larger in
conductance measurements whereas electron transfer occurs on larger distances than in transient electrochemistry.
replaced by electrodes, a steady-state current flows; hence, a
conductivity through the bridge can be estimated. Development
of the mechanically controllable break junction (MCBJ) tech-
nique or the scanning tunneling microscopy break junction
(STMBJ) technique has presently reached the single-molecule
limit6ꢀ9 of molecular conductance determination in the junction.
Theoretical formulations relevant for the diverse experimental
setups differ in the way the electronic and vibrational states are
taken into account. For a molecular entity, there is generally a
single electronic state to consider, but a continuous distribution
of vibrational states is involved through the so-called Franckꢀ
Condon factor:
1. INTRODUCTION
Evaluation of electron transport properties of molecular
structures is under increasing focus, the aim being to provide not
only guidance for building efficient signal transduction for future
bottom-up devices1,2 but also to enable deeper insight into
chemical/electrochemical processes. Several experimental ap-
proaches are relevant in this field. Among them, transient
spectroscopy has proven to be useful to initiate electron transfer
between an acceptor A and a donor D separated by a bridge in a
molecule.3,4 Electrochemical techniques that involve replace-
ment of A or D by an electrode allow a current to be registered
toward or from a redox center that is incorporated into the
bridge.5 Both of these types of techniques afford rate constants
and thus kinetic parameters of thermalized electron transfer.
Furthermore, though in voltammetry the method is statistical,
being performed onto a large number of molecular systems, only
a single electron per molecule is transferred, creating a perma-
nent change in the molecule. Conversely, when both A and D are
2
ADÞ =4λkBT
eꢀðλ þ E
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
F ¼
ð1Þ
4πλkBT
Received: February 2, 2011
Published: April 25, 2011
r
2011 American Chemical Society
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Scheme 1. Molecular Systems Considered in the Present
Work
nature of their redox center, bridging unit, and metal-contacting
atoms but have similar size (about 1.9 nm). Whereas it is
relatively easy to measure molecular conductance when conduc-
tions are rather high, it is conversely more difficult to accurately
determine fast electrochemical rate constants because ohmic
losses in the solution filter the electrochemical information. We
addressed this problem by the employment of microelectrodes
with a specific potentiostat that allows compensation of ohmic
losses with a sweep rate up to 2.5 megavolts per second in cyclic
voltammetry. This setup is equivalent to a few tens of nanose-
conds resolution21ꢀ23 so that transient electrochemistry is now
useful to investigate fast transduction which is obviously the most
interesting domain for future practical applications of molecular
electronic devices.
2. EXPERIMENTAL DETAILS
2.1. Synthesis. The detailed synthesis of compounds 1ꢀ3 is
reported in the Supporting Information.
2.2. Adsorption Conditions. The adsorption conditions were
optimized for each compound. For 1, a gold single crystal was immersed
into a CH3CN solution of 1 (0.1 mM) for 5 min, and then for 10 min in
the pure solvent. For 2, the electrode was first immersed into a 0.05 mM
CH2Cl2 solution of 2 for 1 h at 4 ꢀC and then for 1ꢀ2 h in pure solvent
after a thorough rinsing. The self-assembled monolayer of 3 was formed
by soaking the electrode overnight in a chloroform solution containing
0.1 mM 3 and 0.1 mM pentanethiol 0.1, the latter being used as a diluent
to minimize hairpin adsorption of 3 by both thiol functions on the
surface (see below). After being thoroughly rinsed with chloroform,
the electrode was immersed in pure chloroform for 2ꢀ4 h to remove
physically adsorbed molecules.24
2.3. STM Experiment. Experiments for 1 and 2 were performed
using an Agilent 5100 microscope. Gold tips were prepared
electrochemically25 and then insulated using Apiezon wax to obtain a
leakage current of less than a few picoamps. A gold 111 crystal from
Mateck was used for adsorbing the molecules. Prior to the STMBJ
experiment, an image of the substrate was recorded to ensure that a
single monolayer was obtained. Approach and retraction of the tip were
performed using the custom spectroscopy mode in Picoscan 5.4. The tip
was driven toward the surface, and then it was held at a constant distance
for typically 200 ms in order to form some molecular junctions. Then the
tip was retracted at a typical speed of 5 nm sꢀ1. The feedback was re-
established between each measurement.
