The kinetics for interfacial electron transfer (ET) from a transparent conductive oxide (tin-doped indium oxide, ITO, Sn:In2O3) to molecular acceptors 4-[N,N-di(p-tolyl)amino]benzylphosphonic acid, TPA, and [RuII(bpy)2(4,4′-(PO3H2)2-bpy)]2+, RuP, positioned at variable distances within and beyond the electric double layer (EDL), were quantified in benzonitrile and methanol by nanosecond absorption spectroscopy as a function of the thermodynamic driving force, −ΔG°. Relevant ET parameters such as the rate constant, ket, reorganization energy, λ, and electronic coupling, Hab, were extracted from the kinetic data. Overall, ket increased as the distance between the molecular acceptor and the conductor decreased. For redox active molecules within the Helmholtz planes of the EDL, ket was nearly independent of −ΔG°, consistent with a negligibly small λ value. Rips–Jortner analysis revealed a non-adiabatic electron transfer mechanism consistent with Hab < 1 cm−1. The data indicate that the barrier for electron transfer is greatly diminished at the conductor–electrolyte interface.

Predictive models to describe electron transfer rate constants at metal–electrolyte interfaces have been invaluable for the development of solar energy conversion technologies, batteries, and electrochemical engineering processes. Semiclassical interfacial electron transfer theory was adapted from related homogeneous models, with particular attention to metallic interfaces functionalized with redox active molecular complexes.1–11 The main conceptual difference between interfacial and intramolecular electron transfer lies in the delocalized continuum of electronic states associated with a metal.4,11 Each electronic state within the metal can undergo an electron transfer event to or from an isoenergetic electronic state within the molecule. Integration over the continuum of metallic states results in the ensemble interfacial electron transfer rate constant. In other words, the interfacial electron transfer rate constant is determined by the energetic overlap between the continuum of electronic states of the conductor and the molecular distribution (Fig. 1). As described by the Fermi golden rule, the degree of energetic overlap, and thus the interfacial electron transfer rate constant, is defined by the same fundamental parameters that govern both interfacial and intermolecular electron transfer kinetics—the Gibbs free energy ∆G°, the electronic coupling between the donor and acceptor Hab, and the free energy required to reorganize the bonds and surrounding solvent λ.

FIG. 1.

A theoretical representation of interfacial electron transfer from a metal to a molecular acceptor. Assuming the low-temperature limit of the Fermi–Dirac distribution f(E, EF), the interfacial electron transfer rate constant is proportional to the integration over the continuum of electrode states ρ(E)f(E, EF) and the distribution of activation energies for reduction of the molecule, W(E). The total reorganization energy λ defines the width of W(E). The driving force in eV for a one-electron process is defined as −∆G° = eE°′ − EF = e(E°′ − Eapp), where E°′ is the formal reduction potential of the molecule, EF is the Fermi level in eV, Eapp is an externally applied potential, and e is the elementary charge.

FIG. 1.

A theoretical representation of interfacial electron transfer from a metal to a molecular acceptor. Assuming the low-temperature limit of the Fermi–Dirac distribution f(E, EF), the interfacial electron transfer rate constant is proportional to the integration over the continuum of electrode states ρ(E)f(E, EF) and the distribution of activation energies for reduction of the molecule, W(E). The total reorganization energy λ defines the width of W(E). The driving force in eV for a one-electron process is defined as −∆G° = eE°′ − EF = e(E°′ − Eapp), where E°′ is the formal reduction potential of the molecule, EF is the Fermi level in eV, Eapp is an externally applied potential, and e is the elementary charge.

Close modal

This semiclassical framework for the prediction of an interfacial electron transfer rate constant, ket, from a metal to a molecule is depicted in Fig. 1 and described by Eq. (1).3,11,12 The continuum of metal electronic states is represented by ρ(E)f(E, EF), where ρ(E) is the density of states of the metal and f(E, EF) is the Fermi–Dirac distribution describing the occupancy of these states in relation to the electrode Fermi level, EF. The distribution of activation energies associated with reduction of the molecule is represented by W(E) [Eq. (2)] with a full width at half maximum determined by the reorganization energy, λ,

ket=2πρEfE,EFHabE2WEdE,
(1)
WE=14πλkBTexpΔG+λ24λkBT.
(2)

The utilization of an electrode in place of a molecular donor affords a distinct advantage to the study of interfacial electron transfer over that of intramolecular donor–acceptor complexes. Systematic variation of the driving force −∆G° in donor–acceptor complexes requires considerable synthetic chemistry. However, in interfacial reactions, −∆G° is defined by the difference between the molecular formal reduction potential, E°′, and the Fermi level EF of the metal, as described in Eq. (3), where e is the elementary charge,

ΔG=eEEF.
(3)

Because the application of externally applied potentials (Eapp) to a metallic electrode readily controls the Fermi level, Eapp = EF/e, −∆G° can be precisely tuned with a potentiostat.

