Energy Transfer between Quantum Dots and Conjugated Dye

Article pubs.acs.org/JPCC

Energy Transfer between Quantum Dots and Conjugated Dye Molecules Gary Beane, Klaus Boldt, Nicholas Kirkwood, and Paul Mulvaney* School of Chemistry and Bio21 Institute, University of Melbourne, Parkville VIC 3010, Australia S Supporting Information *

ABSTRACT: Energy transfer from quantum dots (QDs) to variable-length, dye-labeled peptides is reported. We find that existing models used to calculate the efficiency of energy transfer from steady-state measurements are insufficient for nanoparticle− dye interactions. To accurately measure the distance dependence as a function of separation, the effects of both multiple valencies and variations in the luminescence quantum yield of the acceptor dye with separation need to be taken into consideration. Using Poisson statistics, we account for the distribution of QD/dye ratios. Nevertheless, we find that the actual dependence of the energytransfer efficiency as a function of QD−dye separation obeys an R−n dependence with n = 6.1 ± 0.1 as predicted by Förster resonance energy transfer (FRET) theory.

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INTRODUCTION

In particular, there have been numerous studies of energy transfer from semiconductor nanocrystals (QDs) to acceptor dyes. These systems are very attractive for biological labeling studies because QDs have large absorption coefficients; their emission can be tuned by controlling the size of the nanocrystal; and they exhibit enhanced photostability, which facilitates long, time-dependent fluorescence studies. However, there are several key challenges to using QDs for FRET studies. These are the questions of (i) whether QDs can be considered as point dipoles, (ii) whether conjugated dye molecules are free to rotate, and (iii) how to account for multiple dye molecules being adsorbed to a single QD donor. Nevertheless, despite these concerns, FRET has been applied to describe energy transfer between QD donors and dye-molecule acceptors.8−16 Literature reports about the applicability of using FRET to describe systems involving QD donors and dye acceptors vary, with many workers in the area arguing that QDs are well described as point dipoles,8−12 without the need for either higher multipolar interactions or the calculation of the full electronic interactions. Pons et al.5 found that the quenching of a CdSe/ZnS core−shell structure by dyelabeled peptide sequences was consistent with the standard FRET theory, in which the QD is treated as a point dipole. There are, however, several problems with their analysis; specifically, they used the method of Yu et al.17 to calculate the QD concentration, which was shown by Jasieniak and co-workers to underestimate the extinction coefficient, resulting in a lower real concentration.18 This means that the QD-to-dye ratios were underestimated. It is also of note that the shortest QD-to-dye

Understanding the photophysics behind the phenomenon of excitation energy transfer has been an area of intense research for over 85 years.1−5 Much of this research has focused on understanding how the transfer of energy from an excited “donor” fluorophore to a nearby ground-state “acceptor” fluorophore depends on distance. Following the pioneering works of Cario and Franck,1 Perrin6 and Perrin and Choucroun,2 Theodor Förster formulated a quantitative model to explain the relationship between energy-transfer efficiency and the spatial separation of the fluorophores based on dipole−dipole coupling.3 Förster’s theory was subsequently substantiated by Stryer and Haugland, who used rigid polyproline peptides to vary the separation of an α-naphthyl donor at the C-terminus and a dansyl acceptor at the N-terminus.4 Förster’s theory has become the dominant model now used to describe energy transfer between organic fluorophores, where it is commonly known as Förster resonance energy transfer (FRET).7 The ubiquitous use of FRET theory has arisen because, although it makes several key assumptions, it fits experimental observations surprisingly well and requires only a few experimental parameters to be measured. Indeed, in many biological situations, FRET provides a very useful “spectroscopic ruler”4 relating easily measurable macroscopic quantities to the nanoscale separation between donors and acceptors. Although Förster originally formulated his theory for the case of conjugated fluorescent molecules of low molecular weight, many new fluorophores have been discovered that are of high molecular weight such as conducting polymers, green fluorescent proteins, and semiconductor nanocrystals or quantum dots (QDs). © 2014 American Chemical Society

