Generation of Long-Lived Redox Equivalents in Self-Assembled

Feb 27, 2017 - The resulting photocathode and its nanostructured indium–tin oxide analog absorb visible light and convert it into injected holes wit...
0 downloads 12 Views 1MB Size
Download PDF
Article pubs.acs.org/JPCC

Generation of Long-Lived Redox Equivalents in Self-Assembled Bilayer Structures on Metal Oxide Electrodes Bing Shan, Byron H. Farnum,† Kyung-Ryang Wee,‡ and Thomas J. Meyer* Department of Chemistry, The University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, United States S Supporting Information *

ABSTRACT: We report on the synthesis and photophysical properties of a photocathode consisting of a molecular bilayer structure self-assembled on p-type NiO nanostructured films. The resulting photocathode and its nanostructured indium−tin oxide analog absorb visible light and convert it into injected holes with injection yields of ∼30%, measured at the first observation time by nanosecond transient absorption spectroscopy, and long-lived reducing equivalents that last for several milliseconds without applied bias. An initial quantum yield of 15% was achieved for photogeneration of the reduced dye on the p-NiO electrode. Nanosecond transient absorption experiments and detailed analyses of the underlying electron transfer steps demonstrate that the overall efficiency of the cell is limited by hole injection and charge recombination processes. Compared with the highly doped indium−tin oxide photocathode, the NiO photocathode shows superior photoconversion efficiencies for generating reducing equivalents and longer lifetimes of surface-bound redox-separated states due to an inhibition toward charge recombination with the external assembly.

■

We describe here the application of a “donor−dye” bilayer structure to explore the assembly motif for controlling electron transfer on NiO surfaces. The structure of the assembly is shown in Figure 1. It was investigated on the surfaces of NiO and nanoITO electrodes for interfacial electron transfer processes and on a ZrO2 surface for intra-assembly electron transfer steps without the complication from charge injection.32

INTRODUCTION Photocathodes have been proposed that could be used with conventional TiO2-based photoanodes1−4 to split water5−8 with enhanced photocurrents by minimizing internal kinetic losses.5,9−14 The efficiencies of most tandem devices are usually very low due to limitations on the photocathode side, where rapid charge recombination thermalizes the energy stored in the photogenerated electron/hole pairs.5−8 In order to prolong the lifetime of redox-separated (RS) states, efforts have been made mainly to lengthen the distance between the RS centers.9,15−19 Relatively long-lived RS states in the dyesensitized photocathodes only last for tens of microseconds,16,20 on time scales far more rapid than their counterpart photoanodes, which limits their performances in dye-sensitized photoelectrochemical cells. We have taken a different approach to control the structure by using bilayer/trilayer assemblies attached to metal oxide surfaces through phosphonate surface bonding.21−26 The assemblies consist of appropriate organic donors and acceptors linked by ZrIV−phosphonate bridges, which also provide separation between sites as a way to control intersite electron and energy transfer dynamics. The facile bonding of ZrIV− phosphonate was initially investigated by Mallouk et al. and further developed by other groups for formation of layer-bylayer functional assemblies/films.27−31 In a recent report, we described a family of “acceptor−dye−donor” trilayer assemblies on nanostructured ITO films (nanoITO) with site-to-site distance approaching 60 Å.26 They were remarkable in demonstrating an approach for preparing long-lived, molecular RS states with lifetimes of several seconds on the photoanode side and milliseconds at the analogous photocathode side.26 © XXXX American Chemical Society

Figure 1. Structure of the “donor−dye” bilayer assembly on the surfaces of mesoporous NiO, nanoITO, and ZrO2 with [RuII(4,4′(PO3H2)2-2,2′-bipyridine)2(2,2′-bipyridine)]2+ as the light absorber and the dianiline electron donor. Blue arrows show the direction of hole transfer after light excitation of the dye. Asterisks indicate chloride or aquo ligands coordinated to the ZrIV center. Received: December 9, 2016 Revised: February 21, 2017 Published: February 27, 2017 A

DOI: 10.1021/acs.jpcc.6b12416 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

DA and MOX|-RuP22+ were prepared by using the same conditions as described above. Surface Loading. RuP22+ on MOX Films. Surface coverages (Γ in mol/cm2) of RuP22+ were evaluated by UV−vis absorption measurements on an Agilent 8453 UV−visible photodiode spectrophotometer with spectra recorded in pH 1 aqueous solutions. Γ(RuP22+) was estimated from Γ = ΔA465 nm/(ε465 nm × 1000) with ε465 nm = 16 800 M−1 cm−1 determined from the solution spectrum of RuP22+ in pH 1 aqueous solution. DA on MOX Films. For DA on nanoITO and NiO films, in double-step chronocoulometry experiments, a potential step at 1.1 V vs NHE, past the two-electron oxidation of DA, at E(DA2+/0) = 0.56 V in acetonitrile vs Ag/AgCl,26 was held until the oxidation was complete, followed by a reverse step at 0 V. Data were analyzed by using Anson plots of the charges passed versus t1/2 for the forward and reverse steps.38 Background charges were evaluated from the film samples without DA and were subtracted from the total charges of the DA samples. Surface coverages of DA were calculated from the charges of the two-electron oxidation of DA. Samples were purged with N2 for at least 30 min prior to experimentation. Surface coverages of DA on ZrO2 films (mol/cm2) were evaluated according to Γ(DA) = Γb(RuP22+)/r, where r is the ratio Γ′b(RuP22+)/Γ′(DA), determined with nanoITO samples. Since Γ(RuP22+) is always larger than Γ(DA) on the electrodes investigated, there is a small amount of RuP22+ molecules loaded on surface particles that are not linked through DA−Zr bridges. Γb(RuP22+) is the amount of bridged RuP22+ on ZrO2 samples, which was determined by a coloading method. UV−vis absorption spectra of the samples MOX|-DA-ZrRuP22+ (MOX: NiO, nanoITO, ZrO2) are shown in Figure S1 and S2 of the Supporting Information (SI) with surface coverages of RuP22+ and DA listed in Table 1. The margin of error of the three sets of parallel data was less than 15%. From the data, the ratio of DA to RuP22+ is close to 1:1 with a slight excess of RuP22+

The bilayer structure was self-assembled in a sequence of stepwise loadings of a dianiline electron transfer donor (DA), a ZrIV bridge, and a ruthenium(II) polypyridyl chromophore (RuP22+) on the metal oxide films. The lifetime of the resulting RS states, NiO(h+)/RuP2+, is on the tens of millisecond time scale due to the relatively slow back electron transfer. The bridging feature dictates the microscopic details of the assembly and interfacial dynamics at oxide surfaces. Our results are clear in providing evidence for the importance of film structure in modifying transient redox properties to obtain high concentrations of long-lived RS states at the interface of these mesoporous film environments.

