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Dispersive Electron-Transfer Kinetics of Rhodamines on TiO2: Impact of Structure and Driving Force on Single-Molecule Photophysics Jenna A. Tan, John T. Rose, James P. Cassidy, Simran K. Rohatgi, and Kristin L. Wustholz* Department of Chemistry, The College of William and Mary, P.O. Box 8795, Williamsburg, Virginia 23187, United States S Supporting Information *

ABSTRACT: The effects of dye structure, driving force of photoinduced electron transfer, and adsorption affinity on the dispersive electron-transfer dynamics of rhodamines on TiO2 films are investigated using single-molecule microscopy. The time-dependent emission (i.e., blinking dynamics) of rhodamine-sensitized TiO2 films are quantified using maximum likelihood estimation (MLE) and quantitative goodness-of-fit tests based on the Kolmogorov−Smirnov (KS) statistic to determine the best fit to the photophysical data. Although the observation of significant p-values (i.e., ranging from 0.16 to 0.53) seems to support the power-law model for the on-time distributions, only a minor subset of the data are actually represented by power laws (i.e., ∼15−20% of events). Instead, the MLE/KS analysis reveals that log-normal distributions, not power laws, most closely represent the entire on-time and off-time distributions for RB, R6G, R123, and 5-ROX on TiO2. Monte Carlo simulations based on the Albery model for dispersive electron transfer (i.e., activation barriers to electron transfer are Gaussian distributed) demonstrate that the log-normal fit parameters (i.e., μon/off and σon/off) are dependent on the average rate constants for injection and recombination as well as the extent of energetic dispersion about the mean activation barrier. The single-molecule results for RB, R6G, R123, and 5-ROX on TiO2 are interpreted in the context of ensemble-averaged spectroscopic and electrochemical characterization and suggest that heterogeneity in electronic coupling and reorganization (i.e., static and dynamic disorder) play a decisive role in the observed dispersive kinetics.

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semiconductor.16,28,29 The observation of power-law distributed emissive (“on”) and nonemissive (“off”) events is consistent with so-called dispersive kinetics, where the rate constants for dark-state population and depopulation (i.e., injection and charge recombination) are distributed.21,30 Although power laws and the power-law exponent are often used to interpret single-molecule results,21,30−42 data that are qualitatively fit by power laws on log-log axes may not actually be power-law distributed.43−47 For example, we recently used single-molecule blinking measurements in combination with rigorous statistical analyses based on maximum likelihood estimation (MLE) and Kolmogorov−Smirnov (KS) tests to interpret the dispersive electron-transfer dynamics of rhodamine B (RB) and rhodamine 6G (R6G) on TiO2.47 Using this approach, we demonstrated that power laws fit only a portion of the ontime distributions and that corresponding off-time distributions are log-normally distributed. These observations were reproduced using Monte Carlo simulations based on the Albery model48 for dispersive electron-transfer kinetics (i.e., where the activation barriers to electron transfer are normally distributed).

INTRODUCTION As global energy demands continue to rise, the need for inexpensive and sustainable energy sources is escalating.1,2 Dyesensitized solar cells (DSSCs) containing nanocrystalline TiO2 decorated with chromophore sensitizers represent one promising strategy for solar energy conversion.3−5 Upon photoexcitation of the sensitizer (e.g., organic and inorganic dyes), electrons are injected from the molecular excited state into the conduction band or energetically accessible surface states of the semiconductor. Dyes are then regenerated by electron donation from an electrolyte or through back electron transfer from TiO2. Although the interfacial electron-transfer dynamics of dyes on nanocrystalline TiO2 films have been measured for many systems, the reported kinetics are complex and multiphasic.6−14 The origins of these kinetic inhomogeneities are difficult to decipher using ensemble-averaged approaches, because nanoscale spatial and temporal heterogeneity as well as molecular aggregation are operative. Therefore, recent studies have focused on single-molecule measurements of interfacial electron transfer to understand the complex electron-transfer dynamics occurring in DSSCs.15−29 For example, single-molecule studies of porphyrin sensitizers on nanocrystalline TiO2 films have demonstrated that the temporal duration of nonemissive events are fit by power laws, with power-law exponents that vary with sensitizer and © XXXX American Chemical Society

Special Issue: Richard P. Van Duyne Festschrift Received: February 25, 2016 Revised: April 1, 2016

