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A Stochastic Model for Energy Transfer from CdS Quantum Dots/Rods (Donors) to Nile Red Dye (Acceptors) Suparna Sadhu,† Masanori Tachiya,*,‡ and Amitava Patra*,† Department of Materials Science, Indian Association for the CultiVation of Science, Kolkata 700 032, India, and National Institute of AdVanced Industrial Science and Technology, AIST Tsukuba Central 5, Tsukuba, Ibaraki 305-8565, Japan ReceiVed: July 1, 2009; ReVised Manuscript ReceiVed: September 14, 2009
We propose a stochastic model for the kinetics of energy transfer from quantum dots or rods of CdS to Nile Red dye molecules. We assume that the distribution of the dye molecules around quantum dots or rods follows Poisson statistics. By analyzing time-resolved fluorescence decay curves of quantum dots or rods, we obtained the average number of dye molecules attached to the surface of quantum dots or rods as a function of the concentration of dyes and that of quantum dots or rods. The equilibrium constants for attachment/detachment of dye molecules to/from the surface of quantum dots or rods were evaluated. The quenching rate constants per dye molecule attached to the surface of quantum dots or rods were also estimated. 1. Introduction A number of experimental studies exist on quantum dot (QD)based fluorescence resonance energy transfer for many potential applications.1-4 It is now well established that QDs are used in fluorescence resonance energy transfer (FRET) because of their narrow emission and broad excitation spectra to reduce background.1 Medintz et al.1a reported the potential of luminescent semiconductor quantum dots for development of hybrid inorganicbioreceptor sensing materials. They demonstrated the use of luminescent CdSe-ZnS QDs as energy donors in FRET-based assays with organic dyes as energy acceptors in QDs-dye-labeled protein conjugates. Burda et al.1e demonstrated the applicability of CdSe QD for photodynamic therapy via the activation of photosensitizer (Pc4) using FRET. Furthermore, the large size of QDs as compared to organic dyes also provides the design of such configuration where multiple acceptors could interact with a single donor, which enhances FRET efficiency and thus measurement sensitivity.1 FRET is commonly used for biological research to measure molecular distances or donor-to-acceptor proximity.5 Fluorescence resonance energy transfer (FRET) is a process involving the radiationless (nonradiative) transfer of energy from a “donor” fluorophore to an appropriately positioned “acceptor” fluorophore. This process results from dipole-dipole interactions and strongly depends on the center-to-center distance of donor and acceptor. It also requires a nonzero spectral overlap integral between the donor emission and acceptor absorption.5 According to the Fo¨rster theory,6 the rate of energy transfer for an isolated single donor-acceptor pair separated by a distance r is given by
kT(r) )
( )
1 R0 τD r
6
(1)
where τD is the lifetime of the donor in the absence of the acceptor, and R0 is known as the Fo¨rster distance, the distance at which the * Corresponding author. E-mail:
[email protected] (A.P.); m.tachiya@aist. go.jp (M.T.). † Indian Association for the Cultivation of Science. ‡ National Institute of Advanced Industrial Science and Technology.
transfer rate kT(r) is equal to the decay rate of the donor in the absence of the acceptor. The Fo¨rster distance (R0) is defined as
R60 )
9000(In10)κ2φD 128π5Nn4
J(λ)
(2)
where φD is the quantum yield of donor in the absence of acceptor, N is Avogadro’s number, n is the refractive index of the medium, J(λ) is spectral overlap integral, which is defined as J(λ) ) ∫0∞FD(λ)εA(λ)λ4dλ, where FD(λ) is the normalized emission spectrum of the donor, εA(λ) is the absorption coefficient of the acceptor at wavelength λ (in nm), and κ2 is the orientation factor of two dipoles interacting. The value of κ2 depends on the relative orientation of the donor and acceptor dipoles. For randomly oriented dipoles, κ2 ) 2/3, and it varies between 0 and 4 for the cases of orthogonal and parallel dipoles, respectively. Thus, the efficiency of FRET depends on the distance of separation between donor and acceptor molecules. In our previous study,2b we have reported the shape-dependent resonance energy transfer between nanoparticles and dye. We also demonstrated2c that the composition of quantum dots plays a significant role in energy transfer between QD donor and proximal dye acceptors, because the spectral overlap varies with changing the composition without changing the particle size. It is