Activation Energies for Electron Transfer from TiO2 to Oxidized Dyes

Activation Energies for Electron Transfer from TiO2 to Oxidized Dyes: A Surface Coverage Dependence Correlated with Lateral Hole Hopping Renato N. Sampaio, Brian N. DiMarco, and Gerald J. Meyer* Department of Chemistry, University of North Carolina at Chapel Hill, CB 3290, Chapel Hill, North Carolina 27599, United States ABSTRACT: Three ruthenium(II) sensitizers, [Ru(L)2(dcb)]2+, were anchored to mesoporous TiO2 thin films where the ligand L = 4,4′-(CH3)2-bpy (dmb), 4,4′(C(CH3)3) 2-bpy (dtb), and 4,4′-(CF3)2-bpy (bpyCF3) controls the thermodynamics and electronic coupling for self-exchange intermolecular RuIII/II “hole hopping”. Apparent electron difussion coefficients, Dapp, were reported to increase in the order bpyCF3 ≪ dtb < dmb. Nanosecond transient absorption measurements made over an 80° temperature range were conducted to abstract average charge recombination rate constants, kcr, under conditions of sub-percolation and saturated sensitizer surface coverages. For sensitizers [Ru(dmb)2(dcb)]2+ and [Ru(dtb)2(dcb)]2+, the kcr values at saturation coverages were significantly larger than those at low coverages, by a degree that followed the trend in Dapp. The inability of [Ru(bpyCF3)2(dcb)]2+ to introduce hole transport was afirmed by recombination kinetic data that were insensitive to the sensitizer surface converage. An Arrhenius analysis indicated that lateral RuIII/II hole hopping decreased the barrier for electron transfer that ultimately led to faster recombination rates. time scales.1,2 The kinetic data acquired from transient absorption measurements are highly nonexponential and have been widely modeled by the Kohlrausch−Williams−Watts (KWW) function. This function was first proposed empirically by Kohlrausch and was first derived by Scher and Montroll based on a random walk kinetic model.14 Since that time it has become a paradigm for quantifying transport in disordered materials. Nelson and co-workers have extended the random walk model to the dye-sensiztied interface and have used it to model charge recombination kinetic data wherein the injected electrons undergo a randon walk involving TiIV/III trapping/ detrapping.3,5,15 Tachiya and co-workers reported a “time of flight” model in which the trapped electrons can access a delocalized conduction band that enables transport beyond nearest neighbors.6,7 Note that in these charge recombination models, the oxidized dye is assumed to be fixed at the injection site. It has previously been demonstrated that sensitizers anchored to metal oxides can transport charges across the semiconductor surface through lateral self-exchange reactions, a process referred to as “hole hopping”.16−20 Related hole-

T

he mechanism(s) by which electrons in a semiconductor recombine with oxidized dyes has been the subject of many studies.1−11 Much of this work, including this study, was accomplished with pulsed laser excitation of the dyes (termed sensitizers) to initiate excitedstate injection, eq 1, with spectroscopic characterization of the recombination reaction under conditions where the numbers of oxidized sensitizers and injected electrons were equal, eq 2. TiO2 |‐S + hv → TiO2 (e−)|‐S+

(1)

TiO2 (e−)|‐S+ → TiO2 |‐S

(2)

In bulk semiconductor materials the presence of surface electric fields, i.e. depletion layers, are expected to inhibit charge recombination by efficiently sweeping the injected electrons away from the oxidized sensitizer and toward the semiconductor bulk.12 For intrinsically doped ∼20 nm anatase TiO2 nanocrystallites, the field magnitude is less than thermal energy and hence depletion layers are not expected to influence charge recombination.1,13 This Letter describes new experimental studies of charge recombination in dye-sensitized TiO 2 mesoporous thin films as a function of temperature and the sensitizer surface coverage. Charge recombination in dye-sensitized TiO2 nanostructures is known to occur on the tens of microseconds to millisecond © XXXX American Chemical Society

Received: August 17, 2017 Accepted: September 13, 2017

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http://pubs.acs.org/journal/aelccp