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DOI: 10.1021/acs.jpcc.6b01960 J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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EXPERIMENTAL SECTION Bulk Characterization. Solution ultraviolet/visible (UV/ vis) and fluorescence measurements were performed on PerkinElmer Lambda 35 and PerkinElmer LS-55 spectrophotometers, respectively. UV/vis reflectance measurements of dyes on TiO2 anatase (Acros Organics, 98+%) films on glass slides (Fisher) were performed on a Cary 60 spectrophotometer equipped with a fiber-optic coupler and diffuse reflectance probe. Titania films on glass were immersed in 10−4 M solutions of the dyes in acetonitrile for 12 h and rinsed thoroughly with acetonitrile prior to absorbance measurements. The absorbance from dyed films was measured after repeated rinsing and soaking in acetonitrile over 72 h periods to ensure that residual unbound dyes were removed from the films. Electrochemical measurements (CH Instruments 620D) were performed in analytical grade acetonitrile (Sigma-Aldrich) with 0.1 M tetrabutylammonium hexafluorophosphate (TBAPF6) electrolyte in a standard three-electrode cell, with a standard calomel reference electrode (SCE). Platinum working and auxiliary electrodes were thoroughly polished with 0.5 μm alumina powder paste on a cloth-covered polishing pad and then rinsed with water and acetonitrile before each scan. Samples were degassed for 10 min with Ar prior to cyclic voltammetry (CV) measurements. Potentials were scanned between −1 and 2 V vs SCE at a scan rate of 200 mV/s. Ferrocene was used as an internal standard (i.e., observed at 389 mV vs SCE as compared to the expected value at 400 mV vs SCE in acetonitrile). Sample Preparation. RB (99+%), R6G (99%), and R123 (99+%) were used as received from Acros Organics. 5-ROX (5carboxy-X-rhodamine, triethylammonium salt) was obtained from ThermoFisher Scientific. Titanuim isopropoxide (98+%), isopropanol, and hydrochloric acid were used as received from Sigma-Aldrich. Deionized water (18.2 MΩ cm) was obtained using a water purification system (ThermoScientific, EasyPure II). Glass coverslips (Fisher Scientific, 12-545-102) were cleaned in a base bath for 24 h, thoroughly rinsed with deionized water, and dried using clean dry air (McMaster Carr, filter 5163K17). Colloidal suspensions of anatase TiO2 nanoparticles were synthesized by the hydrolysis of titanium isopropoxide.52 Briefly, 2 mL of titanium isopropoxide in isopropanol was slowly injected into 20 mL of acidified water (pH ∼1.5, adjusted with HCl). The resulting colloidal suspension exhibited an absorbance maximum at approximately 280 nm. All dye solutions were prepared in deionized water using base-treated glassware. For single-molecule measurements on bare glass, samples were prepared by spin-coating 35 μL of a 10−9−10−10 M dye solution onto a clean coverslip using a spin coater (Laurell Tecnhologies, WS-400-6NPP-LITE) operating at 3000 rpm. For single-molecule measurements on TiO2, 100 μL of ∼10−9 M dye solution was diluted to a final concentration of ∼10−10 M with 900 μL of colloidal TiO2 (∼500 mg/L). A 35 μL aliquot of the resulting 10−10 M dye/ TiO2 solution was spin-coated on a clean glass coverslip at 3000 rpm. The resulting samples were mounted in a customdesigned flow cell for environmental control and flushed with dry N2 throughout the single-molecule experiments. Single-Molecule Confocal Microscopy. Samples for single-molecule studies were placed on a nanopositioning stage (Queensgate, NPS-XY-100B or Physik Instrumente LP E545) atop an inverted confocal microscope (Nikon, TiU). Laser excitation at 532 nm (Spectra Physics, Excelsior) was focused

These results demonstrated that power laws are not a universal feature of single-molecule emission on TiO2 and motivated additional questions about the significance of the log-normal distribution and its associated fit parameters. In particular, how are changes to the underlying electron-transfer kinetics (e.g., with driving force or binding to TiO2) manifested in the observed log-normal distributions? To address this question, the present study investigates single-molecule interfacial electron-transfer kinetics for a series of rhodamine dyes (Figure 1) with varying structure, driving

Figure 1. Chemical structures and normalized ensemble-averaged absorbance spectra of R123 (green), R6G (black), RB (red), and 5ROX (blue) measured in water.

