Electrochemistry and bioelectrochemistry towards the single-molecule level: Theoretical notions and systems

Electrochimica Acta 50 (2005) 3143–3159

Electrochemistry and bioelectrochemistry towards the single-molecule level: Theoretical notions and systems Jingdong Zhang a , Qijin Chi a , Tim Albrecht a , Alexander M. Kuznetsov b , Mikala Grubb a , Allan G. Hansen a , Hainer Wackerbarth a , Anne C. Welinder a , Jens Ulstrup a,∗ a

b

Department of Chemistry, Building 207, Nano. DTU, Technical University of Denmark, DK-2800 Lyngby, Denmark The A.N. Frumkin Institute of Electrochemistry of the Russian Academy of Sciences, Leninskij Prospect 31, 117071 Moscow, Russia Received 12 September 2004; received in revised form 7 December 2004; accepted 8 December 2004

Abstract Surface structures controlled at the nanometer and single-molecule levels, with functions crucially determined by interfacial electron transfer (ET) are broadly reported in recent years, with different kinds of electrochemically controlled nanoscale/single molecule systems. One is the broad class of metallic and semiconductor-based nanoparticles, nano-arrays, nanotubes, and nanopits. Others are based on self-assembled molecular monolayers. The latter extend to bioelectrochemical systems with redox metalloproteins and DNA-based molecules as targets. We overview here some recent achievements in areas of interfacial electrochemical ET systems, mapped to the nanoscale and singlemolecule levels. Focus is on both experimental and theoretical studies in our group. Systems addressed are organized monolayers of redox active transition metal complexes, and metalloproteins and metalloenzymes on single-crystal Au(1 1 1)-electrode surfaces. These systems have been investigated by voltammetry, spectroscopy, microcantilever technology, and scanning probe microscopy. A class of Os-complexes has shown suitable as targets for electrochemical in situ scanning tunnelling microscopy (STM), with close to single-molecule scanning tunnelling spectroscopic (STS) features. Mapping of redox metalloproteins from the three major classes, i.e. blue copper proteins, heme proteins, and iron–sulfur proteins, at the monolayer and single-molecule levels have also been achieved. In situ STM and spectroscopy of redox molecules and biomolecules have been supported by new theoretical frames, which extend established theory of interfacial electrochemical ET. The electrochemical nanoscale and single-molecule systems discussed are compared with other recent nanoscale and single-molecule systems with conspicuous device-like properties, particularly unimolecular rectifiers and single-molecule transistors. Both of these show analogies to electrochemical in situ STM features of redox molecules and biomolecules. © 2005 Elsevier Ltd. All rights reserved. Keywords: Electrochemical nanoscience; STM of redox molecules; Biomolecular conductivity; Tunnelling spectroscopy; Single-molecule devices

1. Introduction “Nanoscience” refers to the exciting areas of science, where target objects display novel size-dependent properties [1]. Nanoscale and ultimately single-molecule systems also hold multi-farious technological perspectives, best recognized in electronics industry with focus on information stor∗

Corresponding author. Tel.: +45 4525 2419; fax: +45 4588 3136. E-mail address: [email protected] (J. Ulstrup).

0013-4686/$ – see front matter © 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2004.12.044

age, electronic components, sensors, etc. [2] but nanoscience penetrates many areas of physical, chemical, and biological sciences including electrochemistry. Metal and semiconductor structures, nanoscale electrode arrays, and nanoparticle assemblies, are in focus in recent electrochemical nanotechnology, broadly represented at the Second ISE Spring Meeting in Xiamen, China [3]. Nanoscale electrocatalysis [4,5] and fuel cell design [6,7] are other perspectives. No less central in evolving pure and applied nanoscale electrochemistry is a wealth of monolayer systems [8,9]. Electrochemistry of

3144

J. Zhang et al. / Electrochimica Acta 50 (2005) 3143–3159

biomolecules, such as proteins [8,10,11] and DNA [12–15] in monolayer and single-molecule surface structures has also evolved. Central objectives in nanoscale electrochemistry and bioelectrochemistry are: • to construct and control the electrode–solution interface at the nanometer scale, as suitable environment for electrochemical and bioelectrochemical target system functions; • to control supramolecular properties of immobilized molecules at the monolayer and single-molecule levels, including molecular structures with electrochemically controlled electronic properties [16,17] (e.g. “smart” molecules [18]); • to insert molecules into nanoconfigurations, such as STM or between nanogap electrodes, where device-like function can be evoked. This also offers clues to the mechanisms of interfacial ET and single-molecule electronic conductivity. Reported nanoscale systems resting broadly on interfacial ET between the molecules and the enclosing electrodes testify that such objectives are being approached [19–25]. To this come the powerful frames of theoretical ET science [26–28]. Nanoscale electrochemistry has also disclosed novel ET phenomena [29], posing new theoretical challenges. In this overview, we address some electrochemically based interfacial chemical and biological systems characterized to nanoscale or single-molecule resolution. The systems are based on monolayers of redox active molecules self-assembled on single-crystal metal surfaces to create favourable electrochemical environment for molecular ET function. Sophisticated nanostructures based on metal deposition [30], nanoparticles [31], carbon nanotubes [32], and nanopits [33] are also reported in increasing numbers but will not be discussed here. In Section 2, we overview some theoretical notions of electrochemical ET, followed in Section 3 by a discussion of nanoscale configurations, particularly in situ STM. The theoretical discussion is illustrated by recent cases of interfacial ET of redox molecules and biomolecules. The combination of state-of-the-art electrochemistry and in situ STM with biological macromolecules is here emphasized. In Section 4, we discuss single-molecule conductivity, single-electron tunnelling, amplification, and rectification with reference to the theoretical frames. Section 5 offers some concluding observations.

2. Some theoretical notions of interfacial ET theory Experimental and theoretical characterization of chemical and biological ET in solution has reached high sophistication [26–28]. Similar detail in electrochemical ET has been more elusive. Crucial to the interfacial ET scenarios are multifarious static and dynamic environmental effects, imposing multi-phonon character on the ET process (Fig. 1). The electrochemical current is composed of contributions from all the

Fig. 1. Electronic energies of the electrode and redox molecule (left), and Gibbs free energy surfaces (right) for electrochemical (cathodic) ET at metal electrodes [27].

levels of the (here, metal) electrode. These views carry over to nanoscale systems and are summarized in the following. The (cathodic) current density, j(η) at the overpotential η is:
j(η) = dεf (ε)ρ(ε)i(ε; η); i(ε; η) = eΓox W(ε; η) (1) W(ε; η) is the rate constant and i(ε; η) the current density from a given electronic level ε, f(ε) the Fermi function, ρ(ε) the electronic level density, Γ ox the population of the oxidized state of the redox molecules, and e is the electronic charge. Eq. (1) applies to monolayer electrochemistry. Generalization to mobile reactants is straightforward. W(ε; η) holds all information about nuclear reorganization, overpotentialdependence, and electron tunnelling. Eq. (2) applies broadly [26]:   ωeff [Er + eη − (ε − εF )]2 W(ε; η) = κel exp − 2π 4Er kB T  κel = κel (ε; η) = [T␧A (ε; η)]2

4π3 2 E r kB T h ¯ 2 ωeff

(2)

Er is the nuclear reorganization free energy, ωeff the effective vibrational frequency, εF the Fermi energy of the electrode, kB Boltzmann’s constant, and T the temperature. κel is the electronic transmission coefficient (tunnelling factor), the most important part of which is the electron exchange energy, T␧A (ε; η), which couples the molecular level (A) with the metallic level ε. Energy levels around ε ≈ εF dominate broadly, and combination of Eqs. (1) and (2) gives, j = jdiab ≈ eΓox ko/r ; k

o/r

  ωeff (Er + eη)2 ≈ κeff exp − 2π 4Er kB T

κeff ≈ 4πκel (εF ; η = 0)ρ(εF )kB T, if κeff  1, otherwise

(3)

J. Zhang et al. / Electrochimica Acta 50 (2005) 3143–3159

3145

Fig. 2. Spatial dependence of metallic electron density (jellium representation) in electrochemical ET. Left: positive electrode charging (σ > 0). Middle: electrically neutral electrode surface (σ = 0). Right: negative electrode charging (σ < 0).

j = jad

  ωeff (Er + eη)2 ≈ eΓox exp − , i.e. κeff → 1 2π 4Er kB T (4)

κeff is thus the “effective” electronic transmission coefficient over broad overpotential ranges. Eqs. (3) and (4) apply to the weak- and strong-coupling diabatic and adiabatic limits, respectively. Eq. (3) can also be recast using the electrode–molecule electronic density overlap, M(η) [34]:   (Er + eη)2 ωeff j = jdiab ≈ eΓKel (η) exp − ; 2π 4Er kB T  4π3 Kel (η) ≈ (V␧A )2 M(η) (5) 2 Er kB T h ¯ 2 ωeff where V␧A is the physical electrode–molecule interaction. Some intriguing overpotential effects appear in the preexponential tunnelling factor, illustrated by Fig. 2: M(η) ≈ A exp [−βmet (a − z¯ )] + B exp [−βmol (a − z¯ )]

(6)

where A and B are constants, a the distance of the molecule from the electrode surface, z¯ the position of the metallic electron density front (e.g. jellium front), and βmet and βmol the density decay factors of the metal and molecule, respectively. The metallic electron density depends on the surface charge, leading the density overlap to increase as the density expands on negative electrode charging, and to decrease as the density contracts on positive charging. The following modification, applies for strong electrode–molecule interactions [35–37]:   (Er + eη)2 (Er + eη)2 ∆ ∆2 → + ln 4Er 4Er 2π ∆2 + (Er + eη)2 (7) i.e. the level broadening ∆ now lowers significantly the activation free energy. Eqs. (1)–(7) have been introduced as a reference for nanoscale systems discussed in the following. Comprehen-