Measurement of the kinetic response to −∆G° provides a straightforward method to experimentally probe W(E) and to quantify both λ and Hab. Contrary to the inverted region theorized and observed in intramolecular electron transfer,13,14 interfacial electron transfer theory predicts ket to increase with −∆G° to a maximum attainable value, kmax, when −∆G° > 2λ. When −∆G° = λ, ket is 12kmax, and values of ket normalized to kmax provide a convenient means to quantify λ, Eq. (4). Assuming the low temperature limit of f(E, EF), kmax reports on Hab and ρ, both of which are also considered to be independent of the applied potential [Eq. (5)],

ketkmax=121erfΔG+λ2λkBT,
(4)
kmax=2πHab2ρ.
(5)

The explicit experimental disentanglement of λ, Hab, and −∆G° is hence uniquely accessible for interfacial electron transfer through this analysis. This theory has been experimentally validated through an expansive body of research on thermal electron transfer with gold electrodes with self-assembled monolayers (SAMS).15–20 

More recently, researchers have utilized transient absorption spectroscopy to quantify interfacial electron transfer kinetics from a transparent conductive oxide (TCO) electrode to surface-anchored molecular acceptors as a function of −∆G°. This approach requires a means to photo-initiate the desired electron transfer reaction in a standard electrochemical cell. Utilization of the theory described above to analyze the data allowed direct quantification of λ and Hab for interfacial electron transfer to ruthenium–polypyridyl and triarylamine complexes relevant to solar water oxidation.12,21–23 These studies exemplify how factors such as proton involvement and proximity to the metal surface impact λ and Hab. A somewhat surprising finding was the apparent insensitivity of λ, Hab, and ket to electrolyte concentration. The utilization of aqueous electrolytes with 0.1M, 0.2M, and 0.5M HClO4 as well as a 0.1M LiClO4 acetonitrile electrolyte resulted in surprisingly similar kinetic behavior. The insensitivity to the electrolyte concentration is in contrast to predictions of Frumkin.11,24 Similarly, the near parity between acetonitrile and water contrasts with experimental17,20,24–28 and theoretical29–39 studies where solvent dynamics were found to play an important role in many interfacial electron transfer reactions.

To explore the impact of solvent on interfacial electron transfer at metal oxide interfaces, kinetic data are reported here in the slowly relaxing solvents methanol (MeOH) and benzonitrile (BzCN). The redox-active molecules were positioned within the electric double layer and the diffuse layer of an Sn:In2O3 (ITO) electrode using a previously reported layer-by-layer approach with ionic bridges.40 Kinetic analysis with semiclassical interfacial electron transfer theory indicated that in all cases, interfacial electron transfer occurred with very low electronic coupling, indicative of a non-adiabatic mechanism. The kinetic data and analysis are discussed in comparison to the recently published results obtained in water and acetonitrile electrolytes.22,23

All materials were used as received without further purification. Perchloric acid (70%, Sigma-Aldrich), zirconyl chloride octahydrate (reagent grade, 98%), and methylene diphosphonic acid were obtained from Sigma-Aldrich. Ethanol (99.5+ %) and methanol (MeOH, 99.8%) were obtained from Acros Organics. Benzonitrile (BzCN, 99%) was purchased from TCI. In2O3:Sn (ITO) nanoparticles (VP ITO TC8) were purchased as a powder from Evonik Industries. Fluorine-doped tin oxide (FTO) glass substrates (15 Ω/sq) were obtained from Hartford Glass. RuP, [RuII(bpy)2(4,4′-(PO3H2)2-bpy)]2+, where bpy is 2,2′-bipyridine, and TPA, 4-[N,N-di(p-tolyl)amino]benzylphosphonic acid, were synthesized as previously reported.41 

The In2O3:Sn (ITO) nanoparticles (20 wt. %) were thoroughly sonicated in 100-proof ethanol with 2-[2-(2-Methoxyethoxy)ethoxy]acetic acid (3 wt. % compared to ITO) to form a stable dispersion. A sol–gel paste was generated by mixing equal volumes of the 20 wt. % ITO dispersion and a 10 wt. % hydroxypropyl cellulose/ethanol solution. The paste was doctor-bladed onto FTO-coated conductive glass using two layers of Scotch tape as a spacer to define the ITO film thickness. The paste was then dried in air for ∼30 min and annealed in a tube furnace at 450 °C under O2 flow for 30 min. Films generated in this way were measured to be 3 µm–4 µm thick by a Bruker DektatXT profilometer.

