Enhancement of Energy Transfer between Quantum Dots: The Impact

Sep 5, 2012 - ... Alan P. Bell , John J. Gough , Graham P. Murphy , Peter J. Parbrook , A. Louise Bradley ... Tanya Hutter , Sumeet Mahajan , Stephen ...
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Enhancement of Energy Transfer between Quantum Dots: The Impact of Metallic Nanoparticle Sizes R.G. West† and S. M. Sadeghi*,†,‡ †

Department of Physics, University of Alabama in Huntsville, Huntsville, Alabama, 35899, USA Nano and Micro Device Center, University of Alabama in Huntsville, Huntsville, Alabama, 35899, USA

‡

ABSTRACT: We investigated the dependency of plasmonic enhancement of Forster energy transfer between CdSe/ZnS quantum dots on the sizes of metallic nanoparticles as well as the distances between these particles and the quantum dots. The results demonstrate how the interdot Forster energy transfer depends upon the relative magnitudes of (i) the Forster energy transfer rates from the donor and acceptor quantum dots to the metallic nanoparticles, according to their transition frequencies, and (ii) the plasmonic field enhancement at the quantum dot emission frequencies. As a result, even in the absence of the donor-induced plasmonic field, one can adjust these processes to stimulate the interdot energy flow from the donor to acceptor quantum dots, increasing its rate significantly.

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INTRODUCTION Because of their tunable emission spectra and high quantum yields, semiconductor quantum dots (QDs) are often used to test and develop Forster’s theory of resonance energy transfer (FRET). This nonradiative energy transfer between nanoparticles is due to dipole−dipole coupling. Perhaps the most basic display of FRET in inorganic systems occurs when two QDs of differing sizes are in close proximity. Under this condition, energy can transfer from the smaller donor QD to the larger acceptor QD nonradiatively. This process is usually indicated by the suppression of the donor’s emission and the enhancement of the acceptor’s. The rate of energy transfer and the initial shape of the resulting spectra depend largely on the irradiation wavelength, surrounding media, QD size distribution, and presence of other nanoparticles.1−3 This sensitivity of interdot FRET has been utilized for various applications such as biological sensors,4 optical diagnostics and switches,5 etc. Most recently, much attention has been given to QD and metallic nanoparticle (MNP) systems as the MNPs introduce localized plasmonic effects and act as another channel for FRET. This leads to applications such as highly efficient lightharvesting structures,6,7 biologically/chemically triggered ultrafast nanoswitches,8 plasmon-controlled flourescent sensors,9 nanothermometers,10 energy nanogates,11 active nanostructures,12 etc. The presence of MNPs in donor−acceptor structures have been known to influence the interdot FRET rate between QDs. This includes enhancing the range over which FRET occurs as well as increasing the FRET rate between QD pairs.13−15 This has been experimentally studied16 using a “sandwich” structure featuring two monolayers of donor and acceptor QDs separated by a monolayer of gold MNPs with polyelectrolyte spacing layers. When the donor and its spacing layer were missing, the acceptor emission was © XXXX American Chemical Society

completely quenched, but when they were replaced in the sandwich structure, the acceptor emission was reacquired. Such an interdot FRET enhancement process has been associated with the plasmonic amplification of the field of the acceptor QDs due to the plasmons induced by the donor QDs (donorinduced plasmonic field enhancement).16,17 According to our previous research,18 in part we concluded that, for a certain range of large gold MNPs, a monodisperse QD solid exhibits emission enhancement as seen by others,19,20 but suppression is characteristic of FRET from the QD to the MNP for small MNPs. The results found by of Li et al. supports this conclusion.21 From the research to date, we can conclude that MNPs have a potent effect on FRET rates and field enhancement for a few differing configurations as well as QDMNP separations. In this paper we have addressed this issue by investigating the effects of MNP sizes and the distances between QDs and MNPs on plasmonic enhancement of the interdot energy transfer. As a result, we reveal the interplay between the interdot FRET and two other processes intrinsic to the donor−acceptor QD systems in the presence of MNPs: (i) FRET from QDs (both donors and acceptors) to MNPs and (ii) plasmonic field enhancement. We show that even in the absence of the donor-induced plasmonic field enhancement16,17 one can control these processes using the frequency dependency of the plasmonic effects to increase the interdot FRET rate. In other words, with fixed QD transition frequencies, interdot FRET can be controlled by adjusting the spectral features of nearby MNPs. Received: February 29, 2012 Revised: September 2, 2012

