Near-Quantitative Yield for Transfer of Near ... - ACS Publications

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Near-Quantitative Yield for Transfer of Near-Infrared Excitons within Solution-Phase Assemblies of PbS Quantum Dots Ki-Ryong Lee,† Stephanie Bettis Homan,† Mohamad Kodaimati, George C. Schatz, and Emily A. Weiss* Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208-3113, United States S Supporting Information *

ABSTRACT: Covalent coupling of colloidal PbS quantum dots (QDs) of two different sizes through amide bond formation yielded assemblies that mediate near-infrared excitonic energy transfer from smaller QDs to larger QDs with 90% quantum yield, in chloroform solution. The energy transfer lifetimes, determined by fitting the kinetic data with a model that accounts for multiple hopping steps and different sizes of QD aggregates, were 113 ± 26 ns and 850 ± 330 ns, which compete favorably with intrinsic exciton decay in 600 ns to 2.5 μs. The high yield of energy transfer was accomplished by optimizing the sizes of the donor and acceptor QDs to maximize spectral overlap, the ratio of donor QDs to acceptor QDs, the coverage of “functional” ligand (8-amino-1-octanethiol on the donor QDs and 8-mercapto-1-octanoic acid on the acceptor QDs) on the QD surfaces, the amount of ethyl-dimethylaminopropylcarbodiimide (EDC) and N-hydroxy-succinimide (NHS) coupling reagents, the degree of steric hindrance for the amide coupling reaction, and the lengths of all involved ligands to maximize the solubility of small QD aggregates. Transmission electron microscopy images show coupling of donor and acceptor QDs into well-mixed heteroassemblies (dimers, trimers, and higher oligomers). The quantum yield for energy transfer was determined by comparing the enhancement of the photoluminescence intensity of acceptor PbS QDs with that of PbS QDs within energy transfer-inactive PbS QD−CdS QD “control” assemblies, which underwent the same chemical treatment as the PbS QD−PbS QD assemblies but do not have an available energy transfer pathway.

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INTRODUCTION

Here we report an exceptionally high yield of excitonic energy transfer (EnT) from smaller PbS QDs (R = 1.6 nm) to larger PbS QDs (R = 1.9 nm) within small assemblies of QDs dispersed in CHCl3. In the vast majority of studies on EnT among colloidal QDs, the QDs have been deposited as a film, and the interparticle distance minimized by ligand exchange from the “native” (as-synthesized) ligand to a shorter ligand.10−27 For EnT of NIR excitons between PbS QDs, this strategy has resulted in reported time constants of 25−200 ns (and reported efficiencies between 35 and 99%).19−26 There are however very few studies of EnT within solution-phase aggregates of QDs,28−33 despite the potential applications of solution-phase FRET in biological and chemical sensing,1,34 flow cytometry,35 and fundamental mechanistic analysis, in part because assembly of donor and acceptor QDs selective enough to realize high, or even measurable, EnT yield while maintaining solubility of the assembly is a challenge, especially in the NIR. The relatively small transition dipole moments of PbS QDs put an intrinsic limit on the rate of EnT achievable using PbS QDs as energy donors but also limit the radiative lifetime of PbS QDs such that radiative decay is not competitive with achievable EnT time scales. The real competition with EnT, then, is electron and hole transfer, which, given that larger QDs

This paper describes the covalent coupling of colloidal PbS quantum dots (QDs) into soluble heteroassemblies, Figure 1A, that mediate Förster resonance energy transfer (FRET) in the near-infrared (NIR) with 90% quantum efficiency from donor QDs to acceptor QDs. Excitonic energy transfer is a critical component of the operation of devices that convert solar energy to electricity or fuel or that sense small molecules or biomolecules. The typical mechanism for excitonic energy transfer is FRET, which occurs through electrostatic coupling of transition dipole moments of a donor and an acceptor.1 FRET in the NIR is especially useful for energy conversion and biological applications1,2 because NIR light is 40% of the solar energy radiation that reaches the earth3 and because water, hemoglobin, and proteins are near-transparent in the NIR.4 Pbchalcogenide QDs are good candidates for NIR FRET mediators.1 Colloidal QDs, in general, are more photostable and have narrower emission spectra than organic dyes.5 PbS QDs have photoluminescence (PL) quantum yields that are a factor of 10−100 larger than organic NIR fluorophores over the entire NIR window (850−1800 nm),6 and their optical spectra are precisely tunable with size, since their excitons experience a greater degree of quantum confinement than other II−VI and III−V QDs.7 Additionally, PbS QDs have excited state lifetimes of 1−3 μs,8 and mediate a downconversion process called multiple exciton generation,9 both of which enhance their ability to convert photons to mobile charge carriers. © 2016 American Chemical Society