Experiments with 3 were performed on a Nanoscope E STM (Veeco,
Plainview, NY) modified to perform conductance measurements. Me-
chanically cut gold STM tips were used after insulation with thermo-
setting polyethylene glue for in situ STM measurements. Platinum wires
were used as both counter- and quasireference electrodes. Voltammo-
grams were recorded on a CHI potentiostat with an SCE reference
electrode and a Pt counter electrode. All potentials for 3 are thus
reported with respect to SCE.
Histograms were obtained by manual selection of conductance traces.
Traces displaying monotonous decay or mechanical vibration were
discarded. A parallel automatic analysis where conductance plateaus
were evaluated numerically by calculation of the current standard
deviation over a given interval gave similar results.
where λ is the reorganization energy of the redox center and
EAD the energy difference between donor and acceptor.4
Conversely, for an electrode, the vibrational level influence
can be neglected but electron transfer may occur from (or to) a
FermiꢀDirac distribution of closely spaced energy levels. In
all approaches, the parameter relevant to characterize the
communication through the bridge is the electronic coupling
factor H.10
In the case where a redox system is incorporated in the bridge
itself, charge transport could become more complicated. Current
modulation or rectification may depend on the redox state of
the redox moiety.11ꢀ16 In such a configuration, immersing the
bridge into an electrolyte poised to a reference electrode allows
the gating command to propagate through the solution. The
reference electrode (i.e., the gate) can be placed far from the
molecular junction under investigation. Therefore, only two
conducting electrodes need to be arranged close enough to form
a nanometric gap. However, mechanisms of charge transport
would be complicated by fluctuations of solvent polarization and
internal modes of the molecule.17,18
Our aim in this study was to contribute to the ongoing discus-
sion about the relationship between conductivity and electron
transfer rate constants in bridges equipped with a redox center.
Indeed, though there is a formal equivalence, there is a big
difference between communicating and localizing electrons or
holes in a structure (as we do by our CV method) and simply
passing charges through the structure by a tunnel effect favored
by the quantum coupling within the structure (as in STMBJ). We
thus selected the three very different molecules 1ꢀ3, displayed in
Scheme 1, with the aim of measuring both their molecular
conductance using the STMBJ technique initially implemented
by Tao et al.7,19,20 and their heterogeneous rate constant by
ultrafast cyclic voltammetry.21 Molecules 1ꢀ3 differ widely in the
2.4. Ultrafast Cyclic Voltammetry. Ultrafast cyclic voltammetry
was performed with a homemade potentiostat, allowing online com-
pensation for ohmic losses.22,23 Electron transfer rates were estimated
from the peak displacement fitting using Laviron plots and supposing a
transfer coefficient R of 0.5. The working, reference, and counter
electrodes were lithographically produced Au band electrodes for 1.26
Since lower scan rates were necessary for 2, gold balls could be used as
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Molecular conductance was determined by the STMBJ method.
Figure 1c displays typical stepwise currentꢀdistance curves
for 1 at a sample potential of ꢀ0.3 V, thus within the stability
region of OsII. The bias voltage was fixed at 50 mV. Approxi-
mately 20% of the curves displayed detectable steps, which agrees
with that reported in the literature.6 The statistical analysis based
on histogram construction displays a characteristic current peak
which is attributed to the conductance current of a single-
molecule junction (Figure 1d). While keeping the sample
potential at ꢀ0.3 V, we varied the applied bias voltage from 10
to 200 mV. The conductance remained constant, confirming the
reliability of our setup (see Figure S3 in Supporting Informa-
tion).