ITO materials were functionalized with redox-active molecules RuP and/or TPA, which were positioned at variable distances from the ITO surface on the Angstrom length scale with ionic bridges.22,23,40,42 Electrodes termed ITO|-(X)n-TPA employed in transient absorption experiments were first sensitized to 50% saturation surface coverage (∼5 × 10−9 mol cm−2) with RuP by reaction of ITO with RuP in methanol.23 Surface coverages were controlled through reaction time. Molecular bridge units were assembled by subsequent reactions of ITO electrodes with 0.1M HClO4 aqueous solutions of 5 mM methylene diphosphonic acid (overnight) then 6 mM ZrOCl2·8 H2O (2 h). Multiple bridge units were assembled by repeating the process. Bridge assemblies were terminated by redox-active molecules, either RuP or TPA, by overnight reaction with RuP/methanol or TPA/ethanol solutions. For spectroelectrochemical measurements, ITO|-(X)n-TPA electrodes were prepared without first sensitizing the ITO with RuP.

A standard three-electrode cell with the ITO was used as the working electrode, a platinum mesh was used as the counter electrode, and a silver wire was used as the quasi-reference electrode. Experiments were performed in Ar-sparged 0.1M LiClO4 MeOH or BzCN solutions. All potentials are reported vs the Normal Hydrogen Electrode (NHE). For spectroelectrochemical measurements, potentiostatic control was coupled with UV-visible absorption spectroscopy measured with an Avantes AvaLight DHc light source and an Avantes StarLine AvaSpec-2048 spectrometer. The baseline spectra utilized for all absorption spectra reported was an ITO electrode that had not been surface functionalized. Formal redox potentials E°′ for ITO|-(X)n-RuIII/IIP and ITO|-(X)n-TPA+/0 were quantified by modeling the absorption change at 455 nm and 680 nm, respectively, with a modified Nernst equation, Eq. (6). Here, ∆A is the normalized absorbance change, Eapp is the applied potential, and α is a non-ideality factor.43 The E°′ values reported represent the equilibrium potential at which the concentrations of the oxidized and reduced species were equal,

ΔA=11+10(EappE)/(59.2α).
(6)

Transient absorption spectroscopy was performed with a previously described apparatus.44 Pulsed 532 nm light excitation was provided by a frequency-doubled, Q-switched, pulsed Nd:YAG laser (Quantel USA, Brilliant B, 5 ns–6 ns FWHM). Laser fluences were adjusted between 1 mJ/pulse and 8 mJ/pulse to generate the same initial concentration of reactants. A white light 150 W xenon arc lamp (Applied Photophysics) aligned perpendicular to the excitation served as the probe beam that was pulsed at 1 Hz for time scales <100 µs. A SPEX 1702/04 monochromator optically coupled to a Hamamatsu R928 photomultiplier tube was used for detection. An optically triggered LeCroy 9450, Dual 330 MHz oscilloscope was utilized to digitize the transient signal. The instrument response time was ∼10 ns. Single wavelength kinetic measurements were generated by averaging the results of 90 laser pulses. The samples were an ITO photo-electrode positioned at a 45° angle to the excitation in a standard three-electrode cell in a glass cuvette. The electrolytes were purged with argon gas before all measurements.

Mesoporous nanocrystalline films of the transparent conducting oxide Sn:In2O3 (ITO) were functionalized with RuP and TPA, as illustrated in Fig. 2. Molecular acceptors were either directly anchored to the ITO through phosphonic acid groups or were positioned away from the surface through ionic bridge units, represented as X, that consisted of a methylene diphosphonic acid molecule coordinated to a Zr4+ Lewis acid.22,23,40,42 The distance between the ITO surface and the redox active center was controlled through the number of bridging units X to produce films abbreviated as ITO|-(X)n-Acceptor, n = 0, 1 or 2.

FIG. 2.

(a) ITO electrodes were functionalized with the redox-active molecules RuP and TPA. (b) Electrodes abbreviated as ITO|-(X)n-RuP were synthesized by a layer-by-layer technique. Each ionic bridge, X, consisted of a methylene diphosphonic acid molecule bound to a Zr(IV) Lewis acidic cation, and the molecule–electrode distance was controlled by the number of linked bridges, n. Electrodes termed ITO|-(X)n-TPA utilized for kinetic measurements also contained RuP anchored directly to the surface. Electron transfer distances were estimated from DFT models of the molecules and a 7 Å interlayer Zr(IV) spacing. Pulsed light excitation of RuP (1) resulted in excited state electron transfer from RuP to ITO (2). If TPA was present, intermolecular electron transfer from TPA to RuIIIP generated TPA+(black 3). Electron recombination (red 3 or 4) with rate constant ket was quantified spectroscopically to either RuIIIP or TPA+.

FIG. 2.

(a) ITO electrodes were functionalized with the redox-active molecules RuP and TPA. (b) Electrodes abbreviated as ITO|-(X)n-RuP were synthesized by a layer-by-layer technique. Each ionic bridge, X, consisted of a methylene diphosphonic acid molecule bound to a Zr(IV) Lewis acidic cation, and the molecule–electrode distance was controlled by the number of linked bridges, n. Electrodes termed ITO|-(X)n-TPA utilized for kinetic measurements also contained RuP anchored directly to the surface. Electron transfer distances were estimated from DFT models of the molecules and a 7 Å interlayer Zr(IV) spacing. Pulsed light excitation of RuP (1) resulted in excited state electron transfer from RuP to ITO (2). If TPA was present, intermolecular electron transfer from TPA to RuIIIP generated TPA+(black 3). Electron recombination (red 3 or 4) with rate constant ket was quantified spectroscopically to either RuIIIP or TPA+.