forces for photoinduced electron transfer, and adsorption affinities to TiO2. Both RB and 5-carboxy-X-rhodamine (5ROX) possess carboxyl groups for potential binding to TiO2, but 5-ROX has a carboxyl group at the para position relative to the xanthylium backbone, which is expected to increase accessibility for binding relative to the ortho-substituted carboxyl group in RB. R6G and rhodamine 123 (R123) do not possess carboxyl groups for binding to TiO2 but are expected to exhibit different driving forces (i.e., Gibbs energy of photoinduced electron transfer) and steric interactions with the TiO2 surface. Using a combination of ensemble-averaged studies as well as single-molecule blinking measurements with MLE/KS analysis, we investigate the impact of chromophore structure, driving force, and adsorption to TiO2 on the dispersive electron-transfer dynamics of RB, 5-ROX, R6G, and R123 on TiO2. The impact of underlying kinetics on the log-normal fit parameters is investigated using Monte Carlo simulations that provide insight into the origin of log-normal behavior as well as the associated fit parameters. B


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probability of excitation (i.e., P1 = k12t) exceeds a random number. An emission event occurs if the random number exceeds the fluorescence quantum yield, Φf = k21/(k21 + k23), in which case a count is added to the macroscopic (i.e., 10 ms) time bin. Simulated fluorescence intensity trajectories were analyzed using thresholding, consistent with previous work.47 All data analyses, fitting procedures, and Monte Carlo simulations were performed in Matlab (version R2015b) with custom code.

to a diffraction-limited spot using a high numerical aperture (NA) 100× oil-immersion objective (Nikon Plan Fluor, NA = 1.3). Excitation powers (Pexc) of ∼1 μW and ∼5 μW at the sample were used for single-molecule measurements on glass and TiO2, respectively. Epifluorescence from the sample was collected through the objective, spectrally filtered using an edge filter (Semrock, LP03−532RS-2S), and focused onto an avalanche photodiode detector (APD) with a 50 μm aperture (MPD, PDM050CTB) to provide confocal resolution. A custom LabView program was used to control the nanopositioning stage in 100 nm steps and collect emission. A z-axis microscope lock (Applied Science Instruments, MFC-2000) was used to maintain the focal plane of the objective during raster scans. Single-molecule emission was established based on the observation of diffraction-limited spots, irreversible singlestep photobleaching, and concentration dependence of the diffraction-limited spot density. The number density of molecules (i.e., ∼10 molecules per 100 μm2) was equivalent for 10−10 M dye spun coat on TiO2 as well as bare glass, demonstrating that single-molecule studies on TiO2 probed the majority of molecules. Blinking dynamics were acquired using a 10 ms integration time for ∼200 s or until the single-step photobleaching event occurred. The blinking dynamics of RB, R6G, R123, and 5-ROX on glass were measured and analyzed as a control. Consistent with previous work,47 the on-time and off-time distributions for rhodamines on glass are modified with respect to the TiO2 data in terms of the probability distribution functions that best represent the data as well as corresponding fit parameters (Supporting Information). Blinking Analysis and Monte Carlo Simulations. Blinking dynamics were analyzed using the change-point detection (CPD) method,49,50 which reports statistically significant intensity change points as well as the number and temporal durations for up to 30 intensity levels. The first and last events were disregarded because they are artificially set by the observation period. The lowest deconvolved intensity state is designated as nonemissive (off). Deconvolved states with intensities greater than one standard deviation above the rms noise (i.e., ∼20% of the maximum emission intensity) are denoted as emissive (on). Throughout the paper, the temporal durations of statistically significant emissive and nonemissive intensity levels are termed on times and off times, respectively. Consistent with previous studies,44,46,47 the experimental ontime and off-time distributions are converted into complementary cumulative distribution functions (CCDFs) that describe the probability of an event occurring in a time greater than or equal to t according to CCDF = 1− (1/N) ∑iti ≤ t. For clarity, we use the term probability distribution for CCDF throughout the paper. The fit parameters and corresponding goodness-of-fit between the experimental CCDFs and the proposed functional forms (i.e., power law, log-normal, Weibull) are quantified using MLE and the KS statistic (i.e., p value) as described in detail elsewhere.43,47 Standard errors in the fit parameters are determined by calculating the inverse of the Hessian matrix (i.e., the second derivative of the loglikelihood with respect to the parameters).43 Blinking dynamics were simulated by generating population trajectories. In particular, consistent with previous studies,21,47,51 a random number is compared to the probability of leaving the occupied electronic state (i.e., Pi = ∑jkijt, where t is the 1 ns computational time step and kij is the rate constant for the transition from state i to state j). For example, excitation from the ground state to the singlet excited state occurs if the