Fig. 3. Three-dimensional structure of azurin and schematic views of azurin assembled on: (A) bare Au(1 1 1); (B) a hydrophobic alkane thiol monolayer self-assembled on Au(1 1 1). Azurin structure from [39] and Protein Data Bank. Molscript Graphics [40].

sive interfacial electrochemical ET theory has received substantial experimental recent support from both physical electrochemistry and bioelectrochemistry. Figs. 3 and 4 show an example [38]. The blue copper protein Pseudomonas aeruginosa azurin can be immobilized on Au(1 1 1)-electrode surfaces either by binding via a protein surface disulfide group (Fig. 3A), or in an opposite orientation via hydrophobic attachment to Au(1 1 1)-electrodes modified by variable-length alkane thiols (Fig. 3B). The highly ordered single-crystal Au(1 1 1)-surface enables high voltammetric resolution, not reached by polycrystalline electrodes. Both quadratic overpotential-dependence and tunnelling through the alkane thiol layer have been characterized (Fig. 4). Such a level of accuracy opens for subtle long-range ET features including electronic density modulation by configurational fluctuations [41,42].

3. Interfacial ET in two- and three-electrode nanoscale systems Focus here is on electronic conductivity of molecular monolayers or single molecules enclosed between a pair of metallic electrodes. The latter can be a pair of nanoscale electrodes, or the substrate and tip in STM. A third electrode is the reference electrode in electrochemical in situ STM or a gate electrode in three-electrode molecular transistors. Transfer of STM from vacuum to electrochemical aqueous environment involves technological and fundamental changes. Electrochemical STM requires independent control of both substrate and tip potential relative to a common reference electrode [43,44]. The bias voltage and substrate overpotential create, further two kinds of “spectroscopic”

3146

J. Zhang et al. / Electrochimica Acta 50 (2005) 3143–3159

Fig. 4. (A) Interfacial ET rate constant (zero overpotential) of P. aeruginosa azurin on variable-length alkane thiols self-assembled on Au(1 1 1), cf. Fig. 3B. (B) Quadratic free energy relations of cathodic and anodic currents of P. aeruginosa azurin monolayer on tetradecanethiol self-assembled on Au(1 1 1) [38].

current–voltage relations. The tunnelling phenomenon is also different from vacuum as the molecular monolayers or assemblies of solvent molecules in the tunnelling gap invoke static and dynamic fluctuational features on the barrier, both enhancing the tunnelling current compared to vacuum [45–47]. Tunnelling through layers of water molecules has been addressed theoretically by schemes, where the time-dependent Schr¨odinger equation is solved in the field of the water assemblies pre-configured by molecular dynamics simulation, i.e. by invoking static configurational fluctuations [46,47]. The electron–water interactions hold a balance between repulsive interactions with the oxygen atoms and attractive interactions with the hydrogen atoms and the electronic polarizability. This leads the electronic density to spread threedimensionally in ways resembling electron tunnelling in redox metalloproteins [48]. Instantaneous water configurations also induce order of magnitude resonance-like features. These may carry the burden of the electronic transmission but no statistical analysis is available. Dynamic configurational fluctuations are crucial in electronic conduction of molecules with conducting orbitals (LUMOs and HOMOs) close to the Fermi level of the enclosing electrodes. This is addressed in Section 3.2. We consider first briefly electronic conduction through monolayers or single molecules with strongly off-resonance conducting orbitals disregarding configurational fluctuations. This area has been reviewed recently [49–52]. 3.1. Molecular conductivity and single-molecule off-resonance tunnelling This limit applies to electronic conductivity in bias or electrochemical overpotential ranges far from the redox potentials. Experimental and theoretical patterns of molecular conductivity in vacuum or non-conducting liquids are available particularly for organic ␣,␻-dithiols and functionalized thiols [24,25,53–57]. Conductivity patterns in three-electrode in situ STM or metallic break junctions are also available for dithiols [58–61], thiol-oligonucleotides [15,62,63], and pyridine derivatives [60]. The notions below apply in prin-

ciple both to single molecules as part of a monolayer or as “isolated” single molecules, and to whole monolayers. In the former cases, the single-molecule conductivity includes interactions from neighbouring molecules, or from rapid conversions between different conformational states. Conductivity patterns of whole monolayers follow similar patterns but the conductivites are now average values over large twodimensional assemblies. Electronic conductivity through off-resonance molecular orbitals (MOs) bears the closest relation to simple tunnelling views, g(Vbias ) =

ditunn ≈ g0 exp [−β(Vbias )z] dVbias

(8)

where g0 is a constant, z the distance from the negatively biased left electrode, and β(Vbias ) is the (bias voltagedependent) tunnelling decay parameter. The following simple consideration illuminates the correlation between β and the electron transmitting MOs [27]. In the off-resonance conductivity case, the current in Eq. (8) is given approximately by:
2e ∞ itunn = dερL (ε)ρR (ε)|TLR (ε; Vbias )|2 fL (ε) h −∞

(9) × 1 − fR (ε − eVbias ) where fL (ε) and fR (ε) are the Fermi functions of the electrode biased negatively and positively, respectively, and ρL (ε) and ρR( ε) are the electronic energy densities of the negatively and positively biased electrode. From high-order perturbation theory (Green’s function formalism), when ET is transmitted through a number of (LUMO and HOMO) MOs, TLR follows: TLR =

N  j=1

γL1 γ12 .....γjR

(εb1 − εFL ) (εb2 − εFL ) ....... εbj − εFL

(10)

εbj is the LUMO or HOMO energy for the jth MO, γ k,k + 1 the electron exchange energy for coupling between the kth and (k + 1)th orbital, εFL the Fermi energy of the negatively biased electrode, and N is the number of contributing MOs. γ L1 couples the negatively biased electrode with the first MO, γ jR the jth orbital with the positively biased electrode.

J. Zhang et al. / Electrochimica Acta 50 (2005) 3143–3159

3147

Eq. (10) reduces to a simple form, when only nearestneighbour interactions are important, all energy gaps replaced by a common value, εbj − εFL = !ε, and all the intramolecular exchange factors by a common value γ,     γL1 γNR 1 !ε exp − ln TLR ≈ z (11) γ a γ where a is the average spatial extension of the conducting MOs. Eq. (11) bridges to Eq. (8) by:   2 !ε(Vbias ) (12) β (Vbias ) ≈ ln a γ Eqs. (8)–(12) offer a frame for current–voltage and current– distance spectroscopy. This applies both to molecules incorporated between enclosing electrodes and to distancedependent electrochemical ET. Some two-electrode current– voltage and current–distance relations are reported in [64,65], and variable-length interfacial electrochemical ET between redox centres and the electrode in [38,66–69]. Puzzles, however, remain when formalism, such as Eqs. (8)–(12) is used as frames for real monolayer or singlemolecule function. Eqs. (8)–(12) apply only to strongly offresonance limits, i.e. when ∆ε/γ 1. As ∆ε/γ approaches small values, a variety of coherent and incoherent electronic– vibrational transmission patterns involving physical electronic LUMO or HOMO population emerge [27]. Conceptual and some formal appreciation of these cases are available but a comprehensive theory to bridge the gaps between these limits is in need. Formalism, such as Eqs. (8)–(12) and as given in sections below also occasionally fail, when macroscopic energetics in the form of redox potentials are associated with the LUMO and HOMO energies. Molecular conductivity in DNA-based molecules [62,63], or interfacial electrochemical ET through oligonucleotide [70,71] or peptide structures [72,73] display, for example, much weaker distanceand energy-dependence than expected. Configuration fluctuations, reflected in huge fluctuations (0.5–1 eV) of the LUMO and HOMO energies could be a cause of such observations [74], and a consideration in real data analysis.

Fig. 5. Electronic energy diagram of in situ STM of a redox molecule, in the case of small bias voltage; γ |eVbias | < Er − eξη. See Eq. (13) and details in the text.