Close modal

The visible absorption spectra of ITO|-(X)n-RuP display a broad characteristic metal-to-ligand charge transfer absorption band centered near 450 nm when submerged in methanol (MeOH) or benzonitrile (BzCN) [Fig. 3(d) and Fig. S1a]. The neutral TPA does not absorb visible light; however, thermal oxidation to yield ITO|-(X)n-TPA+ is accompanied by a significant color change and the appearance of a prominent absorption band centered at 680 nm [Fig. 3(a) and Fig. S1b]. The absorption spectra were within experimental error independent of the number of ionic bridges, n.

FIG. 3.

The visible absorbance spectra of (a) ITO|-(X)n-TPA+ and (d) ITO|-(X)n-RuP in 0.1M LiClO4 MeOH. [(b) and (e)] Visible absorbance spectra measured over the indicated applied potential range vs NHE of (b) ITO-(X)0-TPA and (e) ITO|-(X)0-RuP in 0.1M LiClO4 MeOH. [(c) and (f)] The absorbance change ∆A measured at (c) 680 nm for TPA and (f) 455 wavelength for RuP as a function of applied potential with overlaid fits to a modified Nernst equation, with Eq. (6).

FIG. 3.

The visible absorbance spectra of (a) ITO|-(X)n-TPA+ and (d) ITO|-(X)n-RuP in 0.1M LiClO4 MeOH. [(b) and (e)] Visible absorbance spectra measured over the indicated applied potential range vs NHE of (b) ITO-(X)0-TPA and (e) ITO|-(X)0-RuP in 0.1M LiClO4 MeOH. [(c) and (f)] The absorbance change ∆A measured at (c) 680 nm for TPA and (f) 455 wavelength for RuP as a function of applied potential with overlaid fits to a modified Nernst equation, with Eq. (6).

Close modal

The formal reduction potential, E°′, for both RuIII/IIP and TPA+/0 was determined through spectroelectrochemical experiments with ITO|-(X)n-RuP and ITO|-(X)n-TPA [Figs. 3(b) and 3(e) and Figs. S2–S5). The absorption was as a function of the applied potential at 455 nm for ITO|-(X)n-RuP and 680 nm for ITO|-(X)n-TPA and modeled with Eq. (6).22,43,45 Values of E°′ obtained in 0.1M LiClO4 methanol or benzonitrile were within experimental error insensitive to the distance from the ITO surface or the solvent [Figs. 3(c) and 3(f)]. For ITO|-(X)n-RuIII/IIP, E°′ = 1.55 V vs NHE, and for ITO|-(X)n-TPA+/0, E°′ = 1.02 V vs NHE.

Pulsed 532 nm excitation of RuP resulted in the prompt appearance of the oxidized complex, data consistent with rapid excited state injection, ITO|-(X)n-RuIIP* → ITO(e)|-(X)n-RuIIIP, with kinj > 108 s−1. After pulsed light excitation of ITO|-(X)n-TPA, for which both RuP and TPA were present, rapid intermolecular electron transfer from TPA to light-generated RuIIIP occurred within 10 ns to yield ITO|-(X)n-TPA+. Data collected 50 ns after excitation are shown in Fig. 4 and Fig. S6 for n = 0 for RuP, and n = 0, 1, and 2 for TPA, while there was no spectroscopic evidence for excited state injection after excitation of ITO|-(X)2-RuP in either methanol or benzonitrile electrolytes.

FIG. 4.

Transient absorption spectra measured 50 ns after pulsed 532 nm light excitation (points) for (a) ITO|-(X)n-TPA and (b) ITO|-(X)0-RuP in 0.1M LiClO4 MeOH. Overlaid as black lines are simulations based on the spectroelectrochemical oxidation of the molecule.

FIG. 4.

Transient absorption spectra measured 50 ns after pulsed 532 nm light excitation (points) for (a) ITO|-(X)n-TPA and (b) ITO|-(X)0-RuP in 0.1M LiClO4 MeOH. Overlaid as black lines are simulations based on the spectroelectrochemical oxidation of the molecule.

