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Mapping Emission from Clusters of CdSe/ZnS Nanoparticles Duncan P. Ryan, Peter M. Goodwin, Chris J. Sheehan, Kevin J. Whitcomb, Martin P. Gelfand, and Alan K Van Orden J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b10924 • Publication Date (Web): 24 Jan 2018 Downloaded from http://pubs.acs.org on January 28, 2018

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The Journal of Physical Chemistry

Mapping Emission from Clusters of CdSe/ZnS Nanoparticles Duncan P. Ryan,† Peter M. Goodwin,‡ Chris J. Sheehan,‡ Kevin J. Whitcomb,¶ Martin Gelfand,† and Alan Van Orden∗,¶ †Department of Physics, Colorado State University, Fort Collins, Colorado 80523, United States ‡Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States ¶Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, United States E-mail: Alan.Van [email protected]

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Abstract We have carried out correlated super-resolution and SEM imaging studies of clusters of CdSe/ZnS nanoparticles containing up to ten particles to explore how the fluorescence behavior of these clusters depends on the number of particles, the specific cluster geometry, the shell thickness, and the technique used to produce the clusters. The total emission yield was less than proportional to the number of particles in the clusters for both thick and thin shells. With super-resolution imaging, the emission center of the cluster could be spatially resolved at distance scales on the order of the cluster size. The intrinsic fluorescence intermittency of the nanoparticles altered the emission distribution across the cluster, which enabled the identification of relative emission intensities of individual particles or small groups of particles within the cluster. For clusters undergoing inter-particle energy transfer, donor/acceptor pairs and regions where energy was funneled could be identified.

Introduction Large quantum yields, bandgap tunability, and fluorescence stability make quantum-confined nanoparticles (NPs) enticing for a variety of optical and electronic applications. Many devices, such as films and solids, take advantage of high NP concentrations to add the desirable properties of the individual particles. However, in such systems interactions between the particles can occur due to their close proximity and affect the overall performance of a device. Loss mechanisms that are present in individual NPs, such as charge trapping and fluorescence blinking, can be amplified under conditions where excitons and charge carriers are mobile. Energy transfer between semiconductor NPs has long been a field of intense study. 1–6 In an early study, Kagan et al. 7 demonstrated energy transfer in mixed solids comprised of donor and acceptor populations where the emission lifetimes were quenched due to energy transfer. Systems of nominally monodisperse particles can also show signatures of energy 2


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transfer due to the finite distribution of bandgaps that arise from synthesis-imposed size heterogeniety. 8 Förster resonant energy transfer 9 —the transfer of an exciton from a donor particle to an acceptor via dipole-dipole coupling—is the mechanism typically ascribed to the energy transfer between NPs. Higher-order structures of NPs can take a variety of forms: linked or attached dimers, 10 wire-like “chains”, 11–14 aggregates, 15,16 ordered arrays, 17,18 monolayers, 1,5 and films. 2–4,19 Mapping the complex network of energy transfer pathways in such higher-order structures is experimentally difficult. Because so many emitters can be active at once, ensemble-level measurements cannot typically resolve the individual energy transfer relationships that make up the larger picture of energy flow within such structures. However, single-particle methods can measure properties, such as geometry or fluorescence behavior, specific to a particle or a small cluster. Small and moderate sized clusters, ranging from dimers to a dozen particles, have previously been studied for their collective fluorescence behavior. 16,20–25 The blinking behavior of these clusters does not resemble a simple super-position of multiple binary states from individual NPs. 20 Shepherd et al. 21 proposed a description whereby each configuration of on/off states leads to different effective radiative rates due to inter-particle energy transfer. Frequent transitions between these configurations can produce the rapid intensity modulations. The on/off blinking of a small number of prominent acceptor particles dramatically alters the fluorescence intensity of the entire cluster, resulting in the enhanced blinking previously reported for these clusters. To investigate the structural basis for this enhanced blinking, we report super-resolution fluorescence microscopy measurements of individual NP clusters correlated with SEM images of the same particles. While other groups have used similar methods to investigate individual NPs, 26–28 to our knowledge this is the first application to higher-order NP structures. The structural information from the SEM images reveals how inter-particle interaction affects the fluorescence behavior of clusters, such as how the emission intensity scales with the number

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of particles and how different arrangements of the particles produces unique donor/acceptor relationships for the entire cluster. Super-resolution measurements can observe shifts in the emission center as the constituent particles within the cluster transition between onand off-states. The spatial distribution of the super-resolution results reflects the geometric arrangement of the particles in each cluster. When inter-particle energy transfer is present, donor/acceptor relationships among the particles and energy transport pathways can be identified by examining the spatial distribution and intensities of successive localizations.