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ACS Energy Letters

coverage.16,24 All sensitizers exhibited intense metal-to-ligand charge transfer (MLCT) absorption bands in the visible region.25 Addition of 0.1 M LiClO4 to the neat acetonitrile solutions induced spectral shifts in the MLCT absorption, which have been previously attributed to cation adsorption to the TiO2 interface (Figure 2).26 Spectroelectrochemical experiments, where absorbance changes are monitored after the application of an increasingly positive electrochemical potential, were performed to yield the RuIII/II mole fraction at a given applied potential. The potential where equal concentrations of RuIII and RuII existed was taken as the formal reduction potential, E0(RuIII/II) (Table 1). The

hopping events are commonly initiated with an applied potential and can be utilized to oxidize all the sensitizers present within the mesoporous thin films provided that the sensitizer surface coverage exceeds a percolation threshold.16−21 More recently, time-resolved anisotropy measurements revealed that after excited-state injection, the oxidized sensitizers are in fact mobile by hole hopping to nearest neighbors.22,23 These observations have been the subject of a recent review24 and naturally raise the question of whether hole hopping provides a transport mechanism that brings oxidized sensitizers proximate to injected electrons prior to charge recombination. In an important step toward addressing this question, two research groups have recently reported a correlation between hole hopping and charge recombination dynamics. 10,11 Collectively the data provides compelling evidence that S+/0 self-exchange occurs prior to recombination. This finding suggests that one can tune, or possibly even control, charge recombination through S+/0 self-exchange. Herein, charge recombination rate constants for a series of three Ru(II) polypyridyl sensitizers (Figure 1) with quite different holehopping characteristics are reported to test this suggestion.

Table 1. Sensitizer Reduction Potentials with Excited-State Free Energies and Injection Yields

a

TiO2|-sensitizer

E0(RuIII/II) (V)a

ΔGES (eV)

E0(RuIII/2+*) (V)a

Φinj

TiO2|-Ru(dmb)2(dcb) TiO2|-Ru(dtb)2(dcb) TiO2|-Ru(bpyCF3)2(dcb)

1.45 1.44 1.85

2.14 1.99 2.14

−0.69 −0.55 −0.29

0.95 0.70 0.50

Potentials are versus NHE.

reducing power of the excited state, E0(RuIII/2+*), was obtained through a free energy cycle with the Gibbs free energy stored in the excited-state, ΔGES, as detailed in a previous publication.11 Self-exchange intermolecular RuIII/II electron transfer, commonly termed hole hopping, was previously quantified for sensitizers [Ru(dmb)2(dcb)]2+ and [Ru(dtb)2(dcb)]2+ by chronoabsorptometry experiments.21 The oxidation of the sensitized TiO2 thin films was spectroscopically monitored as a function of time after a potential step 0.5 V more positive than E0(RuIII/II). The absorbance decay, upon oxidation, was monitored at a single wavelength and used to calculate the apparent electron diffusion coefficient, Dapp. The reported values are shown in Table 2 and indicate that cross-surface hole hopping for [Ru(dmb)2(dcb)]2+ was about 20 times faster than that for [Ru(dtb)2(dcb)]2+. Quantification of Dapp for [Ru(bpyCF3)2(dcb)]2+ was not possible as this sensitizer displayed almost no evidence of oxidation under the same experimental conditions with a positive applied potential, indicative of slow or completely absent RuIII/II hole hopping. Pulsed 532 nm light excitation of the sensitized films immersed in 0.1 M LiClO4 acetonitrile solution at room temperature resulted in spectral changes consistent with electron transfer and the formation of a charge-separated

Figure 1. Molecular structure of the sensitizers [RuII(4,4′-(R)2bipyridine)2(dcb)]2+, where R = (−CH3) dmb, (−C(CH3)3) dtb, or (bpy-CF3) bpyCF3 and dcb = 4,4′-dicarboxylic acid bipyridine.