The dependence of Auꢀ1ꢀAu junction conductance on the
potential is reported in Figure 1e. We varied the sample potential
from ꢀ0.3 to 0.3 V while the bias remained fixed at 50 mV.
A cyclic voltammogram obtained on the Au(111) single crystal
used to perform STMBJ measurements is also displayed in
Figure 1e for comparison. There was a clear modulation of the
conductance by the redox switching from 17.8 nS at ꢀ0.3 V to
2.1 nS at þ0.3 V, which provides an onꢀoff ratio of 8.5.
3.2. Phenylenediaminebisthiol. System 2 conversely con-
tains saturated parts in the bridges, so that the redox center is
better isolated from the electrodes. As a consequence, the rate of
electron transfer is much slower: 7 ꢁ 104 sꢀ1. Since the resistance
was higher, we observed more noise in the conductance curves,
and it was more difficult but nevertheless possible to observe
well-defined steps as depicted in Figure 2a. This allows the
determination of a molecular conductance from the histogram
presented in Figure 2b. From the resulting histograms con-
structed at different potentials (see Figure 2c), we deduced that
the conductance shifts from 0.79 nS in the reduced state to
0.33 nS in the oxidized one. Modulation by the potential is thus
smaller than for 1 but still appreciable (see Discussion). In the
case of goldꢀsulfur bonds, reports of so-called “low” and “high”
conductivity peaks (LC and HC) have often been observed in the
literature. The common explanation is that the molecular con-
ductivity depends strongly on the contact configuration, i.e., on
the position of the sulfur atom on the electrode.19,28,29 Tao
initially proposed that when the sulfur is on a hollow site between
three gold atoms, the conductivity is higher than when it stands
on top of a single gold atom. On the other hand, bridgeꢀbridge
geometry has been predicted by Wandlowski to give the higher
conductivity.29 More recently, further studies by the Nichols
group evidenced multiple sets of conductance values caused by
the contact morphology, thus the atomic structure of the
substrate surface.30 The ratio HC/LC is usually around 5. We
also observed a switch in the low conductance, with a shift from
0.13 to 0.09 nS (see Supporting Information).
Figure 1. Cyclic voltammograms of molecule 1 at (a) 10400 V sꢀ1 and
(b) 407000 V sꢀ1, three consecutive scans, no average. Electrolyte: H2O
þ 1 M NaClO4. (c) Some conductance traces obtained for 1 at a sample
potential of ꢀ0.3 V/Pt and a bias of 50 mV. Electrolyte: 0.1 M NaClO4
aqueous solution. (d) Histogram obtained from the selection of 211 out
of 1000 conductance curves. (e) Filled circles: molecular conductance
versus sample potential. Black line: cyclic voltammogram.
working electrodes. The reference was then an SCE, and Pt was used for
the counter electrode.
3. RESULTS
3.1. Osmium Bisterpyridine. The first probe 1 was an
osmiumII bisterpyridine complex that may be reversibly oxidized
to OsIII. Figure 1a and 1b represents two voltammograms
obtained for 1. At “slow” scan rates, a voltammogram with bell-
shape and almost symmetrical is obtained because equilibrium
with the electrode is always sustained. At 407000 V sꢀ1, despite
the very short time scale of the measurement, the peaks are only
slightly shifted compared to their equilibrium position. However,
this shift is significant and allows determination of the hetero-
3.3. Ferrocenebisthiol. Our attempts to perform experiments
with monolayers formed from a solution of 3 alone did not provide
enough curves with clear steps. Therefore, the resulting histograms
did not display clear maxima so that the molecular conductance
could not be properly evaluated. We assign these complications to
the fact that rotation of the cyclopentadienyl rings around the iron
possesses a low activation barrier, thus allowing anchoring of the
molecule onto the surface with both thiol functions, which prevents
single-molecule contacts. In order to avoid this problem, we
coadsorbed pentanethiol to 3. The resulting cyclic voltammograms
of a Au(111) electrode modified with a mixture of 3 and penta-
nethiol are given in Figure 3a. A well-defined couple of redox peaks
is present with a peak potential at 0.22 V vs SCE.