Methods Sample Preparation Commercially synthesized CdSe/ZnS core-shell NPs from Ocean Nanotech (peak emission at 560 nm) were used to construct clusters. Partial removal of the octadecylamine surface stabilizing ligands by an addition of a bad solvent (methanol) to a colloidal suspension of the NPs in toluene begins the cluster formation. Clusters were spin-coated onto SiN TEM grids (SN100-A10Q33 from TEMwindows) that had been prepared with a (3Aminopropyl)triethoxysilane (APTES) surface treatment to ensure good adhesion to the substrate. Because the fluorescence properties of a cluster may be affected by the clustering process that removes stabilizing ligands, two methods were tested. Slow clustering at nanomolar NP concentrations was allowed to run for 20 minutes and the solution directly deposited onto the imaging substrate (see Whitcomb et al. 24 ). This process does not strip a large number of ligands from the NPs surfaces. A rapid, high concentration clustering method was also used that involves crashing the millimolar stock solutions of NPs and filtering through ultracentrifugation (following the method of Xu et al. 10 ) and produced pre-formed clusters which could be stored for later deposition. This method likely strips away a significant number of ligands from the NP surfaces. However, the final photophysical behavior of clusters prepared 4


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with either method were similar. Slow clustering produced primarily dimers and trimers while rapid clustering also produced clusters up to ten NPs. Growing a shell on a NP stabilizes and enhances the fluorescence properties of the particle. However, shell thickness can also be used to manipulate the interparticle coupling efficiency. Clusters containing either thick-shell, 9 nm diameter NPs (QSR-560 lot #101813) or thin-shell, 6 nm diameter NPs (QSP-560 lot #061713) were tested to observe clusters in different interaction regimes: the thick-shell NPs produce inter-particle spacing in the 8–9 nm range where FRET efficiency rapidly drops 6 while thin-shell NPs will have stronger coupling because of the 6–8 nm inter-particle separation distances. See Supporting Information for additional characterization of the NP clusters and details of the clustering methods.

Imaging A total-internal reflection excitation fluorescence microscope equipped with an electronmultiplying charge-coupled device (EMCCD) camera and an active focus lock (see Han et al. 29 ) was used to acquire movies for super-resolution imaging. The 488 nm line from a frequency-doubled continuous-wave diode laser (Coherent) focused at the back focal plane of an oil objective (Olympus Apo N 60×, 1.49 NA) was used to produce through-objective, total-internal reflection evanescent wave excitation. Fluorescence collected through the same objective was filtered by a dichroic beamsplitter (Semrock FF500/646) and a bandpass filter (Semrock FF01-562/40) before the detector. The EMCCD (Princeton Instruments ProEM 512B) captured movies of the fluorescence emission. Magnification of the system was optimized for achieving the highest localization precision at 150×, corresponding to 106 nm pixels. As focus drift can degrade super-resolution results, a feedback loop was used to maintain focus. Lateral stage drift was corrected for in post-processing. The SiN grids were placed, NP-decorated surface facing the objective, on top of a coverslip mounted on the microscope. Although the imaging conditions are not ideal due to the small air gap between the glass and SiN, the NPs were efficiently excited in this configuration 5



with only a small increase of background fluorescence due to the SiN. For the signal to noise ratios achieved, the localization precision was determined to be less than 10 nm. The NPs were excited with 185 W/cm2 at 488 nm. Under these conditions, the average excited state occupancy for a single NP was hNi = 0.055. An individual super-resolution measurement consists of a movie containing 10,000 frames at 100 ms exposure. Recording a large number of frames ensures the clusters have transitioned between multiple on/off configurations and that multiple observations of each configuration are made. Imaging in an electron microscope followed completed fluorescence measurements. For correlation with SEM, the location of each emitter was measured relative to two orthogonal edges of the SiN grid window and a compiled list of all particle positions gave the coordinates used to locate the same particles in the SEM. The grids were imaged in a FEI Magellan 400 XHR-SEM operating in STEM mode at 30 kV and 0.2 nA.