reported7a that the shape of nanoparticles influences the energy transfer process. The core-shell nanoparticles have a significant role in efficient energy transfer process.7b,c In our previous study,2b we have reported that the efficiency of energy transfer and the interaction of donor-acceptor vary with changing the shape of nanoparticles. To our knowledge, there is no kinetic model for energy transfer between different shaped quantum dots and dye molecules. The distribution of acceptor molecules around QDs is essential to understand the kinetics of energy transfer by using a suitable model because this would be a governing factor for efficient energy transfer. In the present study, we try to understand the interaction between the excited state of quantum dot (QD) and quantum rod (QR) of CdS nanoparticles with dye molecules and present a quantitative
10.1021/jp906160z CCC: $40.75 2009 American Chemical Society Published on Web 10/15/2009
Energy Transfer from CdS QDs to Nile Red Dye
J. Phys. Chem. C, Vol. 113, No. 45, 2009 19489
estimation about the number of dye molecules attached to the surface of nanoparticles, using a simple kinetic model. 2. Materials and Methods The synthesis of CdS quantum dots (QDs) and quantum rods (QRs) was described previously.2b 0.5 mM (0.133 g) cadmium acetate in 5 mL of oleylamine was heated to 150 °C under Ar flow for 20 min to form a clear solution. Separately, an oleylamine-sulfur solution was prepared by dissolving 0.5 mM (0.016 g) of sulfur powder in 2.5 mL of oleylamine and quickly injected into the above hot reaction mixture under gentle stirring. The reaction mixture was kept at the desired growth temperature (150 °C). The reaction was quenched after 8 h by the addition of a large volume of anhydrous toluene into the reaction mixture. The CdS nanocrystals (QD) were separated from the toluene solution by the addition of ethanol and centrifuged. The yellow precipitate was then redispersed in n-hexane. For the preparation of CdS quantum rod (QR), the ratio of cadmium and sulfur precursor was taken as 1:3 (0.5 mM:1.5 mM). The same procedure was followed as before. For optical study, the excess ligands and reaction precursors were removed by repeated precipitation and centrifugation. Solvents were of spectroscopic grade. A series of CdS QDs/QRs (donor) and Nile Red dye (acceptor) solutions were prepared in n-hexane. Absorption and fluorescence spectra of CdS QDs and QRs samples in n-hexane (spectroscopic grade) solution were obtained at room temperature with a Shimadzu UV-2450 UV-vis spectrometer and a Horiba Jobin Yvon FluoroMax-P fluorescence spectrometer, respectively. For the time correlated single photon counting (TCSPC) measurements, all samples were excited at 375 nm using a picosecond diode laser (IBH Nanoled-07) in an IBH Fluorocube apparatus. The pulse duration is about 200 ps. The repetition rate is 500 kHz. The fluorescence decays were collected at a Hamamatsu MCP photomultiplier (C487802). Photoluminescence quantum yields (QY) were obtained by comparison with a standard dye Coumarine 500 in methanol (QY ) 90%).2b The calculated quantum yields values are 63% and 38% for QDs and QRs, respectively.
Figure 1. (a) Emission spectrum of CdS QD (or QR) and (b) absorption spectrum and (c) emission spectrum of Nile Red dye in n-hexane.
3. Results and Discussion Steady-State Study. Figure 1 shows the photoluminescence (PL) spectra of dots and rods of CdS nanoparticles (QD and QR) and the absorption and photoluminescence spectra of Nile Red dye in n-hexane. The PL peaks are at 472 and 478 nm for QDs (dots) and QRs (rods), respectively, under excitation at 370 nm. The absorption spectrum of Nile Red dye shows peaks centered at 487 and 507 nm, and the PL spectrum shows peaks at 524 and 563 nm. As the absorption spectrum of dye overlaps with the PL spectrum of QD and QR of CdS nanoparticles, they are good donor-acceptor pairs. The quenching of PL intensity of QD and QR of CdS nanoparticles in the presence of Nile Red dye is presented in Figure 2. Photoluminescence intensity of QD and QR of CdS nanoparticles decreases as the molar ratio of Nile Red dye to QD and QR of CdS nanoparticles is increased, and PL intensity of Nile Red dye increases. The efficiency of quenching is calculated from the following equation:
φET ) 1 - I/I0
(3)
where I0 and I are the relative integrated PL intensities of QD and QR of CdS nanoparticles in the absence and presence of the Nile Red dye. The observed PL quenching efficiencies are
Figure 2. Quenching of photoluminescence emission of QD (or QR) at different Nile Red dye/QD (or QR) ratios.