Close modal

Following excited state injection and [for ITO|-(X)n-TPA] intermolecular electron transfer, the desired interfacial electron transfer reaction was monitored spectroscopically at 402 nm [ITO(e)|-(X)n-RuIIIP → ITO|-(X)n-RuIIP] or 690 nm [ITO(e)|-(X)n-TPA → ITO|-(X)n-TPA+]. Kinetics for the interfacial electron transfer were measured as a function of the applied potential (Eapp). Typical data for ITO|-(X)n-TPA in 0.1M LiClO4 MeOH are shown in Fig. 5, while data for ITO|-(X)n-TPA in 0.1M LiClO4 BzCN and ITO|-(X)n-RuP are given in Figs. S7 and S8. The kinetic data were non-exponential, and the reciprocal of the time required for the reaction to reach 12 of the initially formed reactants was taken as an estimate of the interfacial electron transfer rate constant, ket. The magnitude of ket increased with increasingly negative Eapp and was most rapid for molecules anchored directly to the oxide surface. However, the sensitivity of the kinetic data to Eapp was smallest for ITO|-(X)0-TPA. Note that after pulsed light excitation of ITO|-(X)1-RuP, transient spectral data indicated that reduction of the RuP* excited state took place, thus lowering the yield of excited state injection (Fig. S9).46 As increasingly negative potentials were applied, the timescales of charge recombination and excited state reduction became similar, precluding accurate ket quantification. As such, ITO|-(X)1-RuP is excluded from further kinetic analysis.

FIG. 5.

The absorption change ∆A measured at 690 nm after pulsed 532 nm light excitation of ITO|-(X)0-TPA (left), ITO|-(X)1-TPA (center) and ITO|-(X)2-TPA (right) immersed in 0.1M LiClO4 MeOH as a function of the applied potential vs NHE.

FIG. 5.

The absorption change ∆A measured at 690 nm after pulsed 532 nm light excitation of ITO|-(X)0-TPA (left), ITO|-(X)1-TPA (center) and ITO|-(X)2-TPA (right) immersed in 0.1M LiClO4 MeOH as a function of the applied potential vs NHE.

Close modal

The interfacial electron transfer rate constant ket, quantified as the inverse half-life, measured as a function of the driving force is given in Fig. 6(a) and Fig. S10(a). For ITO|-(X)0-RuP and ITO|-(X)n-TPA, values of ket increased with increasing driving force before reaching a saturation value, kmax. Furthermore, for a given ΔG, ket decreased with distance from the ITO surface. Normalization of ket by kmax resulted in plots shown in Fig. 6(b) and Fig. S10(b), which were well-modeled by semiclassical heterogeneous electron transfer theory [Eq. (4)] to extract the total reorganization energy λ (Table I). Values of Hab were extracted from kmax using Eq. (5). This equation includes the density of electronic states of the electrode, ρ, which has been previously estimated from Drude analysis of the near infrared plasmon absorption to be 0.45 eV−1 for mesoporous ITO.12 This estimate, however, requires knowledge of the number of surface atoms in ITO capable of undergoing interfacial electron transfer with a molecule, which adds uncertainty to calculated Hab values. For the present analysis, a single surface atom was assumed.

FIG. 6.

(a) Values of ket quantified as a function of −∆G° = e(E°′ − Eapp) for kinetic data measured in 0.1M LiClO4 MeOH. (b) Plots of ket normalized by kmax in 0.1M LiClO4 MeOH with overlaid fits to Eq. (4). When ket = 12 kmax, −∆G° = λ, as illustrated by dashed lines.

FIG. 6.

(a) Values of ket quantified as a function of −∆G° = e(E°′ − Eapp) for kinetic data measured in 0.1M LiClO4 MeOH. (b) Plots of ket normalized by kmax in 0.1M LiClO4 MeOH with overlaid fits to Eq. (4). When ket = 12 kmax, −∆G° = λ, as illustrated by dashed lines.

Close modal
TABLE I.

Relevant interfacial electron transfer kinetic parameters.

BzCNMeOH
R (Å)aλ (eV)kmax × 106 (s−1)Hab (cm−1)λ (eV)kmax × 106 (s−1)Hab (cm−1)
ITO|-(X)0-RuP 7.4 0.38 ± 0.03 31 0.7 0.56 ± 0.03 33 0.7 
ITO|-(X)0-TPA 4.6 0.08 ± 0.04 30 0.7 0.09 ± 0.03 31 0.7 
ITO|-(X)1-TPA 15 0.58 ± 0.03 11 0.4 0.63 ± 0.01 2.5 0.2 
ITO|-(X)2-TPA 24 0.52 ± 0.04 1.5 0.2 0.72 ± 0.01 0.8 0.1 
BzCNMeOH
R (Å)aλ (eV)kmax × 106 (s−1)Hab (cm−1)λ (eV)kmax × 106 (s−1)Hab (cm−1)
ITO|-(X)0-RuP 7.4 0.38 ± 0.03 31 0.7 0.56 ± 0.03 33 0.7 
ITO|-(X)0-TPA 4.6 0.08 ± 0.04 30 0.7 0.09 ± 0.03 31 0.7 
ITO|-(X)1-TPA 15 0.58 ± 0.03 11 0.4 0.63 ± 0.01 2.5 0.2 
ITO|-(X)2-TPA 24 0.52 ± 0.04 1.5 0.2 0.72 ± 0.01 0.8 0.1 
a

Estimated by DFT in Refs. 22 and 23.