■

EXPERIMENTAL SECTION Sample Preparation. Materials. Zirconyl chloride octahydrate, 70% perchloric acid (99.999% purity), zirconium isopropoxide, nickel(II) chloride hexahydrate, lithium perchlorate, tetrabutylammonium hexafluorophosphate (>99.0%), Carbowax 20M, hydroxypropyl cellulose (Mw ∼ 80 000, 20 mesh particle size), and Synperonic F-108 were used as received from Sigma-Aldrich. In2O3:Sn (ITO) dispersion in ethanol (TC8 DE, 20 wt %) was obtained from Evonik Industries. Ethanol (Decon Laboratories, 200 proof) and acetonitrile (Optima LC/MS) were purchased from Fisher Scientific. Distilled water was further purified with a Milli-Q Ultrapure water purification system (Milli-Q water). Fluorinedoped tin oxide (FTO; resistance 15 Ω/sq) glass was purchased from Hartford Glass Inc. and cut into 10 mm × 40 mm strips as substrates for doctor-blading of metal oxide pastes. The chromophore ([RuII(4,4′-(PO3H2)2-2,2′-bipyridine)2(2,2′-bipyridine)]Cl2; RuP22+) and the electron donor [N,N,N′,N′-((CH2)3PO3H2)4-4,4′-dianiline; DA] were synthesized according to the previously published procedures.26 Loading solutions of RuP22+ (0.1 mM), DA (3.6 mM), and ZrOCl2 (3 mM) were prepared by dissolving the chemicals in 0.1 M perchloric acid (in Milli-Q water) and stored in the dark at room temperature before use. Metal Oxide Films. Mesoporous nanoITO and ZrO2 thin films were prepared according to the published procedures with an area of 10 mm × 10 mm and a typical thickness of 4.0 μm.33,34 The nanoITO films prepared by this method have a doping density of about 3 × 1020 cm−3.34 NiO paste was prepared on the basis of a literature sol−gel method.35−37 Briefly, 1.0 g of NiCl2·6H2O was dissolved in 3.0 g of Milli-Q water, followed by sonication until a clear green solution was obtained, and then 1.0 g of copolymer F-108 was added to the solution. Ethanol (6.0 g) was pipetted to the mixture by portions. Stirring was continued until the solution turned clear. The solution was then allowed to sit for 3 days, followed by centrifugation at 3000 rpm for 15 min, after which the supernatant was doctor-bladed on thoroughly cleaned FTO glass slides. The films were dried in a box oven at 110 °C for 15 min and sintered at 450 °C for 30 min in air. The doctorblading and sintering steps were cycled twice before ∼1.8 μm thick NiO films were obtained. Film thicknesses was determined with a Bruker Dektak XT profilometer. Photocathode Assembly. Sequential loading of layers was carried out by soaking the metal oxide films in DA (3.6 mM) for 12 h, ZrOCl2 (3 mM) for 2 h, and RuP22+ (0.1 M) for 12 h, in a stepwise manner. The photocathode assemblies prepared by this method have the structure of MOX|-DA-Zr-RuP22+ (FTO is omitted for simplicity). Control samples of MOX|-

Table 1. Surface Coverages (Γ, mol/cm2) of DA and RuP22+ on ZrO2, nanoITO, and NiO Filmsa surface coverages Γ(DA)/10−8 Γ(RuP22+)/10−8 Γ(DA):Γ(RuP22+)

ZrO2 (3.5 μm thick)

nanoITO (3.5 μm thick)

NiO (1.8 μm thick)

6.54 ± 0.72 6.86 ± 0.53

5.76 ± 0.68 5.80 ± 0.66

2.21 ± 0.29 2.46 ± 0.37

0.95

0.99

0.90

Γ = total surface coverages of DA or RuP22+ in the MOX|-DA-ZrRuP22+ assemblies. a

Steady-State Emission. Steady-state emission spectra for MOX|-RuP22+ and MOX|-DA-Zr-RuP22+ films were acquired with a PTI 4SE-NIR Quanta Master fluorimeter with 488 nm light excitation at room temperature. Samples were immersed in 0.1 M LiClO4 acetonitrile solutions and degassed with N2 for 30 min before measurements. Emitted light intensities were acquired and integrated from 520 to 800 nm with data shown in Figure S3 and S4 (SI). The resulting quenching efficiencies were calculated by averaging three sets of data from parallel experiments for each set of MOX|-RuP22+ and MOX|-DA-Zr-RuP22+ samples, with margin of errors all below 5%. B

DOI: 10.1021/acs.jpcc.6b12416 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C Nanosecond Transient Absorption (TA). TA measurements were performed with a nanosecond TA spectrometer that is based on a Nd:YAG (Spectra-Physics Quanta-Ray Lab170) and OPO (VersaScan, 5−7 ns, 1 Hz, 0.5 cm beam diameter) laser system. The white light probe pulses were generated by a pulsed 450 W Xe lamp and passed through a 345 nm long pass filter before reaching the samples to avoid direct band gap excitation of the films. A 488 nm notch filter was placed before the detector to reject unwanted scattered excitation light. Single wavelength TA changes of the samples upon excitation by 488 nm laser pulses (3.7 mJ/pulse) were detected by a monochromator/PMT (Hamamatsu R928) system and monitored by using a digital oscilloscope. For TA experiments with applied bias, the potentials versus a nonaqueous Ag/Ag+ reference electrode were held constant for the duration of each TA experiment. TA measurements were initiated after the onset of stable plateau currents under each bias. All samples were degassed with N2 for 30 min before measurements.

Scheme 1. Light-Induced Electron Transfer Steps

assembly (eqs 4 and 5) (see Scheme 1). Free energy changes for the reactions are also included from the redox potentials26 of DA+•/DA, RuP22+/RuP2+, and RuP22+*/RuP2+ and the valence band potential (0.37 V vs NHE)40 for this type of pNiO films. The formation and decay of RS states following laser flash excitation at 488 nm are shown for MOX|-RuP22+ and MOX|-DA-Zr-RuP22+ in the nanosecond TA spectra in Figure 3.

