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Measurement of
Single-Molecule
Conductance
Fang Chen, Joshua Hihath, Zhifeng Huang,
Xiulan Li, and N.J. Tao
Department of Electrical Engineering and Center for Solid State Electronics
Research, Arizona State University, Tempe, Arizona 85287;
email: [email protected]
Annu. Rev. Phys. Chem. 2007. 58:535–64
Key Words
First published online as a Review in Advance
on November 29, 2006
molecular electronics, break junction, quantum point contact
The Annual Review of Physical Chemistry is
online at http://physchem.annualreviews.org
Abstract
This article’s doi:
10.1146/annurev.physchem.58.032806.104523
c 2007 by Annual Reviews.
Copyright All rights reserved
0066-426X/07/0505-0535$20.00
What is the conductance of a single molecule? This basic and seemingly simple question has been a difficult one to answer for both
experimentalists and theorists. To determine the conductance of a
molecule, one must wire the molecule reliably to at least two electrodes. The conductance of the molecule thus depends not only on
the intrinsic properties of the molecule, but also on the electrode
materials. Furthermore, the conductance is sensitive to the atomiclevel details of the molecule-electrode contact and the local environment of the molecule. Creating identical contact geometries has
been a challenging experimental problem, and the lack of atomiclevel structural information of the contacts makes it hard to compare
calculations with measurements. Despite the difficulties, researchers
have made substantial advances in recent years. This review provides an overview of the experimental advances, discusses the advantages and drawbacks of different techniques, and explores remaining
issues.
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1. INTRODUCTION
The ability to measure and control electrical current through a molecule is a critical
requirement toward the goal of building electronic devices using individual molecules
(1, 2). This ability also offers us a unique opportunity to understand charge transport,
an important phenomenon that occurs in many chemical and biological processes
(3, 4), on a single-molecule basis. Furthermore, it allows us to read the chemical
information of a single molecule electronically (5), which opens the door to chemical
and biosensor applications based on the electrical detection of individual molecular
binding events (6).
The most fundamental quantity that describes the electrical properties of a bulk
material is conductivity, based on which materials are often divided into conductors,
insulators, and semiconductors. Conductivity is defined as σ = (I/V) × L/A, where
I is the electrical current, V is the applied bias voltage, L is the length, and A is the
cross sectional area of the material. For a small molecule, A and L are difficult to
define precisely, and a more well-defined quantity is the conductance, G, given by
G = I/V. So a basic question in molecular electronics is, what is the conductance of
a single molecule?
To determine the conductance of a molecule, one must first bring it into contact
with at least two external electrodes (Figure 1). The contact must be robust, reproducible, and able to provide sufficient electronic coupling between the molecule and
the electrodes (7–11). One way to meet the contact requirements is to attach the
molecule covalently to the electrodes via proper anchoring groups at two ends of the
molecule. Clearly, the measured conductance depends not only on the molecule, itself,
but also on the properties of the electrodes and the atomic-scale molecule-electrode
contact geometry (12–17). Another factor that may affect the measured conductance
is the local environment of the molecule, which includes solvent molecules (vacuum
or air), pH, and ions (18, 19). Finally, an electron traversing through the molecule
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Molecular electronics:
science and technology
related to the
understanding, design, and
fabrication of electronics
devices based on molecules
Contact geometry: the
atomic-scale geometry of an
electrode, and the binding
site and orientation of a
molecule on the electrode
a
b
I
I
Vbias
Vbias
Figure 1
(a) Current through a molecule covalently bound to two electrodes. (b) Current through a
metal atom attached to two electrodes made of the same metal.
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may exchange energy with the vibration modes of the molecule or surrounding solvent molecules (20, 21). Consequently, the measured conductance may be sensitive
to temperature (22–24). Precisely controlling these measurement details, especially
the molecule-electrode contacts, has been a difficult task, which is a major reason
for the large disparities between different measurements for even a relatively simple
molecule, such as alkanedithiols (25, 26). In this chapter, we review recent experimental advances and discuss remaining issues in measuring single-molecule conductance.
A related problem is to determine the conductance of a single metal atom or a
linear chain of metal atoms bridged between two electrodes made of the same metal
as the atoms in the chain (27–32). This system is known as a quantum point contact.
For metals, such as Au, the conductance of a quantum point contact is close to G0 =
2e2 /h = 77.4 μS, where e is the electron charge, h is the Planck constant, and S is
the conductance unit. G0 is the conductance quantum unit corresponding to 100%
transmission of electrons from one electrode to the other through the point contact.
Therefore, the conductance of a molecule given in units of G0 tells us how conductive
the molecule is in comparison with a metal atom, which is why we use G0 as the unit
of conductance here.
Molecular electronics is a diverse and rapidly growing field, and many excellent
reviews have appeared in recent years, covering general concepts (4, 33–36), theoretical aspects (21, 37, 38), and experimental methods (39–42). In the present review,
we mainly focus on the measurements of single molecules covalently bound to two
electrodes. We refer the readers interested in molecule-film measurements to recent reviews by Metzger (42) and Wang et al. (41). The remainder of the chapter is
arranged as follows: Section 2 provides a brief overview of experimental tools that
measure the conductance of molecular thin films, and Section 3 describes techniques
and methods for single-molecule conductance measurements, in which we discuss
both the advantages and difficulties of different techniques. Section 4 addresses some
critical issues that affect single-molecule conductance, and Section 5 provides a summary and outlook.
Molecule-electrode
contact: contact between a
molecule and an electrode
provides sufficient and
stable electronic coupling
between the molecule and
the electrode
Quantum point contact: a
small constriction between
two conducting regions
through which electrons
traverse ballistically and
experience a quantum
waveguide effect
Conductance quantum
unit: a basic unit of
conductance given by G0 =
2e2 /h, where e is the
electron charge and h is the
Planck constant
2. MEASUREMENTS OF MOLECULAR FILMS
To date, many experimental techniques have been developed to measure and control
current through molecules. We can divide these techniques into two broad categories:
molecular film and single-molecule measurements. We briefly describe the first category in this section, whereas we discuss single-molecule conductance measurements
in more detail in Section 3.