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FABRICATION AND EXPERIMENTAL SETUPS To examine the behavior of FRET from donor to acceptor QDs, it is necessary to understand (i) how the donor and acceptor QDs interact when mixed in the absence of MNPs, (ii) how the QDs behave in the presence of MNPs of various sizes without interdot FRET (when they are not mixed), and (iii) how the QDs behave when mixed in the presence of MNPs. As long as the donor and acceptor concentrations are correctly maintained in these three cases and the separation between the QDs and MNPs are known, a direct comparison of how the individual and mixed QDs interact with various MNPs should reveal how plasmonic enhancement of interdot FRET depends upon the MNPs’ sizes. To make accurate comparisons between unmixed and mixed QDs on MNPs with regard to the impact of MNP sizes, we fabricated a special substrate, or plasmonic template (PT). The template contained an array of nanoislands created by thermal evaporation of ∼10 nm of gold on a glass substrate followed by thermal annealing at 500 °C for 30 min. A mask was placed over the substrate so as to produce a gradient of evaporated gold that, when annealed, congregates into nanoislands of various sizes. The MNPs mean size changes continuously from the center of the template at region A (r = 0 mm) to region D (r ≈ 3.6 mm) where we do not expect any MNPs. The scanning electron microscopy (SEM) images of the sample for these regions are shown in Figure 1. We used a visible super

Figure 2. The plasmonic absorption peaks of the plasmonic template according to sample radius. Beginning at region A (r = 0 mm) at the center of the sample, following the arrow to region C (r = 3.0 mm) by increments of 0.6 mm. The arrow shows the direction from center (r = 0 mm) to the side (r = 3.0 mm) of the template.

solution of toluene and polymethyl methacrylate such that, when spin-coated on glass, their peak emission intensities were similar after FRET and remained consistent along the sample. The spin coating started with a 15-s spread at 170 rpm followed by 60 s of spinning at 4000 rpm. According to ref 22, under such conditions, a polymethyl methacrylate solution with the weight percentage as ours (0.2%) should form a film with about 1−2 nm thickness. In our samples, however, this thickness varied somewhat by the fact that our solutions contained QDs of core size ∼4 nm with the ZnS shell and ligands in addition. Since QD656 had a lower quantum yield, we had to increase its concentration in the mixture such that in the absence of MNPs its emission spectra was comparable to the intensity of the donor spectra after FRET. Therefore, the ratio of the concentrations of QD656 and QD616 is about two, suggesting that each donor interacts with roughly two acceptors. All spectral results in this paper have been obtained in a single day using a thermoelectrically cooled spectrometer. The samples were irradiated by an Ar laser of 514 nm wavelength at a moderate 7.7 W cm−2 intensity in order to avoid abrupt photoionization activation23 or photo-oxidation24 which can affect the emission spectra. Also, spectral data was taken within 1 s of irradiation to ensure consistency among sample sets.

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Figure 1. Schematic illustration of the sample. The QDs were deposited on radially distributed MNPs (plasmonic template). Between the QDs above (donors are small, acceptors are large) and the MNPs (solid circles below) there was a silica spacing layer with 15 nm thickness (Δs = 15 nm). The inset shows the schematic of the metal deposition and the mask. A, B, C, and D refer to four regions of the sample along its radius. Below are the SEM images from the plasmonic template in these regions. The scale is 200 nm.