■

RESULTS AND DISCUSSION In the series of experiments, the key is to explore the ability of NiO-modified assemblies to generate the surface-bound redox states (NiO(h+)/RuP2+) and extend the lifetime of the reducing equivalents at RuP2+. In the assemblies, independent measurements have shown that reduction potentials for the RuP22+*/+ and RuP22+/+ couples in acetonitrile are 1.04 and −1.10 V vs NHE, respectively.26 For the quencher DA, the first and second oxidations occur at 0.69 and 0.96 V vs NHE.26 The assembly components are also easy to monitor spectrophotometrically with absorption maxima in the visible at 510 nm for RuP2+ and at 475 nm for DA+. (Figure 2). The underlying steps in the overall scheme are shown in eqs 1−5 of Scheme 1 for the NiO photocathode. They include light excitation to NiO|-DA-Zr-RuP22+* (eq 1), reductive quenching to NiO|-DA+•-Zr-RuP2+ (eq 2), interfacial hole injection to NiO(h+)|-DA-Zr-RuP2+ (eq 3), and intra-assembly and interfacial back electron transfer to the initial electrode

Figure 3. TA spectral changes following excitation of MOX|-RuP22+ and MOX|-DA-Zr-RuP22+ (MOX = NiO, nanoITO) at 488 nm in degassed acetonitrile with 0.1 M LiClO4 electrolyte.

There is clear evidence in the TA difference spectrum for RuP2+, which absorbs at 510 nm (Figure 2). The importance of the electron-donating base, DA, can be seen by comparing parts a/c and b/d of Figure 3, with a considerable increase in absorbance of RuP2+ seen in Figure 3b,d. For nanoITO|RuP22+, the excited state, RuP22+*, is known to undergo rapid electron injection into the conduction band of nanoITO34 (Figure 3c). The -DA-Zr- bridge between the electrode surface and RuP22+ in NiO|-DA-Zr-RuP22+ provides both long distance and electronic decoupling effects between the oxide surface and the assembly. Photoeneration of Reducing Equivalents (RuP2+). Quenching. The reductive quenching of RuP22+* was investigated with the assemblies on ZrO2, which is inert toward injection by either RuP22+* or the oxidized donor. Quenching efficiencies, ηq, were calculated from eq 6 with Ia and I0 being the integrated emission intensities for RuP22+* in MOX|-DA-ZrRuP22+ and MOX|-RuP22+, respectively. F0/Fa is the ratio of the light absorption factions by RuP22+ in MOX|-RuP22+ and MOX|DA-Zr-RuP22+. Results are summarized in Table S1 (SI). For all the three metal oxides, the quenching yields are above 90%.

Figure 2. Extinction coefficient differences in MOX|-DA-Zr-RuP22+ photocathodes from spectroelectrochemical and chronocoulometry measurements on samples in N2-degassed acetonitrile with 0.1 M TBA(PF6). Extinction coefficients were calculated from UV−vis absorption spectral changes following electrochemical oxidization or reduction.26 [The absorption spectrum of the one-electron oxidized NiO (blue curve) is different from that in the literature39 because of the differences in structure and electrochromic properties of NiO arising from the different preparative methods.] C

DOI: 10.1021/acs.jpcc.6b12416 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C ⎛ I F⎞ ηq = ⎜1 − a 0 ⎟ I0 Fa ⎠ ⎝

the spectral data, the values of ηinj are 0.33 for NiO|-DA-ZrRuP22+ and 0.26 for nanoITO|-DA-Zr-RuP22+ without bias. The loss of injection at 50 ns is due to either the slow injection itself or, more likely, the interfacial charge recombination within the first 50 ns. According to the Gerischer model for interfacial charge injection in wide-band-gap semiconductors, the rate of interfacial charge transfer at an electrode surface is proportional to the overlap of the occupied donor states and the unoccupied acceptor states.41−43 In the case of p-type semiconductors, the donor distribution function is thought to be dependent on the applied bias at room temperature.43−45 The bias dependence of ηinj for both electrodes was investigated by using TA measurements, 50 ns after the laser pulse in Figure 5. Given

(6) +.

Hole Injection from DA to MOX. After the formation of the intra-assembly RS states, MOX|-DA+•-Zr-RuP2+, DA+• injects holes into NiO or nanoITO to form the interfacial RS states, MOX(h+)|-DA-Zr-RuP2+, which are characterized in the TA spectra in Figure 3b,d. The full TA data in the visible region (380−700 nm) from 50 ns to 9 μs after the laser pulse were fit by using the extinction coefficients of RuP22+/+ and DA+/0 and the transient absorptive changes of NiO upon hole injection (Figure 2) according to eq 7. The time-resolved changes of the fractions of DA+• in Figure 4 were deconvoluted from a global

Figure 4. Percentage of DA+• remaining after fixed time delays following the laser excitation of NiO|-DA-Zr-RuP22+ and nanoITO|DA-Zr-RuP22+ samples at 488 nm under open circuit conditions. Laser light intensity: 3.7 mJ/pulse. Medium: N2-degassed acetonitrile with 0.1 M LiClO4 electrolyte. The DA+• percentage was deconvoluted from global fitting of the full TA spectra by using eq 7 and molecular extinction coefficients in Figure 2. Sample fitting curves are shown in Figure S5 (SI).

Figure 5. Hole injection yields, ηinj, of NiO|-DA-Zr-RuP22+ (blue) and nanoITO|-DA-Zr-RuP22+ (pink) samples in degassed MeCN/0.1 M LiClO4 as a function of applied bias. ηinj is calculated from the expression 1 − Γ(DA+•)/Γ(RuP2+), with TA of RuP2+ (510 nm) and DA+• (475 nm) at 50 ns after the laser pulse.

analysis of the full TA spectra with the initial value of Γ0(DA+•) taken from the same Γ0(RuP2+) value obtained at 50 ns after laser excitation.

the fact that the quenching yields should be invariant to bias, the difference in ηinj values arises from the bias-dependent, interfacial electron transfer processes (charge injection and interfacial back electron transfer) that occur within the first 50 ns. The high values of ηinj for samples under negative bias are attributed to greater driving force for hole injection into the nanoITO electrode46 and/or enhanced electron occupation at the NiO surface.40 As the bias is increased positively, ηinj decreases more rapidly, because the yield of RuP2+ drops significantly under positive bias (vide infra) due to faster charge recombination. From the results of some earlier studies on hole injection into valence band/trap states of NiO by surface attached dye molecules, the injection yields are higher when probed at much earlier time delays (1 or 10 ns).47,48 From those data, the injection at 1 ns does not exhibit bias-dependent behaviors,47 while the injection probed at a later time delay reveals a bias dependence similar to the one observed here.48 The above observations indicate that the loss of injection yields of our NiO samples is presumably from interfacial charge recombination that decreases the holes at NiO and electrons carried by RuP2+ within the first 50 ns. As shown in Figure 5, there is a considerable difference in injection efficiencies between the two electrodes under negative bias. Reducing Equivalents. The efficiencies for photogeneration of reducing equivalents, RuP2+, in the assemblies, MOX|-DA-Zr-