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Sadhu et al. k0
QD*n (or QR*) n 98 QDn (or QRn) nkq
QD*n (or QR*) n 98 QDn (or QRn)
(4)
(5)
where QDn* (or QRn*) stands for excited-state quantum dots (QDs) or quantum rods (QRs) with n dye molecules attached, while QDn (or QRn) stands for ground-state QDs (or QRs) with n dye molecules attached. k0 is the decay constant due to unimolecular process of the excited-state donor in the absence of acceptor molecules; kq is the rate constant for energy transfer per one dye molecule. When a QD (or QR) with n dye molecules is excited, the rate constant of the excited -state decay for that QD (or QR) is given by k0 + nkq, and the total energy transfer rate constant is nkq. In this kinetic model, it is also taken into account that the number of dye molecules attached to one quantum dots (or quantum rods) is distributed. It is assumed that the distribution of the number of dye molecules attached to one QD (or QR) follows a Poisson distribution:9
Φ(n) ) (mn/n!) exp(-m)
Figure 3. Time-resolved fluorescence decay curves of QD (or QR) at different Nile Red dye/QD (or QR) ratios. Red curves show the result of fitting the curves with eqs 9 and 10.
(6)
where m is the mean number of dye molecules attached to one QD. Therefore, the ensemble averaged decay curve of the excited QDs (or QRs) with the mean number of dye molecules attached is given by10 ∞ I(t, m) ) I0Σn)0 Φ(n) exp[-(k0 + nkq)t]
88.2%, 44.7%, and 36.4% for the molar ratio of dye:quantum dot ) 3:1, 1:1, and 0.7:1, respectively. For nanorod samples, the PL quenching values are 81.5%, 76%, and 64% for the molar ratio of dye:quantum rod ) 8:1, 6:1, and 4:1, respectively. It is seen that the PL quenching varies with changing the molar ratio of dye to nanoparticles. It clearly suggests that this PL quenching is mainly due to energy transfer2a from semiconducting nanoparticles to dye molecules. Time-Resolved Fluorescence Study. To confirm the energy transfer from semiconducting nanoparticles to dye molecules, time-resolved fluorescence study was performed because decay time measurements are more sensitive than PL quenching efficiencies where errors come from the fluctuations in the lamp intensity. The interaction of dyes with quantum dots and quantum rods can be monitored by their effect on the exciton lifetime, which is measured by time-correlated single-photon counting (TCSPC). We used pulsed excitation (375 nm) to measure the decay times of these QDs and QRs at their maximum PL peak. Figure 3 shows the time-resolved fluorescence decay curves of QDs and QRs of CdS nanoparticles without and with Nile Red dye solution. The decay profiles are well fitted with stretched exponentials.8 The average decay times are 19.65, 14.47, 12.57, and 6.02 ns for the molar ratio of dye: QD ) 0:1, 0.7:1, 1:1, and 3:1, respectively, and the average decay times are 16.51, 12.63, 8.72, and 7.18 ns for the molar ratio of dye:QR ) 0:1, 4:1, 6:1, and 8:1, respectively. The decrease in lifetime further confirms the energy transfer from CdS nanoparticles and nanorods to Nile Red dye. Kinetic Model. Let us assume that the energy transfer occurs in competition with unimolecular decay processes:
∞ (mn/n!) exp(-m) exp[-(k0 + nkq)t] ) I0Σn)0 ∞ ) I0 exp(-k0t - m)Σn)0 {[m exp(-kqt)]n/n!} ) I0 exp(-k0t - m) exp[m exp(-kqt)] ) I0 exp{-k0t - m[1 - exp(-kqt)]}
(7)
The above kinetic model is a simplified version of the model developed by Tachiya11 for luminescence quenching in micelles. His general model is described by eq 1 in ref 11, and the decay curve of the excited quantum dots/quantum rods is given by his eq 2′. If the detachment rate constant k- defined in his eq 1 is much smaller than kq and k0, his eq 2′ reduces to the above eq 7. Let us consider the decay profile predicted from eq 7. If kq is much larger than k0, I(t,m) decays rapidly at short times because of the factor exp(-kqt), but at long times it decays exponentially according to the following equation:
I(t, m) ) I0 exp(-m) exp(-k0t)
(8)
According to eq 8, the slope of the decay curve at long times is given by the unimolecular decay rate constant k0 of excited quantum dots and rods of CdS nanoparticles in the absence of Nile Red dye and should be equal in the absence and presence of dye molecules. This behavior is in accord with the decay curves in Figure 3. According to eq 7, the decay curve in the absence of dye molecules should be exponential over the whole time range. However, according to Figure 3, the decay curve in the absence of Nile Red dye is not exponential at short times, although the