geneous rate constant kET (see Supporting Information): kET
=
2.0 ꢁ 106 ( 0.5 ꢁ 106 sꢀ1. This value is smaller than the one
determined by the same method for the complex Py(CH2)2-
PyOsCl(bpy)2 (kET = 4 ꢁ 106 sꢀ1, Py standing for pyridine) by
the same group27 despite a shorter bridge length. This suggests
that the reorganization energy for the Os(tpy)2 redox center is
probably higher than for PyOsCl(bpy)2. Since the coordination
sphere has nearly the same size, it is likely that the difference
stems from a higher internal reorganization.
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Figure 2. (a) Some conductance traces obtained at a sample potential of ꢀ500 mV and a bias of 100 mV for 2. (b) Histograms at a sample potential of
ꢀ500 mV. 165 out of 1000 curves were selected. (c) Filled circles: conductance as a function of electrode potential (left y axis). Black line: cyclic
voltamogram of 2 (right y axis). Electrolyte: 0.1 M tetraethylammonium tetrafluoroborate aqueous solution.
Figure 3. (a) Cyclic voltamograms of 3 coadsorbed with pentanethiol (see text) at 0.02, 0.05, and 0.1 V sꢀ1 in H2O þ 0.1 M HClO4. (b) Topography
of mixed SAMs of 3 and C5H11SH adsorbed on Au(111) in 0.1 M HClO4 solution at a substrate potential of 0.2 V (100 nm ꢁ 100 nm), It = 15 pA,
bias = ꢀ0.1 V, Z-scale = 1 nm).
Figure 3b shows the STM image of the mixed SAM surface.
The STM image is composed of big bright spots of diameter 4 to
6 nm ascribed to 3 on a relatively darker background attributed to
the underlying pentanethiol monolayer for which molecular
resolution is achieved. Several effects may explain the large
diameter of the spots. First, similar to that proposed by Tour,31ꢀ33
the bright spot corresponds to the tip structure imaged by the
protruding redox molecules so that the size of the spot is not
representative of the size of the molecule. Second, since the
molecule in our system is less diluted than in Tour’s work, single
molecules are not always resolved, and the bright spots may
correspond to molecular aggregates of the redox molecules alone
or with the pentanethiol diluent. However, the nearly ideal
voltametric response demonstrates that interactions between
electroactive entities are minimal, suggesting that pentanethiol
is likely inserted in the aggregate. More importantly, single-
molecule junctions would anyway be formed in the final stage
upon tip withdrawl regardless of the original number of mol-
ecules present in the aggregates (see below). Third, rotation over
the Cp ring to get a twisted conformation would also enlarge the
apparent diameter. The height and diameter of the spots
remained unchanged upon potential variation from reduced
(ꢀ0.1 V) to oxidized state (0.4 V) which serves as the first
indication of possible conductance invariance with potential
(see below).
intermediate (þ0.2 V) redox states of 3 which forms mixed
SAM with pentanethiol. This presents the advantage to prevent a
looping around the cyclopentadienyl ring that could allow an
anchoring with both thiols onto the electrode. As can be seen in
Figure 4, clear steps could be observed, allowing histogram
construction for either high or low conductance. Very surpris-
ingly, the molecular conductance remained almost unchanged
with potential, at a value close to 9.4 nS for HC and 2 nS for LC.