ΔODt = Γt (RuP2+) Δε(RuP2+) + Γt (DA+•) Δε(DA+•) + Γt (MOX (h+)) Δε(MOX (h+))

(7)

On the basis of the data in Figure 4, without added bias, the rate of hole injection from DA+• to nanoITO within the first 50 ns is comparable to, but slightly more rapid than, that to NiO. At high light intensities, the driving force for injection from DA+• to NiO or to nanoITO is estimated to be ∼0.3 and ∼0.4 eV, respectively, from the band potentials of the two films34,40 and the formal potential of the DA+•/DA couple.26 The more rapid injection rate for the nanoITO sample can be attributed largely to the higher driving force for hole injection. Given the quenching/injection scheme in eqs 2 and 3 (Scheme 1), an important factor in limiting redox separation in the photocathodes is the relatively slow charge injection to the electrode from the assembly following excited state quenching. Hole injection yields, ηinj, the fraction of holes reaching the electrode within the first 50 ns after excitation, were also evaluated from the nanosecond TA measurements. The latter were obtained from measurements of 1 − Γ(DA+•)/Γ(RuP2+) by using the difference between transiently formed RuP2+ and DA+• observed at the 50 ns after the laser pulse. On the basis of D

DOI: 10.1021/acs.jpcc.6b12416 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C RuP22+, were also estimated from the TA data. In this analysis, quantum yields (ηQY) were evaluated according to eq 8, with Γ(RuP2+) being the surface coverage of RuP2+ obtained from TA data at 510 nm at 50 ns time delay. The photon flux, Γ(photon flux), was evaluated by a published actinometric method based on the ground-state bleach of Ru(bpy)32+ in degassed acetonitrile as the reference.49 In this equation, f is the fraction of light absorbed by RuP22+ in the assembly. ηQY =

Γ(RuP2+) Γ(photon flux)f

the effect slowly decreasing as the bias is increased toward the first reduction potential of DA+/0 at E(DA+•/DA) = 0.69 V vs NHE.26 The decrease in ηQY with bias is probably due to the slower hole injection and faster interfacial back electron transfer. The initial yield of RuP2+ following quenching is independent of bias. Under negative bias, the injected holes are withdrawn to the back contact, forming a depletion layer that slows down the interfacial back electron transfer. At more positive bias, the width of the depletion layer is decreased, enhancing the interfacial charge recombination. When the bias is sufficiently positive, an accumulation layer is formed that greatly accelerates the interfacial charge recombination. At the same time, a more positive bias decreases the yield of charge injection from DA+• to NiO valence band/trap states, leaving more DA+• accepting electrons from RuP2+. Back Electron Transfer. Intra-Assembly. Following excitation and reductive quenching in eqs 1 and 2, a competition exists between the intra-assembly back electron transfer (eq 4) and hole transfer to the electrode (eq 3) (see Scheme 1). Back electron transfer within the assembly was investigated on ZrO2 films because there are no low-lying levels on the oxide for charge injection. Figure S6 (SI) shows the nanosecond TA spectra following excitation of the assemblies ZrO2|-RuP22+ and ZrO2|-DA-Zr-RuP22+ at 488 nm in degassed acetonitrile/0.1 M LiClO4. A comparison between the two sets of data in Figure S6 (SI) shows that, with added DA, RuP22+* decays much faster, as both DA+ and RuP2+ appear in the difference spectra of the right figure. The time dependence of the intra-assembly back electron transfer within the association complex (eq 9) is shown in the time-resolved decay of RuP22+ in Figure S7 (SI), from which a half-life of ∼25 μs was obtained.

(8)

On the basis of the TA data, under open circuit conditions, ηQY is 15% for NiO|-DA-Zr-RuP22+ and 4.9% for nanoITO|DAZr-RuP22+. The quantum efficiencies, measured at 50 ns time delay, arise from the sequence of reactions shown in eqs 1−3 (Scheme 1). In this interpretation, ηQY is the product of three individual efficiencies: quenching efficiency (ηq), hole injection efficiency (ηinj), and the survival probability (ηb) of RuP2+ after formation of the interfacial RS states. The survival probability, ηb, comes from the efficiency loss in charge recombination. On the basis of the photophysics data, with ηq ∼ 1 and ηinj from the values reported above, ηb is estimated to be ∼48% for NiO|-DA-ZrRuP22+ and 19% for nanoITO|-DA-Zr-RuP22+. Both are comparable to their injection yields under open circuit conditions. On the basis of this analysis and the data above, one of the contributors to the efficiency loss occurs from the relatively slow injection from DA+. to the electrode, probably due to the nonconjugating anchoring groups. Another efficiency loss factor is attributed to the recombination seen in the low ηb values. The lower ηb of nanoITO electrode, relative to that of NiO, arises from its thin depletion layer under negative bias and its high hole mobility both under bias and open circuit conditions, given its high doping density of ∼3 × 1020 cm−3.34 The quantum yield of RuP2+ in the assemblies was also investigated under bias, with the results shown in Figure 6. On the basis of these measurements, with the reduced dye well separated from the surface, the effect of the bias on the reduced dye arises from its interaction with the electrode surface. From the data, there is a decrease in ηQY with bias above −0.2 V, with

ZrO2 |−DA+•−Zr−RuP2 2 + → ZrO2 |−DA•−Zr−RuP2 2 + (9)

On the basis of the initial amplitudes of the TA traces for ZrO2 samples, measurements of back electron transfer within the assembly show that, following excitation and quenching, the amount of the RS states measured by nanosecond TA is diminished due to rapid intra-assembly back electron transfer. For the nanoITO and NiO samples, due to competitive hole injection (eq 3), the contribution from intra-assembly back electron transfer to DA+• is significantly reduced (vide infra). Assembly to Electrode. For NiO and nanoITO photocathodes, photogenerated RuP2+ undergoes back electron transfer with both DA+• (eq 4) and the oxidized MOX (eq 5) (see Scheme 1). Since the nanosecond TA spectra at 510 nm show the decay of RuP2+ caused by these two back electron transfer processes, the kinetics of both can be obtained by analyzing the decay traces of RuP2+. Following photogeneration of the intra-assembly RS states in NiO and nanoITO photocathodes, there is a competition between hole transfer from DA+• to the electrode and to the reduced dye, as shown in eqs 3 and 4 (see Scheme 1), respectively. Because of these two competitive processes, the intra-assembly charge recombination between DA+• and RuP2+ in these photocathodes does not follow equal-concentration second-order kinetics as observed on ZrO2. In our analysis of the data, a non-equal-concentration fitting model, as derived in eq S7 (Supporting Information), is applied to account for the decay of RuP2+ contributed by the intra-assembly back electron transfer. For the interfacial electron transfer, the kinetic behavior is multiexponential due to the random distribution of the injected charges on the