3.2. STM and in situ STM of redox molecules and biomolecules

γ |eVbias | < Er − eξη

More detailed electronic conductivity patterns emerge, when low-lying redox levels can be addressed in suitable bias voltage or overpotential ranges. The levels then become temporarily populated in different dynamic or sequential modes. This offers insight in electronic and electronic–vibrational coupling patterns, in the form of negative differential resistance, or “spectroscopic” current–voltage features. New ET phenomena are also observed. Molecules with low-lying single or multiple electronic levels offer, secondly, analogies to electronic components, such as amplifiers and diodes. Fig. 5 illustrates the redox level of a molecule enclosed between two metallic continua. The empty oxidized state

has a significantly higher equilibrium free energy than the populated reduced state, if the ionization energy exceeds the solvation (electronic–vibrational) free energy. Resonance between the initially vacant (oxidized) level and metallic levels close to the Fermi level of the negatively biased (“left”, L) electrode can then be induced in three ways: (1) The bias voltage, Vbias , can be raised. As the redox level is exposed to part of the voltage, this level follows monotonously the bias voltage. (2) Environmental nuclear fluctuations lead to molecular resonance, from which electrons are transferred. After temporary trapping on the molecule, electrons are transmitted to the positively biased (“right”, R) electrode. (3) The substrate and tip potentials are controlled separately in electrochemical STM. This offers an additional spectroscopy as the redox level can now also be tuned to resonance with the Fermi level by the overpotential of the substrate electrode. This resembles three-electrode single-molecule field transistors, for which a number of cases have been reported [75–77]. When, first the bias voltage is “small”, only a narrow |eVbias |range is available for electron transmission. The notion “small” depends on the overpotential and reorganization energy as [78]: (13)

where ξ and γ are the fractions of the overpotential (ξ) and bias voltage (γ) at the redox site. As the overpotential is raised, the cathodic current first rises but drops as the reduced level is trapped below the Fermi levels. Renewed thermal activation induces the second ET step, generating a region of “negative differential resistance”. This is quite different from electrochemical ET at a single surface, where the current rise is followed by a wide plateau of constant current [26,27]. A new pattern arises, when the redox level is strongly coupled to the enclosing electrodes and both ET steps belong to the adiabatic limit [8,78]. As the temporarily populated redox level relaxes across the energy gap between εFL and εFR , a multitude of electrons, up to two orders of magnitude,

3148

J. Zhang et al. / Electrochimica Acta 50 (2005) 3143–3159

can be transmitted coherently. This is a new ET phenomenon that evokes much higher current rise in the peak overpotential region than in the weak-coupling diabatic limit, where only a single electron is transmitted. Multi-ET is, secondly more conspicuous at large bias voltage, when the inverse Eq. (13) applies. The temporarily occupied level is then trapped between the Fermi levels, where multi-electron transmission continues. The current drops after further overpotential increase, giving a plateau in the current/overpotential relationship: Er − γ |eVbias | < eξη < |eVbias | (1 − γ)

(14)

The following notions frame these views [8,78], where we focus on the adiabatic limit. A broadly valid tunnelling current form for small bias voltages, Eq. (12), is: iadiab tunn = e (eVbias ) κel ρ

ko/r kr/o ko/r + kr/o

(15)

ko/r and kr/o are the rate constants for oxidation and reduction of the redox molecule, respectively, at the tip and substrate. The rate constants follow patterns as in Eqs. (3) and (4), suitably modified:   ωeff (Er − eξη − eγVbias )2 o/r k ≈ exp − 2π 4Er kB T

k

r/o



2  Er + eξη − (1 − γ)eVbias ωeff ≈ exp − 2π 4Er kB T

(16)

The appearance of the electronic transmission coefficient, here taken as the same for the two metals, in the adiabatic tunnelling current, Eq. (15) reflects the coherence and multi-ET character in this limit. The number of electrons transmitted is thus: no/r ≈

|eVbias | ; !ε

!ε ≈

1 κelL ρL

+

1 κelR ρR

≈

2 κel ρ

(17)

In the adiabatic limit !ε  kB T and no/r is large. Eq. (17) recasts Eq. (15) in terms of no/r : iadiab tunn = 2eno/r

ko/r kr/o ko/r + kr/o

(18)

Eqs. (15) or (18) combined with Eq. (16) give the following attractive form:   1 ωeff Er − eVbias adiab itunn = e (eVbias ) κel ρ exp − cosh−1 2 2π 4kB T    1 2 − γ eVbias − eξη  × (19) 2kB T An important implication is that  1 1 η = ηmax = − γ Vbias ξ 2

iadiab tunn

shows a maximum at: (20)

Fig. 6. Overpotential-dependence of normalized in situ STM tunnelling current through a temporarily populated redox redox level, at fixed, small bias voltage. Fully adiabatic limit, cf. Eqs. (15)–(19); eξη in units of kB T. Left: γ = 0.75. Middle: γ = 0.50. Right: γ = 0.25; Er = 8 kB T.

The maximum appears at the equilibrium redox potential ηmax = 0 for a symmetric configuration (i.e. γ = 1/2) but is shifted positively and negatively if the redox site is closer to the substrate and the tip, respectively, for positive bias voltages. This is illustrated in Fig. 6. The character of the tunnelling process changes, when the bias voltage is large and the reduced level trapped between the Fermi levels, i.e. the inverse Eq. (13) applies [6,78] (Fig. 7). The notion of the average (quantum mechanical) level population, n, is then important:

n =

∆L ; ∆L + ∆ R



2 ∆M = π T␧M A ρN ;

M = L, R (21)

n is taken as constant in the energy region between εFL and εFR . ∆M are the level broadenings caused by electronic interactions of the redox level with the electrodes. The tunnelling current is determined by the equilibrium population of the oxidized state [8,78]: iadiab tunn =

e e 1   cox = τ τ 1 + k˜ ox k˜

(22)

red

The tilde on the rate constants refers to the partially populated state, 0 < n < 1, and partial ET, when the redox level is trapped between the Fermi levels. τ can be viewed as an electronic “relaxation time”: τ=

h ¯ h ¯ 2¯h + = ∆L ∆R ∆

if ∆L = ∆R = ∆

(23)

Eq. (22) can be recast as: iadiab tunn =

e 1    ;

n(1− n)E r − n(eξη+eγVbias ) τ 1 + exp kB T

0 < n < 1

(24)

which applies for both small and large overpotentials as long as the reduced level is trapped between the Fermi levels. If

J. Zhang et al. / Electrochimica Acta 50 (2005) 3143–3159

3149

Fig. 7. Left: schematic view of the oxidized and reduced levels at “large” bias voltage γ |eVbias | > Er − eξη. Right: overpotential-dependence of fully adiabatic in situ STM tunnelling current (normalized to e/τ), at fixed bias voltage; |eVbias | = 0.4 eV; Er = 0.1 eV.

n = 1, then: iadiab tunn =

1 e ∆ L ∆R    ; n → 1, or h ¯ ∆L + ∆R 1 + exp − eξη+eγVbias kB T

(25) iadiab tunn

e ∆ L ∆R = ; h ¯ ∆L + ∆ R

(26)

at large overpotentials, where both oxidized and reduced levels are accommodated between the Fermi levels. The current here is high and activationless. Eqs. (22)–(26) suggest that the current–bias voltage relation displays a rectifying feature, going from low, thermally activated, and strongly bias voltage-dependent current at small |Vbias | to large, activationless, and bias voltage-independent values at high |Vbias |. A similar switch is expected upon overpotential variation at given large bias voltage. These equations could represent cases of redox molecules, where strong and bias voltageindependent STM contrast over certain ranges is observed, with poor contrast outside these ranges [78]. At larger overpotentials εox remains above εFL , while εred is trapped below εFR , cf. Eq. (9). The current again reduces to Eq. (15), which can also be converted to the form:  2 ko/r kr/o π e adiab itunn = (2eVbias ) (27) τ Er kB T ωeff ko/r + kr/o suitable for interpolation between Eqs. (15) or (27) and Eq. (24). n = 1 in Eqs. (15) and (27), while 0 < n < 1 in Eq. (24). Fig. 7 shows a current–overpotential relation based on Eqs. (24) and (27). The current plateau and the decreases on either side are apparent. 3.3. Tunnelling spectroscopy of redox molecules Cases of tunnelling spectroscopy through a localized ET centre and current–voltage peaks or negative differential resistance in two-electrode configurations have been reported. The negative differential resistance is caused by different mechanisms and can be reflected in the conduc-

tivity (ditunn /dVbias ) or directly in the current. The enclosing electrodes are constituted either by a STM substrate and a tip, or by a pair of micro- or nanoscale electrodes. The environment could be ultra-high vacuum, ambient atmosphere, or non-conducting liquid. Covalently attached ferrocene [22] and metalloporphyrins [79], heteropolytungstates [23], phthalocyanines [80], organic molecules with functionalizing substituents [24,25,81], and cytochrome c [82] have been target molecules. The mechanism of electron transmission in the peak region is either a redox process, or significant electronic structural changes and electronic density shifts in the different molecular charge states, coupled to “gating” nuclear motion. 3.3.1. In situ STM and tunnelling spectroscopy of transition metal complexes Some recent cases of switch- or transistor-like behaviour in four-electrode in situ STM of redox molecules [16,17,81] open an experimental dimension in this area. A clear advantage of these systems in a device context is that they operate at room temperature, in contrast to other three-electrode single-molecule transistors that were operated only at cryogenic temperatures [75–77]. The opening of ET channels by redox levels in the in situ STM mode was illustrated by Tao’s studies of iron protoporphyrin IX (FePP) on highly oriented pyrolytic graphite (HOPG) [16]. FePP resolved to the single-molecule level showed a strong resonance in the current–overpotential relation at the formal equilibrium potential. This follows adiabatic two-step ET. Some questions as to possible changes of spin state and ligand sphere in the oxidation–reduction cycle remain open but this could add to the importance of this system. Schiffrin and co-workers reported STM of a 6 nm gold particle linked to a gold substrate by ␣,␻-20-methylenedithiol with a pyridinium group in the centre [81]. This configuration also offers an approach to the single-ET views in Section 3.4. Fig. 8 illuminates a recent case of in situ STM and tunnelling-overpotential spectroscopy of a redox couple, viz. [Os(bipy)2 (p2p)2 ]2+/3+ on Au(1 1 1)-electrodes (bipy: 2,2 -

3150

J. Zhang et al. / Electrochimica Acta 50 (2005) 3143–3159

Fig. 8. (A) The [Os(bipy)2 (p2p)2 ]2+/3+ complex structure. (B) Cyclic voltammogram (dotted line), and in situ STM tunnelling current/overpotential correlations (full line) of [Os(bipy)2 (p2p)2 ]2+/3+ monolayers on Au(1 1 1)-electrodes. Positive tunnelling current: positive bias voltage (+0.1 V); negative tunnelling current: negative bias voltage (−0.1 V). Details in [17].