EXPERIMENTAL RESULTS In our samples, the Au MNPs can play three major roles: (i) enhancing the field experienced by the QDs,14,25 (ii) setting up an energy drain for both donor and acceptor QDs via FRET,17 and (iii) enhancing the interdot FRET rate between donors and acceptors.14 As discussed in this section, our results should be indicative of a combination of these processes, and the level at which these processes present themselves in our system should be dependent on the MNP sizes and center-to-center distance R. Our gauge for the presence of each of these processes is based on the QD’s relative emission. So, to compare the spectral data for each data point in a consistent manner, we compare averages of integrated spectra for each sample set. In this way, the radiative energy for each region of the sample may be compared. At this point, it must be noted that the experimental systems are highly heterogeneous. However, the data presented here are an ensemble average of the response of these systems. Though the limitations of our experiment require us to observe the average response of an ensemble of QDs and MNPs, the results are favorably consistent and hardly heterogeneous at the scale

continuum source to measure plasmonic absorption peaks of the PT from the center (region A) to the edge (region D). Consistent with the SEM images, the results reported in Figure 2 suggest a strong plasmonic peak at the center. As we reach region D, however, the peak disappears. The fluctuating features seen in this figure is partially because of the large power variations of the white source along the spectrum. A silica spacing layer of thickness Δs = 15 nm was sputtered on top of the plasmonic template. Thereafter, prepared QD solutions were spin-coated atop the silica spacing layer for each sample made. Relative concentrations of two colloidal CdSe/ ZnS QDs manufactured by NN-Laboratories, with emission at 616 nm (QD616) and 656 nm (QD656), were mixed into a B

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of the ensemble. The excited regions of the sample are sufficiently localized and observed spectra are consistent such that general trends may be observed and compared within error. This common practice of gathering data from ensemble averages of QD and QD-MNP systems is valuable for validating the presence of FRET when the donor/acceptor distribution is random26 and plasmonic enhancement of FRET when the distribution of the MNP size and shape is heterogeneous.2 A. Interdot FRET in the Absence of MNPs. First, we report what is occurring in regions A, B, C, and D of each sample from a purely objective standpoint. Individual and mixed QDs were spin-coated on a glass substrate so as to determine the impact interdot FRET has on the spectra without MNPs. Figure 3a shows the spectra of our donor QD

Figure 4. (a) The integrated intensities of unmixed QD616 (circles) and QD656 (squares) and their ratio (triangles in (c)) along the plasmonic template. (e) Variation of the plasmonic emission enhancement factor for QD616 (circles) and QD656 (squares) with distance r along the sample. (b, d, and f) Similar to a, c, and e, respectively, but when QD616 and QD656 were mixed. The dashed lines represent the ratio of QD656 to QD616 emission intensities on glass when they were unmixed (c) and mixed (d). A, B, C, and D refer to the approximate positions of regions A, B, C, and D, respectively.

that the emission of QD616 in region A is less than in region D. Additionally, we observe a dip around r = 1.8 mm, wherein the MNPs reach a critical size and distance from the QDs for which the emission spectra are suppressed. The situation is different for the case of QD656 wherein the emission of QDs in region A is slightly more than that in region D. This is an indication of the interplay between FRET from the monodispersed QDs to MNPs and the plasmonic field enhancement when both the sizes of the MNPs and their distances from the QDs are changed. As discussed in the next section, such interplay also depends on the positions of the wavelengths of the laser field and the emission of the QDs relative to the plasmonic absorption peak. As seen in Figure 4c, the ultimate result of energy transfer is that for midsized MNPs (regions B and C) QD656 has lost less energy to the MNPs by this FRET process. Figure 4e shows the plasmonic emission enhancement factor (Eenh) for QD616 (circles) and QD656 (squares). Here, Eenh = 0 plas Iplas and I0i refer to the integrated emission of i /Ii where Ii these QDs in the presence and absence of MNPs, respectively. Note that in Figure 4c we expected the ratio of acceptor to donor QDs in region D to become the same as that on the glass. Also, in region A, this ratio should be more than that on glass, since in this region the emission of the donor QDs is suppressed more significantly via FRET to the MNPs than of that of the acceptor QDs. Nonetheless, the standard deviations of these data sets partially overlap, as seen in the figure. Comparing this data to the results in the analysis section, the trend of this function is likely intact but offset, suggesting a systematic error in this particular data set. Yet, the plasmonic emission enhancement of this data set, shown in Figure 4e, seems to remain intact. C. Plasmonic Effects on the Interdot FRET. The results in subsection A demonstrate the intrinsic energy transfer between QD616 and QD656 in the absence of MNPs. To study the impact of plasmons on such a process we spin coated

Figure 3. (a) The emission spectra of unmixed monodisperse QD616 and QD656 on glass. (b) The spectral sum of the unmixed monodisperse QDs (dashed line) and the spectrum of the mixture of QD616 and QD656 on glass (solid line). (c) The emission spectra of disperse (mixed) QD616 and QD656 on metallic nanoparticles in region A.