Received: July 9, 2016 Revised: September 12, 2016 Published: September 13, 2016 22186

DOI: 10.1021/acs.jpcc.6b06880 J. Phys. Chem. C 2016, 120, 22186−22194

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The Journal of Physical Chemistry C

case, >1 nm, Figure S1) where EnT outcompetes charge transfer. Here, we utilize long organic linkers to minimize the probability of charge transfer, and to allow the QDs to couple with high yield into soluble aggregates.20 Our covalent coupling strategyformation of amide bonds between amine-functionalized donor QDs and carboxylate-functionalized acceptor QDsalso allows for highly selective formation of heteroassemblies, where donors and acceptors are most finely mixed, given that EnT yield is highest when it occurs from smaller to larger QDs (heteroassemblies vs homoassemblies).15,16,30,31,36−38 Selective donor−acceptor assembly for EnT has been accomplished using CdSe/ZnS core/shell QDs and gold nanoparticles that are oppositely charged28 and using CdTe of two different sizes that are oppositely charged33 but, until now, has not been accomplished using molecular covalent or noncovalent assembly.29,31 We demonstrate here that our strategy of covalent assembly with donor−acceptor distances of ∼1.5 nm results in 90% quantum yield of EnT in the NIR.

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RESULTS AND DISCUSSION We chose the sizes of the donor and acceptor PbS QDs to satisfy the requirements for Förster EnT: the PL of the DQDs (R = 1.6 nm), centered at 1023 nm (Figure 1B, black solid line), overlaps with the first excitonic absorption of the AQDs (R = 1.9 nm), centered at 1135 nm (Figure 1B, red solid line). Figure 1A (inset) shows the frontier orbital energies (i.e., conduction and valence band-edges) of the DQD and AQD when capped with thiolates, their final surface chemistry in the coupled assemblies. The valence band-edge energies were measured previously for thiolate-capped QDs by photoelectron spectroscopy,39 and the conduction band-edge energies equal the valence band-edge energies plus the optical bandgaps of the QDs. The energy level diagram shows that, in addition to EnT, both electron and hole transfer from a photoexcited DQD to AQD are energetically allowed. We therefore detect EnT (and calculate EnT yield) through an increase in PL quantum yield of the AQD rather than a decrease in PL quantum yield of the DQD, because the latter could also be caused by charge transfer. The mechanism of covalent assembly of the QDs is amide coupling, so we functionalized the DQDs with 8-amino-1octanethiol (AOT) and the AQDs with 8-mercapto-1-octanoic acid (MOA) (Figure 1A). Details of the ligand exchange procedure are in the Experimental Methods section of the Supporting Information. Both functional ligands bind to the QD surface through their thiolate groups, which have a higher binding affinity for the Pb2+ ions on the surfaces of the QDs than do the carboxylate groups of the native oleate ligands. 1H NMR confirms that all MOA and AOT ligands added to the QD dispersion bind to QDs (see the Supporting Information, Figures S2 and S3), and displace the oleate. We hypothesized that the quantum yield of EnT from DQD to AQD will be maximized when the heteroassembly contains one donor and multiple proximate acceptors. To maximize the number of adsorption sites per DQD, we synthesized DQDs with 40% of available binding sites occupied by AOT and AQDs with 20% of available sites occupied by MOA. The resulting AOT-capped DQDs and MOA-capped AQDs are well-dispersed in organic solvents, including the solvent used in this study, CHCl3. The MOA-capped QDs begin to precipitate when MOA occupies >20% of the total ligand sites on the QD surface (180 per AQD), and the AOT-capped QDs begin to precipitate when

Figure 1. (A) Schematic diagram of a QD assembly containing a small PbS QD (R = 1.6 nm) as an energy donor (DQD) and large PbS QDs (R = 1.9 nm) as energy acceptors (AQD). The DQD and AQDs are linked with amide bonds formed by coupling 8-amino-1-octanethiol (AOT) on the DQD and 8-mercapto-1-octanoic acid (MOA) on the AQDs. The QDs are otherwise coated with 1-hexadecanethiol (HDT). Inset: Energies of the valence band (VB) and conduction band (CB) edges of DQD and AQD. (B) Normalized absorbance spectra of DQD (black dotted line) and AQD (red solid line) and PL spectra of DQD (black solid line) and AQD (red dotted line) in CHCl3. The excitation wavelengths used to acquire the PL spectra are 850 nm (DQD) and 900 nm (AQD). Apparent “shoulders” in the PL spectra are due to reabsorption of emitted photons by CHCl3 solvent. The Supporting Information describes how the solvent response was partially subtracted from the absorption spectra.