bipyridine; p2p: 1,2-4,4 -ethylenedipyridine) [17]. This system offers the following merits in the quest for singlemolecule device-like behaviour: (a) The system is robust in both oxidation states, with no change in spin or ligand states. (b) A negative differential resistance feature around the for mal equilibrium potential, E0 = +0.60 V (versus SCE) is highly conspicuous, with an on/off ratio of ≈50. (c) The tunnelling spectroscopic feature is supported by other data, particularly monolayer voltammograms and highresolution in situ STM images. (d) The current–overpotential maximum follows systematically the bias voltage, Eqs. (14)–(15). (e) Preliminary data for a second Os-complex [Os(bipy)2 (p0p)Cl]+/2+ (p0p: 4,4 -bipyridine) indicate that the spectroscopic maximum also follows the formal equilibrium potential. (f) The complexes are linked to the Au(1 1 1)- or Pt(1 1 1)surface, by pyridine-based ligands. These are not as strongly bonded as thiol-linkers but give a weaker interfering STM contrast. Overall, the physical and chemical properties of this class of transition metal complexes offer new and promising prospects for single-molecule device-like target systems. 3.3.2. Approaches to single-molecule electrochemical biological function Approaches to nanoscale and single-molecule electrochemistry have extended to biological macromolecules. Redox metalloproteins and enzymes are presently in our focus. Bioelectrochemistry of redox metalloproteins and metalloenzymes was initiated over 20 years ago [10,11] and has long held multi-farious fundamental and technological biological surface science perspectives [8,83,84] in contexts, such as the understanding of adsorption dynamics, mechanisms of interfacial ET and enzyme catalysis, and applications as biosens-

ing devices. These areas have evolved recently into a new dimension resolving information down to the nanoscale and single-molecule levels. Nanoscale and single-molecule bioelectrochemistry can be addressed from two sides. One rests on biotechnology and bioelectrochemical surface chemistry [83,84]. Objectives are the construction of electrochemically controlled biological redox chains [83], and a variety of physical (electrochemical, optical, magnetic, etc.) control mechanisms of the signal transmission between adsorbed biomolecules and external circuits [84]. Mutant proteins and de novo synthetic proteins are other parts of this approach. The other approach is rooted in state-of-the-art physical electrochemistry, with focus on the use of single-crystal electrodes, and therefore, well-defined local environments, and on cyclic, linear, and differential pulse voltammetry. This is further combined with comprehensive other interfacial techniques including electrochemical impedance spectroscopy, in situ STM, in situ microcantilever technology and X-ray photo-electron spectroscopy (XPS). Imaging of single biomolecules, such as DNA-based molecules and proteins based on interfacial conductivity was an early vision in STM. Mapping of metalloproteins by in situ STM with potential control to single-molecule resolution began in the mid-1990s with horse heart cytochrome c [85], horseradish peroxidase [86], and Pseudomonas aeruginosa azurin [87] as targets. This was followed by other studies of azurin [38,88,89], plastocyanin [90], and representatives of the two other major classes of ET metalloproteins, i.e. the heme protein yeast cyt c [91,92] and the iron–sulfur protein Pyrococcus furiosus ferredoxin [93]. Other proteins characterized to single-molecule resolution include de novo designed 4-␣-helix proteins [94] and the metalloenzyme Achromobacter xylosoxidans (copper) nitrite oxidase [95]. Other proteins in aqueous solution have been studied without electrochemical potential control [96].

J. Zhang et al. / Electrochimica Acta 50 (2005) 3143–3159

3151

Fig. 9. Overview of structures of metalloproteins and DNA-based molecules recently characterized to single-molecule resolution under potential control. Top left: 4-␣-helix synthetic carboprotein [94]. Top middle: thiol-anchored oligonucleotides [15]. Top right: P. aeruginosa azurin [8,38,88,89]. Bottom left: Saccharomyces cerevisiae yeast cytochrome c [91,92]. Bottom middle: Achromobacter xylosoxidans copper nitrite reductase [95]. Bottom right: Pyrococcus furiosus ferredoxin [94].

Fig. 9 shows an overview of redox proteins and an oligonucleotide studied in our group. In situ STM was used in all cases to map the adsorbate molecules to the single-molecule level and was supported comprehensively by other physical electrochemistry. High-resolution voltammograms were, particularly, obtained using singlecrystal bare and surface-modified Au(1 1 1)-electrode surfaces, with the proteins immobilized in well-organized mono- or sub-monolayers through protein disulfide or thiolate groups, or by non-covalent hydrophobic or electrostatic interactions, and ET or enzyme function largely preserved. Single-molecule imaging under conditions, where immobilized proteins are active in interfacial ET or enzyme function was thus achieved. Direct single-molecule electronic function and redox-based “switch” features in the in situ STM contrast similar to those for the transition metal complexes have, however, been elusive. Observed contrast changes around the redox potential of P. aeruginosa azurin have been taken as evidence for two-step tunnelling through oxidation–reduction cycles of the Cu-centre [78,89], and the effects referred to the large-bias voltage limit with coherent ET [78]. Structural features in current–bias voltage relations of horse heart cyt c [82] and P. aeruginosa azurin in two-electrode systems without potential control have also been taken as indications of two-step ET [97]. Inverse aqueous micelles were the environment in the former study, which showed most details. The STM contrast showed a sub-molecular feature and two strong conductivity peaks for both positive and negative bias voltage, indicative of a por-

phyrin ring-based transition in addition to the Fe2+/3+ ET process. 3.4. Interfacial electrochemical single-ET and coulomb blockade effects In addition to STM of redox molecules electrochemical single-ET (SET) based on scanning electrochemical microscopy [98], ET on nanoscale (2–3 nm) Pt–Ir tip electrodes [20], and electrochemistry of nanoscale gold particles protected by variable-length organic thiolates [21] have emerged as a broader class of other interfacial single-ET (SET) systems. SET effects in double-layer capacitances and voltammetry arise, when the electrostatic energy of the interfacial capacitance, C, exceeds the thermal energy kB T [99], e2 > kB T (28) 2C This is a reflection of Coulomb blockade, i.e. following a given single-ET event subsequent ET is blocked by repulsion from the electron first transferred and temporarily located on the particle. This notion has been used in single-molecule solid state contacts (see Section 4). The notion is essentially heuristic and offers a transparent explanation of electrostatically based successive charging, but is not needed in detailed electronic structure descriptions. Successive oxidation or reduction of molecules is also physically rooted in electrostatic effects but the notion is not commonly used here. Onset of Coulomb blockade is a prime reflection of nanoscale dimenel.stat. = ESET

3152

J. Zhang et al. / Electrochimica Acta 50 (2005) 3143–3159

sions and quantum-size effects, where the electronic properties of the objects are significantly affected by the object size. Capacitances in the attofarad (10−18 F) range are needed for Eq. (28) to apply at room temperature but this has now become reality in electrochemical and solid state interfacial ET systems. Quantized capacitance charging and ET proceed in a succession of single-ET events, separated by the potentials:   n − 21 e 0 Ez,z−1 = Epzc + (29) C z represents the charge state, and n is the number of electrons transferred to the nanoparticle. Epzc is the potential of zero charge of the particle. Conspicuous charge peaks appear, for example, in capacitive charging and differential pulse voltammograms of 1–3 nm Au-particles [21]. SET can also be envisaged as Coulomb staircases in electrochemical ET and in situ STM [100], incorporated by the following generalization of Eqs. (1) and (2): ∞
ωeff  dερ(ε)f (ε) exp j(η) = eΓox κeff 2π n=1    2  2    Er + eη + n − 21 eC − (ε − εF )   × −   4Er kB T   (30) The step height is approximately: !j(η) ≈ j(η)

e2 2kB TC

(31)

The discrete term is important, when it exceeds kB T. The data in Ref. [20] accord with a capacitance of 2.4 aF, and step heights of 70 mV, close to e/C. From Eq. (31), the observed step height of 100 aA corresponds to a reorganization free energy of 0.75 eV. Analogous forms apply to in situ STM with nanosize metal particles in the tunnelling gap (Fig. 10). The following generalization of Eq. (14) applies close to equilibrium, when the

redox level is coupled to a metal nanoparticle in the tunnelling gap [100]:   Er ωeff exp − (η = 0) = e exp iadiab tunn 2π 4kB T   γ(1 − γ)eVbias C(2) 

× (1) θ C + C(2) kB T n  (2)     C 1 − n− (32) × Vbias e 2 where C(1) is the capacitance of the contact holding the redox molecule and C(2) the capacitance of the particle-tip contact. Such equations represent nanoscale switches with a metal cluster and a redox addressable group, such as the viologen–Au cluster [81]. 3.5. Stochastic effects in ultra-small electrochemical junctions Approaches to single-molecule electronics enhance the importance of fluctuations in observable molecular properties. Fluctuations are reflected, for example, in distributions of STM contrasts [79], in turn fingerprints of binding modes and single-molecule conductivity. In condensed matter environment, the latter are affected by huge fluctuations in the HOMO–LUMO energies [74], lowering tunnelling barriers [45] and eroding macroscopic energy differences in the oxidation and reduction potentials. There are a few reports of HOMO/LUMO and redox level fluctuations in STM of non-redox and redox molecules. Distributions of peak potentials in STM current–bias voltage correlations of metalloporphyrins were observed [79]. Single-molecule oligonucleotide conductivity shows, further, much less distance-dependence than expected from macroscopic oxidation/reduction potentials [15,62]. A different kind of fluctuation is associated with random electronic level population and depopulation, denoted as “telegraphic noise”, in nanoscale metal–oxide–metal [101] and semiconductor junctions [102], and in polyaniline enclosed between electrochemical nanoscale Au-electrodes

Fig. 10. In situ STM junction with a Au-nanoparticle as contact. Left: the physical configuration. Middle: the electronic energy diagram. Right: the corresponding equivalent circuit.