(solid line) and acceptor QD (dashed line) solutions on glass substrate before mixing. The results show QD616 emitted about 2.5 times more than QD656. Figure 3b shows the sum of the spectra of the pure solutions for the donor and acceptor QDs (dashed line) overlaid by the spectra of the mixed solution (solid line), which takes shape after interdot FRET. These results show efficient energy transfer between the donor and acceptor QDs. B. Plasmonic Enhancement of the Donor and Acceptor QD Emission. To investigate the impacts of the MNPs and variations of their sizes on the donor and acceptor QDs, we studied the emission spectra of the unmixed QD616 and QD656 solutions when spin-coated on the plasmonic template. This also allows us to study how plasmonic effects are influenced by the emission wavelengths of the QDs to some extent and how these effects depend on the center-to-center distance between these QDs and the MNPs, with change in the MNP size. The results showed significant variations in spectral intensities from region A to D (Figure 4a). These results show C

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ment consisted of mixed QDs on glass (no MNP). This system exhibited the inherent FRET that occurs between donor and acceptor QDs in all systems, similar to a previous work.26 Our second experiment with individual QDs atop our plasmonic template demonstrated two other channels by which energy transfer occurs: FRET from both donor and acceptor QDs to the MNPs and absorption of the MNP plasmonic field by the QDs. The rate at which energy is transferred by these mechanisms depends upon the transition wavelengths of the donor and acceptor QDs, which we have fixed by using the same QDs throughout. When donor and acceptor QDs were placed together atop the plasmonic template, QD-MNP FRET and plasmonic enhancement act as channels of energy transfer which regulate the interdot FRET rate. Disperse QD systems in the vicinity of various MNPs have been studied in the past;21 however, this research is unique in that we exhibit the role of FRET from QD to MNP in interdot energy transfer. To understand how MNP sizes influence plasmonic enhancement of interdot FRET, in this section we present a model that treats the major governing processes in our samples. We intend, therefore, to model the following major parameters which affect the interdot FRET rate γint F : FRET from both donor (d) and acceptor (a) QDs to the MNP γiM F (i = d and a) and the plasmonic field enhancement factor due to the MNP Penh. This can be verified by analyzing their effects on donor and acceptor QD emission. As a result, with fixed excitation and QD transition wavelengths, we can indirectly verify the control of interdot FRET due to the independent variables, MNP size, and QD-MNP distance. In this model we consider MNPs as perfect spheres. Though the Au nanoislands in our samples are not at all perfect spheres, the goal of this model is simply to show the trend for the QD emission that should be expected. For simplicity, since the concentration of QD616 is half of QD656, in our model we consider one donor (QD1) and two acceptors (QD2) to interact with one MNP. As shown schematically in Figure 5,

the mixed solution used in subsection A on a PT as used in subsection B. The results presented in Figure 4b show variations of the integrated emission of QD616 and QD656 under these conditions. To obtain these values we used the emission spectra of unmixed QD616 (filled circles) and QD656 (filled squares) in the presence of MNPs (Figure 4a) as a fitting spectra to the emission spectra of mixed QD616 and QD656. The results shown in Figure 4b show distinct differences compared to those in Figure 4a. To make this clearer, in Figure 4d we show the ratio of the emission of QD656 to QD616 (filled triangles). These results are significantly different as compared to the same ratio in the absence of MNPs (dashed line) and when they are unmixed (Figure 4c). In consideration for FRET from these QDs to MNPs and the change in R, we see that the major symptom of interdot FRET is the relative quenching of the donor emission. This is highlighted in Figure 3c, where the spectrum of the mixed QDs in the presence of the largest MNPs (region A) is shown. As discussed in the following section, this suggests that for large MNPs FRET from QD616 to QD656 is stronger. The decreasing trend about region C is similar for both the individual QD and mixed QD cases, indicating that interdot FRET diminishes along with decreasing plasmonic enhancement. In region D, however, due to the lack of MNPs, no significant MNP-mediated FRET exists, and the results match with the case of the absence of MNPs. Such results indicate these various MNPs can affect the balance between FRET from individual QDs to MNPs and plasmonic field enhancement. We model this process in the next section and show how interdot FRET rate changes with the MNP size and associated QD-MNP center-to-center distance. Figure 4f shows the variation of the plasmonic emission enhancement factor for the donor and acceptor QDs when mixed.