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RESULTS AND DISCUSSION Ensemble-Averaged Photophysics and Electrochemistry of Rhodamines. The absorbance spectra of R123, R6G, RB, and 5-ROX in aqueous solution demonstrate single maxima at 500, 526, 554, and 578 nm, respectively (Figure 1). Corresponding ensemble-averaged fluorescence studies demonstrate the dyes exhibit Stokes shifts of ∼22 nm in solution (Supporting Information). To probe the extent of molecular adsorption to TiO2, we measured the diffuse reflectance spectra of rhodamine dyes on titania films. For these studies, TiO2 films on glass were immersed in solutions containing 10−4 M dye and thoroughly rinsed with acetonitrile prior to measurement. The resulting absorbance spectra of R123, R6G, RB, and 5-ROX on TiO2 demonstrate relatively broad maxima at approximately 515, 520, 520, and 575 nm, respectively (Figure 2). R6G and

Figure 2. Normalized absorbance spectra of (a) 5-ROX (blue), (b) RB (red), (c) R123 (green), and (d) R6G (black) in solution (solid lines) and adsorbed to nanocrystalline TiO2 films (dashed lines). 5-ROX and RB adsorb to TiO2 and exhibit hypsochromic shifts and broadening relative to solution, consistent with the formation of dye aggregates on TiO2.52,56−58 R123 and R6G do not adsorb or aggregate significantly on TiO2.

R123 on TiO2 exhibit modest maximum absorbance (Amax) values of 0.10 and 0.17, respectively, consistent with poor adsorption to TiO2 due to the absence of carboxyl groups that promote binding. R123 exhibits slightly more adsorption to TiO2 relative to R6G, which may be related to steric considerations (i.e., R123 has less steric bulk than R6G). In contrast, both carboxyl-containing RB and 5-ROX exhibit persistent absorbance on TiO2 after repeated rinsing, as evidenced by Amax values of 0.68 and 1.0, respectively. These observations are consistent with the fact that 5-ROX has a carboxyl group at the para position relative to the xanthylium backbone, which results in increased accessibility for binding C


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1.52 ± 0.01, − 1.71 ± 0.03, and −1.52 ± 0.01 eV, respectively.64 Figure 3 presents an energy level diagram that

relative to the ortho-substituted RB.52 Ultimately, the data in Figure 2 demonstrate that the relative adsorption to TiO2 decreases as follows: 5-ROX > RB > R123 > R6G. The absorbance spectra of 5-ROX and RB on TiO2 also exhibit hypsochromic shifts and significant broadening relative to solution. For example, the absorbance spectra of 5-ROX in solution and on TiO2 exhibit main absorbance peaks at approximately 575 nm, corresponding to full width at halfmaximum (fwhm) values of 36 and 143 nm, respectively. The absorbance peak at 554 nm for RB in solution (fwhm = 31 nm) is blue-shifted by >30 nm and broadened upon adsorption to TiO2 (i.e., fwhm = 93 nm). Although previous studies have demonstrated hypsochromic shifts due to the photodegradation of RB in suspensions of semiconductor particles (i.e., CdS, TiO2),53,54 substantial spectral shifts were observed only after several hours of continuous visible-light illumination. Here, the dye-sensitized films were prepared and stored in the dark. Previous studies of chalcogenorhodamine dyes have demonstrated the controlled formation of H-aggregates on TiO2 by tuning chromophore structure and anchoring mode (e.g., the position of carboxylic and phosphonic acid anchors relative to the xanthylium backbone).52,55−57 For example, chalcogenorhodamines with 3-thienyl-2-carboxy groups adsorbed in amorphous monolayers to TiO2, consistent with the steric influence of the 2-carboxy group to prevent coplanarity and H aggregation. In contrast, 2-thienyl-5-carboxy-substituted dyes exhibited H aggregation, because the 5-carboxy group has little steric impact on the xanthylium backbone and enables coplanarity of the dyes.56,58 Therefore, the formation of Haggregates (i.e., from plane-to-plane π stacking) on TiO2 represents a more plausible explanation for the observation of blue-shifted and broadened absorbance for 5-ROX and RB on TiO2 relative to solution.13,59,60 Although aggregation does not play a role in molecular photophysics at single-molecule concentrations, the preferential orientation of dyes on TiO2 is expected to play a role in electron-transfer dynamics. The absorbance spectra of R123 and R6G are relatively unchanged upon adsorption to TiO 2, consistent with amorphous adsorption of dye monomers to TiO2. To estimate the driving force of photoinduced electron transfer (ΔG) for R123, R6G, RB, and 5-ROX on TiO2, the redox potentials of the dyes in solution were measured using cyclic voltammetry (CV). R123, R6G, RB, and 5-ROX exhibit oxidation potentials at 1.05 ± 0.03, 1.03 ± 0.01, 1.22 ± 0.03, and 1.03 ± 0.01 V vs SCE, respectively, with the error corresponding to the standard deviation from the mean, consistent with previous CV measurements of rhodamines by Park and Bard.61 The driving force for electron injection is estimated using the equation for the Gibbs energy of photoinduced electron transfer:62 ΔG = Eox (D/D+) − Ered(A /A−) − E00