Received: February 26, 2014 Revised: July 1, 2014 Published: July 8, 2014 18079

dx.doi.org/10.1021/jp502033d | J. Phys. Chem. C 2014, 118, 18079−18086

The Journal of Physical Chemistry C

Article

separation in the study by Pons et al.5 already had a center-tocenter separation of 25 Å. This is significant, as the assumption of a point dipole is expected to be more accurate the farther the dye is from the QD surface. Several studies have already concluded that the point-dipole approximation breaks down when describing energy transfer between QDs and dye molecules when the dye molecules are near the particle surface.19−24 Indeed, Blaudeck and co-workers20 suggested that photoexcited electrons in a QD can tunnel into the local environment, out to 5 Å for a 3.5-nm-diameter CdSe QD, which raises the possibility of additional luminescence quenching due to electron transfer from QDs to adsorbed dye molecules. A further complication is that there could be multiple dye-molecule acceptors for every QD donor, a situation that does not normally arise for dye−dye energy transfer and that makes the analysis more complex, as well as raising the issue of interactions between adsorbed dye molecules. A further consideration that must be addressed for any energytransfer systems involving QD−dye systems is the rigidity of the linker used. Several groups that have studied the effects of using biopolymer and DNA spacers in dye−dye FRET systems have found that significant corrections must be introduced to account for (i) the steric restriction of labels25 and (ii) the variability in the separation caused by the inherent flexibility of the linker.26−28 The effect of linker rigidity was also investigated by Boeneman et al., who found that, especially for biotin−streptavidin-type linkers, the assumption of a single, well-defined donor−acceptor separation is invalid.29 Given the inherent variability in these QD−linker−dye systems, it is worth reflecting on the original choice of linker used to validate FRET theory experimentally. Stryer and Haugland used what they assumed to be a rigid molecule in their early confirmation of FRET, a polyproline helix4 (see Figure 1). The rigidity of this molecule arises through

Figure 2. Comparison of the two common helices that polyproline (shown is a 10-proline sequence) can adopt. The top helix, known as the PPII configuration, is the one most commonly found because it has a comparatively lower ground-state energy than the more compact PPI helix. All of the peptide sequences in this study had the PPII structure, which was found to be the dominant form in ethanol.30

based on the use of polyproline spacers. We find that there exist significant deviations from the standard FRET model unless several important corrections are made, including (i) accounting for the statistical distribution of dye molecules, (ii) ensuring that the dye is separated by a sufficient distance from the donor to enable the point-dipole model to be applied, (iii) accounting for the changes in the intrinsic dye quantum yield (QY) due to the change in environment when bound to the QD, and (iv) confirmnig the relative rigidity of the linker used. We propose a revised model based on the experimental data that accounts for the distance dependence of energy transfer from a QD to a dye acceptor when using peptide spacers.

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EXPERIMENTAL METHODS Synthesis of CdSe/CdS/ZnS Nanoparticles. Nanoparticles were synthesized according to the method described by Boldt et al.32 Solvents were sourced from Sigma-Aldrich and were either high-performance liquid chromatography (HPLC) or spectroscopic grade for the fluorescence measurements. Aminopentanol (95%) was purchased from Aldrich. All chemicals were used as received. Synthesis of Dye-Labeled Peptides. Fmoc Solid-Phase Peptide Synthesis. N,N′-Diisopropylethylamine (DIPEA), piperidine, hydroxybenzotriazole (HBT), 4-dimethylaminopyridine (DMAP), and 1-[bis(dimethylamino)methylene]-1H1,2,3-triazolo[4,5-b]pyridinium 3-oxid hexafluorophosphate (HATU) were all obtained from GLBiochem, Shanghai, China. Dimethylformamide (DMF), dichloromethane (DCM), and diethyl ether were obtained from Ajax Chemicals (Melbourne, Australia). Wang Resin was sourced from NovaBiochem. Chloranil and 2,4,6-trinitrobenzenesulfonic acid (TNBS), which were used to test for the presence of primary amines during the final deprotection, were obtained from Sigma-Aldrich. The N-methyl amino acids N-(9-fluorenylmethoxycarbonyl)-Lproline (Fmoc-Pro-OH), N-(tert-butoxycarbonyl)glycine (BocGly-OH), and N-(9-fluorenylmethoxycarbonyl)-L -proline (Fmoc-Gly-OH) were obtained from GLBiochem, whereas the C-terminal amino acid Nα-Fmoc-Nβ-Boc-L-2,3-diaminopropionic acid [Fmoc-Dap(Boc)-OH] was sourced from ChemImpex International. The fluorescent dye label 5-carboxy-Xrhodamine succinimidyl ester (5-ROX SE) was sourced from Life Technologies.