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ANALYSIS The main goal of our experiment was to demonstrate the effect of various MNP sizes and QD-MNP distances on interdot FRET. To analyze our results, note that in general excitons in QDs can decay radiatively and nonradiatively through various channels. In the absence of MNPs, nonradiative decay includes those channels associated with surface defects, deep trap states on the surface of the QDs, carrier ejection from the QDs, Auger recombination, and interdot FRET rate to larger QDs. In the presence of MNPs the radiative and nonradiative decay rates of QDs are influenced by the plasmonic effects. The near-field enhancement of plasmons increases the radiative decay rates of QDs. On the contrary, interaction between excitons and plasmons allows QDs to transfer their energy to MNPs through the FRET mechanism, increasing their nonradiative decay rates. The competition between these two processes depend on the size of the MNPs and their distances from the QDs. It has been found that the QD to MNP energy transfer process has a more dominant impact for smaller MNPs,21 while for a range of QDMNP distances, larger MNPs can enhance the radiative decay rates of QDs.19,20 Additionally, the impact of plasmons on the decay rates of QDs also depends on the intensity of the laser field used to excite them. At high laser intensities photoionization activation and photo-oxidation of QDs can increase their nonradiative decay rates.23,24 Therefore, as mentioned in section II, to avoid these processes we used a low-intensity laser (7.7 W cm−2). Under consideration of these issues, using a fixed-wavelength irradiation source for all our measurements, our first experi-

Figure 5. Schematic illustration of energy relaxation and energy transfer among the donor, acceptor, and MNP.

QD1 and QD2 can transfer their energy to the MNP with rates aM of γdM F and γF , respectively, while the interdot FRET from QD1 to each acceptor QD2 is γint F /2. Additionally, the radiative and nonradiative rates of QD1 and QD2 are represented by γdr (γdnr) and γar (γanr), respectively. Since the large MNPs in our samples are widely distributed in region A and the small, dense MNPs of C have small dipole moments, we ignored coupling between the MNPs. By use of the SEM images (Figure 1), we determined the mean sizes of the particle distribution ranges D

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from ∼2 nm in region C to ∼22 nm in region A. Therefore, in our model we adopt the same range. Additionally, in our treatment we ignored the amount of plasmonic enhancement of interdot FRET caused by the excitation of plasmons by QD1 (donor-induced plasmonic field enhancement).16,25 This is due to the fact that our samples mostly support interdot FRET between adjacent QDs, and therefore, the angle of separation between QD1 and QD2 from the center of the MNPs is small.17 Additionally, in our experiment the laser excitation wavelength was 514 nm, which is shorter than that of the plasmonic peak of our MNPs (see Figure 2). Therefore, although our treatment includes plasmonic enhancement during the excitation process, its impact at the laser wavelength is not significant. The emission peaks of the QDs were, however, in the longer wavelength side of the plasmonic peak of the MNPs in order that the plasmonic enhancement of their emission rates can be significant. We calculated the plasmonic field enhancement factor defined as Penh = |E/E0|2, where the E refers to the field in the presence of any MNPs and E0 to that in the absence of MNPs at the same location (see Figure.6). To calculate Penh, note that for the