Figure 3. Energy level diagram showing the ensemble-averaged driving forces for electron injection and recombination for rhodamine dyes on TiO2. Driving forces (ΔG) for electron transfer are estimated from the oxidation potentials of the dyes in solution and their corresponding singlet energy (E00) values. RB, red; R6G, black; R123, green; and 5ROX, blue.

summarizes the estimated driving forces for electron injection and recombination. Ultimately, the ensemble-averaged characterization of R123, R6G, RB, and 5-ROX demonstrates that the dyes exhibit a range of driving forces for electron transfer as well as a distribution of adsorption geometries on TiO2. Single-Molecule Photophysics of Rhodamines on TiO2. To probe the impact of chromophore structure, energetics, and surface adsorption on the dispersive electrontransfer kinetics of rhodamine dyes on TiO2, the blinking dynamics of ∼100 molecules of R123, R6G, RB, and 5-ROX were measured and compiled into on-time and off-time probability distributions (i.e., CCDFs).44,47 Figure 4 presents the resulting on-time and off-time probability distributions for 91, 141, 70, and 150 molecules of R123, R6G, RB, and 5-ROX, respectively, on TiO2. The event-duration distributions are broad and peaked at short times. For example, the on-time distribution for 5-ROX on TiO2 contains 555 events, with individual values ranging from 0.02 to 42.36 s and an average on time of 1.82 s (Figure 4a). The corresponding off-time distribution for 5-ROX/TiO2 contains 327 events, with an average off time of 18.52 s and individual values ranging from 0.05 to 138.26 s (Figure 4b). Identifying the functional forms of the on-time and off-time distributions is critical to establish the physical mechanism that is responsible for blinking. For example, previous single-emitter studies on TiO2 have observed power-law distributions, consistent with a dispersive-kinetics model wherein the energy barriers to electron transfer are exponentially distributed.65 Marcus and co-workers also demonstrated that the power laws observed in single-molecule measurements on TiO2 are reproduced using a reaction-diffusion mechanism.31,32 However, several studies have also shown that single-emitter data, which appear to follow a power law on log−log axes using leastsquares fitting, may not actually be power-law distributed.44,46,47 For example, although the dispersive electrontransfer recombination dynamics of RB and R6G on TiO247 are qualitatively fit by power laws, MLE/KS analysis revealed the data is log-normally distributed, consistent with the Albery model48 for electron transfer (i.e., where the activation barriers

(1)

+

In eq 1, Eox(D/D ) is the oxidation potential of the donor, Ered(A/A−) the reduction potential of the acceptor (i.e., −0.49 V vs SCE for TiO2),63 and E00 the singlet energy of the fluorophore, which is obtained from the intersection of the normalized aqueous absorption and fluorescence spectra of the dye in TiO2.62 Using this equation, the driving forces of photoinduced electron injection for R123, R6G, RB, and 5ROX to TiO2 were found to be −0.88 ± 0.03, − 0.78 ± 0.01, − 0.47 ± 0.03, and −0.56 ± 0.01 eV, respectively. Corresponding driving forces for charge recombination from TiO2 to the HOMO of R123, R6G, RB, and 5-ROX are −1.54 ± 0.03, − D