are easier to reduce and oxidize than smaller QDs, will always be thermodynamically favorable when EnT is favorable. In order to maximize the yield of EnT, we must find the donor− acceptor geometry that maximizes the rate of EnT while preventing charge transfer. Both EnT and charge transfer depend on the donor−acceptor distance (rDA), but the rate of charge transfer decreases as exp(−rDA), whereas the rate of Förster EnT decreases as rDA−6. It is therefore, in principle, possible to find a range of donor−acceptor distances (in our 22187


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Scheme 1. Mechanism of Formation of Hetero-QD Assemblies by EDC/NHS-Facilitated Amide Coupling of AOT-Capped DQDs and MOA-Capped AQDsa

a

The text contains the detailed procedure for the coupling reaction.

Figure 2. Representative large-area TEM images of a mixture of DQDs (R = 1.6 nm) and AQDs (R = 1.9 nm) in a 0.67:1 molar ratio stirred for 2 days in the absence (A, “Mixed”) and presence (B, “Coupled”) of EDC/NHS. (C−F) Cryo-STEM images of the coupled product of “dummy” mixtures of small PbS/CdS core/shell QDs (R = 2.1 nm) and larger PbS/CdS core/shell QDs (R = 3.0 nm) to form a heterodimer (C), a heterotrimer (D), a heteropentamer (E), and a hetero-oligomer (F). The core/shell architecture allowed us to achieve a large size difference between the AOT-functionalized QDs and the MOA-functionalized QDs, and thereby convincingly demonstrate the interspersion of DQDs and AQDs within heteroassemblies. Analysis of more than 30 TEM images of the coupled samples shows that 94% of small core/shell QDs are incorporated into heteroassemblies, Table S2 in the Supporting Information. The core/shell QDs were not used for EnT studies because of their low PL quantum yields.

oleate (possibly through displacement by the Cl− counterion of EDC). The agglomeration was marked by a shift of the absorbance and PL peaks of the sample to lower energies and a decrease in PL intensity (see the Supporting Information, Figure S4). We know that assembly of MOA/oleate-coated and AOT/oleate-coated QDs is not merely due to nonspecific aggregation of QDs upon oleate desorption, because assembly does not occur in these systems without partial functionalization of the QDs by MOA and AOT (see the Supporting Information, Figures S5 and S6). To chemically stabilize the QD surfaces after assembly, we replaced the remaining oleate ligands with 1-hexadecanethiol

AOT occupies >40% of the total ligand sites (128 per DQD); see the Supporting Information, Table S1. Amide coupling of AOT-capped DQDs and MOA-capped AQDs was facilitated by simultaneous addition of ethyldimethylaminopropylcarbodiimide (EDC) and N-hydroxysuccinimide (NHS) (in a 1:1 molar ratio), as shown in Scheme 1. After EDC and NHS were added, the mixture was stirred for 2 days. We used 0.5 EDC/NHS per total remaining oleate ligand (the sum of oleate ligands per DQD and oleate ligands per AQD) for all coupling reactions, because we found that the QDs began to agglomerate when the ratio of EDC/NHS to bound oleate was greater than 0.55−0.6 due to desorption of 22188