The results of calculation for the typical case where the radius of MNP is 22 nm is shown in Figure 6 (dashed line). For the FRET rate from QDs to MNPs (γiM F , i = d and a) we used the following8,25 ⎛ 2ξμ 2 a3 ⎞ γFi M = Im⎜⎜ 212 6 ⎟⎟ ⎝ ℏεeff R ⎠

where μ12 is the transition dipole moment for a 1−2 transition exciton and the effective dielectric constant εeff = (2ε0 + εs)/ 3ε0, as εs is the dielectric constant of the QD. Similar to the case of plasmonic field enhancement factor, here we averaged over θ. The solid line in Figure 6 shows the results for the corresponding case of γdM F . For large MNPs, the offset nature of these peaks allows for the donor QD to transfer energy to the MNPs at a higher rate than the acceptor, and the acceptor will experience a more enhanced plasmonic field, directly influencing the interdot FRET rate. The relative intensities in the experimental data are evidence of this interplay. In our model, we consider the interaction of the laser field with the systems to be linear as the laser intensity was low. The density of recombining excitons in one QD (nexc) correlates directly to the emission intensity. For a donor QD, the emission intensity is expressed as Iemis = ndexcγdr Penh(ωde ), where Penh(ωde ) is the plasmonic enhancement factor at the donor’s emission frequency.25 A similar expression also holds for the acceptor QD. If Idabs is the absorption rate of photons (laser field) by the donor, the rate equation for ndexc can be written as follows d dnexc d d d = Iabs Penh(ωSd) − (γtot + γFdM + γFint)nexc dt

Figure 6. Variation of γdM F (solid line) and Penh (dashed line) as a function of frequency for a Au MNP with a radius of 22 nm in a silica host. Here, the center-to-center distance is considered 39 nm. This includes the radius of the QD, considered to be 2 nm, and 15 nm spacing between the QD and the MNP.

⎛ R ⎞6 γFint = 2Penh(ωed)γrd⎜ 0 ⎟ ⎝ d ⎠

(5)

Here R0 contains the overlap integral between QD1 emission and QD2 absorption, refractive index of surrounding medium, and the orientation factor κ2. d is the distance between QD1 and QD2. The case where Penh = 1 is considered to be the conventional FRET rate for mixed QDs in the absence of 29 MNPs (γint In fact, we can write eq 5 as γint F,noplas). F = d int Penh(ωe )γF,noplas. In our analysis γint F,noplas corresponds to interdot FRET on glass (Figure 3b). Since we had increased the acceptor concentration in the QD solid mixture 2-fold, each acceptor receives half the excitons that one donor contributes to interdot FRET. Thus, the rate equation of the nexc for the acceptor is

2

(1)

where a is the MNP radius and R is the QD-MNP center-tocenter distance. In our samples, the plasmonic enhancement changes as we go from the center to the side (increasing r). In our model, R changes with the size of the MNP when Δs is fixed as in the experiment. The dielectric contribution to the enhancement is described by ξ = (εm(ω) − ε0)/(εm(ω) + 2ε0) where ε0 is the dielectric constant of the immediate environment (silica) and εm(ω) is the dielectric function of gold. P̂ and n̂ are the unit vector along the QD dipole field and the center-to-center unitary vector, respectively. Averaging over θ, the angle between these two vectors, leads to the following expression for the plasmonic field enhancement 2|ξ|2 a6 Penh(ω) = 1 + R6

(4)

where γdtot = γdr Penh(ωde ) + γdnr. The FRET rate to metal (γdM F ) as well as the interdot FRET (γint F ) represent two additional channels through which energy transfer occurs. The former, however, acts as a nonradiative decay channel for the QDs at the same scale as γdnr. In consideration of the fact that for each donor we have two acceptors, the interdot FRET rate is

range of wavelengths about the emission wavelength of the QDs, plasmons in the MNPs are induced by the dipoles of the QDs. Therefore, since we consider the MNP polarizability tensor is isotropic, the MNP dipole induced by the QDs is parallel to the QD dipole field.27 For a given direction of the QD dipole field, Penh(ω,θ) is given by28 (3(P ·̂ n)̂ n ̂ − P)̂ ξa3 Penh(ω , θ ) = 1 + R3

(3)

a dnexc 1 d a a a = Iabs Penh(ωSa) − (γtot + γFaM)nexc + γFintnexc dt 2

(6)

where γatot = γar Penh(ωae) + γanr. From these equations we obtained plas the ratio of emission of QD2 (Iplas a ) to QD1 (Id ) when they are mixed in the presence of a MNPs

(2) E

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3 Penh(ωea)γra⎡⎣Penh(ωed)γrd + γnrd + γFdM + 2 γFint ⎤⎦