Figure 6. Quantum yields of reducing equivalents, RuP22+, as a function of applied bias for NiO|-DA-Zr-RuP22+ and nanoITO|-DA-ZrRuP22+ photoelectrodes, obtained from eq 8. E

DOI: 10.1021/acs.jpcc.6b12416 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C mesoporous films.50−53 For the interfacial charge recombination involving surface/bulk trap states, we have applied the “continuous-time random walk” (CTRW) theory, which emphasizes that charge carriers become trapped in localized states with the dynamics of charge transfer dominated by charge hopping from the trap states to the interface.52−57 The kinetics of the interfacial charge recombination for both NiO and nanoITO photocathodes follows the biphasic stretched exponential model, which is consistent with the CTRW model, with one component arising from charge diffusion through a distribution of trap states and the other from interfacial charge recombination between holes at the interface and electrons at RuP2+. As expected from the kinetics, there was no evidence of an intermediate hole transfer from NiO(h+) to the donor, NiO(h+)|-DA-Zr-RuP2+ → NiO|-DA+•-Zr-RuP2+ → NiO|-DAZr-RuP22+, which indicates that the back hole transfer to DA is slow relative to the rapid transfer to RuP2+. By using the interfacial charge recombination model, we were able to resolve the TA data at 510 nm for the decay of RuP22+ to the biphasic stretched exponential model (eqs 10 and 11). The TA data and the fitted curves are shown in Figure 7 and the obtained fitting parameters are listed in Table 2.

∞

is the gamma function: Γ(x) = ∫ t x − 1e−t dt . 58 The 0 distribution width, β, provides insights into the probability densities of the two dynamic phases.59−61 A small β (0.25 V), it is conceivable that the external rate is limited by hole-hopping between surface states, shown as an increase of k2 in Figure 8. On the basis of the data in Table 2 and Figure 8, the reducing equivalents in the cell upon exciting the NiO photocathode are stored at RuP2+ for several milliseconds. Under these conditions, delivery of reductive equivalents to an external acceptor (a water/CO2 reduction catalyst) in a dye-sensitized photoelectrosynthesis cell should be complete.

⎡ ⎛ ⎞β⎤ t A(RuP2+)t = A(RuP2+)t − ia + A1 exp⎢ −⎜ ⎟ ⎥ + A 2 ⎢⎣ ⎝ t1 ⎠ ⎥⎦ ⎡ ⎛ ⎞β⎤ t exp⎢ − ⎜ ⎟ ⎥ ⎢⎣ ⎝ t 2 ⎠ ⎥⎦ ⎡⎛ t ⎞ ⎛ 1 ⎞⎤−1 k1 = ⎢⎜ 1 ⎟Γ⎜ ⎟⎥ ⎣⎝ β ⎠ ⎝ β ⎠⎦

⎡⎛ t ⎞ ⎛ 1 ⎞⎤−1 k 2 = ⎢⎜ 2 ⎟Γ⎜ ⎟⎥ ⎣⎝ β ⎠ ⎝ β ⎠⎦

(10)

(11)

■

CONCLUSIONS We report here on the use of a molecular assembly approach for modification of p-type NiO and a degenerately doped nanoITO electrode. The key feature is the physical separation between the reduced dye in the assembly and the electrode surface. Photophysical measurements on the assembly provide clear evidence that the approach can be successfully used to achieve hole injection to the electrode and photogeneration of reducing equivalents in the assembly. The resulting redoxseparated states last several milliseconds after excitation of either photocathode. Under open circuit condition, an initial quantum yield of 15% was achieved for photogeneration of reducing equivalents at the reduced ruthenium polypyridine dye on p-NiO photocathode. Nanosecond TA experiments and detailed analyses of each electron transfer step demonstrate that

Figure 7. Transient absorptive changes at 510 nm following excitation of NiO|-DA-Zr-RuP22+ at 488 nm in degassed acetonitrile with 0.1 M LiClO4 electrolyte: green, open circuit; blue, with −0.445 V applied bias; pink, with 0.225 V applied bias vs NHE; scatter, TA data; lines, fitted curves based on eqs 10 and 11.

In eq 10, A(RuP2+)t‑ia is the absorbance of RuP2+ at time t that undergoes intra-assembly charge recombination. A1 and A2 are the absorbance of the initial RuP2+ that undergoes the interfacial charge recombination. β is a stretching parameter that inversely reflects the heterogeneity of the kinetics, providing a distribution width of the lifetimes. k1 and k2 are the observed rate constants (s−1) for the two components. Γ(x) F

DOI: 10.1021/acs.jpcc.6b12416 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

Table 2. Bias-Dependent Kinetic Fitting Parameters for the TA Traces at 510 nm Acquired for NiO|-DA-Zr-RuP22+ in Degassed Acetonitrile with 0.1 M LiClO4 Electrolyte bias/V vs NHE β k1/s−1 k2/s−1 A1%a A2%a a

open circuit 0.23 3.7 × 104 2.2 × 102 0.70 0.30

−0.445 0.30 2.1 × 104 1.0 × 102 0.73 0.27

−0.345 0.25 2.1 × 104 1.1 × 102 0.69 0.31

−0.245 0.27 2.9 × 104 1.4 × 102 0.72 0.28

−0.145 0.28 6.2 × 104 1.2 × 102 0.75 0.25

−0.045 0.25 8.9 × 104 1.9 × 102 0.73 0.27

0.055 0.27 8.4 × 104 1.8 × 102 0.77 0.23

0.155 0.25 9.1 × 104 1.1 × 102 0.76 0.24

0.255 0.34 3.9 × 104 1.9 × 103 0.73 0.27

0.355 0.28 1.6 × 104 1.8 × 103 0.73 0.27

A1 and A2 are the amplitudes of the stretched exponential terms in eq 10. A1% = A1/(A1 + A2); A2% = A2/(A1 + A2).