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The Journal of Physical Chemistry C (HDT) upon completion of the coupling reaction. HDT does not desorb in the presence of EDC/NHS. We replaced oleate with HDT after, rather than before, the coupling reaction because we have observed that loss of oleate in the presence of EDC/NHS increases the coupling yield, probably by exposing reactive amine and carboxylate sites on the AOT and MOA ligands, which would otherwise be buried in the longer oleate ligand shell. In fact, adding EDC/NHS to HDT-treated QDs with the same coverage of AOT and MOA did not form QD assemblies; the TEM images and PL spectra of the DQD and AQD mixtures with and without EDC/NHS were indistinguishable; see the Supporting Information, Figures S7 and S8. We analyzed coupling products by transmission electron microscopy (TEM). Parts A and B of Figure 2 are representative large-area images of mixtures of AOT-capped DQDs and MOA-capped AQDs (in a ratio of DQD:AQD = 0.67:1), stirred for 2 days in the absence (A) and presence (B) of EDC/NHS. We diluted the mixed and coupled solutions by a factor of ∼20 before depositing them onto TEM grids (carbon film on 400-mesh copper). The image of the DQD− AQD mixture without EDC/NHS (Figure 2A) shows welldispersed, single QDs, whereas the image of DQD−AQD mixtures coupled with EDC/NHS (Figure 2B) shows QD assemblies of varying sizes and very few single particles. The difference in radii of the DQDs and AQDs is only 0.3 nm (which we chose to optimize their spectral overlap for EnT), so these TEM images do not reveal whether we formed heteroassemblies (i.e, whether the reaction led to coupling of DQDs with AQDs or nonspecific assembly). To demonstrate the formation of heteroassemblies, where DQDs and AQDs are well-interspersed, we performed an identical coupling reaction using a “dummy” system of core/shell PbS/CdS QDs with very different radii (R = 2.1 nm and R = 3.2 nm) such that we can differentiate them in the TEM images. The core/shell architecture was a convenient way to produce two sizes of QDs with the same type of ligand shell (oleate-coated, assynthesized) differentiable by TEM, but the core/shell QDs have PL quantum yields too low to be useful for the EnT study due to etching of the PbS core during shell formation.40 We simulated the conditions of the coupling reaction for the EnTactive system exactly for this dummy system, as detailed in the Experimental Methods section of the Supporting Information. Using cryo-STEM (experimental details in the Supporting Information) images of this dummy system, which ensures that any assemblies we see are present in solution and not just a result of drying on the TEM grid, we demonstrate that our coupling reaction and conditions produce hetero-QD assemblies as small as hetero-QD dimers and trimers (Figure 2C,D) and larger oligomers (Figure 2E,F). We observe that 94% of the small core/shell QDs are incorporated into hetero-QD assemblies upon EDC/NHS coupling, compared to just 5% for uncoupled mixtures (see the Supporting Information, Table S2). The experiment with the dummy core/shell system also provides additional evidence that the assemblies form primarily by covalent coupling, and not by nonspecific aggregation due to oleate loss: the core/shell QDs in Figure 2C−F are separated by gaps of 1−1.5 nm, whereas it was shown previously that core/shell QDs agglomerated due to ligand loss have no detectable interparticle gaps.41 Figure 3 shows the PL and absorbance (insets) of mixtures of DQD and AQD in various DQD:AQD ratios, produced by varying the concentration of DQD while holding constant the concentration of AQD at 0.8 μM; this method results in a linear

Figure 3. PL spectra and absorbance spectra (insets) of mixtures of DQDs and AQDs in a series of molar ratios (DQD:AQD) without (A, “Mixed”) and with (B, “Coupled”) addition of EDC/NHS reagents as outlined in Scheme 1 but otherwise treated identically. The excitation wavelength used to acquire the PL spectra is 970 nm. The Supporting Information shows the deconvolution of these spectra into contributions from DQD (PL peaks at 1080 nm) and AQD (PL peaks at 1195 and 1280 nm). The “dips” in the spectra at ∼1160 nm are due to reabsorption of emitted photons by the CHCl3 solvent. The “0:1” spectrum is that of the control sample, CdS QDs-AQDs, and is slightly shifted relative to the all-PbS QD samples because of the presence of CdS QDs.

increase in the DQD absorbance at 970 nm with increasing DQD concentration and a constant AQD absorbance at 1145 nm across the samples (insets). The two types of samples “Mixed” and “Coupled” are treated identically, including functionalization with AOT and MOA, and postcoupling treatment with HDT, except EDC/NHS was added to the samples in Figure 3B, according to the procedure described above, but not to the samples in Figure 3A. We chose an excitation wavelength of 970 nm for the PL experiments because it maximizes the fraction of photons absorbed by DQDs rather than AQDs. Upon covalent coupling of DQD and AQD, we observe a dramatic change in the shape of the PL spectrum of the mixture. Specifically, the PL on the higherenergy (DQD) side of the spectrum is depressed, and the PL on the lower-energy (AQD) side of the spectrum is enhanced. Fits of the PL spectra to a sum of Gaussian curves (see the Supporting Information, Figures S10−S12) confirm that the integrated DQD contribution to the total spectrum (denoted “PLD”) decreases and the AQD contribution to the total spectrum (“PLA”) increases upon coupling by EDC/NHS. Additionally, the absolute intensity of PL f rom AQDs of the sample increases with increasing concentration of DQD. Given that the concentrationand therefore absorbanceof AQDs in these sets of samples remains constant, an increase in their 22189