Penh(ωed)γrd[Penh(ωea)γra + γnra + γFaM]

(7)

In this expression, we consider the excitation in QD1 and QD2 to be similar. As seen in Figure 3a, Idemis/Iaemis ≈ 2.5, where Iaemis and Idemis are the QD656 and QD616 emissions in the absence of MNPs, respectively. Therefore, due to the higher acceptor concentration, the quantum yield of the donor was actually 5 times that of the acceptor. Therefore, if we consider the radiative decay rates γdr = γar = 0.05 ns−1, comparable to the rate considered by others,30 the nonradiative rates are set to γdnr = 0.35 ns−1 and γanr = 1.6 ns−1. We choose the emission wavelength of QD2 (λa) to be 656 nm and that of QD1 (λd) to be 616 nm, similar to our experiments. We also consider the laser wavelength (λl) to be 515 nm. By application of these parameters to our theory, we replicate parts a, c, and e of Figure 4 in Figure 7 and find a similar trend

Figure 8. Variations of FRET rate from QD1 (QD616) and QD2 (QD565) to MNPs (a) and plasmonic field enhancement factor (c) as a function of MNP sizes when λa = 656 nm, λd = 616 nm, and Δs = 15 nm. (b and d) Results when λa = 548 nm and λd = 528 nm. Solid lines refer to QD1 (donor) and dashed lines to QD2 (acceptor).

radius causes its center-to-center distance from the QDs (R) to increase as well. By use of the model described above, we then calculated the plas linear emission of QD1 (Iplas d ) and QD2 (Ia ) as a function of the MNP radius when the QDs are mixed and Δs = 15 nm. Here we simulate the situation presented in Figure 4b. The results presented in Figure 9a show a minimum when the radius of MNPs is about 10 nm (solid and dashed lines). Figure plas 9c shows that Iplas has some similarities with the results a /Id shown in Figure 4d. Figure 9e shows the emission enhancement factors (Eenh) for the donor and acceptor (solid and dashed lines). Here, dashed line displays similarities with the

Figure 7. (a) The emission of unmixed QD1 (QD616) and QD2 (QD656), their ratio (b), and emission enhancement (c) as a function of MNP radius when Δs = 15 nm. (a, b, and c) Correspond to the experimental data in parts a, c, and e of Figures 4. The dashed line in (b) refers to the ratio of the QD2 to QD1 emission intensities on glass.

for emission intensity across the sample. Despite the fact that the MNP size may not change linearly along the length of the sample, the average response in the experiment and the theoretical calculations are very similar. In consideration of the results shown in Figure 6, such a similarity shows how field enhancement and FRET to MNPs are responsible for the results seen in our experiments. To show this in more detail, we demonstrate the crucial role γiM F and Penh play in the spectral response of the system as a and R changes. The lines in Figure 8a show the results for FRET rates from QD1 (solid line) and QD2 (dashed line) to MNPs as a function of the MNP radius when Δs = 15 nm. The difference between these rates is caused by difference in the wavelengths of these QDs (refer to Figure 6). Figure 8c shows the corresponding variations of the plasmonic field enhancement factors for QD1 and QD2. Note that since here Δs is given (Figure 1), the increase of the MNP

Figure 9. (a) Variation of the emission of QD1 or QD616 (solid line) and QD2 or QD656 (dashed line) and their ratio (c) as a function of MNP radius when they are mixed and Δs = 15 nm. Likewise, for λa = 548 nm (dashed line) and λd = 528 nm (solid line), refer to (b) and (d). (e) Corresponding QD emission enhancement of QD1 and QD2 considered in (a). (f) Corresponds to QD emission enhancement at the same wavelengths as (b) and (d). F