2.1. Bulk Electrodes
The basic idea of the bulk electrode approach is to sandwich a molecular film, either
a monolayer or multiple layers, between two electrodes. The molecules are typically
first immobilized on one electrode surface, via self-assembly or Langmuir-Blodgett
methods (40, 42). Both self-assembly and Langmuir-Blodgett methods provide ordered molecular films, which are highly desired for successful measurement and data
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Molecular junction: a
molecule is attached to two
electrodes to form an
electrode-moleculeelectrode structure
11:34
interpretation. A second electrode is then placed on top of the molecular film, and
the electrical current between the two electrodes is measured as a function of bias
voltage.
The placement of the top electrode is often the most difficult part of the measurement, and many methods have been developed (43). One is to evaporate a metal
layer onto the molecular film in vacuum. To avoid a short circuit between the top
electrode and the bottom electrode, one must ensure that energetic metal atoms do
not damage the molecular film and the deposited metal does not penetrate into the
molecular film via defect sites to reach the bottom electrode (44, 45). To minimize
the short-circuit problem, Akkerman et al. (46) put a conducting polymer layer onto
the molecular film before the deposition of the top electrode. Another method is to
print a metal layer onto the molecular film by transferring a metal film evaporated
on a stamp via direct contact (47, 48).
Electrodeposition methods have also been investigated (49–51). For example,
Manolova et al. (52) used a 4,4 -dithiodipyridine-modified Au electrode to allow Pd
or Pt ions to adsorb preferentially onto the pyridine moiety of the molecules. The adsorbed metal ions were then reduced electrochemically to metallic Pd or Pt that could
serve as the second electrode in a metal ion-free acidic solution (52). Angle-resolved
X-ray photoelectron spectroscopy showed that the second electrode was indeed on
top of the molecular film without penetrating into the molecule film via defect sites.
Instead of using a solid metal as the top electrode, an alternative approach is to place a
drop of mercury onto the molecular layer (53–57). The mercury approach is relatively
simple and has shown high device yields.
2.2. Nanoelectrodes
The molecular film measurements described above involve many molecules, which
can be reduced using nanoscale electrodes. For example, a conducting atomic-forcemicroscope tip with a radius of curvature on the nanometer scale can serve as the
top electrode to measure conductance of a relatively small number of molecules (58,
59). Another method is the cross-wire junction, which sandwiches a molecular layer
between two perpendicular metal wires (60–62). The contact area between the two
wires is small, so a relatively small number of molecules is measured.
One may also reduce the number of molecules by confining the molecular film
inside a nanopore fabricated in a thin solid membrane (63, 64). One side of the
membrane is first covered with a metal layer, and molecules are allowed to form
a monolayer on the metal surface inside of the nanopores. A second metal layer is
then deposited on top of the molecular film in the nanopores. Nanopores can also be
used as templates to fabricate nanoscale metal-molecule-metal junctions (65). Metal
is first deposited electrochemically into the nanopores in an alumina membrane to
partially fill up the nanopores. Sample molecules are then allowed to adsorb on the
metal surface inside of the nanopores, which is followed by the chemical deposition
of a top metal layer into the nanopores to form nanoscale molecule junctions. After
dissolving the alumina, these molecular junctions in a solution are assembled onto
electrode arrays for conductance measurements.
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The molecular film measurements have played an important role in the understanding of the electron-transport properties of molecules (66, 67) and for demonstrations of many device functions, including rectification (44, 68–70), molecular switching (62, 71, 72), and negative differential resistance effects (56, 63, 73). When applying
these techniques to a particular sample molecule, one needs to consider the following
factors: First, not all the molecules of interest can form well-ordered films, which
limits the choice of molecules for the studies. Second, molecular films often have defects, and additional defects may be created during the fabrication of the top electrode
(51) and application of bias voltage (61). It is important to ensure that the defects and
electromigration-induced effects do not dominate the measured conductance. Third,
in a close-packed film, a molecule interacts with the neighboring molecules, which
may suppress its conformational change and affect its electron-transport properties
(74). As a result, the average conductance per molecule calculated from the molecular
film measurements may not be directly comparable with single-molecule conductance
measurements. Finally, the molecules in the films are not exposed to the outside world,
which makes it difficult to introduce a gate electrode and prevents one from studying
molecular binding processes between the sample molecules and analytes.
Electromigration:
transport of material caused
by the movement of the ions
in a conductor owing to the
momentum transfer
between conducting
electrons
STM: scanning tunneling
microscopy
AFM: atomic force
microscopy
3. MEASUREMENTS OF SINGLE MOLECULES
To determine the conductance of a single molecule, one must (a) provide a signature
to identify that the measured conductance is a result of not only the sample molecules,
but also a single sample molecule, (b) ensure that the molecule is properly attached to
the two probing electrodes, and (c) perform the measurement in a well-defined environment. The current methods fall into three categories: scanning probe methods,
fixed electrodes, and mechanically controlled molecular junctions.
3.1. Scanning Probe Techniques
Scanning tunneling microscopy (STM) has played a unique role in the field of molecular electronics (75). This is because it allows one to image individual molecules adsorbed on a conductive substrate with submolecular resolution. By placing a scanningtunneling-microscope tip over a molecule, one can perform tunneling spectroscopy
measurements on the molecule (76–78). In addition, the tip can be used to manipulate atoms and molecules on surfaces (79). A closely related technique is atomic
force microscopy (AFM). Although AFM has typically a lower resolution than STM,
it measures both the mechanical and electrical properties of molecules when a conducting tip is used (80, 81). To date, STM and AFM have revealed many interesting
phenomena important to the development of molecular electronics. Examples include reversible redox switching (82–85), an electromechanical molecular amplifier
(86), the negative differential resistance-like effect (59, 87–89), molecular switching
(90, 91), and the study of field effects on electron transport in molecules (92).