J. Zhang et al. / Electrochimica Acta 50 (2005) 3143–3159

[103]. It is directly associated with forward and reverse interfacial ET between the electrodes and redox states in a random, stochastic mode. The data by Tao and co-workers [103] are illustrative. Two-level electronic “switching” between conducting (“on”) and non-conducting (“off”) states was controlled by the electrochemical potential. The on-state is operative at high electrochemical potentials, where the polymer is oxidized; the reduced form characterizes the non-conducting off-state at low potentials. The system displays random transitions between “on” and “off” states with millisecond lifetimes at the small bias voltage 20 mV. The amplitudes depend on the electrode potential, ranging from a fraction of a nA at low potentials to several tens of nA at high potentials. This accords with the above views on in situ STM single-molecule conductivity of redox molecules, when the redox levels are close to the Fermi levels, and the nuclear reorganization free energy does not exceed a few multiples of kB T. The average lifetime of the oxidized “on” state, i.e. the time between on → off transitions is: −1  τon ≈ ko/r

(33)

ko/r is given by Eq. (16). The average lifetime of the “off”

−1 state is τoff ≈ kr/o . The current amplitude at the singlemolecule level is, however, different from the steady-state current given by Eqs. (15)–(19). The single-molecule amplitudes follow instead a superexchange mode given by: iampl ≈

e ; τ

τ≈

h ¯ h ¯ 2¯h + ≈ ∆L ∆R ∆

(34)

cf. Eq. (23). The broadening follows roughly the superexchange energy-dependence: ∆∝

" " T␧

LA

"" " " "TA␧ " R

(εF − εox )

(35)

cf. Section 3.1. An inverse relationship between lifetime and amplitude is thus expected. The overpotential-dependence of the duration and amplitudes of the “on” and “off” states is slightly entangled. Observation of the vacant “on” state entails that εox is close to the Fermi levels, i.e. at a certain negative overpotential. If the level is too close, the lifetime is too short to observe fluctuations. Asymmetry is imposed as the occupied level is trapped further below the Fermi levels than the vacant level above the Fermi levels. The lifetime is, therefore, shortest for the “on” state. The amplitude increases with increasing negative overpotential due to the decreasing energy denominator in Eq. (35). These expectations are broadly as observed. Inverse effects are expected at positive potentials, where the occupied level is close to the Fermi levels and the “on” state, while the vacant state further above these levels would be the “off” state.

3153

4. Interfacial electrochemical ET in nanoscale and single-molecule device-like systems The use of single-crystal electrodes with atomically planar surfaces in mesoscopic or nanoscale multi-electrode systems, such as in situ STM has disclosed phenomena, which approach those of functional electronic devices. The negative differential resistance in current–overpotential and conductivity–bias voltage relations holds conspicuous on/off switching or amplifying features. Current–voltage asymmetry or rectification is another kind of electronic feature, which has acquired reality. A key observation is that reported single-molecule three-electrode solid state transistors are functional only at cryogenic temperatures or in ultra-high vacuum, while the amplifying feature in the redox molecular in situ STM is displayed at room temperature and in a liquid state medium. We discuss first similarities and differences between in situ STM of redox molecules at room temperature and single-molecule transistors at cryogenic temperatures. We then address two-centre molecular electronic rectifiers. 4.1. Analogies and differences between in situ STM and solid state single-molecule transistors The view of in situ STM of redox molecules above rests on shifting the redox level into the energy window between the Fermi levels, by the overpotential or bias voltage. This resembles other single-molecule three-electrode systems recently reported [75–77]. In both cases, discrete electronic or vibrational levels are dragged into the energy window to open new conducting channels. Molecular transistors contain the source, drain, and gate electrode, and two current–voltage relations emerge in either case. The discrete level can be controlled by the in situ STM overpotential or by the transistor gate electrode. New conducting channels display “spectroscopic” or “switch” effects in each case. Conducting channels are also opened by the bias voltage in both configurations. This is followed by saturation as the level continues to transmit electrons at high bias voltage. Multiple levels provide multiple differential resistance features if the level separation is larger than the bias voltage and the nuclear reorganization energy, while current–voltage staircases emerge at large bias voltage. In situ STM of molecules and single-molecule transistors also exhibit differences. The former applies at room temperature and electronic–vibrational coupling causes thermal activation and level broadening. Solid-state molecular transistors have been brought to work only at cryogenic temperatures, where very small vibrational level separations are disclosed. Thermal activation is unimportant, but electronic–vibrational relaxation remains. The nuclear relaxation patterns are also different. Solvent inertial polarization dominates in the in situ STM process, while metal lattice vibrations are dominating collective modes in solid-state molecular transistors. Local mode coupling is important for both cases.

3154

J. Zhang et al. / Electrochimica Acta 50 (2005) 3143–3159

q0i and q0f are the initial and final state equilibrium values of q, and θ(t) the unit step function. (2) The time-dependent overpotential or bias voltage, e.g. a step followed by a linear sweep: eξη(t) =

1 eξη0 (1 + bt) 1 + exp(−νt)

(40)

where ν ( 1) is a constant step height, b a constant sweep rate, and η0 is the starting potential. (3) The average-level populations, n1  and n2 . These follow Eq. (21) and determine the equilibrium nuclear coordinate shifts: Fig. 11. Electronic energy diagram for tunnel contact with two accessible molecular bridge group electronic–vibrational redox levels, ε01 and ε02 .

The two-level system in Fig. 11 illuminates these observations [104]. Vacant levels, ␧01 and ␧02 , are successively brought into the energy window by the gate or bias voltage. Once populated, the levels relax and assume the following dependence on the nuclear coordinate(s) q: ¯ ωg1 q − eξη − eγVbias ε1 (q) = ε01 − h

(36)

ε2 (q) = ε02 − h ¯ ωg2 q − eξη − eγVbias where g1 and g2 are coupling constants, and ω the nuclear vibrational frequency.The current density for tunnelling through a given bridge group level, b (= 1, 2) is, i(t) =

2e π¯h




×#

2

 dεfL (ε) 1 − fR (ε) b=1

∆Lb ∆bR $2 ε − εb q(t) + ∆2b

(37)

fL (ε) and fR (ε) are the Fermi functions, ∆Lb and ∆bR the level broadenings coupling the discrete level to the electrodes, and ∆b = ∆Lb + ∆bR . The relaxation feature is indicated by the time-dependence, q = q(t). Replacing the Fermi functions by unit step functions gives:

q0s = n1 g1 + n2 g2 ;

s = i, f

(41)

Combination of Eqs. (39)–(41) with Eq. (38) offers a scheme for computation of the current–time relations, equivalent to the current–voltage relation, when energy relaxation is unimportant. Fig. 12 shows current–overpotential or gate voltage relations at intermediate and large bias voltage. Two levels are successively brought into the energy window. In Fig. 12, left only one level at a time is accommodated, while both levels are accommodated simultaneously in Fig. 12, middle. The levels leave the window at long times or large overpotentials. Fig. 12, right shows that hysteresis between forward and reverse sweeps arises, when the bias voltage variation is in the same time range as nuclear relaxation. The latter can be slow at cryogenic temperatures. This view follows those for in situ STM with the difference that lowtemperature conditions are in focus. Both approaches incorporate any number of electronic or electronic–vibrational levels of the electron-transmitting unit (molecule, solid-state structure, quantum dot). The overpotential/gate voltage- and bias voltage-dependences are thus composite and determined by an interplay between the external voltage, the molecular level separations, and the electronic–vibrational coupling. Systems that show electronic–vibrational features in low-temperature single-molecule conduction directly related to the formalism include oligothiophenes [75], pphenylenevinylene oligomers [76], transition metal complexes [77], and C60 -fullerene [105]. The C60 -system is illus-

2e  ∆Lb ∆bR i(t) = π¯h ∆b b=1   ¯ ωgb q(t) − eξη(t) − e(1 − γ)Vbias (t) ¯ ωgb q(t) − eξη(t) − eγVbias (t) ε0b − εFL − h ε0b − εFL − h (38) × arctan −arctan ∆b ∆b 2

The time-dependence of the overpotential and bias voltage scans is also shown. Eqs. (37) and (38) offer a transparent approach to the current–voltage characteristics. Parameters are: (1) The relaxation properties of the nuclear coordinate(s), say by the exponential form:

(39) q(t) = q0f + (q0i − q0f ) exp (−t) θ (t)

trative. The core fullerene, C60 , is robust to single-molecule physical manipulation [105] and well-characterized [106]. Six successive anionic states are electrochemically and optically accessible in solution [107] even though only the first state is below the vacuum level [108]. Along with the closely spaced voltammetric peaks (0.3−0.5 V), this is indicative of strong environmental effects even in apolar sol-