The Ru(II) sensitizers were anchored to mesoporous thin films of nanocrystalline TiO2 at saturated surface coverages, Γ ≥ 7 × 10−8 mol/cm2, by overnight submersion in concentrated CH3CN solutions. Sub-percolation surface coverage thin films, Γ < 3 × 10−8 mol/cm2, were obtained by immersion in diluted sensitizer solutions. Note that sub-percolation surface coverages limit the hole mobility across the TiO2 surface through incomplete percolation pathways. Previous literature has demonstrated that the percolation threshold necessary for complete oxidation of all the sensitizers present in the mesoporous thin films is about 60% of the saturation surface

Figure 2. UV−visible absorption spectra of the indicated sensitizers anchored to nanocrystalline TiO2 thin films at sub-percolation and saturation surface coverages immersed in neat CH3CN and 0.1 M LiClO4/CH3CN electrolyte. 2403

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ACS Energy Letters Table 2. Apparent Diffusion Coefficient and Activation Energies kcr (s−1) at 293 K

activation energy, Ea (kJ/mol)b −9

Dapp (×10 TiO2|-Ru(dmb)2(dcb) TiO2|-Ru(dtb)2(dcb) TiO2|-Ru(bpyCF3)2(dcb) a

2

cm /s)

5.3 ± 0.6a 0.24 ± 0.01a −

sub-percolation coverage

saturation coverage

sub-percolation coverage

saturation coverage

23 22.5 22

17 20 22

1.6 × 103 2.7 × 103 2.7 × 103

8.0 × 103 6.0 × 103 2.5 × 103

From ref 17. bValues are Ea ± 1.0 kJ/mol.

Figure 3. (a) Transient absorption data measured at room temperature after pulsed 532 nm laser excitation of the indicated sensitizers at saturation (blue) and sub-percolation (red) surface coverages. The kinetic data was monitored at 460 nm for TiO2|-Ru(dmb)2(dcb) and TiO2|-Ru(dtb)2(dcb) and at 402 nm for TiO2|-Ru(bpyCF3)2(dcb). Overlaid in yellow are fits to the KWW function. Laser energy fluencies were carefully adjusted to ensure the same number of injected electrons per particle, ∼20 TiO2(e−), for experiments at sub-percolation and saturated surface coverages. (b) Representative Arrhenius plot for the averaged charge recombination rate constants under conditions of subpercolation surface coverage (blue) and saturated surface coverage (red). Overlaid are linear fits from which activation energies were abstracted.

state, TiO2(e−)|-S+ (eqs 1 and 2). Electron injection quantum yields were quantified through comparative actinometric methods using a nanocrystalline TiO2 thin film sensitized with Ru(bpy)2(bpy-PO3H2) as the reference actinometer, Φinj = 1.27 For TiO2|-Ru(dmb)2(dcb) and TiO2|-Ru(dtb)2(dcb), the yields were 0.95 and 0.70 respectively, while that of TiO2|Ru(bpyCF3)2(dcb) was 0.50 because of its weaker excited-state reducing power, which lowers the overlap between the Ru excited-state and the electron-acceptor states in the TiO2.28 Excitation irradiances were adjusted to ensure ∼20 TiO2(e−) were present per nanoparticle after pulsed laser excitation for all experiments. This value was chosen as it also represents the average number of TiO2(e−) in dye-sensitized solar cells at operational conditions.29 The kinetic data for charge recombination were quantified through single-wavelength absorption changes monitored at 460 nm for TiO2|-Ru(dmb)2(dcb) and TiO2|-Ru(dtb)2(dcb), while the 402 nm excited-state isosbestic point was chosen for TiO2|-Ru(bpyCF3)2(dcb). Recombination of the injected

electrons, TiO2(e−), with the oxidize sensitizers required micro- to milliseconds to complete and were well-modeled by the Kohlrausch−William−Watts function30 A(t ) = A 0exp[−(kt )β ]

(3)

where β is inversely related to the width of the underlying Lévy distribution of the rate constants, 0 < β < 1; A0 is the initial absorbance; and k is the characteristic observed rate constant. A representative average charge recombination rate constant, kcr, was calculated with eq 4 ⎡ 1 ⎛ 1 ⎞⎤−1 kcr = ⎢ Γ⎜ ⎟⎥ ⎣ kβ ⎝ β ⎠⎦

(4)

where Γ is the Gamma function, and values of β between 0.3 < β < 0.4 provided the best fit. Transient absorption data provided in Figure 3 revealed that charge recombination for TiO2|-Ru(dmb)2(dcb) and TiO2|Ru(dtb)2(dcb) was faster at saturation surface coverages 2404