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The Journal of Physical Chemistry C PL intensity upon addition of DQDs indicates that, in the coupled system, excitons are being transferred from DQDs to AQDs,31 and at least a portion of those transferred excitons are being emitted by AQDs. Fits of the PL spectra in Figure 3 also show that the AQDs comprise two spectroscopically distinct populations, one that emits with a peak at 1195 nm (“PLA1”) and one that emits with a peak at 1280 nm (“PLA2”); see the Supporting Information, Figures S10−S12. We note that the peaks of the DQD and AQD absorbances differ in wavelength by 5−10 nm in the mixed vs coupled samples; this shift is consistent with what we observe when we add EDC/NHS to DQD or AQD samples in the absence of the complementary QD, and probably reflects a slight etching of the QD surface by both EDC and NHS by removal of Pb(oleate)2. Quantitative analysis of the PL spectra in Figure 3 to obtain the quantum yield of EnT requires that we measure the PL spectra and intensity of the AQDs within assemblies under the same chemical conditions but in the absence of an EnT pathway (i.e., a “baseline” PL spectrum). We therefore must construct a control system that is treated, chemically, identically to the DQD−AQD system but cannot mediate EnT. The Supporting Information contains a list of possible influences of the coupling reaction and subsequent treatment of the QDs on their optical properties, and therefore justifies the use of this control. For this purpose, we use CdS QD−PbS QD pairs, where a CdS QD of an appropriate radius replaces the PbS QD that either serves as the AQD or the DQD. When CdS replaces PbS as the AQD (we call this sample “DQD,control”) and we pump the mixture at 970 nm, only the PbS DQD is excited. EnT cannot occur because the absorption of the CdS AQD is at much higher energy than the emission of the PbS DQD. Using the DQD,control system, we obtain the baseline PL spectrum and quantum yield of the PbS DQDs within the assemblies. When CdS replaces PbS as the DQD (we call this sample “AQD,control”) and we pump the mixture at 970 nm, only the PbS AQD is excited. Again, EnT cannot occur, so we obtain the baseline PL spectrum and quantum yield of the PbS AQDs within the assemblies; see the Supporting Information, Figures S13 and S14. Figure 4 is a plot of the percentage EnT quantum yield, defined as the number of excitons transferred from DQDs to AQDs per photon absorbed by a DQD (×100%), as a function of DQD:AQD. We calculate the EnT yield as follows. In the DQD−AQD coupled product, the intensities of light absorbed by DQDs (IDQD) and AQDs (IAQD) are given by eqs 1 and 2, respectively, where I0 is the a IDQD = I0 × (1 − 10−(a + b)) × (1) a+b IAQD = I0 × (1 − 10−(a + b)) ×

IDA IAQD,Cont

=

=

b a+b

⎡ −(a + b) )× ⎣ (1 − 10

(

Figure 4. EnT quantum yieldthe percentage of excitons in DQDs that are transferred to AQDs, (EnT in eq 7 × 100%)of the coupled DQD−AQD system for different ratios DQDs:AQDs in the sample. EnT yields were calculated as described in the text. We observe the highest quantum yields of EnT with the DQD:AQD = 1:1 and 1.5:1 systems (∼90%). The data points are the average of three measurements on three independently prepared samples, where each sample had its own control (CdS QD−AQD) sample. The error bars represent the total range, not the standard deviation, of the three measurements. The raw data for each sample are in the Supporting Information.

intensity of the incident light, a is the optical density of the DQDs, and b is the optical density of the AQDs. The intensity of the photons emitted from the AQDs upon coupling to the DQDs (IDA) is given by eqs 3 and 4, where EnT is the fractional energy transfer yield from DQDs to AQDs, QYPL,AQD (3)

⎡⎛ a ⎞ ⎟ × EnT IDA = ⎢⎜(1 − 10−(a + b)) × ⎣⎝ a + b⎠ b ⎤ + (1 − 10−(a + b)) × ⎥ × I0 × QYPL,AQD a + b⎦

(4)

is

the PL quantum yield of the AQDs, and eq 4 is obtained by substituting eqs 1 and 2 into eq 3. The intensity of light emitted by the AQDs within the CdS QD−AQD control sample (IAQD,Cont) is given by eq 5, where we assume the optical density (b) and the quantum yield (QYPL,AQD) of the IAQD,Cont = I0 × (1 − 10−b) × QYPL,AQD