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Thomas J. Meyer: 0000-0002-7006-2608 Present Addresses †

B.H.F.: Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849. ‡ K.-R.W.: Department of Chemistry, Daegu University, Gyeongsan, 712−714, Republic of Korea. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This research was supported solely by the U.S. Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences, under Award DE-SC0015739.

Figure 8. The k1 and k2 values as a function of applied bias from the fitting of TA data at 510 nm for NiO|-DA-Zr-RuP22+ based on eqs 10 and 11. Each data point with an error bar was obtained from three sets of parallel experiments with the averages shown.

■ ■

ABBREVIATIONS USED RS, redox-separated; CR, charge recombination; DSPEC, dyesensitized photoelectrosynthesis cells

the overall efficiency is limited by hole injection and charge recombination. Compared with highly doped nanoITO, the NiO photocathode shows superior photoconversion efficiency for producing reducing equivalents and longer lifetimes of the redox-separated states, due to an inhibition toward charge recombination with the external assembly. For the nanoITO photocathode, both injection and the quantum efficiency depends on the applied bias given its highly doped nature. Without bias, the nanoITO photocathode gives a lower yield of reducing equivalents, lower efficiency of hole injection, and faster interfacial back electron transfer than those of the NiO photocathode. From the nanosecond TA measurements, differences in efficiencies come from variations in the interfacial charge recombination rates. For the NiO photocathode, evidence from bias-dependent nanosecond TA measurements points to dynamics that are controlled by hole transport between trap states. Our results highlight the value of modifying the interfacial film structures with molecular assemblies to achieve higher efficiencies in p-type dye-sensitized solar cells. Promoting the charge injection yield by engineering the donor structures and further coupling this electrode with catalysis of water reduction are currently under investigation.

■

REFERENCES

(1) Shockley, W.; Queisser, H. J. Detailed Balance Limit of Efficiency of p/n Junction Solar Cells. J. Appl. Phys. 1961, 32, 510−519. (2) Vos, A. D. Detailed Balance Limit of the Efficiency of Tandem Solar Cells. J. Phys. D: Appl. Phys. 1980, 13, 839. (3) Polman, A.; Atwater, H. A. Photonic Design Principles for Ultrahigh-Efficiency Photovoltaics. Nat. Mater. 2012, 11, 174−177. (4) Xu, Y.; Gong, T.; Munday, J. N. The Generalized ShockleyQueisser Limit for Nanostructured Solar Cells. Sci. Rep. 2015, 5, 13536. (5) Nattestad, A.; Ferguson, M.; Kerr, R.; Cheng, Y.-B.; Bach, U. Dye-Sensitized Nickel(II)oxide Photocathodes for Tandem Solar Cell Applications. Nanotechnology 2008, 19, 295304. (6) Nattestad, A.; Mozer, A. J.; Fischer, M. K. R.; Cheng, Y.; Mishra, A.; Bauerle, P.; Bach, U. Highly Efficient Photocathodes for DyeSensitized Tandem Solar Cells. Nat. Mater. 2010, 9, 31−35. (7) Ameri, T.; Dennler, G.; Lungenschmied, C.; Brabec, C. J. Organic Tandem Solar Cells: A review. Energy Environ. Sci. 2009, 2, 347−363. (8) Hagfeldt, A.; Boschloo, G.; Sun, L.; Kloo, L.; Pettersson, H. DyeSensitized Solar Cells. Chem. Rev. 2010, 110, 6595−6663. (9) Gibson, E.; Smeigh, A.; Le Pleux, L.; Fortage, J.; Boschloo, G.; Blart, E.; Pellegrin, Y.; Odobel, F.; Hagfeldt, A.; Hammarström, L. A pType NiO-Based Dye-Sensitized Solar Cell with an Open-Circuit Voltage of 0.35 V. Angew. Chem., Int. Ed. 2009, 48, 4402−4405. (10) Pellegrin, Y.; Le Pleux, L.; Blart, E.; Renaud, A.; Chavillon, B.; Szuwarski, N.; Boujtita, M.; Cario, L.; Jobic, S.; Jacquemin, D.; et al. Ruthenium Polypyridine Complexes as Sensitizers in NiO Based pType Dye-Sensitized Solar Cells: Effects of the Anchoring Groups. J. Photochem. Photobiol., A 2011, 219, 235−242. (11) Odobel, F.; Pellegrin, Y.; Gibson, E. A.; Hagfeldt, A.; Smeigh, A. L.; Hammarström, L. Recent Advances and Future Directions to

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b12416. Photoluminescence quenching, UV−vis absorption spectra, spectroelectrochemistry, extinction coefficients, and transient absorption spectra of ZrO2 samples (PDF) G

DOI: 10.1021/acs.jpcc.6b12416 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