Figure 1. Generalized structure of the α-naphthyl−polyproline−dansyl donor−acceptor construct used in Stryer and Haugland’s validation of the FRET model.4 In their work, n spanned from 1 to 12.

the formation of a characteristic helix, known as the polyproline type II helix (PPII) (see Figure 2). This is reported to have a rigid, rodlike structure in ethanol, as evidenced by the welldefined circular dichroism of solutions containing this molecule.30 However, recent work by Schuler et al.31 called into question the rigidity of this molecule and showed, through Monte Carlo simulations, that a “wormlike-chain” (WLC) model provides a better description of this molecule. Moreover, they showed that, for polyproline lengths much larger than about 20 prolyl residues, it is necessary to explicitly include the chain flexibility when calculating accurate energy-transfer efficiencies. Notwithstanding these considerations, polyproline remains the obvious choice as a rigid linker as long as the number of prolyl residues remains low.26 What is still missing in the literature, and is clearly needed, is a systematic experimental validation of FRET theory for energy transfer between QD donors and dye-molecule acceptors for a range of QD/dye ratios and for a wide range of clearly defined donor−acceptor separations. We report herein an approach 18080



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Sample Preparation. The diameter of CdSe/CdS/ZnS nanoparticles in solution was determined to be 5.8 nm by TEM (see Supporting Information). Samples for fluorescence measurements were all prepared in ethanol (HPLC-grade, Sigma-Aldrich) by ligand exchange with aminopentanol. For steady-state experiments, sample concentrations of 200 nM with a 1:1 ratio of QDs to dye were used, unless stated otherwise. The absorbance of the samples at the excitation wavelength was adjusted to be 10 molar excess) was added to ∼2 mmol of peptide prepared to ∼10 μg/ μL in dry DMF. Excess 0.4 M DIPEA/DMF (dry) was added to the solution until it had a grainy texture. The reaction mixture was covered and vortexed to thoroughly mix the peptide and dye label. The solution was then allowed to sit for 16 h with occasional mixing. The final dye-labeled peptide was purified by HPLC with a 1% acetonitrile gradient over 20 min on a Phenomenex Jupiter C4 column (300 Å). Electrospray ionization time-of-flight mass spectrometry confirmed the purity of the resultant dye-labeled peptides, which are denoted G(Dap)-ROX and GPn-(Dap)ROX, where n = 0, 4, 8, 12, 16, and 20.

Table 1. General Photophysical Properties of the Different Chemical Species Useda

QDsc 5-ROX Rh6G

λabs,max (nm)

λPL,max (nm)

ε(400 nm)b (M−1 cm−1)

τ (ns)

QY

525 568 529

542 604 553

8.2 × 105 1363 5031

5.2 ± 0.1 4.3 ± 0.1 −

0.49 ± 0.02 0.80 ± 0.04 0.9533

a

All data are for species in ethanol. bAll measured extinction coefficients have errors less than 5%. cD = 5.8 ± 0.7 nm.

Instrumentation. UV−visible absorbance, excitation, and photoluminescence (PL) spectra were collected using a ThermoElectron Varioskan multimode plate reader, with excitation at 400 nm for PL spectra. Time-resolved emission measurements were carried out in solution using a confocal microscope in epiillumination configuration, with an oil-immersion objective (Olympus, PlanApo NA 1.4) focusing the light from a 470 nm pulsed diode laser set at a 10 MHz repetition rate (PicoQuant, LDH-P-C-405). A 550-nm short-pass filter was used to remove emission originating from the dye, and the light was focused onto an avalanche photodiode (Perkin-Elmer, SPCM-AQR-15). For the measurement of the PL decay times of the individual particles, the photon-counting card (PicoQuant, TimeHarp 200) was set to time-tagged time-resolved mode (TTTR), and the decays were then generated by time-correlated single photon counting (TCSPC). All steady-state and time-resolved samples were prepared in triplicate.

