Role of Solvent Dielectric Properties on Charge Transfer from PbS

pubs.acs.org/NanoLett

Role of Solvent Dielectric Properties on Charge Transfer from PbS Nanocrystals to Molecules Byung-Ryool Hyun,*,† A. C. Bartnik,† Jin-Kyun Lee,‡ Hiroaki Imoto,| Liangfeng Sun,† Joshua J. Choi,§ Yoshiki Chujo,| Tobias Hanrath,§ Christopher K. Ober,‡ and F. W. Wise† †

School of Applied and Engineering Physics, ‡ Department of Materials Science and Engineering, § School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14850, and | Department of Polymer Chemistry, Graduate School of Engineering, Kyoto University, Kyoto, Japan ABSTRACT Transfer of photoexcited charge from PbS nanocrystals to ligand molecules is investigated in different solvents. We find that the charge transfer rate increases dramatically with solvent dielectric constant. This trend is accounted for by a modified Marcus theory that incorporates only static dielectric effects. The choice of solvent allows significant control of the charge transfer process. As an important example, we find that PbS nanocrystals dispersed in water exhibit charge transfer rates 1000 times higher than the same nanocrystals in organic solvent. Rapid charge extraction will be important to efficient nanocrystal-based photovoltaic and photodetector devices. KEYWORDS Charge transfer, nanocrystal, molecule, dielectric constant, reorganization energy, solvent

T

ransfer of charge to and from semiconductor nanocrystals (NCs) is a process at the frontier of fundamental science with applications in NC-based photovoltaic1 and optoelectronic devices,2 and photocatalysis.3 Thus, an understanding of the charge-transfer (CT) dynamics of NC-charge acceptors/donors is of both scientific and technological importance. Further, the ability to control CT dynamics is critical to NC photodevice applications. Fast CT will be indispensible, for example, for efficient photovoltaic and photo devices.

kCT )

] (1)

where τCT is the charge transfer time, HDA is the electronic coupling between the initial and final states, λ is the reorganization energy, ∆G0 is the total Gibbs free energy change for the electron transfer reaction, kb is the Boltzmann constant, and T is the temperature. At fixed temperature and after selecting a QD size, the driving force (∆G0) and the electronic coupling strength (HDA) are specified, leaving only the reorganization energy (λ) as an adjustable parameter. The reorganization energy includes all structural changes of both the reactants and the solvent during the charge transfer. Looking first at the effect of the solvent only, the reorganization energy can be written as18,20

NCs could open up new ways to utilize multiple charge carriers excited by a single photon.4-6 Multiple-exciton generation (MEG)7-10 has the potential to increase the efficiency of photovoltaic devices, although the MEG yield in NCs is a topic of strong debate.11-13 A prerequisite to MEG-based devices is extraction of charge from NCs on the time scale of the multiexciton lifetime, typically ∼100 ps.14,15 Hyun et al. showed that electron transfer from PbS QDs to TiO216 and SnO217 nanoparticles occurs in 10-100 ns. It is important to understand this slow transfer and to find parameters that can allow sub-100 ps CT for any size of NC.

λsolvent )

(

1 1 1 8π εop εst

)∫

(Di - Df)2 dv

(2)

Where εst and εop are the static and optical dielectric constants of the solvent, and Di and Df are the inductions created in the medium by the distribution of charges in the reactants and products. The dielectric properties of solvent or host materials clearly impact the CT dynamics. It is wellknown that CT in molecular systems is strongly affected by solvents.21,22 Solvent effects offer a way to control CT from NCs to charge acceptors, and more broadly, to extend Marcus theory to NC-molecule systems. Kamat and coworkers have found that CT from CdSe NCs is consistent with the normal regime of Marcus theory,23 but no systematic study has been reported. Lead-salt NCs have become a model system for nanoscale photovoltaic devices owing to their optimal overlap with the

For guidance, we turn to Marcus theory, the dominant model of CT dynamics in molecules. The CT rate can be expressed as18,19

* To whom correspondence should be addressed. E-mail: [email protected]. Received for review: 10/29/2009 Published on Web: 12/07/2009 © 2010 American Chemical Society

[

1 1 2π (λ + ∆G0)2 ) |HDA | 2 exp τCT p 4λkbT √4πλkbT

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DOI: 10.1021/nl903623n | Nano Lett. 2010, 10, 318-323

FIGURE 1. (a) Energy levels of various sizes of PbS NCs. The measured levels of the PbS NCs (red circles) are obtained from absorption spectra and CV measurements. The calculated energy levels for PbS NCs are represented by solid red. Blue line: LUMO level of DAT. Green line: HOMO level of 4-hydroxythiophenol (HTP) radical (HS-C6H4-O-). (b) Schematic of DAT-capped PbS nanocrystal. (c) Emission spectra of PbS NCs (D ) 5.6 nm, i.e., subcritical) with (blue line)/without (red line) DAT molecules in TCE. (d) Fluorescence spectra of 3 nm (i.e., supercritical) diameter PbS NCs in toluene (red line) and DAT-PbS NC in toluene (blue line). Fluorescence is measured with 633 nm excitation. The inset shows the expanded fluorescence spectra of DAT-PbS NCs.