(5)

AQDs are the same within the DQD−AQD sample and the CdS QD−AQD control sample. The ratio of photons emitted from AQDs in the coupled donor−acceptor assemblies to photons emitted from AQDs within the control is then given by eq 6, and by rearranging eq 6, we obtain the definition

(2) a a+b

IDA = (IDQD × EnT + IAQD) × QYPL,AQD

) × EnT + (1 − 10−(a+b)) × a +b b ⎤⎦ × I0 × QYPL,AQD I0 × (1 − 10−b) × QYPL,AQD

((1 − 10−(a+b)) × a +a b ) × EnT + (1 − 10−(a+b)) × a +b b (1 − 10−b)

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(6)


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The Journal of Physical Chemistry C of the fractional quantum yield of energy transfer, eq 7. This yield is plotted in Figure 4.

EnT =

⎡ IDA(1 − 10−b) − (1 − 10−(a + b)) × ⎣⎢ IAQD,Cont

b ⎤ ⎥ a + b⎦

((1 − 10−(a+b)) × a +a b )

(7)

The maximum enhancement of AQD PL due to EnT (a factor of ∼3.0) occurs at DQD:AQD = 1.5:1−2:1, but the maximum QY of EnT, ∼90%, occurs at some DQD:AQD ratio between 1:1 and 1.5:1. We believe the QY of EnT is maximized in this range because (i) each DQD needs at least one proximate AQD in order to capture its exciton (so having DQDs in large excess is not optimal) and (ii) as the fraction of photons absorbed by DQD increases, there is a higher probability of exciting a DQD that has a proximate AQD; that is, we sample more arrangements of heteroassemblies (so having AQDs in large excess is not optimal). We have also anecdotally observed, though not proven, that, as the discrepancy between the total number of AOT ligands (on the DQDs) and MOA ligands (on the AQDs) increases, the coupling yield decreases, so having one or another type of QD in large excess could decrease the EnT yield by making the coupling reaction less effective. We emphasize that, if we assume, as we saw in the core/shell dummy system, that 94% of DQDs are incorporated into heteroassemblies within our optimized (DQD:AQD = 1.5:1) coupled sample, then the EnT yield when only considering DQDs within heteroassemblies is 91/94 = 97%. In other words, if a DQD has a proximate AQD, the EnT yield is nearly unity. Finally, we measured the rate constant for EnT using transient absorption (TA) measurements (details in the Supporting Information) of the formation of the AQD excited state, by monitoring its bleach feature at a probe wavelength of 1150 nm after pumping the system at 970 nm. There is no contribution from the DQD excited state at the probe wavelength of 1150 nm. The vast majority of excited state evolution in this system occurs on the nanosecond time scale (see the Supporting Information, Figure S15, for TA spectra and kinetic traces on the picosecond time scale). Figure 5 shows kinetic traces extracted from the TA spectra of the CdS QD−AQD control sample, where no EnT occurs, and of the DQD−AQD coupled mixtures in various ratios. The AQD excited state within the control system decays by two processes with time constants of 612 ns and 2.5 μs. The 2.5 μs time constant (τ3) is typical for radiative recombination of excitons in PbS QDs. The 612 ns time constant (τ2) most likely corresponds to electron or hole trapping to sites formed upon chemical treatment of the QDs during the coupling procedure (which is simulated in producing the control sample). The kinetic traces for the DQD:AQD = 1:1, 1.5:1, and 2:1 EnT-active coupled mixtures have similar shapes, and were globally fit with a rate equation, eq 8, derived from a model of the exciton ⎧ ⎪ d 1 Pi(t ) = Pi(t )⎨− − ⎪ dt τ ⎩ i