In the STM or AFM method, a molecule adsorbs onto a substrate to form a
well-defined molecule-substrate contact, but the tip-molecule contact is often less
well defined, which prevents one from determining the absolute conductance of the
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a
b
Tip
Tip
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Metal particle
Substrate
Substrate
Figure 2
(a) Scanning tunneling microscopy (STM) study of electron transport through a target
molecule inserted into an ordered array of reference molecules. (b) STM or conducting atomic
force microscopy (AFM) measurement of conductance of a molecule with one end attached to
a substrate and the other end bound to a metal nanoparticle.
molecule. One way to reduce this problem is to embed a molecule of interest into
the matrix of another, often less conducting molecule (Figure 2a). Bumm et al. (90)
used this approach to study current through molecular wire candidates inserted into
an insulating alkanethiol monolayer and observed much higher current through the
molecular wires than through the surrounding alkanes. Tao (82) studied Fe-porphyrin
coadsorbed in the ordered array of porphyrin molecules in an electrochemical cell.
Fe-porphyrin is redox active, whereas porphyrin is similar in structure but redox
inactive. The work shows that the current through the redox active molecule is much
higher than that through the redox inactive molecule when the electrode potential is
tuned near the redox potential of Fe-porphyrin.
Another STM approach demonstrated by Langlais et al. (93) is to attach one end
of a molecule to a step edge on a metal substrate. The STM image of the molecule and
the metal substrate provides spatially resolved electronic penetration of the metallic
electronic states from the step edge into the molecule, which the researchers used to
determine the electron tunneling decay constant along the molecule.
A third approach is to attach one end of a molecule onto a substrate and the
other end to an Au nanoparticle covalently (Figure 2b). One then places a scanningtunneling-microscope tip (94) or a conducting atomic-force-microscope tip (7) on top
of the nanoparticle. Because Au nanoparticles are typically coated with an organic
surfactant layer, the tip and the nanoparticle form a tunneling junction. Consequently,
the nanoparticle behaves similar to a Coulomb island, and the electron transport
between the tip and the substrate via the nanoparticle exhibits Coulomb blockade
effect (7, 94). By fitting the measured I-V curves with the Coulomb blockade model,
one can extract the conductance of the sample molecule between the nanoparticle
and the substrate (95, 96).
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Ho et al. (97) recently made a significant step toward the goal of creating a metalmolecule-metal junction with atomic-scale precision. They assembled a copper(II)
phthalocyanine molecule bound to two Au atomic chains on an NiAl(110) surface
by manipulating individual Au atoms and copper(II) phthalocyanine molecules with
a scanning-tunneling-microscope tip. The spatially resolved electronic spectroscopy
revealed that the electronic states of the metal-molecule-metal junction change significantly when varying the number of Au atoms in the chains one by one. The
NiAl(110) is conducting, so the electronic coupling between the molecule and the
substrate is strong. To reduce the electronic coupling, Repp et al. (98) introduced an
insulating layer of NaCl between the sample molecule (pentacene) and a Cu substrate.
By manipulating an Au atom with a scanning-tunneling-microscope tip, they created
an Au-pentacene contact and studied the dependence of the molecule’s electronic
states on the formation of the Au-molecule contact (Figure 3). These STM studies not only provided the atomic-scale structural information of the metal-molecule
contacts but also determined the mixing of the electronic states of the molecules with
those of the metal electrodes.
Figure 3
Making and breaking a chemical bond between a single pentacene molecule and an Au atom
on an NaCl bilayer supported by a Cu(100) substrate. (a) Scanning tunneling microscopy
(STM) image showing the molecule and the Au atom before bond formation. (b) Image
showing a molecule-metal complex (6-Au-pentacene) after resonant tunneling through the
lowest unoccupied molecular orbital of the pentacene molecule. (c) Calculated geometry of the
adsorbed 6-Au-pentacene complex. C, H, and Au atoms are represented by gray, white, and
gold spheres, respectively. Reprinted with permission from Reference 98.
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In both examples described here, the metal electrodes, consisting of a single or
several Au atoms, are too small to develop full continuous density of states of metallic
character. The coupling between the molecule and metal substrate is reduced by the
thin NaCl layer, but it is still finite as it is needed for STM imaging. Therefore, the
results may not be compared directly with the molecular conductance measurements
that use large or bulk metal electrodes. Another challenge is to connect the metal
electrodes to two external electrodes to carry out electron-transport measurements
on the molecular junctions created by STM.
3.2. Fixed Electrodes
A conceptually simple method to measure single-molecule conductance is to fabricate a pair of facing electrodes on a solid substrate and then bridge the electrodes
with a molecule terminated with proper anchoring groups that can bind to the electrodes (Figure 4a). A key requirement of this method is to fabricate electrodes with a
molecular-scale gap, which has been a difficult task. This is because most molecules are
a few nanometers or less, and fabrication of such a small gap between electrodes is beyond the reach of conventional micro- and nanofabrication facilities. Unconventional
Figure 4
a
Schematic illustrations of
single-molecule
conductance studies using
different methods. (a) A
single molecule bridged
between two electrodes
with a molecular-scale
separation prepared by
electromigration,
electrochemical etching or
deposition, and other
approaches. (b) Formation
of molecular junctions by
bridging a relatively large
gap between two
electrodes using a metal
particle. (c) A dimer
structure, consisting of
two Au particles bridged
with a molecule,
assembled across two
electrodes.
Source
Drain
Oxide
Gate
b
Metal
particle
Electrode
Electrode
Substrate
c
Au
Au
Electrode
Electrode
Substrate
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fabrication techniques—such as electromigration (99, 100), electrochemical etching
or deposition (101–104), and other novel methods (105–109)—have been developed
to create electrodes separated with a molecular-scale gap.
