Single-Nanocrystal Reaction Trajectories Reveal Sharp Cooperative

Letter pubs.acs.org/NanoLett

Single-Nanocrystal Reaction Trajectories Reveal Sharp Cooperative Transitions Aaron L. Routzahn† and Prashant K. Jain*,†,‡,§,∥ †

Department of Chemistry, ‡Department of Physics, §Frederick Seitz Materials Research Lab, and ∥Beckman Institute for Advanced Science and Technology, University of Illinois, Urbana−Champaign, Illinois 61801, United States S Supporting Information *

ABSTRACT: Whereas pathways of chemical reactions involving small molecules are well-understood, the dynamics of reactions in extended solids remain difficult to elucidate. Frequently, kinetic studies on bulk materials provide a picture averaged over multiple domains or grains, smearing out interesting dynamics such as critical nucleation phenomena or sharp phase transitions occurring within individual, often nanoscale, grains, or domains. By optically monitoring a solid-state reaction with single nanocrystal resolution, we directly identified a unique, previously unknown, reaction pathway. Reaction trajectories of single cadmium selenide nanocrystals undergoing ion exchange with silver reveal that each individual nanocrystal waits a unique amount of time before making an abrupt switch to the silver selenide phase on a few hundred millisecond time scale. The gradual reaction progress of ensemble-scale cation exchange is actually comprised of these sharp single-nanocrystal switching events. Statistical distributions of waiting times suggest that the reaction is a cooperative transition rather than a diffusion-limited cation-by-cation exchange, which is confirmed by a stochastic reaction model. Such insight, achievable from single nanocrystal reaction studies, furthers mechanistic understanding of heterogeneous reactions, solid-state catalysis, bottomup nanostructure growth, and materials’ transformations and degradation in reactive environments. KEYWORDS: Quantum dot, cation exchange, CdSe/CdS, single-particle spectroscopy, cooperativity, nucleation

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crystals,9 thought to be due to easy diffusion of ions into a nanocrystal lattice with a high surface/volume ratio. Nanocrystals of ca. 5 nm undergo the reaction in seconds at room temperature, whereas a bulk crystal can require days to months at elevated temperatures. (b) During cationic replacement, the anionic framework of the crystal appears to be largely maintained as seen from past transmission electron microscopy studies.10 As a result, the size, shape, and morphology of the nanocrystals are preserved during the reaction. (c) From X-ray crystallography and related structural studies, the transformation appears topotaxial, allowing products with nonequilibrium or metastable crystal structures to be templated.11 An in-depth mechanistic understanding would allow cation exchange to be exploited for atomically precise templating of complex semiconductor nanostructures with utility in photovoltaics, light-emitting diodes, and display applications.12−14 Characterization of cation exchange in nanocrystals has been somewhat informative, but studies involving a large ensemble typically a colloidal solution or thin filmof nanocrystals do not provide a dynamic picture of how ions exchange. To avoid the loss of dynamic information by ensemble-averaging, we monitored single nanocrystals undergoing cation exchange in a microfluidic cell (methods detailed in the Supporting Informa-

ven in macroscale solid-state systems, chemical, structural, or electronic transitions are frequently initiated or nucleated within nanometer-sized clusters of atoms. Some key examples, where this has been directly verified, include the formation of atmospheric aerosols,1 calcium carbonate scale formation,2 crystallization of iron oxide and oxyhydroxide from solution,3,4 and formation of dopant metal clusters in silicon carbide.5 The ability to probe nanoscale regions of an extended solid undergoing a transition enables mechanistic, potentially atomistic, insights. Conventional bulk techniques for monitoring transitions, while informative, are limited for developing such insight. This limitation is because these techniques average over large numbers of nanoscale nuclei. Since different nuclei are not temporally in phase with each other during a transition and because heterogeneities exist between different nuclei, ensemble averaging results in the loss of dynamic information and the plethora of accompanying mechanistic information. A process ubiquitous in solid-state materials is the mineral replacement reaction,6,7 recently popularized in the form of ion exchange in semiconductors,8 for example, + 2+ CdSe(s) + 2Ag(MeOH) ⇋ Ag 2Se(s) + Cd(MeOH)

where the cadmium ions in a cadmium selenide (CdSe) crystal are replaced by silver ions (Ag+), which results in the formation of a silver selenide (Ag2Se) crystal and the release of cadmium ions (Cd2+) into the solution. The reaction is mechanistically rich due to several reasons: (a) The kinetics are rapid in nanosized © 2014 American Chemical Society

Received: November 28, 2013 Revised: December 26, 2013 Published: January 8, 2014 987

dx.doi.org/10.1021/nl4044289 | Nano Lett. 2014, 14, 987−992

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tion (SI)). Akin to the approach used in single-molecule biophysics/enzymology/catalysis,15−20 we employed in situ optical imaging (Scheme 1) to obtain kinetic trajectories of ion exchange of individual nanocrystals. Single-nanocrystal reaction trajectories reveal the ion exchange process is more akin to a sharp cooperative phase transition rather than a diffusion-limited exchange. In situ liquid-phase transmission electron microscopy21 remains a powerful alternative for such single-nanocrystal studies, but chalcogenides and silver ions are both susceptible to electron beam effects, making it difficult to monitor the reaction without significant perturbation, especially in reactive environments. We took advantage of the excitonic photoluminescence of CdSe nanocrystals22 as a single-nanocrystal-sensitive probe of the cation exchange reaction. The CdSe nanocrystals, typically 3.5 nm in diameter, were surface passivated with an inorganic layer of cadmium sulfide (CdS) to enhance the brightness23 and photostability of their photoluminescence under microfluidic imaging conditions. The CdS layer is known not to modify the propensity for cation exchange or the attributes of the reaction.10 We performed an ensemble-level titration (Figure 1) to demonstrate that the excitonic photoluminescence of CdSe/ CdS nanocrystals at 2.05 eV can serve as a reliable probe of cation exchange conversion. With increasing Ag+ addition, the photoluminescence of the nanocrystal ensemble progressively decreased in intensity as attributable to an increasing degree of cation exchange.24 The product Ag2Se/Ag2S nanocrystals have an infrared band gap with no visible photoluminescence. The point in the titration where the photoluminescence intensity