J. Zhang et al. / Electrochimica Acta 50 (2005) 3143–3159

3155

Fig. 12. Low-temperature in situ tunnelling current/overpotential or /gate voltage scans represented by the scan time for the electronic-level configuration in Fig. 11, Eqs. (21) and (38)–(40) [104]. Fixed bias voltage and step-wise/linear potential sweep: b = 0.1; ␯ = 10; eξη0 = 1; ∆1 = ∆2 = ∆ = 0.1l; n1 = n2 = 0.8; s = T1 /T2 = 2. Left: small bias voltage and successive level accommodation in the energy window; eVbias = 0.1; ε02 − εFL = 1.7. Correlation shown from the time that ε02 crosses εFL . Middle: large bias voltage and both levels accommodated simultaneously in the energy window; eVbias = 3.6; ε02 − εFL = 2.8. Right: bias voltage-dependence of in situ tunnelling current showing hysteresis in forward and reverse scan. Constant overpotential or gate voltage eξη0 = 2; eV0 = 0.1. Other parameters as above.

vents. Single-C60 can be brought to display transistor function between a pair of nm separated gold electrodes combined with a doped silicon gate [105] and shows current–bias voltage staircases in a wide gate voltage range, corresponding to mono- or dianion formation. The correlations show a 33 mV step from excitation of the lowest frequency deformational mode (270 cm−1 ), but is dominated by a sequence of steps of only 5 mV (40 cm−1 ), assigned to centre-of-mass hindered n− translational motion of adsorbed C60 (n = 0, 1). Manifolds of 5 mV levels separated at the low temperature (1.5 K) were thus successively brought into the window between the two Fermi levels, assisted by vibrational relaxation. 4.2. The molecular diode and single-molecule electronic rectification The molecular transistor is the “simplest” device in the sense that electronic function is effected by a single redox centre. The molecular diode gives another electronic function, namely a larger current in one bias direction than in the opposite direction. This notion is commonly reserved, when the diode function arises from molecules with both electron donor and acceptor moieties. Molecular rectification was the earliest proposed molecular device principle [109] in a twoelectrode environment with only a source and a drain electrode. Single-molecule rectification rests on general principles with different molecular mechanisms [19,110]. Current asymmetry can involve surface dipole formation (“Schottky rectifiers”). Rectification also arises if the molecular switch is located asymmetrically between the electrodes, related to the

parameters γ and ξ. The third and most fundamental rectification feature is induced by intrinsic asymmetry of the donor and acceptor MOs in two-centre molecules, either energetic or electronic in origin. Fig. 13 is a natural extension of the schemes for singlecentre molecules and illuminates molecular rectification, without considering mechanistic detail. A D–␴–A molecule is inserted between two metallic conductors (D, donor; A, acceptor; ␴, a non-redox bridge group that ascertains charge localization). In the simplest case, the donor level is below and the acceptor level above both Fermi levels at zero bias voltage. On application of positive bias voltage to the right electrode, both levels are lowered but the acceptor level faster. This level, therefore, crosses the donor level at a certain bias voltage, triggering electron flow from left to right, " " M1 |D − σ − A| M2 → M1 "D+ − σ − A− " " " " " M2 M1 "D+ − σ − A− " M2 → M1+ "D − σ − A− " M2 → M1+ |D − σ − A| M2−

(42)

In contrast, the donor–acceptor energy gap is increased, when the right electrode is biased negatively, blocking electron flow from left to right. Both electronic rectification and bias voltage thresholds for onset of electronic current flow are, therefore, inherent in such schemes. The general scheme can be combined with specific molecular mechanisms. The four-electrode in situ STM system and the three-molecular transistor can first be introduced. This offers current–overpotential/gate voltage relations, in addi-

Fig. 13. Schematic view of bias voltage threshold and rectified ET via a donor–acceptor molecule from negatively (left) to positively biased electrode (right) [110]. Left: zero bias voltage. Middle: positive bias voltage to induce resonance from donor to acceptor group. Right: relaxation of occupied acceptor level. Negative bias voltage increases the donor–acceptor energy gap, with insignificant current flow in the opposite direction.

3156

J. Zhang et al. / Electrochimica Acta 50 (2005) 3143–3159

tion to current–bias voltage relations. The levels are, secondly, broadened. One effect is electronic interactions with the metallic continua, the other one electronic–vibrational interaction with local and collective nuclear modes. The latter imposes multi-phonon character on the rectification process and paves the way for rectifying devices in solid-state matrices. This view offers an immediate connection to theoretical ET science, with multifarious ET patterns [110]. The following observations are central: (a) In the limit of fully diabatic interfacial ET, rectification can be viewed as a sequence of interfacial and intramolecular single-ET steps in Eq. (42). The order of the steps is different in different overpotential or bias voltage ranges. (b) Effective rectifying conduction requires good contacts between the redox centres and the adjacent electrodes, i.e. interfacial ET must belong to the adiabatic limit. Intramolecular donor–acceptor ET should not be hampered by small tunnelling factors either, and this step should also be adiabatic or at least weakly diabatic. If the metallic contact with one of the levels is strong and the level significantly broadened, the pattern will resemble in situ STM with a single redox level. (c) In fully adiabatic interfacial ET, the intramolecular ET step is intercepted by fast interfacial ET, leaving the intermediate D+ –␴–A− state as vibrationally unrelaxed or “dynamically populated”. As in adiabatic single-level in situ STM, this is different from the diabatic limit, where the intermediate state is fully relaxed. The following current form applies approximately for the scheme shown in Fig. 13 [110]: iadiab rect

 % & ωeff ErD + ErA = 2ecκDA tanh eVbias exp 2π 4ErD ErA kB T    × − 

(ErD + ErA + eξD η + eγD Vbias −eξA η − eγA Vbias )2 4ErA kB T

    

(43)

“D” and “A” refer to the donor and acceptor, respectively. κDA (≤1) is the transmission coefficient for intramolecular ET, and c the concentration of donor–acceptor molecules in the initial D–␴–A state. In a more complete scheme, other possible initial states, such as D+ –␴–A, D–␴–A- , and D+ –␴–A− should be included as well. Fig. 14 shows current–bias voltage relations based on the full scheme of equations, such as Eqs. (42) and (43). The correlations show pronounced asymmetry with current onset roughly at Vbias ≈ ErD /eξD and rectification ratios exceeding an order of magnitude. Further diagnostic evidence is inherent in the current sensitivity to the voltage distribution (γ D and γ A ) and charge density shifts in the oxidized and reduced forms of the D- and A-groups.

Fig. 14. Normalized current/bias voltage for the donor–acceptor system in Fig. 13. Different potential distributions in the gap: γ D = 0.2; γ A = 0.4; ErD = ErA = 0.2 eV. Solid line: eξηD = eξηA = 0. Dotted line: eξηD = −10 mV; eξηA = −20 mV. Dashed line: eξηD = −25 mV; eξηA = −50 mV.

Common features of different molecular mechanisms are organized molecular layers with accessible electronic states suitable for temporary electronic population and depopulation. A number of mono- and multi-layer organic donor–acceptor systems based on different system types with high rectification have been reviewed recently by Metzger [19]. These include: condensed aromatic ring systems [111], carbon nanotubes [112], ␣,␣ -xylyl dithiolate [54], biphenyl thiolates in asymmetric Au/TiO2 /Au contacts [113], molecular three-layer photodiodes (donor, sensitizer, acceptor) [114], disulfide-TCNQ monolayers (TCNQ: tetracyanonquino dimethane) [115], thiophene (donor)–thiazole (acceptor) combined with variable-length alkylthiolate monolayers [116], and a binuclear Co(I)Pc–Co(III)Pc monolayer (Pc: phthalocyanine) [117]. The most comprehensive studies are based on hexadecyl-quinolinium tricyanodimethanide and related molecules over the last 15 years [19]. So far only Fujihira’s photodiodes [114] constitute an electrochemical molecular rectifier. Further, apart from the photodiode, probably only the hexadecyl-quinolinium tricyanodimethanide-based molecules, the thiophene-thiazol [116], and the Co(I)Pc–Co(III)Pc monolayer systems [117] show rectifying effects solely within the molecules themselves. Rectification by the zwitterionic hexadecylquinolinium tricyanodimethanide has been addressed by the multi-phonon two-level ET view [110]. The nuclear reorganization energy determined from the optical charge transfer bandwidth was significantly smaller than the threshold bias voltage energy. This pointed to the intermediate charge transfer state as a dynamically populated state. The high structural symmetry of the thiophene-thiazol and Co(I)–Co(III)Pc monolayer rectifiers and their positioning in a tunnelling gap make these systems attractive in other analysis. The systems were studied by (ambient, ex situ) STM, at Au/mica and HOPG substrates, respectively, imaged to single-molecule

J. Zhang et al. / Electrochimica Acta 50 (2005) 3143–3159

resolution and showed strong (ex situ) STM current/bias voltage rectification, with thresholds of about 1 V. Appropriate data for oxidation/reduction potentials, optical charge transfer characteristics, or ionization potentials and electron affinities are, however, absent. This is prohibitive for a detailed comparison with our analysis of the hexadecyl-quinolinium tricyanodimethanide system [110].