Super-resolution Analysis Super-resolution algorithms return position coordinates, intensity, and background count rates by fitting images to a parametric model point-spread function (PSF). Two algorithms were used to analyze the fluorescence movies from the correlated super-resolution experiment: ThunderSTORM 30 and DAOSTORM. 31 Both are maximum likelihood estimation based methods that consider a Poisson noise model, but differ in the degree of complexity given to the model PSF. ThunderSTORM is an ImageJ plugin that uses analytic PSFs, such as the pixel-integrated Gaussian derived by Smith et al., 32 as fit models for rapid processing. DAOSTORM (based on the astronomy software DAOPHOT II 33 ) uses a Gaussian PSF and corrects for inconsistencies by incorporating a globally characterized residual image based on examining multiple point-emitters from a sample frame. Artifacts due to the instrument response function of the microscope are better addressed by DAOSTORM and this algorithm produced better overall localization precision than ThunderSTORM (see Supporting Information for comparison and discussions about using other physical PSFs). The fiducial drift 6


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correction incorporated in ThunderSTORM was used to correct for lateral drift on results from both algorithms. As discussed in detail by Engelhardt et al., 34 super-resolution localization can be inaccurate if dipole effects are not considered, potentially returning misleading structures. Model functions that incorporate orientation information are necessary for many emitters including NPs which have a 2D emission plane. 35–37 However, the imaging configuration of the fluorescence measurements reported here—the combination of an air gap and a high-numerical aperature objective—results in axisymmetric PSFs that do not contain orientation information. Therefore, simple PSF models can be used and the complications from multiple overlapping dipole emitters do not need to be taken into account for fitting. A more detailed discussion of the dipole considerations and supporting analysis can be found in the Supporting Information.

Results Intensity Scaling for Clusters With correlated fluorescence and SEM imaging, the maximum fluorescence intensity as a function of the number of particles in a cluster can be measured. Such measurements suggest additional loss mechanisms develop in the CdSe/ZnS system when only a few NPs are involved. Other NPs systems, such as Si nanoparticles, 16 have shown opposite results, demonstrating emission enhancement when formed into higher-order structures. The results for both thick-shell NPs and thin-shell NPs of this study are plotted in Fig. 1. Also presented is the predicted intensity assuming it was proportional to the total number of particles, based on measurements of single NP emission intensities. Significantly, the emission from clusters of both NP types is far below what it would be from the same number of non-interacting, independent NPs. While there are variations of single particle quantum yield, the distributions observed from these samples do not account for the observed data. Because the thick7



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particles in cluster Figure 1: Maximum emission intensity as a function of the number of NPs in a cluster (solid lines). Thick-shell clusters (blue) and thin-shell clusters (green) both produce lower emission rates than would be expected if the intensity were directly proportional to the number of absorbers (dashed lines and encompassing shaded region). Furthermore, thin- and thickshell NPs have comparable emission reduction. The standard deviation of the maximum intensities of each cluster size group is represented by the shaded regions.

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and thin-shell systems both exhibit the same intensity reduction, energy transfer does not appear to be the mechanism responsible. Batches of NPs are known to contain populations of dark particles 28,38–40 —particles that are never emissive, to be differentiated from particles that are only temporarily in an off-state due to blinking. The dark fraction can range from 2%–50% depending on the synthesis and particle quality. Hence, there is the potential for dark particles to be incorporated into clusters that could explain the scaling observed. A significant dark population would result in broader intensity distributions as the number of NPs increases, which is not indicated in the observed scaling: the standard deviations for small and large clusters are similar. Furthermore, the discovery of a NP during SEM imaging that was not present in the fluorescence imaging was rare, suggesting a small dark population in the samples measured here.