For ITO|-(X)0-RuP and ITO|-(X)n-TPA, Hab values were within experimental error indistinguishable between MeOH and BzCN. Values of λ, however, were systematically smaller for interfacial electron transfer occurring in BzCN. For ITO|-(X)2-TPA, where λ is expected to approach homogeneous solution values,11,22,23λ ≈ 0.6 eV in BzCN, while in MeOH, λ ≈ 0.75 eV.

The kinetics for interfacial electron transfer from ITO to acceptors physically located within the electric double layer and the diffuse layer were quantified as a function of the free energy change in both benzonitrile (BzCN) and methanol (MeOH). The kinetic approach required a high surface area mesoporous thin film conductive electrode so that the desired reaction could be photoinitiated and quantified as a function of −ΔG°. Marcus–Gerischer analysis provided estimates of the reorganization energy and the electronic coupling. These data compliment previously reported measurements of the same materials in water and acetonitrile (MeCN), providing an opportunity to evaluate the impact of solvent on interfacial electron transfer at technologically relevant oxide interfaces.22,23 It is important to emphasize that the formal reduction potentials and absorption spectra of the molecules were insensitive to the number of bridge units and were only weakly solvent dependent. However, the interfacial electron transfer rate constants, ket, were highly sensitive to the number of bridge units with a more acute solvent dependence. Below, we discuss these data, first with regard to the reorganization energy followed by the electronic coupling.

The quantified λ values were largest when the distance from the oxide–electrolyte interface was greatest and decreased to λ ≈ 0.1 eV at the smallest distance. Dielectric continuum theory predicts that λo should decrease with the donor–acceptor distance, as described by Eq. (7),

λo=q221εop1εst1a12R.
(7)

Here, εst and εop are the solvent static and optical dielectric constants, a is the radius of a spherical cavity occupied by the molecular acceptor,6,47 and R is the distance between the ITO and the molecule.11,48 Values of R were estimated as the distance between the redox center of the molecule (N for TPA and Ru for RuP) and a plane through the O atoms of the phosphonic anchoring group, as shown in Fig. 2. Distances in the RuP, TPA, and diphosphonic acid were estimated by density functional theory, and the Zr(IV) interlayer spacing was estimated to be 7 Å.22,23 Experimental reorganization energies in this study were best modeled with a = 4.8 Å and are represented as a function of distance in Fig. 7 (solid lines), assuming εst = 32.7 and εop = 1.76 for MeOH and εst = 25.2 and εop = 2.33 for BzCN.49 This dielectric continuum expression predicts the smaller λ values obtained for BzCN and the decrease in λ near the surface, but fails to predict the vanishingly small λ measured for ITO|-(X)0-TPA when the redox center of the TPA is a mere ∼4.6 Å from the surface. Note that these molecular acceptors have negligibly small inner-sphere reorganization energies (λi)50,51 such that the total reorganization energy λ is approximately equal to the outer-sphere reorganization energy λo, i.e., λ = λo + λiλo.

FIG. 7.

Experimentally extracted reorganization energies λ for interfacial electron transfer as a function of distance between the molecule and electrode R in MeOH (black points) and BzCN (red points). Solid lines represent dielectric continuum predictions of λ as a function of R, assuming εst = 32.7 and εop = 1.76 for MeOH, and εst = 25.2 and εop = 2.33 for BzCN.

FIG. 7.

Experimentally extracted reorganization energies λ for interfacial electron transfer as a function of distance between the molecule and electrode R in MeOH (black points) and BzCN (red points). Solid lines represent dielectric continuum predictions of λ as a function of R, assuming εst = 32.7 and εop = 1.76 for MeOH, and εst = 25.2 and εop = 2.33 for BzCN.

Close modal

Values of λ near 0 for ITO|-(X)0-TPA in MeOH and BzCN align with recent data obtained in H2O and MeCN, which also found λ ≈ 0.1 eV.22,23 That these λ values in MeOH, BzCN, H2O, and MeCN are within experimental error equal suggests that inductive effects recently reported by Matyushov,52 which would predict λ to be significantly larger in bulkier solvents, are not significant here. In these studies, the unexpectedly small λ at the metal oxide/electrolyte interface was attributed to the electric double layer (EDL). Although descriptions of the EDL have evolved over time, the polarized metal electrode is generally thought to have specifically adsorbed ions and rigidly oriented solvent molecules at the interface.11,53 This is often called the inner-Helmholtz plane. The outer-Helmholtz plane, for which a strong electric field is also present, consists of solvated ions. Beyond this, a diffuse layer of solvent and solvated ions progressively screens the electric field. Gouy and Chapman’s model assumed that the field decays continuously from the metal surface, while Stern separated potential decay in the EDL and the diffuse layer.54 

Experimental evidence for a loss of the rotational freedom in water molecules within the EDL that drastically reduces εst has been previously reported,55–60 although the behavior of non-aqueous interfaces has been less thoroughly explored.38,61 The dielectric constant in the diffuse layer increased until bulk solvent properties are measured far from the interface. That λ for interfacial electron transfer in ITO|-(X)0-TPA is near zero in H2O, MeCN, MeOH, and BzCN suggest that within the Helmholtz planes, εst approaches εop for each solvent. This manifests in nearly identical electron transfer rate constants for ITO|-(X)0-TPA regardless of the solvent (Fig. 8). The generality suggests near-activationless interfacial electron transfer to be a general effect within the Helmholtz planes of a conductor–electrolyte interface.