solar spectrum and critical role in studies of MEG. They also attract interest as near-infrared photodetectors. The basic features of lead-salt nanocrystals are reviewed in ref 24. As mentioned above, experiments find CT from photoexcited PbS NCs to be much slower than CT from CdSe NCs.23 To investigate the mechanisms that underlie this slow transfer, we study a model system that includes only the NC and acceptor without intermediate linking molecules. Candidate charge-acceptor molecules must satisfy several demanding conditions, (1) to accept the electrons the LUMO (lowest unoccupied molecular orbital) of the molecule should be lower than that of the NC, or, to accept the holes, the HOMO (highest unoccupied molecular orbital) of the molecule should be higher than that of the NC, (2) it must be possible to disperse the molecule in several organic solvents to tune the dielectric constant, and (3) the molecule should bind directly to the surface of the NCs. To satisfy the third requirement, the thiol (SH-) group was chosen as a binding functional group because it is known to bind strongly with the Pb ion of the NCs.25,26 Primarily mono- and bidentate thiol ligand molecules have been used to develop photovoltaic and photodetector devices based on lead-salt NCs.27-30 To satisfy the second requirement, molecules with a long alkyl chain are required. Toward this end, 10-dodecylanthracene-9-thiol (DAT) was newly synthesized (see the Supporting Information for the © 2010 American Chemical Society

detailed synthesis procedure). DAT is attractive to this application because anthracene molecules are known as excellent conductors.31 To verify proper energy level alignment, cyclic voltammetry (CV) was used. The left side of Figure 1 summarizes the key energy levels, including previously measured levels of PbS NCs.16 The measured reduction potential (LUMO, -3.94 eV vs vacuum) of DAT (see Figure S1 of the Supporting Information) should allow electron transfer from PbS NCs less than 4.5 nm in diameter. From optical measurements, the energy gap of this ligand is over 2 eV, which places the HOMO level well below that of PbS NCs and precludes hole transfer. Colloidal PbS QDs were synthesized with energy gaps between 0.8 and 1.8 eV by literature procedures32,33 that build on Murray’s approach.34 The size of PbS NCs was estimated by comparing the first absorption peak of the NCs with the k·P model.35 Only the PbS NCs were optically excited in the present study. CT from different NC sizes and in different solvents was investigated with time-integrated fluorescence, timeresolved fluorescence using time-correlated single photon counting (TCSPC), and femtosecond transient absorption spectroscopy. DAT molecules were mixed with PbS NCs in organic solvents with a molar ratio of NCs to DAT molecules around 1:10000. The binding of DAT to PbS NCs was 319

DOI: 10.1021/nl903623n | Nano Lett. 2010, 10, 318-323

FIGURE 2. (a) Transient fluorescence traces of DAT-PbS NCs in toluene with 3.0, 3.5, and 3.7 nm diameters. The inset shows the fluorescence decay of 3.0 nm diameter PbS NCs in toluene. (b) Typical fluorescence traces of 3.7 nm diameter PbS NCs in toluene (orange line), chloroform (blue line), and dichloromethane (red line). Cyan line is the instrument response. The fluorescence traces are offset vertically for clarity.

FIGURE 3. (a) Size dependence of electron transfer time of DAT-PbS NCs in toluene. The lines are theoretical models explained later in the text. (b) Electron transfer time vs static dielectric constant of solvents. The lines are theoretical fits, numbered in the inset to indicate the value of the parameter λΓ in the model. The inset shows the same graph over a larger range of dielectric constant.

confirmed by NMR measurements (see the Supporting Information). First, we investigated the dependence of the charge transfer on NC size. We tested NCs below and above the critical size, 3.0 and 5.6 nm diameter. The 5.6 nm NCs do not show any fluorescence quenching, as expected (Figure 1c). The emission spectra of the 3.0 nm NCs in toluene (red line) and coupled to DAT in toluene (blue line) are shown in Figure 1d. The NC fluorescence is quenched dramatically (over 99%) in the presence of DAT, which is a strong indication of charge transfer. The observed ∼60 nm red shift of the emission is typical with thiol ligands. These results support the value of the LUMO of DAT in Figure 1a. To study the dependence on ∆G0, we measured fluorescence transients from three sizes of NCs below the critical diameter, 3.0, 3.5, and 3.7 nm. The inset of Figure 2a shows that the fluorescence of the 3.0 nm PbS NCs decays with a time constant of 2.7 µs, which is a typical value for oleatecoated lead-salt NCs.25,36-38 Emission from the 3.5 and 3.7 nm NCs decays with time constants of 1.9 and 2.2 µs, respectively. When coupled to DAT, the decay times decrease to the ∼10 ns range (Figure 2a). The energy difference between the LUMO of the NCs and the LUMO of the DAT are 0.39, 0.22, and 0.15 eV, respectively. Because the CT rate increases with energy difference, the process must be in the normal region of Marcus theory.18,19 To gain a deeper understanding of the Marcus theory applied to CT from QD © 2010 American Chemical Society