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TABLE 1: Overview of the Values of Quenching Parameters Using the Kinetic Model molar ratio of Nile Red dye/ QD(or QR) QD
k0 (ns-1)
0:1 0.7:1
kqt (ns-1)
mt 1.09 0.93
0.0182
QR
0.88 1.04
0:1 4:1
2.45 3.12 0.0214
K (M-1)
f
0.62
0.461
0.63
0.84
0.87 1.79
0.453 0.412
0.68 0.65
0.78 0.54
1.84
0.896
0.74
0.42
2.42 2.98
0.798 0.871
0.73 0.77
0.44 0.35
0.108 1.91 2.23
long-time decay is exponential, and the slope is equal to those in the presence of Nile Red dye. This behavior of the decay curve may be due to unidentified traps existing on the surface of quantum dots and rods of CdS nanoparticles. If the distribution of the number of unidentified traps on the surface of quantum dots and rods of CdS nanoparticles follows a Poisson distribution with the average number mt, the decay curves of the excited state of quantum dots and quantum rods of CdS nanoparticles in the absence and presence of dye molecules are described by
I(t, 0) ) I0 exp{-k0t - mt[1 - exp(-kqtt)]}
(9)
I(t, m) ) I0 exp{-k0t - mt[1 - exp(-kqtt)] - m[1 exp(-kqt)]} (10) where the quenching rate constant (kqt) by unidentified traps may be different from that (kq) by dye molecules. At long times, they reduce to
I(t, 0) ) I0 exp(-mt) exp(-k0t)
(11)
I(t, m) ) I0 exp[-(mt + m)] exp(-k0t)
(12)
The average number m of Nile Red dye attached to one QD is related to the total concentration [A] of Nile Red dye added in solution and the concentration [QD or QR] of QD or QR added in solution through
[A] ) m[QD or QR] + [Asolv]
(13)
m ) K[Asolv]
(14)
where [Asolv] is the concentration of dye in solvent phase. K ) k+/k- and k+ and k- are the attachment and the detachment rate constants defined in eq 1 of ref 9. Using eqs 13 and 14, we have
m ) K[A]/(1 + K[QD or QR])
kq (ns-1)
0.0715
1:1 3:1
6:1 8:1
m
(15)
Because the concentrations of dye molecules and quantum dots or quantum rods of CdS nanoparticles added in solution are experimentally known, we can calculate the value of K from the obtained value of m. On the other hand, the fraction of Nile Red dye attached to quantum dots or quantum rods among all
dye molecules added in solution is given by
f ) m[QD or QR]/[A]
(16)
We have determined the values of the parameters mt, kqt, k0, m, and kq by fitting eqs 9 and 10 to the decay curves in the absence and presence of dye molecules. The resulting fits are represented by red solid lines in Figure 3. We fitted the decay curves in the presence of dye molecules by fixing the unimolecular rate constant (k0) to 0.018 and 0.021 ns-1 for quantum dots and quantum rods, respectively. The fitted results are summarized in Table 1. It is seen that the model describes the decay curves reasonably well. The values of K and f are calculated using the fitted values of m. These values are also included in Table 1. As seen from the values of f in Table 1, the fractions of dye molecules attached to nanostructures are in the range 0.84-0.54 and 0.42-0.35 for QDs and QRs, respectively. The remaining fractions of the dye molecules are in the solution. This indicates that the chemical interaction between a dye molecule and an amine-capped nanostructure is not so strong. In this kinetic model, kq is considered as the rate at which energy transfer occurs from an exciton to one neighboring dye molecule, and it is extracted from the fits. The average values of the energy transfer rate (kq) are 0.442 ((0.03) and 0.855 ((0.05) ns-1 for quantum dots and quantum rods, respectively. The rate of energy transfer (kq) for QRs is much higher than that for QDs. This may be due to the difference in dipole moment of spherical and rod-shaped particles. Thus, the shape of nanoparticles influences the energy transfer rate. The average values of K are 0.65 and 0.75 for quantum dots and quantum rods of CdS nanoparticles, respectively. The value of K evaluated from the value of m and the concentrations [A] and [QD or QR] of acceptors and nanostructures added in the solution is also independent of the stoichiometry and depends only on the nature of interaction between an acceptor and a nanostruture. Thus, the binding constant K (k+/k-) does not depend on the stoichiometry. The detachment rate constant k- should be independent of the surface area of a nanostructure, while the attachment rate constant k+ should increase with increasing surface area. This seems to explain at least partly why the value of K is larger in QRs than in QDs. The efficiency of quenching given by eq 3 can also be calculated on the basis of the same kinetic model. According to this model, I/I0 in eq 3 is given by ∞ ∞ I/I0 ) {Σn)0 Σn)0 (mne-m/n!)