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regions of large MNPs, displaying the overpowering effect of FRET from both QDs to the MNPs. The end result is a slightly increased interdot FRET rate for large MNP size and QD-MNP distance (Figure 10b). Note that the ratio of the QD emission on glass (in the absence of MNPs) in Figure 4d to that in Figure 4c can serve as a direct measure of the efficiency of the interdot FRET. In the presence of MNPs, however, because of FRET from QDs to MNPs, the situation is more complicated. In fact, performing the equivalent theoretical calculation, that is, dividing Figure 9c by Figure 7b, produces a function very different and opposite of the trend expected for the interdot FRET rate, as seen Figure 10. This function (not shown) is actually smallest for large MNPs and rises to a maximum for when the MNPs are not present. On the other hand, our theoretical results confirmed that the ratio of emission of the acceptor to donor QDs in the presence of MNPs shown in Figure 4d properly represents the trend of enhancement of interdot FRET (Figures 9c and 10).

squares in Figure 4f (QD656), while the solid line is similar to the circles (QD616). The above results (Figure 9) were obtained considering γint F follows eq 5. To emphasize how this rate changes with MNP size and distance from the QDs, we show the results of our modeling for its variations with the MNP radius in Figure 10a

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CONCLUSIONS We studied plasmonic enhancement of interdot FRET between two monodisperse QDs with disparate transition energies by simultaneously varying the MNP sizes and their center-tocenter distance from the QDs. Our results showed that even in the absence of donor-induced plasmonic field enhancement interdot FRET can be enhanced due to the frequency dependency of the plasmonic effects. For large MNPs, we observed enhancement of interdot FRET. For smaller MNPs such emission enhancement reduces while FRET rate to the metal dominates. Under this condition the interdot FRET rate falls to a level at which no MNPs are present. For mediumsized MNPs the interplay between the amount of plasmonic field enhancement and the rate of FRET to the MNPs was such that a dip in the emission intensity was observed. This feature was successfully exhibited by our model. The theoretical interdot FRET rate in our system does not exhibit such a minimum, which was in accordance with the results shown Figure 4d. Our results conclude that one of the controlling factors for interdot FRET enhancement among disperse donor and acceptor QDs in the presence of MNPs is the frequency dependency of the plasmonic effects.

Figure 10. (a) The interdot FRET rate between QD1 (QD616) and QD2 (QD656) as a function of the MNP radius when Δs = 15 nm (solid lines) and when the center-to-center distances between MNPs and the donor and acceptor QDs are 39 nm (dashed lines). (b) is similar to (a) but for QD emission wavelengths λa = 548 nm and λd = 528 nm.

(solid line). These results suggest an increase of about 75% when the radius of the MNP reaches 22 nm. In this case, since the QDs were separated from the MNPs with a spacer layer with a given thickness, i.e., the edge-to-edge distance was constant (Δs = 15 nm), the sizes of the MNPs and the centerto-center distances between the QDs and MNPs changed simultaneously. The enhancement and quenching, however, are most relevant to the center-to-center distance. To deconvolute the impact of these parameters and study how the interdot FRET rate changes with the radius of the MNPs when R remains constant, in our model we vary the MNP radius while considering R = 39 nm. The corresponding results shown in Figure 10a (dashed line) suggest a sharp reduction of this rate as the sizes of the MNPs are reduced. Note that the value of R here corresponds to the center-to-center distance between the QDs and the MNPs when a = 22 nm, Δs = 15 nm, and the QD radius is about 2 nm. In this paper we discussed how frequency dependencies of the plasmonic effects influence the interdot FRET between two monodisperse QDs. For given MNP structures, one can equivalently study the effects of the wavelengths of the donor and acceptor QDs. This is particularly appealing since chemical synthesis of QDs provides a great control over the sizes of QDs and, thus, their wavelengths. To further clarify the effects of donor and acceptor wavelengths in the processes discussed above, we consider the possibility where wavelengths of QD1 and QD2 are 528 and 548 nm, respectively. The results shown in parts b and d of Figure 8 show that, compared to λa = 565 and λd = 616 nm (parts a and c of Figure 8), for these wavelengths the plasmonic field enhancement and FRET to metal for the donor and acceptor are reversed (see Figure 6). Therefore, the resulting emission intensities of both QDs are changed, as seen in parts b and d of Figure 9. Though the plasmonic field is enhanced for both QDs, the FRET to metal causes the emission enhancement decrease for both QDs in

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The work was supported by the U.S. National Science Foundation MRI Grant No. ECCS-1040019 and by the financial aid of the University of Alabama in Huntsville.

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REFERENCES

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