Viologen Phosphonate Compounds. J. Am. Chem. Soc. 1993, 115, 11767−11774. (29) Katz, H. E. Multilayer Deposition of Novel Organophosphonates with Zirconium(IV). Chem. Mater. 1994, 6, 2227−2232. (30) Fang, M.; Kaschak, D. M.; Sutorik, A. C.; Mallouk, T. E. A “Mix and Match” Ionic-Covalent Strategy for Self-Assembly of Inorganic Multilayer Films. J. Am. Chem. Soc. 1997, 119, 12184−12191. (31) Massari, A. M.; Gurney, R. W.; Wightman, M. D.; Huang, C. K.; Nguyen, S. T.; Hupp, J. T. Ultrathin Micropatterned Porphyrin Films Assembled via Zirconium Phosphonate Chemistry. Polyhedron 2003, 22, 3065−3072. (32) Lemon, B. I.; Liu, F.; Hupp, J. T. Electrochemical, Spectral, and Quartz Crystal Microgravimetric Assessment of Conduction Band Edge Energies for Nanocrystalline Zirconium Dioxide/Solution Interfaces. Coord. Chem. Rev. 2004, 248, 1225−1230. (33) Heimer, T. A.; D’Arcangelis, S. T.; Farzad, F.; Stipkala, J. M.; Meyer, G. J. An Acetylacetonate-Based Semiconductor−Sensitizer Linkage. Inorg. Chem. 1996, 35, 5319−5324. (34) Farnum, B. H.; Morseth, Z. A.; Brennaman, M. K.; Papanikolas, J. M.; Meyer, T. J. Application of Degenerately Doped Metal Ox-ides in the Study of Photoinduced Interfacial Electron Transfer. J. Phys. Chem. B 2015, 119, 7698−7711. (35) Sumikura, S.; Mori, S.; Shimizu, S.; Usami, H.; Suzuki, E. Syntheses of NiO Nanoporous Films Using Nonionic Triblock Copolymer Templates and Their Application to Photocathodes of pType Dye-Sensitized Solar Cells. J. Photochem. Photobiol., A 2008, 199, 1−7. (36) Li, L.; Gibson, E. A.; Qin, P.; Boschloo, G.; Gorlov, M.; Hagfeldt, A.; Sun, L. Double-Layered NiO Photocathodes for p-Type DSSCs with Record IPCE. Adv. Mater. 2010, 22, 1759−1762. (37) Wood, C. J.; Summers, G. H.; Clark, C. A.; Kaeffer, N.; Braeutigam, M.; Carbone, L. R.; D’Amario, L.; Fan, K.; Farre, Y.; Narbey, S.; et al. A Comprehensive Comparison of Dye-Sensitized NiO Photocathodes for Solar Energy Conversion. Phys. Chem. Chem. Phys. 2016, 18, 10727−10738. (38) Bard, A.; Faulkner, L. Electrochemical Methods: Fundamentals and Applications; John Wiley & Sons, Inc., 2001. (39) Boschloo, G.; Hagfeldt, A. Spectroelectrochemistry of Nanostructured NiO. J. Phys. Chem. B 2001, 105, 3039−3044. (40) Natu, G.; Hasin, P.; Huang, Z.; Ji, Z.; He, M.; Wu, Y. Valence Band-Edge Engineering of Nickel Oxide Nanoparticles via Cobalt Doping for Application in p-Type Dye-Sensitized Solar Cells. ACS Appl. Mater. Interfaces 2012, 4, 5922−5929. (41) Gerischer, H. Electrochemical Techniques for the Study of Photosensitization. Photochem. Photobiol. 1972, 16, 243−260. (42) Gerischer, H.; Willig, F. Reaction of Excited Dye Molecules at Electrodes. Physical and Chemical Applications of Dyestuffs; Springer Berlin Heidelberg: Berlin, 1976. (43) Fabregat-Santiago, F.; Mora-Seró, I.; Garcia-Belmonte, G.; Bisquert, J. Cyclic Voltammetry Studies of Nanoporous Semiconductors. Capacitive and Reactive Properties of Nanocrystalline TiO2 Electrodes in Aqueous Electrolyte. J. Phys. Chem. B 2003, 107, 758−768. (44) Bailes, M.; Cameron, P. J.; Lobato, K.; Peter, L. M. Determination of the Density and Energetic Distribution of Electron Traps in Dye-Sensitized Nanocrystalline Solar Cells. J. Phys. Chem. B 2005, 109, 15429−15435. (45) Bisquert, J.; Fabregat-Santiago, F.; Mora-Seró, I.; GarciaBelmonte, G.; Barea, E. M.; Palomares, E. A Review of Recent Results on Electrochemical Determination of the Density of Electronic States of Nanostructured Metal-oxide Semiconductors and Organic Hole Conductors. Inorg. Chim. Acta 2008, 361, 684−698. (46) Farnum, B. H.; Morseth, Z. A.; Brennaman, M. K.; Papanikolas, J. M.; Meyer, T. J. Driving Force Dependent, Photoinduced Electron Transfer at Degenerately Doped, Optically Transparent Semiconductor Nanoparticle Interfaces. J. Am. Chem. Soc. 2014, 136, 15869−15872. (47) D'Amario, L.; Antila, L. J.; Pettersson Rimgard, B.; Boschloo, G.; Hammarström, L. Kinetic Evidence of Two Pathways for Charge

Optimize the Performances of p-Type Dye-Sensitized Solar Cells. Coord. Chem. Rev. 2012, 256, 2414−2423. (12) Walter, M.; Warren, E.; McKone, J.; Boettcher, S.; Lewis, N.; Mi, Q.; Santori, N. S. Solar Water Splitting Cells. Chem. Rev. 2010, 110, 6446−6473. (13) Chen, Z.; Jaramillo, T.; Deutsch, T. G.; Turner, J.; Dinh, H.; et al. Accelerating Materials Development for Photoelectrochemical Hydrogen Production: Standards for Methods, Definitions, and Reporting Protocols. J. Mater. Res. 2010, 25, 3−16. (14) Haussener, S.; Xiang, C.; Spurgeon, J.; Ardo, S.; Lewis, N.; Weber, A. Modeling, Simulation, and Design Criteria for Photoelectrochemical Water-Splitting Systems. Energy Environ. Sci. 2012, 5, 9922. (15) Ji, Z.; Natu, G.; Huang, Z.; Wu, Y. Linker Effect in Organic Donor-Acceptor Dyes for p-Type NiO Dye Sensitized Solar Cells. Energy Environ. Sci. 2011, 4, 2818−2821. (16) Le Pleux, L.; Smeigh, A. L.; Gibson, E.; Pellegrin, Y.; Blart, E.; Boschloo, G.; Hagfeldt, A.; Hammarstrom, L.; Odobel, F. Synth-esis, Photophysical and Photovoltaic Investigations of Acceptor-Functionalized Perylene Monoimide Dyes for Nickel Oxide p-Type DyeSensitized Solar Cells. Energy Environ. Sci. 2011, 4, 2075−2084. (17) He, M.; Ji, Z.; Huang, Z.; Wu, Y. Molecular Orbital Engineering of a Panchromatic Cyclometalated Ru(II) Dye for p-Type DyeSensitized Solar Cells. J. Phys. Chem. C 2014, 118, 16518−16525. (18) Lefebvre, J.; Sun, X.; Calladine, J. A.; George, M. W.; Gibson, E. A. Promoting Charge-Separation in p-Type Dye-Sensitized Solar Cells Using Bodipy. Chem. Commun. 2014, 50, 5258−5260. (19) Hao, Y.; Wood, C. J.; Clark, C. A.; Calladine, J. A.; Horvath, R.; Hanson-Heine, M.; Sun, X.; Clark, I. P.; Towrie, M.; George, M. W.; et al. Can Aliphatic Anchoring Groups Be Utilised with Dyes for pType Dye Sensitized Solar Cells? Dalton Trans. 2016, 45, 7708−7719. (20) Gennari, M.; Légalité, F.; Zhang, L.; Pellegrin, Y.; Blart, E.; Fortage, J.; Brown, A. M.; Deronzier, A.; Collomb, M.; Boujtita, M.; et al. Long-Lived Charge Separated State in NiO-Based p-Type DyeSensitized Solar Cells with Simple Cyclometalated Iridium Complexes. J. Phys. Chem. Lett. 2014, 5, 2254−2258. (21) Hanson, K.; Torelli, D. A.; Vannucci, A. K.; Brennaman, M. K.; Luo, H.; Alibabaei, L.; Song, W.; Ashford, D. L.; Norris, M. R.; Glasson, C. R. K.; et al. Self-Assembled Bilayer Films of Ruthenium(II)/Polypyridyl Complexes through Layer-by-Layer Deposition on Nanostructured Metal Oxides. Angew. Chem., Int. Ed. 2012, 51, 12782−12785. (22) Hanson, K.; Brennaman, M. K.; Ito, A.; Luo, H.; Song, W.; Parker, K. A.; Ghosh, R.; Norris, M. R.; Glasson, C. R. K.; Concepcion, J. J.; et al. Structure−Property Relationships in PhosphonateDerivatized, RuII Polypyridyl Dyes on Metal Oxide Surfaces in an Aqueous Environment. J. Phys. Chem. C 2012, 116, 14837−14847. (23) Hanson, K.; Brennaman, M. K.; Luo, H.; Glasson, C. R. K.; Concepcion, J. J.; Song, W.; Meyer, T. J. Photostability of Phosphonate-Derivatized, RuII Polypyridyl Complexes on Metal Oxide Surfaces. ACS Appl. Mater. Interfaces 2012, 4, 1462−1469. (24) Nayak, A.; Knauf, R. R.; Hanson, K.; Alibabaei, L.; Concepcion, J. J.; Ashford, D. L.; Dempsey, J. L.; Meyer, T. J. Synthesis and Photophysical Characterization of Porphyrin and Porphyrin-Ru(ii) Polypyridyl Chromophore-Catalyst Assemblies on Mesoporous Metal Oxides. Chem. Sci. 2014, 5, 3115−3119. (25) Ashford, D. L.; Gish, M. K.; Vannucci, A. K.; Brennaman, M. K.; Templeton, J. L.; Papanikolas, J. M.; Meyer, T. J. Molecular Chromophore−Catalyst Assemblies for Solar Fuel Applications. Chem. Rev. 2015, 115, 13006−13049. (26) Farnum, B. H.; Wee, K.; Meyer, T. J. Self-Assembled Molecular p/n Junctions for Applications in Dye-Sensitized Solar Energy Conversion. Nat. Chem. 2016, 8, 845−852. (27) Cao, G.; Hong, H. G.; Mallouk, T. E. Layered Metal Phosphates and Phosphonates: From Crystals to Monolayers. Acc. Chem. Res. 1992, 25, 420−427. (28) Vermeulen, L. A.; Snover, J. L.; Sapochak, L. S.; Thompson, M. E. Efficient Photoinduced Charge Separation in Layered Zirconium H