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an 80° temperature range. Collectively, the data provides compelling evidence that a composite mechanism for charge recombination exists wherein the injected electron and the oxidized sensitizer first form an encounter complex prior to charge recombination. Sensitizers capable of rapid holehopping self-exchange promote encounter complex formation that results in a larger representative kcr value. Lowering the sensitizer surface coverage, or using a sensitizer such as [Ru(bpyCF3)2(dcb)]2+ that does not show hole hopping, increases the barrier for charge recombination and slows this unwanted electron-transfer reaction.

compared to surface coverages below the percolation threshold for hole hopping. This is evident in both the raw experimental data and in the average rate constants abstracted from the KWW model. Large average rate constants for charge recombination at saturation surface coverages have previously been reported10,11 and are consistent with a model wherein rapid hole transfer facilitates formation of an encounter complex between the TiO2(e−) and the oxidized sensitizer. In contrast, the transient data for TiO2|-Ru(bpyCF3)2(dcb) were, within experimental error, the same at both saturated and subpercolation surface coverages, providing strong evidence that hole transport is inhibited for this sensitizer; thus, charge recombination dynamics remain unaffected by the surface coverage conditions. To access further detailed mechanistic information, charge recombination kinetic data were measured over an 80° temperature range. Arrhenius plots based on the calculated kcr are shown in Figure 3b. For all sensitizers, the charge recombination rate increased with temperature. With exception of TiO2|-Ru(bpyCF3)2(dcb), experiments performed at saturation surface coverages showed faster charge recombination over the entire temperature range compared to those with low coverages. Arrhenius analysis of kcr values extracted from eq 4 provided activation energy, Ea, for charge recombination reactions for all three sensitizers under study (Table 2). ln(kcr) = ln(A) −

Ea 1 RT

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EXPERIMENTAL SECTION Materials. All reagents and materials were used as received from the indicated commercial suppliers: acetonitrile (CH3CN; Burdick & Jackson, spectrophotometric grade); lithium perchlorate (LiClO4; Sigma-Aldrich, 99.99%); argon gas (Airgas, > 99.998); titanium(IV) isopropoxide (Sigma-Aldrich, 97%); fluorine-doped SnO2-coated glass (FTO; Hartford Glass Co., Inc., 2.3 mm thick, 15 Ω/□); and glass microscope slides (Fisher Scientific, 1 mm thick). Synthesis. Synthetic producers for all sensitizers investigated herein can be found elsewhere.32,33 Preparations. Transparent mesoporous nanocrystalline TiO2 thin films were prepared as previously described in the literature.32 Sensitization was achieved by immersing the thin films in concentrated (∼mM) acetonitrile sensitizer solutions overnight to yield saturation surface coverages, Γ > 7 × 10−8 mol/cm2. Low surface coverages, Γ < 3 × 10−8 mol/cm2, were obtained by immersing the thin films in diluted sensitizer solutions. Surface coverage conditions were determined using a modified Beer−Lambert law34

(5)

Previous work by Moia et al. combined theoretical models and experimental evidence to demonstrate that dispersive hole transport and spatial inhomogeneity at the sensitizer−semiconductor interface could contribute to the observed charge recombination data.10 The new temperature-dependent recombination data provides the first quantitative test to show how hole transport and charge recombination are linked. When sensitizer surface coverages were below the percolation threshold, hole transport was inhibited and the activation energies were the same within experimental error, Ea = 22.5 ± 0.5 kJ/mol, for all three sensitizers. At saturation surface coverages, the activation energy decreased for those sensitizers capable of hole transport, Ea = 18.5 ± 1.5 kJ/mol. In contrast, for TiO2|-Ru(bpyCF3)2(dcb) that showed no evidence of lateral hole hopping, the activation energies were independent of the sensitizer surface coverage. Hence, the data support the previously proposed model and indicate that lateral selfexchange hole-hopping chemistry directly influences the barrier for charge recombination. Apparent diffusion coefficients reported for Ru(II) sensitizers anchored to TiO2 thin films are generally ∼10−9 cm2/s in acetonitrile electrolyte solution, while diffusion coefficients for electron transport on TiO2 are highly dependent on electron density, 10−8 < Ddiff < 10−4 cm2/s.31 Under the conditions studied in this work, the observation that hole transport influences the observed charge recombination rate constants indicates that the hole diffusion and electron transport are of a similar magnitude. The degree to which the charge recombination activation energy decreases with hole hopping can be understood as the formation of a more favorable encounter complex between the injected electron and the oxidized sensitizer: TiO2(e−) + S+ → TiO2(e−)|-S+ prior to charge recombination. In summary, charge recombination kinetics were measured at saturation and sub-percolation sensitizer surface coverages over