⎫ ⎪ k ∑ i ,j⎬⎪ + ⎭ j≠i

Figure 5. AQD kinetic traces, monitored on the nanosecond-tomicrosecond time scale, extracted at the red edge of the ground state bleach of AQD from the TA spectra of a coupled CdS QD−AQD control sample (black) and the coupled DQD−AQD samples at various ratios DQD:AQD = 1:1 (blue), D:A = 1.5:1 (green), and D:A = 2:1 (orange), after excitation at 970 nm. The probe wavelength is 1135 nm for the control sample and 1150 nm for the three EnT-active samples. The lines are the result of a global fit of the data to eq 8, where we assume that all three DQD−AQD samples have the same intrinsic EnT lifetimes (lifetimes for EnT between an adjacent DQD and AQD without intervening exciton hopping). The model yields intrinsic EnT lifetimes for DQD to AQD1 of τEnT1 = 113 ± 26 ns and for DQD to AQD2 of τEnT2 = 850 ± 330 ns. The kinetic traces are positioned at “time-zero” (here, 1 ns) according to their respective amplitudes at 1 ns in the ultrafast TA experiment. The ultrafast TA data is in the Supporting Information, Figure S15, and the kinetic traces acquired at other probe wavelengths within the AQD ground state bleach are in Figure S17.

details.42,43 We incorporated both radiative and nonradiative contributions to exciton decay in the AQDs into τi by assigning each QD in the simulation a value of τi that corresponds to either τ for the radiative process (2.5 μs) or τ for the nonradiative process (612 ns), with a probability equal to each process’ respective fractional amplitude in the fit of the kinetic trace of the control sample. The master equation was solved by propagating the QD populations in time within 100 hexagonally close packed (HCP) structures of the QD assemblies, with sizes and interparticle distances estimated from our TEM images. We created the initial excited state population within each assembly by randomly exciting a number of DQDs and AQDs commensurate with their respective extinction coefficients at 970 nm. In each assembly, a fraction of the QDs, determined from the experimentally measured quantum yields of 21% (DQD) and 15% (AQD), undergo nonradiative trapping on the hundreds of ns time scale that competes with EnT. The model includes two “intrinsic” (direct EnT without an intervening hopping step) DQD-toAQD EnT rates to account for EnT from DQDs to the two AQD populations (AQD1 and AQD2) that are observed experimentally. We determined the relative populations of AQD1 and AQD2 from their relative emission intensities (in the steady-state PL experiment), and assuming the two populations have the same PL quantum yield. We determined the intrinsic EnT rates between donor and acceptor QDs, ki,j, by globally fitting the rate equation (8) to the kinetic traces for the formation and decay of the AQD ground state bleach, Figure 5, for a series of DQD:AQD ratios. The resulting intrinsic lifetimes are τEnT1 = 113 ± 26 ns for EnT from DQD to AQD1 (the better spectral overlap case) and

∑ kj ,iPj(t ) j≠i

(8)

dynamics in the PbS QD assemblies, where Pi(t) and Pj(t) represent the photoexcited populations of each type of QD i or j, τi is the time constant for relaxation of the AQD excited state without EnT, and ki,j are the rate constants for EnT between adjacent QDs i and j; see the Supporting Information for 22191


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The Journal of Physical Chemistry C τEnT2 = 850 ± 330 ns for EnT from DQD to AQD2 (the less optimal spectral overlap case). We note that the formation of the AQD excited state by EnT on the 100 ns time scale competes with its decay on the 1 μs time scale, so we do not expect the amplitude of the ground state bleach at its peak to reflect the population of excited states created by EnT, as does the steady-state PL spectra of the samples. The growth in the ground state bleach feature of AQD in time is indicative of EnT and not CT, because this growth is also observed in the timeresolved PL of the AQDs, which indicates that the process we are measuring with TA creates an emissive species, not an ion pair (see the Supporting Information, Figure S16). The Supporting Information, Table S7, lists the values of all fitting parameters and all fixed input parameters for our exciton hopping model.

HDT, (iv) the absolute and relative amounts of EDC/NHS added, and (v) the time of reaction. The coupling reaction performed here needs at least 2 days to complete. The main disadvantages of this coupling chemistry are that (i) it is irreversible, so heteroassemblies cannot be made to be dynamic or reconfigurable, and many assemblies are kinetically trapped structures, and (ii) selective synthesis of lower-order assemblies (dimers and trimers) is difficult because the coupling yield drops dramatically when we lower the coverage of “functional” ligand (AOT and MOA) below 20% for AOT on DQD and 10% for MOA on AQD. The second issue is of little consequence to the current study, since even the larger aggregates remain soluble, and we can incorporate aggregates of different sizes into our simple kinetic model. Further mechanistic study of this process would benefit from selective production of lower-order oligomers, which has been accomplished in the coupling of metal nanoparticles, and CdSe/ZnS core/shell QDs with metal nanoparticles through DNA templating and subsequent chromatography,45,46 and by coupling QDs with rigid organic spacers followed by density gradient ultracentrifugation to isolate dimer and trimer fractions.41 The latter approach does produce a relatively low yield of small oligomers (1−5% for dimers, for example). Even with these limitations, we have shown that amide coupling chemistry leads to selective donor−acceptor coupling of QDs, and can be optimized to yield 90%-efficient transfer of near-IR excitons from donors to acceptors, despite the relatively slow energy transfer process (∼100 ns). Both the slow energy transfer and the high yield of energy transfer are, interestingly, related to the long excited state lifetime of PbS QDs (1−3 μs), which is caused by a weak transition dipole moment for the radiative transition but allows even nanosecond-time scale processes like energy transfer to compete with radiative decay of the exciton. The “forgiving” PbS QD excited state also allows us to lengthen the interparticle distance such that charge transfer is prohibitively slow but EnT can still occur with high efficiency. These conformationally flexible linkers, whether joined by an amide bond or another type of interaction, also increase the probability of coupling EnT donors and acceptors, even if they are both large objects, like QDs or proteins.