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RESULTS We have constructed a series of analogues of the original αnaphthyl−polyproline acceptor systems that also meet some additional specific requirements. Foremost among these is that the peptide−dye structures must be capable of binding directly to the surface of the QDs, a condition that is met by incorporating a primary amine into the peptide sequence (by means of a glycine residue at the N-terminus of the peptide). Moreover, we require an orthogonal approach to deprotection, as we ultimately want one primary amine to be labeled with dye and another amine to bind to the surface of the QDs. This is achieved using a combination of tert-butoxycarbonyl (Boc) and fluorenylmethoxycarbonyl (Fmoc) protection on the (Nβ) amine side chain of the 2,3-diaminopropionic acid (Dap) residue and the N-terminus (Nα), respectively. It is desirable that the donor be excited at a particular wavelength at which the acceptor does not absorb any of the incident light. This is indeed the case for the present system, as 18081



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Figure 4. (A) Photoluminescence spectra of three ethanolic solutions containing 200 nM green QDs (green trace), 200 nM G(Dap)-ROX (blue trace), and 200 nM of each QDs and G(Dap)-ROX (magenta trace). The solution containing equimolar concentrations of QDs and dye shows a marked reduction of the PL of the QDs at a wavelength of 530 nm and an enhancement of the PL of the dye at a wavelength of 600 nm. The excitation wavelength was 400 nm. (B) Excitation spectra (green, blue, magenta) corresponding to those shown in panel A, where the PL of the dye at a wavelength of 630 nm was monitored while scanning the excitation wavelength from 350 to 620 nm. It is evident from panel B that the origin of the enhanced PL of the dye is from energy transfer from the QD donor to the dye acceptor. Note that the QY of G(Dap)-ROX in solution is different from the QY when G(Dap)-ROX is bound to the QDs, as is evident from the decreased PL of the dye at wavelengths at which the QDs do not absorb. The traces in gray and orange are those of GP4(Dap)-ROX and GP8(Dap)-ROX, respectively, and demonstrate that the QY of the dye increases with the length of the linker.

Figure 3. (A) Optical extinction spectra of 5-ROX (red trace, left axis) and QDs (blue trace, left axis), along with their corresponding PL spectra (magenta and green traces, respectively, right axis). (B) Normalized optical absorption spectrum of 5-carboxy-X-rhodamine (5-ROX) (red trace, left axis) and the normalized PL spectrum of CdSe/ CdS/ZnS particles with 2 ML of each CdS and ZnS used in this study (green trace, right axis). The shaded area between the two spectra is indicative of the spectral overlap.

one can see in Figure 3A that, at 400 nm, the extinction coefficient of the QDs (8.2 × 105 M−1 cm−1) is 600 times higher than that of the dye (1363 M−1 cm−1). One can also see from this same figure that the QD PL and the dye PL have significant spectral separation, which enables the emission from just the donor or just the acceptor to be measured. The structure shown in the upper right-hand corner of Figure 3A is a general structure for the dye acceptor used throughout this study, 5-carboxy-Xrhodamine (5-ROX), where the substituent R represents the different peptides that this acceptor labels. A concise summary of some of the key photophysical characteristics of the dye acceptor (5-ROX) and the QD donor is presented in Table 1. If one considers the photoluminescence spectra of the QD donor in Figure 4A in the absence and in the presence of 1 stoichiometric equivalent of the shortest, dye-labeled spacer G(Dap), one can see that the PL of the QD donor is significantly quenched. It can be observed that, in the absence of the QDs, the dye PL at the same concentration is much lower than the dye emission in the

presence of the QDs, that is, the dye emission is enhanced. From these data alone, we conclude that there is energy transfer from the QD donor to the dye acceptor. To confirm this, one can also monitor the excitation spectra of the two fluorophores. In Figure 4A, the PL is shown for excitation at 530 nm. One can see that the PL at 630 nm is much lower for a solution containing the dye than for a solution containing equimolar concentrations of QDs and dye. As the QDs have negligible PL at this wavelength, one must infer that the emission from the dye in the presence of the QDs originates primarily from the absorption of light by the QDs; thus, there must be energy transfer. An important complication in these systems is that the dielectric environment around the dye changes as the dye binds to the QD surface. This causes a dramatic reduction in the intrinsic QY of the dye.34 This effect can be seen by examining the emission of the dye at 630 nm upon excitation at a 18082