to molecules, we investigated the dependence of the dielectric constant of the solvent medium. Specifically, we dispersed the 3.7 nm NC-DAT complexes in various organic solvents. The measured fluorescence decays of 3.7 nm diameter PbS NCs in toluene, chloroform, and dichloromethane exhibit a dramatic dependence on the solvent (Figure 2b). We model our fluorescence decays as a sum of exponential decays. Even though the choice of model is somewhat arbitrary, some choice is necessary in order to have quantitative values for the time scales involved, and this model has been successful in molecular systems.39 The intensityweighted average lifetimes ( ) Σiaiτi2/aiτi39,40) of the DATPbS NCs in toluene are 10, 13, and 19 ns for the 3.0, 3.5, and 3.7 nm NCs, respectively. The electron-transfer rate41

kCT )

1 1 τQD+DAT τQD

is plotted versus NC size in Figure 3a. Because the quenching is so rapid, the fluorescence decay is a good approximation to the CT process. The solvents we studied are listed in Table 1 along with their static and optical dielectric constants. Results obtained with water as the solvent will be presented below. The solvent reorganization energy is theoretically proportional to (1/εop - 1/εst) (eq 2), but a plot of CT rate (or time constant) versus this quantity shows no correlation (see the Supporting 320

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FIGURE 4. (a) The transient absorption kinetics of 3 nm diameter HTP-PbS NCs in water (orange), excited and probed at 800 nm. Inset shows the trace for oleic acid capped PbS NCs in TCE. The 1/e decay time is 21 ps. (b) The transient absorption kinetics of 4.5 nm diameter HTP (orange line) and MUA (green line)-PbS NCs, excited and probed at 1230 nm. The 1/e decay time is 77 ps.

Information). On the other hand, a plot of CT time constant versus the static dielectric constant of the solvent shows a clear trend (Figure 3b). Guided by this experimental observation, we propose to model the reorganization energy with only static dielectric effects. That is, we simply calculate the difference in electrostatic energy between initial and final configurations. We approximate the system as two dielectric spheres with the transferred charge spread evenly over their surface, embedded within a structureless dielectric medium. This model has been used successfully to model CT reactions.22,42,43 The radius of the molecule is chosen to be 1.0 nm, as a reasonable approximation to its actual size, and its dielectric constant is set to 1.0. The dielectric constant of the PbS NC was set to the bulk value of 170.44 In addition, since we do not model the reorganization energy of either reactant, we set λtotal ) λΓ + λs, where λs is the solvent energy calculated as above and λΓ is the unknown energy of the reactants. We left λΓ as a free parameter, though independent of solvent or NC size. Figure 3a,b shows fits with various values of this parameter in the 0-150 meV range. Finally, the electronic coupling parameter |HDA|2 was adjusted to set the proper scale of the transfer times. The value inferred from the fit is ∼70 µeV (HDA), which indicates that the CT between PbS NC and DAT is through a nonadiabatic reaction.45 This model produces a good fit to the variation of CT time with dielectric constant (Figure 3b), and a reasonable qualitative fit to the trend with NC size (Figure 3a). The best fit to the measured trend with QD size is obtained with λΓ ) 0, although this causes the transfer time to increase by many orders of magnitude as the dielectric constant approaches that of water (inset of Figure 3b). With slightly larger values of λΓ, the transfer time will either remain roughly constant or decrease further for large values of the dielectric constant. Unfortunately this trend cannot be addressed directly with the DAT molecules; to our knowledge, there are no viable organic solvents with static dielectric constants that large. Considering the simplicity and approximations of the theoretical approach, the agreement with experiment is good. © 2010 American Chemical Society