5. Some concluding observations Surface structures based on robust redox active molecules, with interfacial ET as a common functional denominator, characterized at the nanoscale and towards the singlemolecule levels have been reported broadly over the last few years. Studies have extended to biological macromolecules, redox metalloproteins in particular, the bioelectrochemistry of which is being combined with state-of-the-art physical electrochemistry and other surface science. Electrochemical nanoscale molecular systems can be brought to retain functional integrity at the nanoscale and single-molecule spatial levels and novel ET phenomena can arise, for example, stochastic “noise”, single-molecule tunnelling spectroscopy, and coherent multi-ET phenomena. Nanoscale electrochemical systems can display electron transport features, which resemble device-like function, such as amplification, transistor function, and unimolecular rectification. This suggests that electrochemical nanoscale ET systems are also in a class with other recent single-molecule device systems with solid-state unimolecular transistors and rectifiers in the strongest focus but significantly different operational conditions. Solid-state single-molecule transistors, for example, so far only operate at cryogenic temperatures, whereas in situ STM redox switches operate at room temperature or in ultra high vacuum. By multifarious experimental approaches and comprehensive theory of molecular ET processes, the functional electron transport principles are, however, becoming understood. Finally, novel electrochemistry and bioelectrochemistry at the nanoscale and single-molecule levels hold immediate technological perspectives. One perspective is that singlemolecule enzyme sensing and DNA-based screening could be within reach. Another one would be the combination of functional molecules and biomolecules with nanoscale metallic and semiconductor structures and arrays into multifunctional sensing devices (novel types of “labs-on-a-chip”). Construction of molecular electronic “circuits” would hold other novel but much debated perspectives, which would be a forthcoming major phase towards molecular electronics [118–120].

Acknowledgements Financial support from the Danish Technical Science Research Council, NanoScience Center, University of Copen-

3157

hagen, and Russian Foundation for Basic Research (Grant no. 03-03-32935) is acknowledged.

References [1] M.A. Ratner, D.I. Ratner, Nanotechnology, Prentice Hall, Upper Saddle River, 2003. [2] R. Waser (Ed.), Nanoelectronics and Information Technology: Advanced Electronic Materials and Novel Devices, Wiley-VCH, Weinheim, 2003. [3] Z.-Q. Tian (Ed.), Proceedings of the Second Spring Meeting of the International Society of Electrochemistry: Electrochemistry at Nano-scale—Structuring, Characterization and Theories, Xiamen University, 2004. [4] M.S. El-Deab, T. Ohsaka, J. Electroanal. Chem. 553 (2003) 107. [5] X. Zhang, K.Y. Chan, Chem. Mater. 12 (2003) 451. [6] S.J. Han, Y.K. Yun, K.W. Park, Y.E. Sung, T. Hyeon, Adv. Mater. 15 (2003) 1922. [7] J.X. Wang, S.R. Brankovic, Y. Zhu, J.C. Hanson, R.R. Adzic, J. Electrochem. Soc. 150 (2003) A1108. [8] J. Zhang, Q. Chi, A.M. Kuznetsov, A.G. Hansen, H. Wackerbarth, H.E.M. Christensen, J.E.T. Andersen, J. Ulstrup, J. Phys. Chem. B 106 (2002) 1131. [9] H.A. Finklea, in: A.J. Bard, I. Rubinshtein (Eds.), Electroanalytical Chemistry, vol. 19, M. Dekker, NY, 1996, p. 109. [10] J.J. Davis, H.A.O. Hill, A.M. Bond, Coord. Chem. Rev. 200 (2000) 411. [11] F.A. Armstrong, G.S. Wilson, Electrochim. Acta 45 (2000) 2623. [12] S.O. Kelley, N.M. Jackson, M.G. Hill, J.K. Barton, Angew. Chem. Int. Ed. 38 (1999) 941. [13] N.M. Jackson, M.G. Hill, Curr. Opin. Chem. Biol. 5 (2001) 209. [14] D. Kambhampati, P.E. Nielsen, W. Knoll, Biosens. Bioelectron. 16 (2001) 1109. [15] H. Wackerbarth, M. Grubb, J. Zhang, A.G. Hansen, J. Ulstrup, Angew. Chem. Int. Ed. 43 (2004) 198. [16] N. Tao, Phys. Rev. Lett. 76 (1996) 4066. [17] T. Albrecht, A. Guckian, J. Vos, J. Ulstrup, Trans. IEEE, in press. [18] V. Balzani, M. Venturi, A. Credi, Molecular Devices and Machines: A Journey into the Nanoworld, Wiley-VCH, Weinheim, 2003. [19] R.M. Metzger, Chem. Rev. 103 (2003) 3803. [20] F.-F. Fan, A.J. Bard, Science 277 (1997) 1791. [21] A.C. Templeton, W.P. Wuelfing, R.W. Murray, Acc. Chem. Res. 33 (2000) 27. [22] C.B. Gorman, R.L. Carroll, R.R. Fuierer, Langmuir 17 (2001) 6923. [23] M.S. Kaba, I.K. Song, M.A. Barteau, J. Vac. Sci. Technol. A 15 (1997) 1299. [24] J. Chen, M.A. Reed, A.M. Rawlett, J.M. Tour, Science 286 (1999) 1550. [25] J. Chen, W. Wang, M.A. Reed, A.M. Rawlett, D.W. Price, J.M. Tour, Appl. Phys. Lett. 77 (2000) 1224. [26] A.M. Kuznetsov, Charge Transfer in Physics, Chemistry, and Biology: Physical Mechanisms of Elementary Processes and an Introduction to the Theory, Gordon and Breach, Reading, 1995. [27] A.M. Kuznetsov, J. Ulstrup, Electron Transfer in Chemistry and Biology: An Introduction to the Theory, Wiley, Chichester, 1999. [28] A.M. Kuznetsov, J. Ulstrup, Electrochim. Acta 45 (2000) 2339. [29] A.M. Kuznetsov, J. Ulstrup, J. Phys. Chem. A 104 (2000) 11531; A.M. Kuznetsov, J. Ulstrup, Errata 105 (2001) 7494. [30] D.M. Kolb, Angew. Chem. Int. Ed. 40 (2001) 1162. [31] M.-C. Daniel, D. Astruc, Chem. Rev. 104 (2004) 293. [32] S.J. Tatis, M. Devoret, H. Dal, A. Thess, R.E. Smalley, L.J. Geeligs, C. Dekker, Nature 386 (1997) 474. [33] Q. Chi, J. Zhang, E.P. Friis, J.E.T. Andersen, J. Ulstrup, Surf. Sci. 463 (2000) 648.

3158

J. Zhang et al. / Electrochimica Acta 50 (2005) 3143–3159

[34] A.A. Kornyshev, A.M. Kuznetsov, J.U. Nielsen, J. Ulstrup, Phys. Chem. Chem. Phys. 2 (2000) 141. [35] Y.G. Boroda, G.A. Voth, J. Electroanal. Chem. 450 (1998) 95. [36] J.-H. Mohr, W. Schmickler, Phys. Rev. Lett. 84 (2000) 1051. [37] A.M. Kuznetsov, I.G. Medvedev, J. Ulstrup, Electrochem. Commun. 2 (2000) 135. [38] Q. Chi, J. Zhang, J.E.T. Andersen, J. Ulstrup, J. Phys. Chem. B 105 (2001) 4669. [39] H. Nar, A. Messerschmidt, R. Huber, J. Mol. Biol. 221 (1991) 765. [40] P. Kraulis, J. Appl. Crystallogr. 24 (1991) 946. [41] M.V. Vigdorovich, A.M. Kuznetsov, J. Ulstrup, Chem. Phys. 176 (1993) 539. [42] A.M. Kuznetsov, V.V. Sokolov, J. Ulstrup, J. Electroanal. Chem. 502 (2001) 36. [43] A.A. Gewirth, H. Siegenthaler (Eds.), Nanoscale Probes of the Solid/Liquid Interface, Kluwer, Drodrecht, 1995. [44] A.I. Danilov, Russ. Chem. Rev. 64 (1995) 767. [45] Y.Y. Gurevich, A.M. Kuznetsov, Soviet Phys. Solid State 17 (1975) 2076. [46] A. Nitzan, Ann. Rev. Phys. Chem. 52 (2001) 681. [47] W. Schmickler, Surf. Sci. 335 (1995) 416. [48] H.B. Gray, J.R. Winkler, Q. Rev. Biophys. 36 (2003) 341. [49] C. Joachim, M.A. Ratner, Nanotechnology 15 (2004) 1065. [50] F. Rosei, M. Schunach, Y. Naitoh, P. Jiang, A. Gourdon, E. Laegsgaard, I. Steensgaard, C. Joachim, F. Besenbacher, Progr. Surf. Sci. 71 (2003) 95. [51] A. Nitzan, M.A. Ratner, Science 300 (2003) 1384. [52] A. Solomon, D. Cahen, S. Lindsay, J. Tomfohr, V.B. Engelkes, C.D. Frisbie, Adv. Mater. 15 (2003) 1881. [53] L.E. Hall, J.R. Reimers, N.S. Hush, K. Silverbrook, J. Chem. Phys. 112 (2000) 1510. [54] W. Tian, S. Datta, S. Hong, R. Reifenberger, J.I. Henderson, C.P. Kubiak, J. Chem. Phys. 109 (1998) 2874. [55] A. Dhirani, P.-H. Lin, P. Guyot-Sionnest, R.W. Zehner, L.R. Zita, J. Chem. Phys. 106 (1997) 5249. [56] M. Di Ventra, S.-G. Kim, S.T. Pantelides, N.D. Lang, Phys. Rev. Lett. 86 (2001) 288. [57] J.M. Seminario, A.G. Zacarias, J.M. Tour, J. Am. Chem. Soc. 122 (2000) 3015. [58] W. Haiss, R.J. Nichols, H. Van Zalinge, S.J. Higgins, D. Bethell, D.J. Schiffrin, Phys. Chem. Chem. Phys. 6 (2004) 4330. [59] X. Xiao, B. Xu, N. Tao, Nanoletters 4 (2004) 267. [60] B. Xu, N. Tao, Science 301 (2003) 1221. [61] X.D. Cui, A. Primak, X. Zarate, J. Tomfohr, O.F. Sankey, A.L. Moore, T.A. Moore, D. Gust, G. Harris, S.M. Lindsay, Science 294 (2001) 571. [62] H. Wackerbarth, M. Grubb, J. Zhang, A.G. Hansen, J. Ulstrup, Langmuir 20 (2004) 1647. [63] B. Xu, P. Zhang, X. Li, N. Tao, Nanoletters 4 (2004) 1105. [64] W. Wang, T. Lee, I. Kretzschmer, M.A. Reed, Nanoletters 4 (2004) 643. [65] W. Wang, T. Lee, M.A. Reed, Phys. Rev. B 68 (2003) 035416. [66] K. Weber, L. Hockett, S. Creager, J. Phys. Chem. B 101 (1997) 8286. [67] J.F. Smalley, S.W. Feldberg, C.E.D. Chidsey, M. Lindford, M.D. Newton, Y.-P. Liu, J. Phys. Chem. 99 (1999) 13141. [68] A. Avila, B.W. Gregory, K. Niki, T.M. Cotton, J. Phys. Chem. B 104 (2000) 2759. [69] A. Murgida, P. Hildebrandt, J. Am. Chem. Soc. 123 (2001) 4062. [70] M.A. O’Neill, J.K. Barton, Top. Curr. Chem. 236 (2004) 67. [71] T. Kawai, T. Takada, S. Tojo, T. Majima, J. Am. Chem. Soc. 125 (2003) 6842. [72] T. Morita, S. Kimura, J. Am. Chem. Soc. 125 (2003) 8732. [73] I. Bediako-Amoa, T.C. Sutherland, C.V.-Z. Li, R. Silerova, H.-B. Kraatz, J. Phys. Chem. B 108 (2004) 704. [74] A.A. Voityuk, K. Siriwong, N. R¨osch, Angew. Chem. Int. Ed. 43 (2004) 624.