Blinking Characteristics of Clusters Fluorescence trajectories of interacting NPs exhibit intermittency that is distinct from those of isolated, non-interacting single NPs. Figure 2 highlights the characteristics of the blinking behaviors. Binary blinking from a single NP is characterized by transitions between on- and off-states and the intensity variations are centered about two well-defined emission rates (the off-state representing the rate associated with the detector dark-count and background fluorescence only). Departures from the strict two-level intensity profile are primarily due to Poisson photon noise, on/off transitions that occur faster than the camera integration time, and grey states. The fluorescence trajectory from an interacting cluster, such as the trimer in Fig. 2, displays rapid modulations between non-distinct intensities to give a distribution of intensity levels. The signal is not the simple superposition of the individual NP behaviors. This collective emission dynamic has previously been linked to energy transfer. 20,21 The energy transfer efficiency in these NP systems can exhibit a spectrum of interaction strengths due to variations of the number of interacting neighbors, the separation distances, or relative orientations, which affect the energy transfer efficiency and, hence, the manifestation of 9


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Figure 2: The fluorescence trajectory of a single NP (top) shows the on/off blinking typically associated with single NPs. In contrast, clusters, such as a trimer (bottom), exhibit enhanced blinking with rapid intensity fluctuations. The blue traces depict the number of photons integrated over the entire PSF of each fluorescent spot and the black traces indicate the background photon count rate taken from a nearby, empty region, which is due to fluorescence from the SiN grid.

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fluorescence intermittency. Each cluster has a unique blinking behavior that is dictated by the specific geometry of the cluster. Enhanced blinking—the fluorescence fluctuations observed from clusters where the constituent NPs interact—is manifestly different from other forms of non-binary blinking. For example, the blinking behavior of single NPs is known to change with excitation intensity due to the intensity-dependent rate of charged exciton generation. 41 Many environmental conditions and structural properties are also known to affect the blinking behavior. 26,42,43 However, under low excitation conditions—the average rate of excitation being much smaller than the relaxation rate—the individual NPs observed in this experiment showed normal blinking behavior. Shepherd et al. 21 showed that fluorescence intensity autocorrelation analysis, which provides a measure of the characteristic time scale of intensity fluctuations, results in a shorter correlation time for clusters than the binary blinking of single NPs. The shorter roll-off times are quantitative indicators of the more rapid fluctuations from clusters. In another study by Whitcomb et al., 24 thresholding the intensity into high and low segments (analogous to the on and off classifications for binary blinking) produced the same power-law blinking statistics for clusters as the single NPs. This suggests the interactions between NPs does not affect the blinking mechanism occurring within individual NPs and that the overall modulation resembles the power-law blinking produced by a single NP. The authors explain the behavior as an acceptor NP acting as the primary source of intensity modulation for the entire cluster as it undergoes its intrinsic blinking. Blinking of donor NPs can further modulate the signal, yielding intermediate intensity levels beyond the binary blinking of an acceptor.

Super-resolution Imaging Super-resolution localization of a single, well-isolated NP provides a baseline for the fit quality that can be achieved under our experimental conditions. Figure 3 depicts the single NP whose intensity trajectory is shown in the top panel of Fig. 2. Position coordinates of each 11



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Figure 3: Super-resolution results (bottom) and the correlated SEM image (top) of the thin-shell NP whose intensity trajectory is shown in the top panel of Fig. 2. SEM and super-resolution images are shown at the same scale (magnification). In the super-resolution image, coordinates from each localization measurement are displayed as a scatter plot. The color scale indicates the emission intensity level of each localization. The extent of the super-resolution image, ∼ 14 nm, is larger than the physical extent, ∼ 5 nm, of the particle.

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frame where the particle was emitting displayed in a scatter plot indicate emission originating from a single, well-defined region. No other NPs or clusters were found within microns of this isolated NP, eliminating the possibility of influence from neighboring fluorescent particles. Compared to the SEM image, shown scaled to the same magnification, the fit (localization) precision is worse than in the SEM image and larger than the physical extent of the NP. Therefore, identification of individual particles in larger structures by inspection of the superresolution images alone may have limited success. single NP