One attempt to avoid the requirement of molecular-scale gaps is to use metal
nanoparticles as bridges (Figure 4b). This technique starts with a pair of electrodes
separated with a gap that is much larger than a sample molecule. After covering the
electrodes with a layer of sample molecules, one drives a metal nanoparticle with a
diameter greater than the electrode gap into the gap to bridge the two electrodes,
either using dielectrophoresis (110) or a magnetic field when Au-coated Ni particles
are used (71). This results in two metal-molecule-metal junctions in series, which
may complicate the data analysis. Dadosh et al. (111) reported another strategy based
on synthesizing a dimer structure, consisting of two Au nanoparticles connected by
a dithiolated organic molecule, and electrostatically trapping the dimer structure
between two metal electrodes (Figure 4c).
Because the fixed electrodes are supported on a solid substrate, the molecular junctions are mechanically stable, which is ideal for studying electron transport through
molecules as a function of temperature, magnetic field, and other external parameters. Another advantage of this approach is that one can use the substrate (e.g., heavily
doped Si) as a gate electrode to control the electron transport through the molecules.
Researchers have applied this approach to study various interesting phenomena, including single-electron charging (99, 100, 107, 112) and Kondo effects (99, 100, 113)
in molecules at low temperatures.
Further improvements are desired to address the following issues. First, the deviceto-device variation is large, which calls for statistical analysis. However, the fabrication
yield is usually rather low, making it difficult to perform statistical analysis (104,
105). Second, for redox molecules, the single-electron charging effect was used as a
signature to identify measurements attributed to a single molecule (99, 100, 107, 112).
But, in general, it is difficult to determine how many molecules are bridged across
the electrodes and how many contribute to the measured current. Because metalnanoparticle complexes often form during the fabrication processes of the molecularscale gaps, it is important to distinguish that the measured transport properties are
a result of the sample molecule rather than the nanoparticles or a nanoparticlemolecule complex (114). Third, even though the molecules have two linker groups,
it is difficult to determine if the molecules are indeed covalently bound to the two
electrodes. Finally, the structure of the electrodes and the position of the molecule
are not precisely known, so a technique that can provide atomic-scale structural
information of the molecular junction is highly desired.
Redox molecule: molecule
that can be reversibly
oxidized or reduced via
electron transfer between
the molecule and electrodes
PZT: piezoelectric
transducer
3.3. Mechanically Formed Molecular Junctions
It is difficult to fabricate electrodes separated with a gap that can fit a sample molecule
precisely. This difficulty may be overcome by bringing two electrodes together or
separating them apart mechanically. Using a piezoelectric transducer (PZT) or other
mechanical actuation mechanisms, one can control the gap with subangstrom precision, making it possible to fabricate molecular junctions and measure the conductance
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of various molecules. Several techniques based on this concept have been developed,
which are described below.
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MCBJ: mechanically
controllable break junction
3.3.1. Mechanically controllable break junction. The basic principle of the mechanically controllable break junction (MCBJ) method (115, 116) is to break a thin
metal wire supported on a solid substrate into a pair of facing electrodes (32). The
process is controlled by bending the substrate with a mechanical actuator, such as
a PZT and stepping motor (Figure 5a). An MCBJ device can be built manually by
fixing a metal wire with a notch near the middle of the wire (116). An alternative
method is to create a nanobridge connecting two microelectrodes on a substrate using electron-beam lithography (Figure 5b) (117). Because the bending is achieved by
fixing two ends of the substrate while pushing the middle part of the substrate vertically, the vertical movement of the PZT is demagnified when the substrate is thin
compared to its width. This allows one to accurately control the width of the gap.
Moreland & Ekin (115) first used the MCBJ to study electron tunneling, and
Muller et al. (116) pioneered the technique to create metallic quantum point contacts
and to demonstrate conductance quantization (29). Reed et al. (118) applied MCBJ
to measure electron transport in molecules. They first formed a molecular-scale gap
between two electrodes and then exposed the electrodes to a solution containing
benzenedithiol. After evaporation of the solvent, they measured a finite current between the electrodes and attributed it to electron transport through the molecules.
Kergueris et al. (119) measured electron transport through oligothiophenes terminated with dithiols using an MCBJ in a similar way. These pioneering works demonstrate the feasibility of studying electron transport in molecules using the MCBJ;
however, how many molecules were involved in the conduction and whether the
molecules were bound to both electrodes were not clear.
Reichert et al. (120) provided strong evidence of single-molecule conductance
measurements using an MCBJ setup. In their experiment, they first applied a droplet
of a solvent containing dithiol molecules to the electrode pair formed with the MCBJ
to allow the molecules to adsorb onto the electrodes. The gap was then closed while
maintaining a fixed voltage across the electrodes, during which time they recorded
the current (Figure 5c). Initially, the current grew exponentially, owing to electron
tunneling across the gap. When the gap was decreased to a certain width, sometimes
the current locked into a stable value weakly dependent on the gap width (121).
At that point, the first molecule was presumably attached to the opposite side. The
measured I-V (Figure 5d) curves were asymmetric for asymmetric molecules, which
suggests a single or a small number of molecules bridging the gap. Smit et al. (122)
reported that a hydrogen molecule forms a stable bridge between platinum electrodes
in their quantum point contact measurements in the presence of H2 . The measured
conductance determined from the hydrogen bridge is close to 1G0 , nearly perfect
conductance or 100% transmission through H2 . They also studied the vibrations of
the molecules using point contact spectroscopy (123).
3.3.2. Scanning-tunneling-microscopy-based break junction. Xu & Tao (124)
developed an STM–break junction method that quickly creates thousands of
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Figure 5
(a) Schematics of a microfabricated mechanically controllable break junction (MCBJ) (88). (b)
Scanning-electron-microscope picture of the lithographically fabricated break junction (92).