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tial)43 distributions. For example, the power law (i.e., P(t) = At−α), is normalized from the onset time for power-law behavior (tmin) to yield P(t ) =

−α α − 1⎛ t ⎞ ⎟ , ⎜ tmin ⎝ tmin ⎠

α>1 (2)

MLE is used to determine the power-law exponent (α), and tmin is determined using the KS test. The corresponding goodnessof-fit is determined using a KS test, which quantifies the distance between the empirical data and hypothesized model in a p-value.43 For example, if p = 0, the empirical data and the model are fundamentally different. A statistically-insignificant pvalue of R6G > R123 > 5-ROX (i.e.,−μon is equal to 1.90 ± 0.05 for RB, 1.52 ± 0.05 for R6G, 1.18 ± 0.09 for R123, and 0.96 ± 0.06 for 5-ROX). The average rate constant for recombination decreases according to RB > R6G > 5-ROX > R123 (i.e., −μoff is −0.70 ± 0.13 for RB, −1.09 ± 0.07 for R6G, −1.7 ± 0.1 for 5-ROX, and −2.2 ± 0.1 for R123). Comparison of the σ values in Table 1 demonstrates that the energetic dispersion is largest for 5-ROX and smallest for RB. What is the physical interpretation of these results? According to Marcus theory, the rate constant for electron transfer is dependent on the driving force of photoinduced electron transfer (ΔG) and the reorganization energy (λ) between reactant and product states: G


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The Journal of Physical Chemistry C ⎡ −ΔG‡ ⎤ ⎡ −(ΔG + λ)2 ⎤ o ⎥ k = A exp⎢ ⎥ = A exp⎢ ⎢⎣ kBT ⎥⎦ 4λkBT ⎦ ⎣

for amorphous adsorption to TiO2 (i.e., for R6G and R123) relative to preferential adsorption (i.e., for 5-ROX) suggests that binding to TiO2 through the para-carboxyl group introduces additional kinetic dispersion (e.g., in electronic coupling29 and reorganization energy83). The observation that RB exhibits relatively low σon/off values that are closest to those for R6G suggests that (1) at single-molecule concentrations RB exhibits nearly amorphous adsorption to TiO2 or (2) binding to TiO2 through the ortho-carboxyl group does not introduce a significant amount of kinetic dispersion. Because the on-time and off-time distributions for individual molecules on TiO2 are log-normally distributed (Supporting Information), dynamic disorder may play a significant role in the observed dispersion. Altogether, the combination of single-molecule studies with robust MLE/KS analysis, Monte Carlo simulations, and ensemble-averaged measurements demonstrates that the lognormal distributions, which report on the dispersive injection and recombination dynamics on TiO2, are dependent on chromophore structure, driving force, and adsorption affinity on the semiconductor surface. Our results also suggest that further experimental and theoretical studies are necessary to investigate the specific roles of dispersive reorganization energy and electronic coupling on the on-time and off-time distributions.

(4)

where A is a pre-exponential factor that depends on the electronic coupling between initial and final states as well as the density of unoccupied acceptor states.75 In other words, the average activation energy for electron transfer (ΔG‡o) can be −(ΔG + λ)2