(mtne-mt/n′!)/[1 + nkq/k0 + ∞ (mtne-mt/n′!)/[1 + n′kqt/k0] (17) n′kqt/k0]}/Σn)0
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Therefore, the quenching efficiencies are 79%, 55%, and 43% for the molar ratio of dye:QD ) 3:1, 1:1, and 0.7:1, respectively. For nanorod samples, the efficiencies are 90%, 77%, and 40% for the molar ratio of dye:QR ) 8:1, 6:1, and 4:1, respectively. The quenching efficiencies calculated using this kinetic model differ from the efficiencies obtained from PL measurements, which we ascribe to experimental uncertainty. In the PL quenching efficiencies, errors come from the fluctuations in the lamp intensity. 4. Conclusions We have proposed a stochastic model for the kinetics of energy transfer from quantum dots or rods of CdS to Nile Red dye molecules. We have assumed that the distribution of the dye molecules around quantum dots or rods follows Poisson statistics. By analyzing time-resolved fluorescence decay curves of quantum dots or rods, we have obtained the average number of dye molecules attached to the surface of quantum dots or rods as a function of the concentration of dyes and that of quantum dots or rods. The equilibrium constants for attachment/ detachment of dye molecules to/from the surface of quantum dots or rods were evaluated. The equilibrium constant evaluated for quantum rods was larger than that for quantum dots. This result is rationalized by considering that the rate of attachment of dye molecules to the surface of quantum rods is faster as compared to that of quantum dots. The quenching rate constants per dye molecule attached to the surface of quantum dots or rods were also estimated. We have found that the quenching rate constant varies with the shape of the particles.
Sadhu et al. Acknowledgment. A.P. thanks The Department of Science and Technology (NSTI) and “Ramanujan Fellowship” for generous funding. S.S. thanks CSIR for awarding a fellowship. References and Notes (1) (a) Medintz, I. L.; Clapp, A. R.; Mattoussi, H.; Goldman, E. R.; Fisher, B.; Mauro, J. M. Nat. Mater. 2003, 2, 630. (b) Goldman, E. R.; Medintz, I. L.; Whitley, J. L.; Hayhurst, A.; Clapp, A. R.; Uyeda, H. T.; Deschamps, J. R.; Lassman, M. E.; Mattoussi, H. J. Am. Chem. Soc. 2005, 127, 6744. (c) Peng, H.; Zhang, L.; Kjallman, T. H. M.; Soeller, C.; Sejdic, J. T. J. Am. Chem. Soc. 2007, 129, 3048. (d) Warner, J. H.; Watt, A. R.; Thomsen, E.; Heckenberg, N.; Meredith, P.; Dunlop, H. R. J. Phys. Chem. B 2005, 109, 9001. (e) Dayal, S.; Lou, Y.; Samia, A. C. S.; Berlin, J. C.; Kenney, M. E.; Burda, C. J. Am. Chem. Soc. 2006, 128, 13974. (2) (a) Chowdhury, P. S.; Sen, P.; Patra, A. Chem. Phys. Lett. 2005, 413, 311. (b) Sadhu, S.; Patra, A. ChemPhysChem 2008, 9, 2052. (c) Sadhu, S.; Patra, A. Appl. Phys. Lett. 2008, 93, 183104–1. (3) Zhou, D.; Piper, J. D.; Abell, C.; Klenerman, D.; Kang, D. J.; Ying, L. Chem. Commun. 2005, 4807. (4) Gao, X.; Cui, Y.; Levenson, R. M.; Chung, K. L. W.; Nie, S. Nat. Biotechnol. 2004, 22, 969. (5) Lakowicz, J. R. Principles of Fluorescence Spectroscopy, 2nd ed.; Kluwer Academic/Plenum Publishers: New York, 1999. (6) Forster, T. Discuss. Faraday Soc. 1959, 27, 7. (7) (a) Sen, T.; Patra, A. J. Phys. Chem. C 2008, 112, 3216. (b) Haldar, K. K.; Sen, T.; Patra, A. J. Phys. Chem. C 2008, 112, 11650. (c) Haldar, K. K.; Patra, A. Chem. Phys. Lett. 2008, 462, 88. (8) Schlegel, G.; Bohnenberger, J.; Potapova, I.; Mews, A. Phys. ReV. Lett. 2002, 88, 137401. (9) Tachiya, M. Chem. Phys. Lett. 1975, 33, 289. (10) Koole, R.; Luigies, B.; Tachiya, M.; Pool, R.; Vlugt, T. J. H.; Donega, C. D. M.; Meijerink, A.; Vsanmaekelbergh, D. J. Phys. Chem. C 2007, 111, 11208. (11) Tachiya, M. J. Chem. Phys. 1982, 76, 340.
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