(c) Change of current recorded during the formation of a molecular junction. After a region of
roughly exponential increase of the current, the current suddenly locks into a remarkably
stable value (plateau), nearly independent of the distance. (d) I-V and dI/dV of a molecular
junction. Images reprinted with permission from References 32, 117, 120, and 121.
molecular junctions by repeatedly moving a scanning-tunneling-microscope tip into
and out of contact with the substrate electrode in the presence of sample molecules
(Figure 6). The molecules in the study have two end groups that can bind to the tip
and the substrate electrodes, respectively. The process can be divided into three steps:
(a) A PZT drives the tip toward the substrate surface until it contacts the molecules
bound to the substrate. During the contact period, one or more molecules may bind
to the tip via the second end group. (b) The tip is pulled away from the substrate, and
then the molecules break contact with one of the two electrodes individually, which
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Figure 6
(a) Measurement of single-molecule conductance using a scanning tunneling microscopy
(STM) break junction. A scanning-tunneling-microscope tip is pushed into contact with
molecules adsorbed on an electrode with a piezoelectric transducer (PZT) in a solution
containing the sample molecules, during which the molecules have a chance to bridge the tip
and substrate electrodes. The tip is then pulled away from the substrate to break the molecules
from contacting the electrodes. (b) The current (conductance) for viologen dithiol (N,
N -bis(6-thiohexyl)-4,4 -bipyridinium bromide) recorded during the pulling process shows
stepwise features. Bias voltage = −0.1 V. These curves reflect the typical current features for
thousands of molecular junctions repeatedly formed under the same conditions.
(c) Conductance histogram constructed from the individual measurements reveals well-defined
peaks near integer multiples of a fundamental value, ∼1 nS, which is identified as the
conductance of a single molecule. Reprinted with permission from Reference 85.
Conductance histogram:
a statistical distribution of
conductance values of a
large ensemble of molecular
junctions with
microscopically different
contact geometries
546
is shown as a series of stepwise decreases in the current (Figure 6b). (c) The process
is repeated until a large number of molecular junctions are created and measured.
The conductance histogram of these molecular junctions exhibits peaks located near
integer multiples of a fundamental value, which is used as a signature to identify a
single-molecule conductance. During the approaching stage, one may control the tip
to either make contact with the substrate to form a quantum point contact or avoid
the formation of a point contact between the tip and the substrate.
Chen et al.
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Unlike most of the MCBJ experiments that record the approaching processes,
this method focuses on the separation process. Because only those molecules bound
to two electrodes can be stretched until breakdown during the separation process,
this method selectively measures the conductance of those molecules bound to both
electrodes. Another difference is that the creation of the molecular junctions and the
measurement of the conductance are performed in an organic solvent or aqueous
electrolyte, so one can easily introduce the sample molecules via the solution and
control the electron transport through the molecules electrochemically. Finally, the
scanning-tunneling-microscope tip images the substrate surface before performing
the electron-transport measurement, so one can place the tip on an atomically flat
area or move the tip laterally to a fresh area of the substrate during the measurement.
This freedom comes at the cost of mechanical and thermal stability, however, which
is typically not as good as the MCBJ. Different groups have used this or similar
approaches to determine the conductance of many molecules (85, 125–127). Despite
the success, several issues remain to be resolved and understood (see Section 4).
3.3.3. Conducting atomic-force-microscopy break junction. The stepwise
change in the conductance curves shown in Figure 6b was attributed to the breakdown of individual molecules during the separation of the electrodes. Xu et al. (80)
confirmed this by measuring the electromechanical properties of the molecular junctions with a conducting atomic force microscope (Figure 7). Each abrupt conductance decrease is accompanied by an abrupt decrease in the force, corresponding to
the breakdown of a molecule from contacting the electrodes. Further pulling causes
only a slight change in the conductance but an approximately linear increase in the
force. When the force reaches a certain threshold, another molecule junction breaks
b
Conductance (10– 4 G0)
a
6
Conductance
8
4
Force
4
2
0
0
Stretching
Figure 7
(a) Simultaneous conductance and force measurements of a molecular junction during
breakdown using a conducting atomic force microscope setup. (b) As the individual molecules
break, the conductance decreases in a stepwise fashion (red), and associated with each
conductance step, the force (blue) also decreases abruptly (83).
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Force (nN)
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down, resulting in additional abrupt decreases in the conductance and the force. The
average breakdown force required to break Au-octanedithiol junctions is ∼1.5 nN
(128), which is about the same as the force required to break an Au-Au bond under
the same conditions, indicating the breakdown probably takes place at the Au-Au
bond. The conducting AFM break junction method also allows one to study the
electromechanical properties of single molecules.
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3.3.4. Other scanning-tunneling-microscopy-controlled point contact measurements. The STM break junction method described above forms a molecular
junction by first contacting the molecules with the tip and then pulling the tip away.
Haiss et al. (129) developed an STM trapping method to bridge molecules between
the tip and the substrate. The tip was brought close to but not into contact with the
substrate covered with the dithiol molecules. They observed sudden jumps in the tunneling current, which they attributed to the spontaneous chemical-bond formation
between the tip and the molecule.
Yasuda et al. (130) showed recently that one can form a molecular junction by
moving the tip toward a given molecule until a chemical bond formed between
the tip and the molecule. They first imaged isolated target molecules [α,ω-bis(acetylthio)terthiophene and α,ω-bis-(acetylseleno)terthiophene] embedded in an
octanemonothiol monolayer. The target molecules are terminated either with two
thiol or selenium groups that can bridge the substrate and the tip, but the octanemonothiols are bound to the substrate via its sole thiol group. They first located
the target molecules and then placed the tip above a molecule and moved it toward
the chosen molecule. When the tip formed a chemical bond with the terminal group
(S or Se) of the molecule, the conductance jumped to a much higher conductance.