). Table expressed in terms of ΔG and λ (i.e., ΔGo‡ = 4λ 2 summarizes the ensemble-averaged driving forces for electron injection and recombination alongside the −μ on/off and σon/off values obtained from single-molecule measurements. Comparison of ΔG and −μon/off values in Table 2 suggests that differences in the electronic coupling and reorganization energy play a decisive role in the electron-transfer kinetics for this series of dyes on TiO2. For example, although RB demonstrates the smallest driving force for electron injection (i.e., ΔGinj = −0.47 eV), single-molecule data reveal that RB/TiO2 exhibits the largest average rate constant for injection (i.e., −μon = ln (kon) = 1.90). Corresponding single-molecule studies of RB, R6G, 5-ROX, and R123 on glass demonstrate that the average injection rate (i.e., relative −μon value) is smaller for molecules on glass relative to TiO2 (Supporting Information), consistent with a decrease in driving force for electron injection to glass as compared to TiO2. The estimated driving force for charge recombination is equivalent within error for R6G, 5-ROX, and R123, but corresponding charge recombination kinetics are distinct (Table 2). These observations are consistent with previous studies of Re- and Ru- complexes on TiO2 that demonstrated charge recombination dynamics are independent of driving force.7,76,77 The hypothesis that electronic coupling and reorganization energy are different for this series of rhodamine dyes on TiO2 is consistent with the observation that carboxyl-containing 5-ROX and RB adsorb appreciably to TiO2 but R123 and R6G do not (Figure 2). For example, previous studies have demonstrated that introducing spacers between a surface anchor (e.g., carboxyl group) and dye sensitizer results in a dramatic decrease in the injection and recombination rate constants, consistent with a reduction in electronic coupling.78,79 Reorganization energy is also dependent on the distance between donor and acceptor as well as binding motif.75,80−82 These observations suggest that it is necessary to account for differences in driving force, reorganization energy, and electronic coupling to accurately model the single-molecule photophysics of rhodamines on TiO2. The dispersion in electron-transfer kinetics (i.e., σon/off) is also modified with sensitizing molecule (Table 2). For example, 5-ROX/TiO2 exhibits the most dispersion in electron-transfer rates, consistent with the highest σon/off values (i.e., σon = 1.48 and σoff = 1.77). Ensemble-averaged measurements indicate that kinetic dispersion is related to the presence of various dye−surface attachments (i.e., through the ortho- and paracarboxyl groups) and therefore a corresponding distribution of rate constants for electron transfer. Whereas 5-ROX has two carboxyl groups for potential binding to TiO2, RB possesses one carboxyl group at a relatively sterically-hindered location. Thus, RB is expected to exhibit less site-to-site heterogeneity than 5-ROX/TiO2, consistent with the observed σon/off values for RB/TiO2 of σon = 1.25 and σoff = 1.56. Interestingly, R6G and R123 exhibit intermediate values for σon/off, demonstrating the contribution to kinetic dispersion due to unspecific adsorption to TiO2. The observation of smaller σon/off values

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CONCLUSION We have used single-molecule spectroscopy to probe the interfacial electron-transfer kinetics of a series of rhodamine dyes that exhibit a range of driving forces for electron transfer as well as adsorption geometries on TiO2. Our results reveal several new insights about the dispersive electron-transfer kinetics of single molecules on TiO2. Although the on-time distributions are indeed power-law distributed above onset times of ∼1 s or longer, for a majority of the data the power-law hypothesis is rejected. Instead, log-normal distributions most closely represent the complete on-time and off-time distributions for RB, R6G, 5-ROX, and R123, on TiO2. Furthermore, the log-normal fit parameters are dependent on the chromophore sensitizer. Monte Carlo simulations based on the Albery model demonstrate that −μon/off is proportional to the average rate constants for injection and recombination, respectively, and values for σon/off are proportional to the extent of energetic dispersion about the mean activation barrier. Altogether, these results demonstrate that the average injection rate constant decreases as follows: RB > R6G > R123 > 5-ROX. The average rate constant for recombination decreases according to RB > R6G > 5-ROX > R123. Energetic dispersion is largest for 5-ROX and smallest for RB. Our results suggest that dispersion in the electronic coupling and reorganization energy (both static and dynamic) plays a decisive role in the electron-transfer kinetics for this series of dyes on TiO2. These observations motivate further experimental and Monte Carlo simulation studies to examine the impact of dispersive electronic coupling and reorganization energy on the on-time and off-time distributions.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b01960. Best-fit parameters and p-values for Weibull distributions as well as rhodamines on glass; ensemble-averaged H


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fluorescence of rhodamines; on- and off-time distributions for an individual molecule on TiO2 (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Tel.: (757) 221-2675. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Acknowledgement is made to the donors of the American Chemical Society Petroleum Research Fund (50873-UNI6) and to the Research Corporation (MI-CCSA #22491) for support of this research. We thank the NASA Virginia Space Grant Consortium for support of this project through Undergraduate Research Scholarships to J.T.R. The Charles Center at the College of William and Mary provided summer funding for J.A.T. through Monroe and Honors fellowships. We thank Wanji Zhang and Prof. William McNamara at the College of William and Mary for assistance with diffuse reflectance and CV measurements as well as helpful discussions. This work was performed in part using computational facilities at the College of William and Mary, which were provided with the assistance of the National Science Foundation, the Virginia Port Authority, Sun Microsystems, and Virginia’s Commonwealth Technology Research Fund. We thank Eric J. Walter for helpful discussions about computations on the SciClone cluster.

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