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dependence obeys Förster theory, it must be shown that the energy-transfer efficiency obeys the equation

wavelength at which only the dye absorbs (575 nm) (Figure 4B). We also note that the emission from the dye-only sample in Figure 4B is significantly greater than that for the QD−dye conjugate when excited at 575 nm. Overall, one can see from the excitation spectra that, although there is significant energy transfer to the dye, the overall emission intensity is substantially lower because of the environmental quenching effect. This additional quenching must be taken into account in calculating energy-transfer efficiencies. The final confirmation that energy transfer occurs is provided by measurement of the QD lifetime after the addition of the dye, which results in strong reductions in PL lifetimes, as seen in Figure 5A.

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E=

1 1 + (R /R 0)γ

(1)

with γ = 6. In dye−dye systems, R0 is given by R 06 =

9 ln(10)κ 2ϕDJ 128π 5ε0NAn0 4

(2)

where κ is the orientation factor, ϕD is the quantum yield of the donor, J is the spectral overlap integral for the donor−acceptor system, and n0 is the refractive index of the solvent. An assumption in eq 1 is that the donor and acceptor fluorophores are in a one-to-one ratio. The energy-transfer efficiency when there are n independent acceptors per QD at a fixed distance R is given by n E(n) = n + (R /R 0)6 (3)

DISCUSSION

The results presented here clearly confirm earlier works, which have demonstrated that energy transfer from QDs to dye molecules is very efficient. However, to confirm that the distance

Until this point we have approached the construction of the QD−dye system in a manner that is analogous to that of Stryer and Haugland’s system; however, we must now consider one way in which the present system is quite dissimilar. Although a molecular system can be constructed so that the donor and acceptor bind in a stoichiometric ratio, this is not easily achieved for quenching of QDs by molecular acceptors such as dyes. Because multiple conjugation groups are attached to each QD surface, addition of the dyes results in a statistical distribution of dye molecules bound to the QDs. If the dye molecules are labile enough that they can exchange with different quantum dots and if the number of possible dye-binding sites is large (typically larger than 20 sites for a mean ratio of 1),35 then the dye distribution will obey Poisson statistics. With these assumptions in place, the observed quenching efficiency Eobs is given by ∞

Eobs =

∑ E(n) P(n) (4)

n=0

where Eobs is the observed, ensemble-averaged energy-transfer efficiency; E(n) the energy-transfer efficiency for QD donors with n dye acceptors; and P(n) is the probability of a QD having n acceptors, which is given by the Poisson equation

P(n) =

e −λ λ n n!

(5)

where λ = dye/QD is the mean number of dye molecules bound to each QD. Combining eqs 3 and 5, the observed energytransfer efficiency is Figure 5. (A) Fluorescence lifetimes of ethanolic solutions of QDs collected by TCSPC for various donor−acceptor spacings. The waveforms are normalized to the maximum number of counts. The solutions were excited using a 470-nm pulsed diode laser with a fwhm of 50 ps, and the emission was collected using a 530-/10-nm short-pass filter. (B) Excitation spectra of the different QD−dye systems from G(Dap)-ROX to GP20(Dap)-ROX, where the dye and QD are in equimolar concentrations. The spectra are normalized to the dye peak at 560 nm. The black trace represents the theoretical maximum-energytransfer situation where only one dye molecule can bind to the donor and there is 100% energy transfer; in this scenario, the excitation spectrum would be the same as the sum of the absorbance spectra of the QD donor and the dye acceptor, when normalized to the acceptor peak.

∞

Eobs =

∑ n=0

n e −λ λ n n + (R /R 0)γ n!