Abs = 1000 × Γ × ε where ε is the molar extinction (absorption) coefficient that was assumed to have the same value when anchored to the surface. Sensitized films were rinsed with neat acetonitrile prior to experimentation. Mesoporous thin films of In2O3:Sn were prepared as described previously.35 Spectroscopy. Steady-state ultraviolet (UV)−visible spectra were obtained on a Varian Cary 60 spectrophotometer at room temperature with sensitized thin films positioned at 45° angle in 1 cm path length quartz cuvettes filled with the desired acetonitrile solutions. Steady-state photoluminescence spectra were obtained with a Fluorolog spectrophotometer (Horiba) at room temperature. The Gibbs free energy stored in the MLCT excited-state, ΔGES, was determined from the photoluminescence onset. Spectroelectrochemistry. Spectroelectrochemical data were performed with an integrated UV−vis spectroelectrochemical system from Pine Research Instrumentation. Briefly, an Avalight Deuterium/Halogen (Avantes) light source was used and the AvaSpec ULS2048 UV−vis (Avantes) was the spectrophotometer. A WaveNow (Pine) potentiostat was used in a electrochemical setup consisting of a standard three-electrode cell with sensitized thin films of In2O3:Sn as the working electrodes, Pt as the counter electrode, and nonaqueous Ag/AgCl as the pseudoreference electrode. Measured applied potentials where converted to the normal hydrogen electrode (NHE) by calibration of the pseudoreference electrode to the ferrocenium/ferrocene half-wave potential (Fe+/0 = +630 mV vs NHE)36 before and after experiments. 2405

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ACS Energy Letters Applied potentials were held for ∼2 min before the UV−vis absorption spectrum was recorded. Concentration curves of the redox species, RuIII and RuII, were analyzed as a function of the applied potential to yield their respective Nernstian redox distribution, from which formal reduction potentials, E0(RuIII/II), were obtained. Note: The highly conductive In2O3:Sn thin films were used for spectroelectrochemical measurements as, unlike TiO2, this material does not require a percolation mechanism for complete sensitizer oxidation. Samples were purged with argon gas for a minimum of 30 min prior to spectroelectrochemical measurements. Transient Absorption. Nanosecond transient absorption measurements were obtained with a previously described apparatus.37 The laser power was adjusted through different measurements to ensure ∼20 electrons were present per TiO2 nanoparticle, TiO2(e−), right after laser excitation. This condition was chosen because it represents the average number of TiO2(e−) in dye-sensitized solar cells at operational conditions.29 Controlled-temperature data were obtained with a liquid nitrogen CoolSpek UV USP-203 four-window cryostat (Unisoku). Relative excited-state electron injection yields were measured by comparative actinometry38,39 on the nanosecond time scale with sensitized TiO 2 thin films of Ru(bpy)2(bpyPO3H2) taken as the reference sample with unity injection efficiency.27 Samples were purged with argon gas for a minimum of 30 min prior to transient absorption measurements.