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time [s] Figure 4: Raw position trajectories (blue) and the signal from Chung-Kennedy filtering (black) with algorithm parameters K = 20, M = 5, and p = 3. The upper trajectory illustrates the typical flat, featureless position trace of a single NP. The filtered signal of a cluster, bottom, depicts clear and sudden position changes. In both trajectories off-periods have been removed to present continuous traces. Position traces extracted from super-resolution fitting reveal distinct differences between single NPs and clusters. Figure 4 plots one of the x, y-coordinates from a single NP (top) and from a cluster (bottom) for a sequential selection of frames. A single NP has a constant position distributed according to the uncertainty arising from the localization precision and 13



fluctuations are uncorrelated in time. The efficacy of the drift correction, as well as validation that such correction does not introduce additional structure to the data, is clearly demonstrated in the scatter plots from single NPs. All well-isolated single NPs in these experiments produced similar featureless position traces. Because the correction algorithm considers all spots within the field of view of the measurement to obtain the drift, the assumption that uncorrelated position changes from individual clusters does not introduce artifacts is valid and is confirmed by the resulting constant trajectories of single NPs. A cluster, by contrast, shows sudden and discrete position changes. These features are unique to clusters and can be explained in terms of the emission configuration for the particular group of NPs: a segment of constant position represents a specific set of the on/off states of the individual constituent particles. Over the duration of a measurement, particles in a cluster transition among the possible on/off configurations. Therefore, the effects of enhanced blinking can be observed in both the intensity trajectory and the motion of the fluorescence center. Blinking events can persist for several frames and post-processing using signal averaging, filtering, or denoising methods can improve the data. Step-preserving filtering, such as the Chung-Kennedy (CK) algorithm 44 and wavelet denoising 45 are often applied to timedependent signals as a smoothing step to extract clearer dynamics or recover discrete levels from overlapping distributions. Figure 4 shows the smoothed position traces from CKfiltering in black. In these processed signals, the random fluctuations that are as large as the position jumps are suppressed, making it possible to visualize the configuration dynamics that would otherwise be obscured. Other signal smoothing methods, such as a moving average filter and wavelet denoising, were found to be similarly effective. Super-resolution scatter plots presented in this work have been processed through the CK filter. An example of the improvement as visualized by scatter plots is given in the Supporting Information.

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Discussion We are concerned about where the various intensity levels that arise from enhanced blinking occur in space. Dimers and trimers are simple structures that have limited sites where localization can occur, and we focus our investigations on these two types of systems. While single NPs, such as in Fig. 3, are observed as primarily a single, high-intensity emission confined to a circular region, clusters behave differently. Their emission can be distributed in space in such a way that indicates cluster geometry and the presence or absence of energy transfer between NPs within the cluster. Figure 5 shows the emission intensity spatial distribution for several thin- and thickshell dimers. The super-resolution images of these clusters show unique and non-uniformly distributed emission that reflect the geometries identified by SEM imaging. In the thickshell examples, Figs. 5(a) and 5(b), two well-separated regions centered over each of the NPs are evident. The distribution of intensity levels in Fig. 5(a) suggest energy transfer occurs between the two NPs with the upper NP acting as the acceptor. Because the single NP intensities for this batch of particles are so narrowly distributed, this feature is more likely to identify a donor/acceptor relationship than dissimilar emission rates of the two NPs. When the acceptor NP transitions to an off-state, the lower intensity emission from the donor is observed. The inhomogeneity and irregularity of the shell thickness for these thick-shell NPs should lead to a broad range of energy transfer efficiencies. Figure 5(b) illustrates the extreme case where the NPs are physically attached, but exhibit an intensity distribution consistent with no energy transfer between the NPs. The few events of the highest intensity (green) occur at the geometric center of the dimer, which represent the cluster configuration where both NPs are in their on-states. The intermediate intensities (red) correspond to single emitting NP, either one of the NPs or the other. The two thick-shell dimers depicted in Figs. 5(a) and 5(b) look nearly identical in the SEM images. There are no structural features in the SEM images that would indicate the large difference we observe in the apparent energy transfer 15



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Figure 5: Super-resolution position scatter plots of dimers made up of thick-shell NPs, Figs. 5(a) and 5(b), and thin-shell NPs, Figs. 5(c) and 5(d). Three of the examples depict high-intensity regions localizing off-center, over one of the NPs: the acceptor. This is indicative of energy transfer within the clusters and their corresponding intensity traces demonstrate enhanced blinking. The example in Fig. 5(b) does not show signs of energy transfer because no bright NP is evident and the maximum intensity fits occur at positions that are the geometric center of the cluster.