4. CRITICAL ISSUES IN SINGLE-MOLECULE
CONDUCTANCE MEASUREMENTS
The mechanical methods, especially when combined with force measurements and
statistical analysis, have the following distinctive features: (a) Peaks in the conductance
histogram located at integer multiples of a fundamental value can be used as a signature
to identify the conductance of a single molecule. (b) The simultaneously measured
force tells us if a molecule is properly bound to two electrodes. (c) Statistical analysis
reduces the chances of mistaking impurities as sample signals. (d ) Mechanical methods
work in solution and in vacuum, which not only makes it easy to introduce various
sample molecules into the measurement, but also provides a controlled and inert
environment for the measurement. However, there are several issues that require
further study.
4.1. Molecule-Electrode Contact Geometry
In STM– or conducting AFM–break junction methods, a large number of molecular
junctions are repeatedly created, but these molecular junctions differ in their contact
geometries (Figure 8). In fact, the conductance of the last step, corresponding to
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Figure 8
(a) Different contact geometries of a 1,6-hexanedithiol molecule bound to two Au electrodes.
(b) Calculated conductance values of the molecule for the different contact geometries plotted
versus the number of atoms protruding out of the crystal planes of the electrodes.
(c) Distribution of conductance values with 1296 different contact geometries. Reprinted with
permission from References 14 and 16.
the formation of a single-molecule junction, varies considerably from one junction
to another, which reflects atomic-scale variations in the contact geometries (13, 14,
16, 17). Guo and colleagues (16) calculated the conductance values of molecules with
hundreds of different contact geometries (Figure 8c). By assuming that the statistical
weight of each geometry is equal, they obtained a distribution of the conductance
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HOMO: highest occupied
molecular orbital
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LUMO: lowest unoccupied
molecular orbital
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values. The distribution for 1,6-hexanedithiol bound to Au electrodes has a peak near
∼2 × 10−3 G0 , which is in good agreement with the experimental peak position at
∼1.2 × 10−3 G0 (124). In addition to various binding sites of the anchoring groups
(e.g., S) on Au electrodes, Muller (14) considered the possibility that the anchoring
groups may bind to one or more Au atoms protruding out of the electrode crystal
planes (Figure 8a). For 1,6-hexanedithiol, most of the 16 different contact geometries
have conductance values close to ∼2 × 10−3 G0 (Figure 8b), in close agreement with
both the experiment and the calculations by Guo et al. (16).
In the case discussed above, pronounced peaks appear in the conductance histogram, which are used to identify the conductance of single molecule. This method
fails if the distribution is too broad, as shown by Ulrich et al. (131). We also found
in our lab that some molecules, especially small conjugate molecules, exhibit welldefined steps in the individual conductance traces, but the conductance histograms
display only broad distributions (132). Another possibility is that for (at least) some
molecules, more than one set of conductance peaks appear in the histograms. Li et al.
(133) studied the conductance of single N-alkanedithiols (N = 6, 8 and 10) covalently
bound to Au electrodes. For each molecule, the conductance histogram reveals three
sets of well-defined peaks near integer multiples of different conductance values.
The two higher conductance sets can be described by the tunneling model with an
identical decay constant of 0.84 Å−1 and interpreted in terms of different moleculeelectrode contact geometries (134). The lowest one is thermally activated, which was
previously reported by Haiss et al. (23), and is attributed to the thermal fluctuation
of the molecular conformation.
The distribution of different contact geometries appears to depend on the way
the molecular junctions are formed. For example, Wandlowski and colleagues (85)
measured the conductance of dithiol molecules using an STM break junction by
carefully avoiding the contact of the tip with the Au substrate. They found one
set of pronounced peaks in the conductance histograms. Conversely, Venkataraman
et al. (127) reported that diamine-terminated molecules gave well-defined peaks in the
conductance histograms by forcing the two electrodes to form a point contact during
the approaching stage. In their case, the formation of point contacts was believed to
be crucial for the formation of an amine-Au bond.
4.2. Molecule-Electrode Energy-Level Alignment
The conductance of a molecule depends on the alignment of the molecular energy
levels, especially the highest occupied molecular orbital (HOMO) and lowest occupied molecular orbital (LUMO), relative to the Fermi levels of the electrodes.
Typically, the Fermi level is positioned in the LUMO-HOMO gap of the molecule
because if the HOMO or LUMO is close to the Fermi level of an electrode, electrons
transfer between the molecule and the electrode, and consequently the molecules are
oxidized or reduced spontaneously. The energy-level alignment is determined by the
intrinsic properties of the molecule and the electrodes, and also by the interactions
between the molecule and the two electrodes, which are often difficult to determine
for both theory and experiment (135, 136).
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Surface spectroscopy techniques, such as ultraviolet photoelectron spectroscopy
and X-ray photoelectron spectroscopy, can provide useful information about the
energy-level alignments of molecules adsorbed on surfaces (137). STM tunneling
spectroscopy has also been used to study the electronic states of molecules adsorbed
on surfaces. Hipps and colleagues combined the tunneling spectroscopy with ultraviolet photoelectron spectroscopy to study metallo-porphyrins and phthalocyanines
on Au (138) and resolved different molecular energy levels and their relative positions
to the Au Fermi level (77).
In electrolytes, one may gain valuable insights into the energy-level alignment
by measuring the oxidization or reduction potentials (Figure 9) (139). One may
even tune the alignment by adjusting the potentials of the electrodes relative to
a reference electrode inserted in the electrolyte. When the LUMO or HOMO is
brought close to the Fermi levels, electrochemical oxidation or reduction occurs. For
molecules that can be reversibly oxidized or reduced, significant changes in the conductance occur. This has lead to electrochemical gate control of the conductance of
single redox molecules that is analogous to field effect transistors (82, 140–142). This
behavior has been observed in several redox systems (82, 140–143). For example,
Haiss et al. (140) reported an interesting potential-dependent conductance in viologen derivatives. Another example is perylene tetracarboxylic diimide terminated with
thiol groups (Figure 9c) (141). The conductance of a single perylene tetracarboxylic
diimide molecule covalently bound to two Au electrodes increases reversibly over
nearly three orders of magnitude as one shifts the LUMO of the molecule toward
the Fermi level of the electrodes.