We tentatively attribute this to the long time scales involved in CT processes studied here, relative to the time scale of molecular motion. The longitudinal relaxation time is less than 10 ps for all the solvents used in this work.48-54 The slow time scale of the transfer relative to orientational relaxation allows the molecules to be in constant equilibrium, so the reorganization is purely electrostatic in nature. In general, the solvent dipoles are not expected to be in instantaneous electrostatic equilibrium with the reactants during CT, and thus a more complex nonequilibrium calculation is required, as reflected in eq 2. The results above naturally motivate investigation of CT in highly polarizable solvents. Water has the high dielectric constant of readily available solvents, but DAT cannot be used due to its poor solubility in water. We selected 4-hydroxythiophenol (HTP) as the ligand because HTP-capped PbS (HTP-PbS) NCs can be dispersed in water containing NaOH (pH ) 12.5) through ligand exchange.25 The HTP radical has its HOMO at -4.7 eV versus vacuum,55 which should lead to hole transfer. Direct quantitative comparison of measurements of CT in this system to the controlled experiments with DAT molecules is not sensible. However, we expect the dependence on dielectric constant to dominate the CT. We speculate that the electronic coupling may not differ drastically between the two systems because both molecules bind to the NCs through the same thiol functional group. The fluorescence emission of 3.0 and 4.5 nm NCs is quenched in the presence of HTP (Figure S3 of the Supporting Information). The fluorescence decay of HTPPbS NCs in water is faster than the ∼1 ns instrument response, so we used transient saturated absorption to monitor the carrier dynamics on the picosecond time scale. Degenerate excitation and probe wavelengths resonant with the lowest exciton transition were chosen. To exclude effects of many-particle interactions, the excitation intensity was kept low enough to create an average exciton population below 0.01 per dot. The lowest exciton population of PbS NCs capped with oleic acid and dis321

DOI: 10.1021/nl903623n | Nano Lett. 2010, 10, 318-323

TABLE 1. Dielectric Constants of Various Solvents solvents

static dielectric constant46

optical dielectric constant47a

tetrachloroethylene toluene carbon disulfide chloroform chlorobenzene dichloromethane water

2.30 2.41 2.64 4.77 5.54 8.51 78.85

2.28 2.23 1.63 2.09 2.32 2.03 1.78

with solvent dielectric constant. This trend is accounted for qualitatively by a modified Marcus theory that incorporates only static dielectric effects. Guided by the model, we investigated charge transfer from PbS NCs coupled to molecules in water, where we observe charge transfer rates at least 100 times higher than reported previously for lead-salt NCs. The rapid charge transfer will be pertinent to photodevices, including those that exploit multiple exciton effects.

a Optical dielectric constants are obtained by the square of the refractive indexes of solvents measured at 589 nm (sodium D line).

Acknowledgment. This work was supported by the Cornell Center for Materials Research (CCMR) with funding from the Materials Research Science and Engineering Center program of the National Science Foundation (cooperative agreement DMR 0520404) and in part the Center for Nanoscale Systems through National Science Foundation Grant EEC-0646547.

solved in TCE shows no change on the 250 ps time scale of the measurement, as expected. When coupled to HTP in water, the initial population in 4.5 nm QDs decays in 77 ps and that of 3 nm NCs decays in 21 ps. The CT is thus 2-3 orders of magnitude faster than is found for lead-salt NCs coupled to molecules in low-dielectric solvents or to oxide electrodes. The energy differences between the HOMO of PbS NCs and the HOMO of the HTP radical are 0.5 and 0.1 eV for the 3 and 4.5 nm NCs, respectively, which are in the same range as the DATcapped NCs. The use of host material with high static dielectric constant allows sub-100 ps CT dynamics from PbS NCs, even for moderate energy differences. To rule out the possibility that the high pH value somehow underlies the rapid CT, we measured the picosecond exciton dynamics of PbS NCs capped with 11-mercaptoundecanoic acid (MUA) in water with the same high pH. Charge transfer to this ligand is not energetically favorable. The fluorescence spectrum is not quenched, and the fluorescence decay is only slightly faster than that of oleate-capped QDs.25 Slight decay is observed over 250 ps (Figure 4b). Thus, we attribute the ultrafast CT to HTP to the solvent’s dielectric properties and not the pH. The results presented here are immediately relevant to extraction of charge from lead-salt NCs in Gra¨eztel-type NC photovoltaic devices,16,56,57 in which the NCs are surrounded by a liquid or polymer electrolyte. The model is more broadly applicable; given the dielectric constants of relevant semiconductors, the dependence on solvent should be similar with other NC materials. A study analogous to this work but with II-IV NCs will be interesting and is planned. Previous studies of CT between CdS58,59 and CdTe58,59 NCs and molecules did find that the Stern-Volmer quenching constant increases with static dielectric constant of the solvent, which lends some support to our model. Experiments on CdS and CdSe NCs coupled to molecules in low-dielectric solvents produce CT times of several picoseconds.60-62 Perhaps these can be pushed into the femtosecond range through choice of solvent. Such fast CT rates would represent an interesting regime, as the assumption of static solvent reorganization would be breaking down. In summary, we find that the rate of charge transfer from PbS NCs to DAT molecules increases dramatically © 2010 American Chemical Society

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