DOI: 10.1021/acs.jpcc.6b12416 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C Recombination in NiO-Based Dye-Sensitized Solar Cells. J. Phys. Chem. Lett. 2015, 6, 779−783. (48) Daeneke, T.; Yu, Z.; Lee, G. P.; Fu, D.; Duffy, N. W.; Makuta, S.; Tachibana, Y.; Spiccia, L.; Mishra, A.; Bäuerle, P.; et al. Dominating Energy Losses in NiO p-Type Dye-Sensitized Solar Cells. Adv. Energy Mater. 2015, 5, 1401387. (49) Kelly, C. A.; Farzad, F.; Thompson, D. W.; Stipkala, J. M.; Meyer, G. J. Cation-Controlled Interfacial Charge Injection in Sensitized Nanocrystalline TiO2. Langmuir 1999, 15, 7047−7054. (50) Yan, S. G.; Lyon, L. A.; Lemon, B. I.; Preiskorn, J. S.; Hupp, J. T. Energy Conversion Chemistry: Mechanisms of Charge Transfer at Metal-Oxide Semiconductor/Solution Interfaces. J. Chem. Educ. 1997, 74, 657. (51) Barzykin, A. V.; Tachiya, M. Mechanism of Charge Recombination in Dye-Sensitized Nanocrystalline Semiconductors: Random Flight Model. J. Phys. Chem. B 2002, 106, 4356−4363. (52) Nelson, J.; Chandler, R. E. Random Walk Models of Charge Transfer and Transport in Dye Sensitized Systems. Coord. Chem. Rev. 2004, 248, 1181−1194. (53) Katoh, R.; Furube, A.; Barzykin, A. V.; Arakawa, H.; Tachiya, M. Kinetics and Mechanism of Electron Injection and Charge Recombination in Dye-Sensitized Nanocrystalline Semiconductors. Coord. Chem. Rev. 2004, 248, 1195−1213. (54) Scher, H.; Montroll, E. W. Anomalous Transit-Time Dispersion in Amorphous Solids. Phys. Rev. B 1975, 12, 2455−2477. (55) Abramowitz, M.; Stegun, I. A. Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables; Dover Publications, 1964. (56) Alidoust, N.; Carter, E. A. Three-Dimensional Hole Transport in Nickel Oxide by Alloying with MgO or ZnO. J. Appl. Phys. 2015, 118, 185102. (57) Gibson, E. A.; Awais, M.; Dini, D.; Dowling, D. P.; Pryce, M. T.; Vos, J. G.; Boschloo, G.; Hagfeldt, A. Dye Sensitised Solar Cells with Nickel Oxide Photocathodes Prepared via Scalable Microwave Sintering. Phys. Chem. Chem. Phys. 2013, 15, 2411−2420. (58) Williams, G.; Watts, D. C. Non-Symmetrical Dielectric Relaxation Behaviour Arising from a Simple Empirical Decay Function. Trans. Faraday Soc. 1970, 66, 80−85. (59) Sillescu, H. Heterogeneity at the Glass Transition: A Review. J. Non-Cryst. Solids 1999, 243, 81−108. (60) Pastore, R.; Coniglio, A.; Ciamarra, M. P. Dynamic Phase Coexistence in Glass−Forming Liquids. Sci. Rep. 2015, 5, 11770. (61) Wu, J. H.; Jia, Q. The Heterogeneous Energy Landscape Expression of KWW Relaxation. Sci. Rep. 2016, 6, 20506. (62) Mandal, D.; Hamann, T. W. Charge Distribution in Nanostructured TiO2 Photoanode Determined by Quantitative Analysis of the Band Edge Unpinning. ACS Appl. Mater. Interfaces 2016, 8, 419− 424.

I

DOI: 10.1021/acs.jpcc.6b12416 J. Phys. Chem. C XXXX, XXX, XXX−XXX