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CONCLUSIONS We have demonstrated the transfer of near-IR excitons from donor PbS QDs (DQD, R = 1.6 nm) to acceptor PbS QDs (AQD, R = 1.9 nm)with near-perfect spectral overlap of donor emission and acceptor absorptionwithin covalent heteroassemblies in CHCl3, with 90% quantum yield and time constants of 113 ns and 850 ns. The heteroassemblies are formed by EDC/NHS-facilitated amide coupling of amineterminated ligands on the smaller DQDs and carboxylateterminated ligands on the larger AQDs. This coupling results in dimers, trimers, tetramers, and higher-order hetero-oligomers of DQDs and AQDs, as imaged by TEM and cryo-STEM. The enhancement of the PL of the AQDs by energy transfer increases with increasing ratio of DQDs to AQDs even after correcting for the absolute number of photons absorbed (and appears to saturate at a factor of 3.0 at DQD:AQD = 1.5:1), but the quantum yield of energy transfer, defined as the percentage of excitons in the DQDs that transfer to an AQD, peaks at 90% at DQD:AQD = 1:1−1.5:1, probably due to a combination of optimal coupling yield and maximum mixing of DQDs and AQDs within assemblies. The time constants for energy transfer, 113 and 850 ns, are within the range of those measured for EnT between PbS QDs in the solid state,19−21,23 and a factor of 2−10 slower than those measured for EnT between CdSe QDs in the solid state,10,12,15,44 although the comparison is not entirely straightforward because the quoted rate constants are directly measured (and therefore could be convoluted with exciton hopping rate constants), while ours are “intrinsic”, i.e., single-step, nearest-neighbor EnT determined from fitting our data with a multipathway kinetic model. Implicit in our analysis is that FRET is a valid model for interparticle EnT in our system. Although we have not explicitly addressed the distance dependence of the EnT rate here, the measured average rate constants for EnT between adjacent QDs, which we obtain from modeling our TA data (113 and 850 ns), are reasonably similar to that predicted by Förster theory for our TEM-measured interparticle distances of 4.9 nm (102 and 205 ns, respectively). The yield of the amide coupling procedure depends on (i) the absolute and relative coverages of the functional ligands, MOA and AOT, (ii) the length and binding affinity of the native ligand (here oleate), which needs to be long enough and tight-binding enough to solubilize the QDs (here, at least 10 carbons long) but have enough time “off” the QD surface to transiently expose the end groups of the functional ligands for reaction with EDC or NHS, (iii) sufficient stability of the QD surface after coupling, achieved here by replacing oleate with

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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.6b06880. Additional experimental methods, photoluminescence spectra of mixed and coupled samples and Gaussian fits, additional electron micrographs, and additional transient absorption and photoluminescence data (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: (847)491-3095. Author Contributions †

K.-R.L., S.B.H.: These authors contributed equally.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This material is based on work supported by the Air Force Office of Scientific Research, under AFOSR Award No. FA22192


Article


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9550-14-1-0005. This work made use of the EPIC facility of the NUANCE Center at Northwestern University, which has received support from the Soft and Hybrid Nanotechnology Experimental (SHyNE) Resource (NSF NNCI-1542205); the MRSEC program (NSF DMR-1121262) at the Materials Research Center; the International Institute for Nanotechnology (IIN); the Keck Foundation; and the State of Illinois. NMR measurements were performed at Northwestern University’s Integrated Molecular Structure Education and Research Center (IMSERC).

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