(6)

where γ is the exponent to be found. There are two ways to determine the values of Eobs in each experiment. The first is by measuring the reduction in quantum yield or lifetime of the donor in the presence of the bound acceptor dye. The efficiency of energy transfer is Eobs = 18083

kD → A

kD → A + kR + kNR

(7)



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where kD→A is the rate of energy transfer, kR is the rate of radiative decay, and kNR is the rate of quenching by all other mechanisms. Equation 7 can be expressed in terms of either the fluorescence intensities or the lifetimes of the donor−acceptor complexes (Iobs or τobs, respectively) and the donor fluorophore by itself (ID or τD, respectively) Eobs =

τ I kD → A = 1 − obs = 1 − obs τD kD → A + kD ID

(8)

−1

where τobs = (kD→A + kD) and kD = kR + kNR. Although eq 8 allows a direct value of the energy-transfer efficiency from the lifetime quenching of the donor fluorophore (τobs) to be obtained, simply monitoring the steady-state quenching of the donor fluorophore (Iobs) provides only a measure of the total amount of quenching, not the amount due to energy transfer. Hence, we prefer to use the change in lifetime to estimate the rate of energy transfer. The second way to measure the energy-transfer efficiency is from the increase in the dye emission in the presence of the donor, from analysis of the excitation spectra. It is well-known that the excitation spectrum and extinction spectrum for a particular chemical species are coincident provided that the absorbance is low.36 From this equivalence, it follows that, in donor−acceptor systems in which 100% of the excitation energy passes from the donor to the acceptor, the sum of the donor and acceptor extinction spectra is the same as the sum of their excitation spectra, provided that both are normalized to unity at the acceptor peak (thus both are unitless). Simply put, if the profile of the donor−acceptor excitation spectrum is the same as that of the extinction spectrum, then energy transfer is unity. The reason for normalizing to the dye acceptor peak is that the magnitude of this peak in the excitation spectra is independent of the degree of energy transfer and serves as a reference for how much donor character, and thus energy transfer, is present in the donor−acceptor complex. For systems in which the energy transfer is less than unity, the efficiency of energy transfer is provided from the normalized extinction spectrum of the donor−acceptor complex, A, which is equal to the sum of the acceptor and donor excitation spectra such that A = χA + EobsχD

Figure 6. (A) FRET efficiencies calculated from either the excitation spectrum data using eq 10 (open black squares) or the fluorescence lifetime measurements using eq 8 (open red circles) to calculate Eobs in eq 6. The black and red dashed lines through the corresponding data sets represent best fits to the data using eq 6. The parameter λ was held constant at 1, with the following fitted: R0 = 79 Å, γ = 5.5 for the steadystate data and R0 = 78, γ = 5.6 for the time-resolved data. (B) FRET efficiencies calculated from excitation spectra for four different stoichiometries, namely, 0.1, 0.3, 1, and 3 equiv of dye per QD (black open circles), and fits to eq 6 with R set to 50.9 Å and λ as the independent variable. Fitting of the experimental data gives a γ value of 6.1 ± 0.08. Error estimates for the efficiencies are one standard deviation, whereas distance estimates assume a 5% variation.

(9)

where χA and χD are the excitation spectra of the donor and acceptor, respectively (normalized to the acceptor peak), and Eobs is the efficiency of energy transfer from the donor to the acceptor fluorophore. Although eq 9 is correct for the case of energy transfer in which the local dielectric environment of the acceptor is constant, in the present system, this is not the case. As can be seen in Figure 4B, the QY of the dye changes with the length of the linker, which complicates the use of eq 9 and neccessitates its revision. Thus, rearranging eq 9 and accounting for the reduced QY of the acceptor, our final equation becomes Eobs =

In Figure 6A, we plot fits of the experimental data from the excitation spectra (black circles) and from the quenching of the QD donor (blue squares) to eq 6. The best fits yield values of γ = 5.6 and 5.5 for the two data sets. Equation 6 should also account for the Poisson distribution, and in Figure 6B, the efficiency of energy transfer is plotted for various dye/QD ratios using the single quencher G(Dap)-ROX; it is again well fit by eq 6 with γ = 6.1. These data all strongly indicate that, for these spacers, the energy-transfer efficiency closely follows FRET theory. It is worth noting that any error in the QD core−shell diameter would result in changes in R0 and not in the value of γ itself (see Figure 7A). Indeed, only errors in parameters that are distancedependent will cause changes in the value of γ. For example, if there are distance-dependent deviations in the orientations of the