The slight decrease observed near the standard potential (9.2 and
1.9 nS) is within the experimental error. The high conductivity is
in agreement with the one determined previously in a MCBJ
experiment without potential control (9.7 nS).34 The conduc-
tance invariance observed for 3 severely contrasts with the
behavior of systems 1 and 2 and with any other redox molecules
that have been reported so far. Moreover, in some cases, we
observed large fluctuations in the current while retracting the tip
(see Figure 5a). This prompted us to stop the tip movement at a
defined current close to high or low conductance and monitor
the current as a function of time. Interestingly, discrete con-
ductance switching around HC or LC was observed, two typical
examples being displayed in Figure 5b and 5c. This subtle
behavior is not directly apparent in the conductance histograms
except for broadening of the histograms. Since it occurs for both
HC and LC, it cannot be attributed to the contact geometry but
rather to a conformational change of the molecule that induces a
change in electronic coupling. Recently, it has been demon-
strated that a direct contact between the tip and an aromatic ring
Under these conditions, single-molecule conductance was
measured at reduced (ꢀ0.1 V), oxidized (þ0.4 V), and
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could be obtained.30,35,36 However, it was also demonstrated that
whenever adsorption by both thiols is possible, conductance
peaks in the histograms are dominated by AuꢀSꢀmoleculeꢀ
SꢀAu configuration. Observation of HC and LC conductance
peaks also confirms that 3 is linked by both thiols to the
electrode, which seems plausible considering that the AuꢀS
interaction is stronger than the Au-Cp one. At the present stage,
it is impossible to identify the precise molecular changes respon-
sible for these variations. Rotation of the cyclopentadienyl rings
may be involved.
Our former ultrafast CV results for molecules 4 and 5 which
possess a similar structure compared to 3 are very useful to relate
with conductance measurements.37 Very similar rate constants of
ca. 5 ꢁ 106 sꢀ1 for both 4 and 5 were obtained. In the case of 5,
a single two-electron wave was obtained, indicating that the
singly oxidized intermediate was thermodynamically as well as
kinetically unstable. The currently accepted explanation is that
the positive charge is delocalized over the whole conjugated body
and thus cannot be stabilized by the solvent.38 Conversely, the
charges are localized in the doubly oxidized molecule, and
solvation brings a stabilization that may overcompensate for
the initial electrostatic repulsion, particularly in polar media. A
dramatic mechanistic change was thus observed when the
intermediate redox center was buried inside a hydrophobic
diluent. The almost independence of electronic coupling with
the molecular length confirmed that phenylenevinylenes are
indeed very good candidates for building efficient molecular
devices.5 Hence, this family provides a relatively high conduc-
tance and very fast electron transfers.
4. DISCUSSION
For electrochemical systems, theories have been developed to
take into account the energy level variations inside the gap when
the redox reaction occurs and different limiting situations may be
encountered. Initially, Schmickler and co-workers evaluated the
case of resonant tunneling when the oxidized or reduced level of
the redox center has an energy level comparable with that of the
electrodes.39 This situation should in principle lead to a current
maximum at potentials close to E0 ( λ (E0 is the standard
potential) upon varying the sample potential. On the other hand,
Ulstrup and co-workers have considered both reduced and
oxidized states and electron hopping possibilities.13,40ꢀ42 Upon
electron transfer, the redox level relaxes to another equilibrium
position. If coupling with the electrodes is very strong, several
electron transfer events may occur during the relaxation. If the
coupling is weak, relaxation occurs first, the electron is trans-
ferred to the second electrode, and relaxation toward the first
equilibrium position ends the cycle. In adiabatic or nonadiabatic
situations a conductance peak should thus be observed in the
vicinity of the standard potential of the bridge. Influence of some
experimental parameters is worth mentioning. First, the local
potential at the redox site may be different because the potential
drop is strongly affected by the tip potential. Second, the access of
solvent molecules to the nanogap is restricted and the effective
dielectric constant may differ, inducing a slower energy reorga-
nization. Finally a conformational change may occur in the
nanogap, hindering the resonance and leading to a so-called
“soft gating” transition,18,40,43 i.e., the one where a monotonous
variation of the conductance is observed. This last point also
Figure 4. Typical conductance traces and histograms for high and low
conductance at different potentials for molecule 3. Potentials refer
to SCE.