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efficiencies within two dimers. NP cores located off-center cannot be identified with SEM imaging and can result in clusters with increased or diminished energy transfer efficiency compared to what a center-of-mass determination would suggest. However, other sources such as poor spectral or transition dipole orientation overlap may be present, which also cannot be determined from SEM images. The low, intermediate, and high intensities from a cluster, whether exhibiting energy transfer or not, correspond to the various emission configurations of the individual NPs. At one extreme, the lowest intensity can generally be assigned to configurations where only a single NP is emitting from the cluster. Likewise, the highest intensity can generally be attributed to the configuration that has all NPs in their bright, emissive states. The intermediate intensities correspond to configurations that lie in between. For example, the intermediate intensity in Fig. 5(a) is likely due to an emitting acceptor and an dark donor. The lack of enhancement from the donor reduces the intensity from the acceptor. However, the intermediate levels of Fig. 5(b) overlap with the lowest intensity levels and represent the intensities distribution of on-states from each NP. Thin-shell dimers have greater potential than thick-shell dimers to demonstrate stronger energy transfer coupling because they have small inter-particle separations and, compared to the irregularly shaped thick-shell NPs, a narrower distribution of separations (see Supporting Information). The thin-shell dimers presented in Figs. 5(c) and 5(d) also generate the features that are attributed to energy transfer, namely the highest intensity emission is localized on a specific NP and is off-center relative to the overall cluster shape. The physical extents of these thin-shell dimers are smaller than the thick-shell dimers, which is reflected in the super-resolution results. Figure 5(d) shows subtle off-center shifting of the emission center. A crescent of intermediate intensities (red) is visible in the lower left of the scatter plot. The intensity trajectory of this cluster also shows enhanced blinking (see Supporting Information Fig. S8), further suggesting this cluster exhibits strong energy transfer between the NPs.

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Figure 6: Super-resolution position scatter plots of trimers. Examples of two geometries are presented for thick-shell clusters, Figs. 6(a) and 6(b), and thin-shell clusters, Figs. 6(c) and 6(d): a linear trimer and the closely-packed triangle structure. Larger clusters exhibit an increase in overall maximum intensity and the distinct geometries of each cluster are represented in the super-resolution results. The highest intensities strongly localize to specific regions of the clusters. The localization precision improvement from higher photon counts and higher signal-to-noise ratios are clear in Fig. 6(a) where the lower intensity upper NP has a broader spatial distribution than the higher intensity of the lower NP. 18


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Trimers are the smallest higher-order structures where several geometric arrangements of the particles are possible: linear chains, angled chains, and close-packed triangles. Furthermore, in larger clusters energy transfer between multiple neighbors generates a more complex energy landscape where hierarchical donor/acceptor relationships occur. Figure 6 shows a selection of correlated super-resolution/SEM results from thick- and thin-shell NPs that include examples of the linear trimer geometry and the closed-packed triangle geometry. The linear chains in Figs. 6(a) and 6(c) exhibit the enhanced blinking and high intensity emission localization signatures consistent with energy transfer. Furthermore, the true geometries of these clusters are evident by the super-resolution representations alone. In both examples, a terminal NP is responsible for the highest intensity emission from the cluster. The distribution of low, intermediate, and high intensities as a continuous gradient along the length of the cluster suggests that energy flow in the thin-shell linear trimer, Fig. 6(c), is driven by a specific ordering of roles: primary acceptor (left-most NP), donor to the primary acceptor (middle NP) that also serves as a secondary acceptor, and donor (right-most NP) that transfers to the secondary acceptor. This arrangement of nested donor/acceptor relationships is supported by the observation that the middle NP emission is more intense than a NP that acts solely as a donor. Emission from the middle is enhanced by the terminal donor NP. While the thick-shell linear trimer, Fig. 6(a), also exhibits an intensity distribution consistent with a terminal acceptor at one end and a terminal donor at the other, emission from the middle NP is absent. As an example of the difficulty even the simplest of clusters present to interpreting specific NP roles, and the limitations of relying on super-resolution results only, we propose the missing emission is due to a dark NP. An explanation that the middle NP emission is quenched due to energy transfer does not seem likely because such complete quenching would require more efficient energy transfer than is even observed for thin-shell NPs. The lower emission intensity from the upper NP can be explained as energy transfer to the dark NP, which can still act as an acceptor without contributing to the