Aζ − χA χD

(10)

where the term ζ is a correction for the difference in QY of bound dye molecules compared to the free dye molecules in bulk ethanol solution. Equations 8 and 10 provide two independent measurements of Eobs. The first assumes that the decrease in QD PL lifetime can be attributed to energy transfer alone, whereas the second records the fractional increase in acceptor emission due to the QDs. We now use both these measurements of Eobs in eq 6 to extract the parameter γ. 18084



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molecules are bound to the QDs; this environmental effect can be taken into account by measuring the dye PL at wavelengths to the red of the QD absorption spectrum when the dye is both bound and free in solution. Moreover, we are forced to assume that the value of κ is a constant and does not change with QD− acceptor separation. Finally, we have assumed strictly dipole− dipole coupling between the QDs and dye molecules and cannot exclude quadrupole−dipole coupling37−39

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CONCLUSIONS Energy transfer has been well studied for dye−dye systems, and its ubiquitous use in the biological sciences has demonstrated countless times the validity of the mathematical formalism. In contrast, the practical application of FRET theory to QD−dye systems has received far less attention, and there are real differences in these systems that set them apart from conventional dye−dye systems. As we have shown in this article, it is imperative that Poisson statistics be used when evaluating energy transfer in QD−dye systems. Moreover, we have also shown that there is an anomalous distance dependence for QD−dye energy transfer, with significantly less energy transfer occurring than would be expected. We attribute these deviations to either variance in the value of the orientation factor κ as a function of separation or some small degree of divergence from the simple dipole−dipole model of energy transfer. We conclude that more work is necessary to fully elucidate the energy-transfer efficiency of QD−dye interactions.

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ASSOCIATED CONTENT

* Supporting Information S

Figure 7. (A) ln(1/Eobs − 1), which is related to the observed efficiency, plotted with respect to the natural logarithm of the donor−acceptor separation. The data (open circles) are well fit (solid black line) using eq 6, which gives values of R0 = 79.0 ± 1.6 and γ = 5.6 ± 0.5 Å. The gray shaded area represents a 20% variation from the mean in the value of R, which would change the value of R0 (lower dashed line is 63 Å; upper trace is 96 Å) but would not change the value of γ. (B) Data (open circles) and fit to the data (γ = 5.6, solid black line) compared with the cases where γ = 6 and γ = 4.

Additional details of the analysis method and ensemble characteristics results. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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donor and acceptor, through the κ2 term, these could account for the observed deviation of γ from 6. One can also see from Figure 7B that a 1/R4 dependence of the efficiency of energy transfer on separation is not valid for this system and fits the experimental data poorly. A 1/R4 dependence has been reported for the quenching of dye photoluminescence by small metal particles. Importantly, it is worth noting that the efficiencies shown in Figure 5 were calculated from the enhancement of the dye PL (which occurs only if there is energy transfer) and the quenching of the PL lifetime of the QDs (which can be caused by either electron or energy transfer). As is immediately apparent from Figure 6, the distance dependence as a function of QD−dye separation is the same for both sets of data, strongly suggesting that electron transfer in the present system is negligible. What is evident from the data presented here is that, although FRET is likely to be a valid formalism for explaining energy transfer in QD−dye systems, it must be used with care, as a number of significant factors must be taken into consideration. For example, it is essential to allow for the Poisson distribution of dye molecules bound to the QDs; failure to do so leads to artificially low values for the FRET exponent and makes the distance dependence look much weaker than it really is. We also found that the intrinsic dye QY is strongly reduced when the dye

ACKNOWLEDGMENTS K.B. acknowledges the support of the Alexander von Humboldt Foundation through a Feodor Lynen research fellowship. N.K. thanks the Melbourne Materials Institute for support through an MMI/CSIRO scholarship. P.M. thanks the ARC for support under Grant DP130102134.

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REFERENCES

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