4.3. Effect of External Force
The mechanical methods can create a molecular junction by controlling the separation between two electrodes. It is natural to ask how the applied force affects the measured conductance of the molecules. In the individual conductance traces recorded
during the breakdown of the molecular junctions, the step is rather flat, which means
the force does not significantly affect the measured conductance until the contact
breaks down. However, carefully examining the steps, one can see a finite decrease,
on average, in the conductance upon stretching. In the case of alkanedithiols, the decrease is only 10%–20% before breakdown (81). Another observation is that the distance over which a molecular junction can be stretched is typically several angstroms.
Clearly a small molecule cannot be stretched over such a large distance without tearing the molecule apart. The reason for such a large stretching distance is that most
of the stretching actually takes place in the Au atoms near the molecule-electrode
contact rather than in the molecule, itself. When the force reaches ∼1.5 nN, the
contact breaks, and the maximum force that one applies to the molecule is ∼1.5 nN.
For molecules such as alkanedithiols, such a force is not sufficient to change the electronic states of the molecules or distort the structure of the molecule significantly.
However, for conjugated molecules, such as oligothiophenes, the force can cause a
much greater change in the conductance, owing to a stronger coupling between the
electronic states and the structures of the molecule than that for alkanedithiols (81).
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(a) A redox molecule is
covalently linked to two
electrodes in an
electrochemical cell.
(Counter electrode is not
shown here for clarity.)
(b) In terms of the energy
diagram, the
electrochemical gate voltage
(Vg ) shifts the molecular
energy levels up and down
relative to the Fermi energy
levels of the source and
drain electrodes, and the
current is driven by a finite
bias voltage (Vsd ) between
the two electrodes. (c) The
current through a single
perylene tetracarboxylic
diimide molecule as a
function of electrochemical
gate voltage (Vg ).
a
Reference electrode
Gate
Working electrode 1
Vg
Source
Working electrode 2
O
O
N
N
O
O
Drain
Vsd
Redox molecule
b
Molecular level
Fermi level
c
Fermi level
10
Current (nA)
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Figure 9
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1
0.1
–0.8
–0.6
–0.4
–0.2
Vg (V vs. Ag/AgCl)
One may also expect a stronger effect of the applied force on the conductance for
softer molecules.
4.4. Effect of Environment
The local environment (such as solvent molecules, ions, pH, and dopants) of a
molecule can significantly affect the conductance of the molecule. Xiao et al. (144)
measured conductance on several oligopeptides terminated with dithiols as a function
of solution pH and observed the dependence of the conductance on pH (Figure 10).
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a
b
4.8
HS
SH
N
H
O
NH 2
G(10–3G0)
O
H
N
4.4
Cysteamine-Gly-Cys
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4.0
0
2
4
6
8
10
12
pH
Figure 10
(a) Molecular structure of a peptide, Cysteamine-Gly-Cys. (b) Dependence of peptide
conductance on the solution pH.
They traced the pH dependence to the protonation or deprotonation of NH2 and
COOH in the peptides, which changes electronic states and local charge distributions
of the molecules. The conductance of a molecule may also depend on the surrounding ions (6). For example, the presence of Cu2+ and Ni2+ in solution changes the
conductance of cysteamine-Gly-Cys by ∼300 and ∼100 times, respectively, owing
to strong binding of the metal ions to the molecule. In a recent study by STM in an
ultrahigh vacuum environment, a charged dangling bond of Si induced a large change
in the electronic states of a nearby adsorbed molecule, and the researchers attributed
this observation to the electric field by the charge (92). In the case of peptides, the
binding of Ni2+ and Cu2+ is strong and known to induce conformational changes in
the peptides. Therefore, in addition to an electrostatic effect, conformational changes
may be responsible for the change in conductance.
For certain molecules, the dependence of conductance on local environment may
be traced to the change in doping. Chen et al. (145) measured the conductance of a
hepta-aniline oligomer attached to Au electrodes in toluene and in electrolyte. The
single-molecule current-voltage characteristic is linear in toluene but displays negative differential resistance in an acidic electrolyte. The conductivity of bulk polyaniline
increases dramatically when it is oxidized in an acidic medium, in which acid plays
the role of doping the polymer materials. Similar to the bulk polyaniline, the conductance of a single aniline oligomer also increases in the oxidized form in acid. These
results show the sensitive dependence of the conductance of the redox molecule on
the solvent, and on the doping condition.
Local heating: heating
effect in a molecular
junction owing to an
electrical current passing
through the junction
4.5. Current-Induced Local-Heating Effects
Local heating is known to be a critical factor in the design of conventional siliconbased microelectronics. When current passes through a single molecule, how hot it
gets is an important question. In a nanoscale junction, the inelastic electron mean free
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path is often large compared with the size of the junction, so each electron is expected
to release only a small amount of its energy to phonons (heat) during transport in
the junction (66, 67). However, substantial local heating may still arise owing to the
large current density and thus power per atom.
Recently, researchers have reported experimental studies of local-heating effects
in quantum point contacts (146, 147). In the case of molecules, the current density
is much lower, but the thermal conduction of molecules may also be poorer than
that of the metal contacts. Theoretical calculations have found a finite increase in
the temperature of the molecules as a result of the inelastic scattering of electrons
(148, 149). Huang et al. (150) reported on an experimental approach to determine
the local temperature in a single molecule covalently bound to two Au electrodes.
They measured the force required to break the attachment of the molecules to the
electrodes. Because the breakdown process is thermally activated, the average breakdown force is sensitive to the local temperature of the molecule-electrode contact and
can be used to estimate the effective local temperature of the molecular junction. For
octanedithiol, the temperature with a bias voltage of 1 V (current ∼20 nA) increases
by ∼25 K above room temperature.