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cluster emission. While this is not the only possible interpretation, it raises the interesting possibility that dark NPs can act as energy transferring donors or acceptors. The results presented for linear trimer chains emphasize how quickly interpreting individual roles of NPs within a cluster becomes complicated. In those geometries, multiple energy transfer events or next-nearest neighbor transfer are necessary for excitons to reach the acceptor NPs (which were at terminal positions in the presented examples). The close-packed triangle geometry represents, in principle, the most efficient conditions for energy transfer to a primary acceptor. In addition to a two-step series of transfer events from the most subordinate donor to the primary acceptor, direct transfer is possible—although orientation conditions can still limit such transfers. Figs. 6(b) and 6(d) show the intensity distributions of such close-packed triangle clusters. Similar to the previous energy transfer examples, these trimers also suggest a primary acceptor from where the highest intensity emission originates. However, the specific donor/acceptor relationships are difficult to gauge in these geometries. The recent work of Nguyen et al. 46 reports spatial mapping of energy transfer within clusters of NPs using single-molecule optical absorption detection by scanning tunneling microscopy (SMA-STM). Their observations of energy funneling to local acceptors among nominally monodisperse NPs support the results from the all-optical approach presented here. Furthermore, with the aid of Monte Carlo simulations, the SMA-STM method identifies the distribution of bandgaps within a cluster. However, SMA-STM measurements can electronically perturb the environment a cluster may experience in isolation. The subtle effects of fluorescence intermittency, charge trapping, and collective behavior may not be captured in a SMA-STM measurement, requiring a different approach. The non-invasive optical approach of super-resolution mapping identifies the same relationships but without perturbing the system and observes the dynamics of the system. However, the distribution of bandgaps, which defines the spectral overlap component of the FRET mechanism, cannot be measured with super-resolution imaging alone and the complimentary methods may provide the measurement capabilities that probe energy transfer systems in situ.

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Conclusions The maximum emission intensity from NP clusters was smaller than would be the case for non-interacting particles. This result suggests limitations to device efficiency based on interparticle interactions. Interestingly, both thick- and thin-shell NP clusters showed the same reduced scaling. Because shell thickness affects the efficiency of energy transfer, this result appears to indicate energy transfer is not the only mechanism responsible for the lower than expected emission enhancement. Mapping the source of emission from a NP cluster by super-resolution imaging suggests how energy flows between the particles and identifies potential donor/acceptor relationships. Correlated with SEM imaging, the true structure of NP clusters can be compared against the emission map, verifying the super-resolution features correspond to real structure. Compared to single NPs, clusters are characterized by various intensity levels localizing to different regions within the cluster and by intensity trajectories that exhibit enhanced blinking. Intensity distributions from clusters exhibiting signatures of energy transfer show high intensity emission localized over specific NPs, identifying them as acceptor NPs, as well as lower intensity regions localized over donor particles. More complex clusters, such as trimers, can have multiple hierarchical donor/acceptor relationships that can be identified from the intensity distributions. This study details a framework by which other cluster systems can be interpreted using the super-resolution localization where there is movement of the fluorescence center brought on by dynamics in the fluorescence. Future work will combine this approach with TEM and other single-molecule microscopy methods to determine the structural basis for energy transport in these higher-order systems.

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Supporting Information Details of the clustering methods, additional NP characterization, comments about the intensity scaling, comments about enhanced blinking from clusters, comparison of raw and filtered super-resolution results, comparison of super-resolution localization algorithms, notes about dipole emission effects, a specific example of the intensity trace from a strong energy transfer cluster, and super-resolution results from larger clusters are given in the Supporting Information.

Acknowledgement Special thanks to D. Shepherd for helpful conversations about cluster behavior and R. Geiss for the TEM imaging work. This work was funded by the National Science Foundation grant MPS/CHE-1059089 and performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. Los Alamos National Laboratory, an affirmative action equal opportunity employer, is operated by Los Alamos National Security, LLC, for the National Nuclear Security Administration of the U.S. Department of Energy under contract DE-AC52-06NA25396.

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