Figure 5. (a) Examples of stepwise conductance fluctuation shown in some conductance traces curves for low conductance. Sample potential 0.2 V vs
SCE, bias: 100 mV for 3. (b) Example of stepwise conductance fluctuations obtained by Iꢀt measurements near the high conductance at different
potentials. Bias: 100 mV. (c) Example of stepwise conductance fluctuations obtained by Iꢀt measurements near the low conductance. Bias: 100 mV.
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Figure 6. Estimated electronic coupling elements from conductance measurements (filled circles) and from ultrafast voltammetry (horizontal lines) for
a range of reorganization energies ranging from 0.6 to 1 eV for 1 (a), 2 (b), and 3 (c). The vertical dashed line indicates standard potential. The potential
scale refers to Pt for panels a and b, and to SCE for panel c.
depends on the precise experimental setup used to construct the
nanogap since it may play a role in the local organization of the
molecules inside the junction.
where e is the elementary charge, and FM is the electronic state
density in the metal (supposedly identical in both electrodes).
ꢀ1 10,52
A currently accepted value for gold is FM = 0.27 state eV
.
H
ET
Experimentally, two different situations have been encoun-
tered in literature. The first class of systems is composed of
electroactive self-assembled monolayers and investigated by
tunneling spectroscopy. In this situation, many systems display
a current maximum when the sample is poised near the standard
potential. This is the case, for example, for a protoporphyrin,44
several osmium and ferrocene complexes,42,45,20 viologens,46 and
azurin, a redox protein.47 The second category is composed of
systems chemically anchored at both ends.24,43,46,48,49 In that
case, only the tetrathiofulvalenebisalkylthiol displayed a maxi-
mum.43 For other systems of this category including ferrocenes
or viologens, a monotonous variation of the conductance was
observed. Perylenetetracarboxylic diimine derivatives displayed
intermediate behavior.16,48
is the electronic coupling energy controlling the electron transfer
rate constant and Hconduc imposes the conductance value.
The coupling factors Hconduc and HET were evaluated for a
range of reasonable reorganization energies. For Hconduc, we
resorted to the high conductance value since it is expected to
be closer to the relaxed conformation of the SAM. Results are
reported in Figure 6. For ferrocene and phenylene diamine
derivatives λ is in the range 0.6ꢀ1 eV.54ꢀ56 No reported λ
value exists for 1, but it may be expected to fall in the same
range (see Supporting Information). Comparison of system 3
with 4 and 5 gives an excellent agreement (Hconduc = 9.2 ꢁ
10ꢀ3 eV ; HET = 9.5 ꢁ 10ꢀ3 eV) for λ = 0.9 eV, a very plausible
value for ferrocenyl derivatives.5,37 This may be correlated to
the invariance of kET with the molecular length.37 For 1 and 2,
For our systems, the absence of any current maximum near the
standard potential indicates a “soft-gating” mechanism, thus
involving configurational dynamics of the molecule in the
nanogap, as depicted by Ulstrup et al.40,43 Electron transfer is
assisted by the redox molecular levels that are not, however, in
resonance with the Fermi levels of the electrode. Here, a
potential variation modulates the coupling factor Hconduc but
the mechanism continues to be a superexchange.50,51 This
demonstrates that large conformational fluctuations occur in
the nanogap. It is noticeable that the larger onꢀoff current ratio
is higher for the more rigid system 1. In the extending nanogap
more degrees of freedom may be available for flexible molecules
which would extend beyond the height of the diluent molecules,
and the situation may thus greatly differ from the behavior in
single-component types of self-assembled monolayers where the
molecules are well-organized. In the framework of superex-
change, theoretical equivalence between conductance measure-
ments through a bridge and electron transfer from an electrode to
a redox center separated from the electrode by the same bridge
has been examined by several authors4,52 and reinforce the
intuitive idea that electron transfer rate constants should be
correlated to single-molecule conductance.53 From the Lewis
formulation,10,52 one deduces the following expressions for kET
and G:
H
conduc obtained at low potentials, therefore in the conforma-
tion for which the SAM is created, is clearly higher than HET
.