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5. OUTLOOK
The conductance of a single molecule depends not only on the intrinsic properties of
the molecule and the probing electrodes, but also on the molecule-electrode contacts
and its local environment. To determine the conductance unambiguously, one wishes
to fabricate a molecular junction with molecule-electrode contacts that are well defined on the atomic scale and carry out the measurement in a controlled environment.
Fabricating such contacts reproducibly has been a challenge. Despite the difficulty,
researchers have made solid advances recently. For example, STM has been used to
create a well-defined metal-molecule-molecule junction by precisely placing individual metal atoms into contact with a molecule adsorbed on a substrate. To measure the
conductance, the remaining challenges are to wire the two metal ends to an external
circuit and to ensure that the electronic coupling between the molecular junction and
the underlying substrate is negligible.
Another important development is various break junction techniques. By combining a mechanical break junction with simultaneous force and conductance measurements, one can determine if the measured conductance is a result of a single
molecule and how the molecule is bound to the probing electrodes. The approach
also allows one to create a large ensemble of molecular junctions with microscopically different molecule-electrode contacts and to perform statistical analysis on the
conductance values of the molecular junctions. A peak in the distribution gives an
averaged conductance of the molecule. The approach is simple and has been used
to measure the electron-transport properties of many different molecules in vacuum
and in solutions. However, the exact molecule-electrode contact geometries created
by the break junction methods are usually unknown, and techniques that can provide
atomic-scale structural information of the molecule-electrode contact will be of great
importance to the field.
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SUMMARY POINTS
1. Determining the conductance of single molecule is a basic task in molecular
electronics.
2. To measure the conductance of a molecule, one must provide a reliable and
reproducible contact between the molecule and two probing electrodes.
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3. Measurement of single-molecule conductance has been difficult owing to
the lack of a technique that can provide reliable and well-defined moleculeelectrode contacts.
4. STM-based methods can place metal atoms into contact with a single
molecule on a substrate with atomic precision. Remaining challenges are
to connect the metal atoms to the external electrodes for conductance measurements and to ensure the electronic coupling between the molecule and
the substrate does not interfere with the conductance measurement.
5. Break junction methods can create a large number of molecular junctions
with different contact geometries. Although these contact geometries are
not known precisely, the methods allow one to perform statistical analysis
and to determine an average conductance of a molecule.
6. The conductance of a molecule depends also on its local environment.
7. By carrying out the measurement in an electrochemical environment, one
can tune the alignment of the molecular energy levels relative to the Fermi
energy levels of the electrodes and thus control the conductance of the
molecule.
8. Future techniques that can fabricate molecular junctions with moleculeelectrode contacts that are well defined on the atomic scale and that can
characterize the atomic-scale structures of the molecule-electrode contacts
will contribute enormously to the field of molecular electronics.
ACKNOWLEDGMENTS
We thank NSF, DOE, VW, and DARPA (via AFOSR) for financial support.
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www.annualreviews.org • Single-Molecule Conductance
25. Compares
experimental results on
low-bias,
room-temperature
conductance of saturated
alkane chains and
conjugate molecules
obtained in different
electrode-moleculeelectrode test
beds.
32. Presents a
comprehensive review of
quantum point contact,
mechanically controlled
break junctions, and
relevant physical concepts
and techniques.
39. Reviews
single-molecule electrical
junctions with emphasis
on the application of
single-electron transistor
theories such as the
Kondo effect and Zeeman
splitting.
40. Summarizes many
different experimental
techniques with a focus
on the self-assembled
monolayer.
41. Presents a
comprehensive study of
the conduction
mechanism of alkane films
sandwiched between two
Au electrodes.
557
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www.annualreviews.org • Single-Molecule Conductance
133. Describes in detail an
STM–break junction
technique for
single-molecule
conductance
measurements, including
experimental setup and
statistical analysis.
563
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Annual Review of
Physical Chemistry
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Contents
Volume 58, 2007
Frontispiece
C. Bradley Moore p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p xvi
A Spectroscopist’s View of Energy States, Energy Transfers, and
Chemical Reactions
C. Bradley Moore p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 1
Stochastic Simulation of Chemical Kinetics
Daniel T. Gillespie p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 35
Protein-Folding Dynamics: Overview of Molecular Simulation
Techniques
Harold A. Scheraga, Mey Khalili, and Adam Liwo p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 57
Density-Functional Theory for Complex Fluids
Jianzhong Wu and Zhidong Li p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 85
Phosphorylation Energy Hypothesis: Open Chemical Systems and
Their Biological Functions
Hong Qian p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p113
Theoretical Studies of Photoinduced Electron Transfer in
Dye-Sensitized TiO2
Walter R. Duncan and Oleg V. Prezhdo p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p143
Nanoscale Fracture Mechanics
Steven L. Mielke, Ted Belytschko, and George C. Schatz p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p185
Modeling Self-Assembly and Phase Behavior in
Complex Mixtures
Anna C. Balazs p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p211
Theory of Structural Glasses and Supercooled Liquids
Vassiliy Lubchenko and Peter G. Wolynes p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p235
Localized Surface Plasmon Resonance Spectroscopy and Sensing
Katherine A. Willets and Richard P. Van Duyne p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p267
Copper and the Prion Protein: Methods, Structures, Function,
and Disease
Glenn L. Millhauser p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p299
ix
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Aging of Organic Aerosol: Bridging the Gap Between Laboratory and
Field Studies
Yinon Rudich, Neil M. Donahue, and Thomas F. Mentel p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p321
Molecular Motion at Soft and Hard Interfaces: From Phospholipid
Bilayers to Polymers and Lubricants
Sung Chul Bae and Steve Granick p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p353
Molecular Architectonic on Metal Surfaces
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Annu. Rev. Phys. Chem. 2007.58:535-564. Downloaded from arjournals.annualreviews.org
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