[75] N.B. Zhitenev, H. Meng, Z. Bao, Phys. Rev. Lett. 88 (2002) 226801. [76] S. Kubatkin, A. Danilov, M. Hjort, J. Cornill, J.-L. Br´edas, N. Stuhr-Hansen, P. Hedegaard, T. Bjørnholm, Nature 425 (2003) 698. [77] J. Park, A.N. Pasupathy, J.I. Goldsmith, C. Chang, Y. Yaish, J.R. Petta, M. Rinkoshi, J.P. Sethna, H.D. Abru˜na, P.L. McEuen, D.C. Ralph, Nature 417 (2002) 722. [78] J. Zhang, A.M. Kuznetsov, J. Ulstrup, J. Electroanal. Chem. 541 (2003) 133. [79] W. Han, E.N. Durantini, T.A. Moore, A. Moore, D. Gust, P. Rex, G. Leatherman, G.R. Sealy, N. Tao, S.M. Lindsay, J. Phys. Chem. Chem. B 101 (1997) 10719. [80] K.W. Hipps, U. Mazur, J. Phys. Chem. B 104 (2000) 4707. [81] D.L. Gittins, D. Bethell, D.J. Schiffrin, R.J. Nichols, Nature 408 (2000) 67. [82] G.B. Khomutov, L.V. Belovolova, S.P. Gubin, V.V. Khanin, A.Y. Obydenov, A.M. Sergeev-Cherenkov, E.S. Soldatov, A.S. Trifonov, Bioelectrochemistry 55 (2002) 177. [83] G. Gilardi, A. Fantuzzi, Trends Biotechnol. 19 (2001) 468. [84] I. Willner, E. Katz, Angew. Chem. Int. Ed. 39 (2000) 1180. [85] J.E.T. Andersen, P. Møller, M.V. Pedersen, J. Ulstrup, Surf. Sci. 325 (1995) 193. [86] J. Zhang, Q. Chi, S. Dong, E. Wang, Bioelectrochem. Bioeng. 39 (1996) 267. [87] E.P. Friis, J.E.T. Andersen, L.L. Madsen, P. Møller, J. Ulstrup, J. Electroanal. Chem. 431 (1997) 35. [88] Q. Chi, J. Zhang, J.U. Nielsen, E.P. Friis, I. Chorkendorff, G.W. Canters, J.E.T. Andersen, J. Ulstrup, J. Am. Chem. Soc. 122 (2000) 4047. [89] L. Andolfi, S. Cannistrarro, G.W. Canters, P. Facci, A.G. Ficca, I.M.C. Van Amsterdam, M.P. Verbeet, Arch. Biochem. Biophys. 399 (2002) 81. [90] L. Andolfi, D. Bruce, S. Cannistrarro, G.W. Canters, J.J. Davis, H.A.O. Hill, J. Crozier, M.P. Verbeet, C.L.K. Wrathmell, Y. Astier, J. Electroanal. Chem. 565 (2004) 21. [91] A.G. Hansen, A. Bojsen, J.U. Nielsen, H. Wackerbarth, I. Chorckendorff, J.E.T. Andersen, J. Zhang, J. Ulstrup, Langmuir 19 (2003) 3419. [92] B. Bonanni, D. Alliata, A.R. Bizzari, S. Cannistrarro, Chewm. Phys. Chem. 4 (2003) 1183. [93] J. Zhang, H.E.M. Christensen, B.L. Ooi, J. Ulstrup, Langmuir 20 (2004) 10200. [94] J. Brask, H. Wackerbarth, K.J. Jensen, J. Zhang, I. Chorkendorff, J. Ulstrup, J. Am. Chem. Soc. 125 (2003) 94. [95] J. Zhang, A.C. Welinder, A.G. Hansen, H.E.M. Christensen, J. Ulstrup, J. Phys. Chem. B 107 (2003) 12480. [96] J.J. Davis, H.A.O. Hill, Chem. Commun. (2002) 393. [97] J.J. Davis, C.L. Wrathmell, J. Zhao, J. Fletcher, J. Mol. Recogn. 17 (2004) 167. [98] A.J. Bard, F. Fan, Acc. Chem. Res. 29 (1996) 572. [99] L.P. Kouwenhoven, D.G. Austing, S. Tarucha, Rep. Progr. Phys. 64 (2001) 701. [100] A.G. Hansen, H. Wackerbarth, J.U. Nielsen, J. Zhang, A.M. Kuznetsov, J. Ulstrup, Russ. J. Electrochem. 39 (2003) 108. [101] C.T. Rogers, R.A. Buhrman, Phys. Rev. Lett. 55 (1985) 859. [102] K.R. Farmer, C.T. Rogers, R.A. Buhrman, Phys. Rev. Lett. 58 (1987) 2255. [103] H.X. He, J.S. Zhu, N. Tao, L. Nagahara, T. Amlani, R. Tsui, J. Am. Chem. Soc. 123 (2001) 7730. [104] A.M. Kuznetsov, J. Ulstrup, J. Electroanal. Chem. 564 (2004) 209. [105] H. Park, J. Park, A.K.L. Lim, E.H. Anderson, A.P. Allvistos, P.L. McEuen, Nature 407 (2000) 57. [106] M.S. Dresselhaus, G. Dresselhaus, P.C. Eklund, Science of Fullerenes and Carbon Nanotubes, Academic, NY, 1996. [107] D. Dubois, G. Moninot, W. Kutner, M.T. Jones, K.M. Kadish, J. Phys. Chem. 96 (1992) 7137.

J. Zhang et al. / Electrochimica Acta 50 (2005) 3143–3159 [108] R. Bauernschmitt, R. Ahlrichs, F.H. Hennrich, M.M. Kappes, J. Am. Chem. Soc. 120 (1998) 5052. [109] A. Aviram, M.A. Ratner, Chem. Phys. Lett. 29 (1974) 277. [110] A.M. Kuznetsov, J. Ulstrup, J. Chem. Phys. 116 (2002) 2149. [111] A. Stabel, P. Herwig, K. M¨ullen, J.P. Rabe, Angew. Chem. 107 (1995) 1768. [112] P.G. Collins, A. Zettle, H. Brando, A. Thess, R.E. Smalley, Science 278 (1997) 100. [113] C. Zhou, M.R. Deshpande, M.A. Reed, L. Jones II, J.M. Tour, Appl. Phys. Lett. 71 (1997) 611. [114] M. Fujihira, Ann. N. Y. Acad. Sci. 852 (1998) 306.

3159

[115] M.L. Chabinyc, X. Chen, R.E. Holmlin, H. Jacobs, H. Skulason, C.D. Frisbie, V. Mujica, M.A. Ratner, M.A. Rampi, G.M. Whitesides, J. Am. Chem. Soc. 124 (2002) 11731. [116] M.-K. Ng, D.-C. Lee, L. Yu, J. Am. Chem. Soc. 124 (2002) 11862. [117] Y.J. Zhang, Y. Li, Q. Liu, J. Jin, B. Ding, Y. Song, L. Jiang, X. Du, Y. Zhao, T.J. Li, Synth. Met. 128 (2002) 43. [118] J.C. Ellenbogen, J.C. Love, Proc. IEEE 88 (2000) 386. [119] A.R. Pease, J.O. Jeppesen, J.F. Stoddart, Y. Luo, C.P. Collier, J.R. Heath, Acc. Chem. Res. 34 (2001) 433. [120] S. Ami, M. Hliva, C. Joachim, Nanotechnology 14 (2003) 283.