FIG. 8.

Interfacial electron transfer rate constants ket as a function of −∆G° for ITO|-(X)0-TPA in the indicated solvents. Circular points represent data from this work. Blue crosses are taken from Ref. 23, and green crosses are taken from Ref. 22. Solid lines represent fits to Eq. (8) (see text below) to extract Sumi–Marcus kinetic parameters in Table II.

FIG. 8.

Interfacial electron transfer rate constants ket as a function of −∆G° for ITO|-(X)0-TPA in the indicated solvents. Circular points represent data from this work. Blue crosses are taken from Ref. 23, and green crosses are taken from Ref. 22. Solid lines represent fits to Eq. (8) (see text below) to extract Sumi–Marcus kinetic parameters in Table II.

Close modal

The remarkable solvent insensitivity of the interfacial electron transfer kinetics for ITO|-(X)0-TPA (MeOH, BzCN, H2O, and MeCN) raises questions about the mechanism of the reaction. As X increases to 1 and 2, a non-adiabatic reaction is reasonably expected over the large distances created by the ionic bridges.15 However, strong coupling at small distances, i.e., for ITO|-(X)0-TPA, might be expected to result in adiabatic electron transfer. While there was no direct spectroscopic evidence for enhanced coupling at short distances in ITO|-(X)0-TPA, researchers have previously identified electron transfer reactions at metal interfaces that depend on the solvent longitudinal relaxation time τL and that have been thus assigned as adiabatic and dynamically controlled.20,24,27,28 Methanol and BzCN are slowly relaxing solvents with large τL, while for H2O and MeCN, solvent motion relaxation occurs ten and twenty times faster, respectively (Table II). As such, if the electron transfer was dynamically controlled, kinetics should be distinct between the two solvent sets. Furthermore, the slow relaxation of MeOH and BzCN may promote solvent control.20,30,34,37,39

TABLE II.

Solvent characteristics and kinetic parameters extracted with Rips–Jortner theory.

SolventεstεopaτL (ps)λ (eV)Hab (cm−1)κ × 10−3b
MeOH 32.7a (2.2)c 1.76 4.39d (66)e 0.08 0.7 8.2 (120) 
BzCN 25.2a (3.3)c 2.33 5.72d (44)e 0.09 0.7 8.6 (66) 
H278.5a (2.5)c 1.78 0.48d (15)e 0.12 0.6 0.4 (14) 
MeCN 35.9a (2.5)c 1.80 0.20d (3)e 0.11 0.6 0.2 (3) 
SolventεstεopaτL (ps)λ (eV)Hab (cm−1)κ × 10−3b
MeOH 32.7a (2.2)c 1.76 4.39d (66)e 0.08 0.7 8.2 (120) 
BzCN 25.2a (3.3)c 2.33 5.72d (44)e 0.09 0.7 8.6 (66) 
H278.5a (2.5)c 1.78 0.48d (15)e 0.12 0.6 0.4 (14) 
MeCN 35.9a (2.5)c 1.80 0.20d (3)e 0.11 0.6 0.2 (3) 
a

Values taken from Ref. 49 

b

Calculated from Eq. (9) using two τL values. The first value is calculated using the εst of the bulk solvent to generate a lower limit of κ. For values in parentheses, τL is calculated using the εst required to model experimentally determined λ values, as to represent an upper limit of κ.

c

Values required to model experimental λ values in Table I with Eq. (7).

d

Calculated with Eq. (10) using bulk εst values from Ref. 49 

e

Calculated with Eq. (10) using εst values that best model experimental λ.

Although there are several theoretical treatments to describe the influence of adiabaticity on interfacial electron transfer,30,32–36,39,62 application of Sumi–Marcus theory as refined by Rips and Jortner is an appealingly straightforward approach,29,39,63–65

kA=ket1+κ.
(8)

Here, the non-adiabatic electron transfer rate constant ket [Eqs. (1) and (4)] is affected by the solvent dynamics through an adiabaticity parameter κ [Eq. (9)] to yield an adiabaticity-corrected rate constant kA,

κ=4πτLHab2λ.
(9)

When the adiabaticity parameter is small, κ ≪ 1, the reaction is non-adiabatic, and kAHab,2 as in Eq. (5). When κ ≫ 1, however, Hab2 factors out of the pre-exponential term, the reaction is adiabatic, and kA ∝ 1/τL. For a reaction to be adiabatic in the Rips–Jortner model, a slowly relaxing solvent environment (large τL), high electrode-molecule electronic coupling (large Hab), and/or a small reorganization energy (λ) are required.