Since electron transfer operates over a longer distance in the
conductance mode, this result is rather surprising, particularly
for 2 whose redox center is connected through long saturated
bridges. In the present study, we do not have a clear reference
for the electrodeꢀtip distance. For the conductance steps
being observed within 0.2 nm, it is possible that while a step is
observed, the molecule is in a stressed conformation, for
example a partially folded or twisted one. Conversely, cyclic
voltammetry is performed onto a relaxed geometry.57ꢀ61 By
temperature measurements of single-molecule conductance
performed in air for dithioalkyls, Haiss et al. demonstrated
that different high energy conformers indeed lead to higher
conduction.62 Conformational changes may be induced by the
current itself,63,64 or by the tip movement while or after the
contact is established. A softer method to realize the contact
could minimize the molecular fluctuations and lead to a better
correlation.8 Other recent evolutions of the STMBJ technique
may also enable analysis and help to resolve this issue by
allowing conductance measurements at various nanogap
widths (i.e., at different molecular conformations).8,65 These
results, and particularly those for 3, although showing a
qualitative correlation between kET and G, highlight the need
for further theoretical and experimental insights to fully
understand the performances of complex molecular systems.
These results also emphasize the need for independent and
complementary experimental methods to estimate the device
possibilities.
rffiffiffiffiffiffiffiffiffiffi
2π2
πkBT
λ
kET
¼
FMHE2T
ꢁ expð ꢀ
Þ
ð2Þ
ð3Þ
h
λ
4kBT
4π2e2
G ¼
Hc2onducF2M
h
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5. CONCLUSIONS
(10) Traub, M. C.; Brunschwig, B. S.; Lewis, N. S. J. Phys. Chem. B
2007, 111, 6676.
Molecular conductance and heterogeneous rate constants
were evaluated for three molecular systems. Qualitatively, it
was observed that fast electron transfer rate constants correspond
to rather high conductances. Conductance variation with the
potential suggests that superexchange, not electron hopping, is
the predominate mechanism for the investigated molecules. The
almost fully conjugated ferrocenebisthiol 3 even displayed a
complete independence of conductance on potential when
constructing histograms from Iꢀd curves. However, slight flips
of conductance ascribable to conformational changes were obser-
ved when the tip movement was stopped after establishing an
otherwise stable molecular junction. Tentative evaluations of
electronic coupling revealed that, except for compound 3, this
parameter is surprisingly higher for steady-state conductance
measurements than for transient electron transfer albeit the
charge had to travel over a larger distance in the former case.
This emphasizes that information derived from molecular struc-
tures should be evaluated through various experimental and
theoretical approaches to elucidate intrinsic molecular complexity.
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’ ASSOCIATED CONTENT
S
Supporting Information. Reorganization energy evalua-
b
tion of molecule 1, additional data for conductance measurement
and ultrafast cyclic voltammetry, synthesis of molecules 1ꢀ3.
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Corresponding Author
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Author Contributions
3These two authors contributed equally to this work.
’ ACKNOWLEDGMENT
In Paris, this work was supported by the CNRS (UMR 8640
and LIA XiamENS), Ecole Normale Supꢀerieure, UPMC, and the
French Ministry of Research through ANR. In China, this work
was supported by the National Natural Science Foundation of
China (Nos. 20973141, 20911130235, and 21003110). X.S.Z.
and N.R. thank ANR and DGRST, respectively, for postdoctoral
grants.
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