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Recombination in Dye-Sensitized Nanocrystalline Semiconductors. Coord. Chem. Rev. 2004, 248, 1195−1213. (8) Clifford, J. N.; Palomares, E.; Nazeeruddin, M. K.; Grätzel, M.; Nelson, J.; Li, X.; Long, N. J.; Durrant, J. R. Molecular Control of Recombination Dynamics in Dye-Sensitized Nanocrystalline TiO2 Films: Free Energy vs Distance Dependence. J. Am. Chem. Soc. 2004, 126, 5225−5233. (9) Haque, S. A.; Palomares, E.; Cho, B. M.; Green, A. N. M.; Hirata, N.; Klug, D. R.; Durrant, J. R. Charge Separation versus Recombination in Dye-Sensitized Nanocrystalline Solar Cells: the Minimization of Kinetic Redundancy. J. Am. Chem. Soc. 2005, 127, 3456−3462. (10) Moia, D.; Szumska, A.; Vaissier, V.; Planells, M.; Robertson, N.; O’Regan, B. C.; Nelson, J.; Barnes, P. R. F. Interdye Hole Transport Accelerates Recombination in Dye Sensitized Mesoporous Films. J. Am. Chem. Soc. 2016, 138, 13197−13206. (11) Sampaio, R. N.; Müller, A. V.; Polo, A. S.; Meyer, G. J. Correlation Between Charge Recombination and Lateral HoleHopping Kinetics in a Series of cis-Ru(phen′)(dcb)(NCS)2 DyeSensitized Solar Cells. ACS Appl. Mater. Interfaces 2017, DOI: 10.1021/acsami.7b01542. (12) Gerischer, H. Electrochemical Photo and Solar Cells Principles and Some Experiments. J. Electroanal. Chem. Interfacial Electrochem. 1975, 58, 263−274. (13) Peter, L. M. Dye-Sensitized Nanocrystalline Solar Cells. Phys. Chem. Chem. Phys. 2007, 9, 2630−2642. (14) Scher, H.; Montroll, E. W. Anomalous Transit-Time Dispersion in Amorphous Solids. Phys. Rev. B 1975, 12, 2455−2477. (15) Nelson, J. Continuous-Time Random-Walk Model of Electron Transport in Nanocrystalline TiO2 Electrodes. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 15374−15380. (16) Bonhôte, P.; Gogniat, E.; Tingry, S.; Barbé, C.; Vlachopoulos, N.; Lenzmann, F.; Comte, P.; Grätzel, M. Efficient Lateral Electron Transport inside a Monolayer of Aromatic Amines Anchored on Nanocrystalline Metal Oxide Films. J. Phys. Chem. B 1998, 102, 1498− 1507. (17) Trammell, S. A.; Meyer, T. J. Diffusional Mediation of Surface Electron Transfer on TiO2. J. Phys. Chem. B 1999, 103, 104−107. (18) Wang, Q.; Zakeeruddin, S. M.; Nazeeruddin, M. K.; HumphryBaker, R.; Grätzel, M. Molecular Wiring of Nanocrystals: NCSEnhanced Cross-Surface Charge Transfer in Self-Assembled RuComplex Monolayer on Mesoscopic Oxide Films. J. Am. Chem. Soc. 2006, 128, 4446−4452. (19) Swierk, J. R.; McCool, N. S.; Saunders, T. P.; Barber, G. D.; Mallouk, T. E. Effects of Electron Trapping and Protonation on the Efficiency of Water-Splitting Dye-Sensitized Solar Cells. J. Am. Chem. Soc. 2014, 136, 10974−10982. (20) Brennan, B. J.; Durrell, A. C.; Koepf, M.; Crabtree, R. H.; Brudvig, G. W. Towards Multielectron Photocatalysis: a Porphyrin Array for Lateral Hole Transfer and Capture on a Metal Oxide Surface. Phys. Chem. Chem. Phys. 2015, 17, 12728−12734. (21) DiMarco, B. N.; Motley, T. C.; Balok, R. S.; Li, G.; Siegler, M. A.; O’Donnell, R. M.; Hu, K.; Meyer, G. J. A Distance Dependence to Lateral Self-Exchange Across Nanocrystalline TiO2. A Comparative Study of Three Homologous RuIII/II Polypyridyl Compounds. J. Phys. Chem. C 2016, 120, 14226. (22) Ardo, S.; Meyer, G. J. Direct Observation of Photodriven Intermolecular Hole Transfer across TiO2 Nanocrystallites: Lateral Self-Exchange Reactions and Catalyst Oxidation. J. Am. Chem. Soc. 2010, 132, 9283−9285. (23) Ardo, S.; Meyer, G. J. Characterization of Photoinduced SelfExchange Reactions at Molecule−Semiconductor Interfaces by Transient Polarization Spectroscopy: Lateral Intermolecular Energy and Hole Transfer Across Sensitized TiO2 Thin Films. J. Am. Chem. Soc. 2011, 133, 15384−15396. (24) Hu, K.; Meyer, G. J. Lateral Intermolecular Self-Exchange Reactions for Hole and Energy Transport on Mesoporous Metal Oxide Thin Films. Langmuir 2015, 31, 11164−11178.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Gerald J. Meyer: 0000-0002-4227-6393 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge support from the National Science Foundation award CHE-1213357.

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REFERENCES

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