To analyze the degree of adiabaticity for ITO|-(X)0-TPA interfacial electron transfer in each solvent, values of k quantified from transient spectral data as a function of −∆G° were modeled with Eq. (8) (Fig. 8). As in modeling with Eq. (4), the range over which the kinetics are sensitive to Eapp reflects λ, and kmax reflects the preexponential factor, now assumed to contain information on both Hab and κ. Values of λ, Hab, and κ quantified using Eqs. (8) and (9) are given in Table II. Values of τL depend on εst as described in Eq. (10), where ε is the high-frequency dielectric constant and τD is the Debye relaxation time, which means τL is likely significantly affected by the EDL,

τL=εεstτD.
(10)

As such, κ values (Table II) were calculated both with the εst of the bulk solvent and the decreased εst required to model the experimental λ values in Table I with Eq. (7). These produce a lower and upper limit of κ, respectively. Interestingly, λ and Hab values quantified by Eq. (8) were within experimental uncertainty equal to those quantified in the non-adiabatic limit [Eq. (4)]. Values of Hab were all exceptionally small, <1 cm−1. Although large τL values in MeOH and BzCN yielded κ values roughly 5–20× greater than those for H2O and MeCN, even the upper limit κ values were all ≪1. This indicates electron transfer at these ITO surfaces, even within the Helmholtz planes and in slowly relaxing solvents, is non-adiabatic.

The assignment of a non-adiabatic interfacial electron transfer with this Rips–Jortner analysis is consistent with the similarity between the interfacial electron transfer rate constants for ITO|-(X)0-TPA in each solvent. No systematic dependence of ket on solvent τL was observed (Fig. S11). Furthermore, ket depended exponentially on the distance from the electrode irrespective of solvent (Fig. S12), and the absorbance spectra of RuP and TPA were insensitive to the molecules’ position in the EDL (Fig. 1 and Fig. S1). All of these experimental measures point to small Hab and non-adiabatic electron transfer. Very weak coupling results in non-adiabatic electron transfer, even when the EDL lowers εst values to slow the solvent longitudinal relaxation and virtually eliminate λ—both factors that promote adiabaticity. Why Hab in these functionalized transparent conductive oxide materials is so low is not readily apparent, as electron transfer reactions between molecules and metallic electrodes on similar length scales are generally considered to be adiabatic.20,24,27,28 It may be that the s orbitals that comprise the conduction band states of ITO couple poorly to anchored molecules.66 It is also possible that surface heterogeneity leads to a subset of electron transfer events that occur non-adiabatically, while others with larger Hab occur adiabatically within the 10 ns instrument response time. While a small fraction of the interfacial electron transfer may occur on shorter time scales, the data reported here are fully in line with a non-adiabatic mechanism.

Interfacial electron transfer kinetics were measured as a function of −∆G° from a mesoporous ITO electrode to tethered, redox-active molecules positioned at various distances from the conductor–electrolyte interface. Absorbance spectra and formal reduction potentials of the molecules were independent of their physical location. Analysis with semiclassical electron transfer theory revealed the reorganization energy λ for the electron transfer to be significantly smaller in BzCN than in MeOH when molecules were distant from the interface in the diffuse layer. Values of λ decreased as molecules approached the interface and were vanishingly small, λ ≈ 0.1 eV, at the shortest attainable distances. This near-activationless electron transfer was attributed to the strong electric field in the Helmholtz planes of the electric double layer, which drastically reduced the solvent static dielectric constant. The impact of the electric double layer on the reorganization energy has now been quantified in MeOH, BzCN, H2O, and MeCN, suggesting that activationless electron transfer in the Helmholtz planes may be a general feature of polar solvents. Exceptionally low coupling between the ITO and the redox-active molecules resulted in non-adiabatic electron transfer, even at the shortest distances, as revealed by Rips–Jortner analysis. This non-adiabaticity manifests in electron transfer rate constants that show no systematic dependence on the solvent longitudinal relaxation time in MeOH, BzCN, H2O, and MeCN. The data reveal that electron transfer barriers are dramatically diminished within the Helmholtz planes of the conductive oxide–electrolyte electric double layer.

See the supplementary material for absortion spectra, spectroelectrochemistry, and transient absorption kinetics of ITO|-(X)n-TPA and ITO|-(X)n-RuP in benzonitrile.

B.M.A.-T. and R.E.B. contributed equally to this work.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

This study is based on the work solely supported by the Alliance for Molecular PhotoElectrode Design for Solar Fuels (AMPED), an Energy Frontier Research Center (EFRC) funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Award No. DE-SC0001011. R.E.B. acknowledges the National Science Foundation for an individual Graduate Research Fellowship under Grant No. DGE-1650116. B.M.A.-T. and R.E.B. appreciate Dr. Eric Piechota’s valuable insight on the subtleties of electron transfer theories. B.M.A.-T. thanks ALN for the feedback provided in the development of this project.

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Supplementary Material