Scheme 1. Imaging Cation Exchange Using SingleNanocrystal Photoluminescence: Schematic of the TotalInternal Reflection Fluorescence Setup Used To Monitor Cation Exchange of Well-Separated Single CdSe/CdS Nanocrystals Immobilized inside a Microfluidic Flow Cella

a A methanolic solution of AgNO3 was flown at a controlled rate using a syringe pump. A 457 nm laser was used to photoexcite the nanocrystals, and the photoluminescent emission was imaged on an electron multiplying charge-coupled device (EMCCD) at a 50 ms time resolution. At the bottom, a caricature of the binocular view of a widefield of individual CdSe/CdS nanocrystals (represented by red dots) converting to Ag2Se/Ag2S nanocrystals (represented by black dots) is shown.

Figure 1. Ensemble test of photoluminescence as a probe of cation exchange: An ensemble-scale titration performed with a solution of CdSe/CdS nanocrystals shows that the CdSe 1Se−1Sh excitonic absorption (left panel) and photoluminescence emission (middle panel) decrease with the addition of increasing amounts of silver nitrate (AgNO3). This decrease is attributable to an increasing degree of cation exchange of Cd2+ with Ag+, resulting in the formation of Ag2Se/Ag2S nanocrystals, which is an infrared band gap material with no excitonic absorption or photoluminescence in the visible region. Note that the Ag2Se/Ag2S nanocrystals formed do exhibit band-to-band absorption in the visible region. This broad featureless absorption was removed by baseline subtraction to emphasize the CdSe excitonic peak, since this peak serves as a reliable probe of the cation exchange conversion %. Uncorrected absorbance spectra containing the contribution from Ag2Se/Ag2S band-to-band absorption are shown in Figure S9 in the SI. X-ray diffraction (XRD) analysis (right panel) shows that the initial nanocrystals have a wurtzite CdSe/CdS crystal structure. At the end of the titration, the nanocrystals exhibit the orthorhombic Ag2Se/monoclinic Ag2S. No remnant CdSe/CdS can be identified in the XRD or in excitonic absorption, ensuring complete cation exchange had occurred by the end of the titration. The titration point where the excitonic absorption and the photoluminescence intensity go to zero is defined as 100% exchange, based on which the % exchange was determined for all other titration points. The final titration point corresponds to 107% exchange, that is, a small excess of added Ag+. On the basis of these ensemble titrations, visible region photoluminescence intensity was chosen as a probe of cation exchange in single nanocrystals. It must be noted that our microscopy setup only acquires visible region (400−800 nm) photoluminescence but is not sensitive in the infrared region, where Ag2Se/Ag2S nanocrystals may exhibit band gap photoluminescence.25,26 988


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Figure 2. Imaging reveals sharp single-nanocrystal transitions: Select-area snapshots from video microscopy of cation exchange (top, left panel) at time t = 0, 4.1, 8.3, and 12.1 s show that photoluminescence intensities of individual nanocrystals turn OFF one-at-a-time. The entire movie is available as SI. ON/OFF switching is highlighted for three representative nanocrystals, marked by white circles. Black trace (top, right panel) shows the time-trajectory of photoluminescence intensity averaged over several hundred nanocrystals in the entire field-of-view. This wide-field intensity decreases sigmoidally with time, representing the ensemble-averaged kinetics of cation exchange. Time trajectories from eight representative nanocrystals are also shown as colored traces (top, right panel), depicting that individual nanocrystals make a rather abrupt switch from having an ON intensity, albeit convoluted with blinking, to having a permanently OFF intensity level, that is, the nonluminescent Ag2Se state. The gradual wide-field trajectory is comprised of several of these discrete single-nanocrystal switching events. A single-nanocrystal trajectory is shown with a magnified time axis (bottom panel) to demonstrate that the single-nanocrystal switch, while much more rapid compared to the ensemble scale conversion, is not instantaneous relative to the 50 ms time resolution of the imaging. A sigmoidal fit to the single-nanocrystal trajectory is also shown in red. For these experiments, the flow rate and concentration of AgNO3 solution were 75 μL/min and 10 μM, respectively. The start of the acquisition t = 0 may not be exactly coincident with the instant at which Ag+ enters the cell, which is difficult to accurately determine. Single nanocrystals subject to flow of methanol with no Ag+ showed only a small, 10%-or-less drop in intensity. This control experiment, results from which can be found in the SI, ensures that over the 100 s time frame of the experiment, nanocrystals are largely stable against intensity losses resulting from photobleaching, photooxidation, or washing off by methanol.

reaches zero corresponds to complete conversion of the nanocrystal ensemble to Ag2Se/Ag2S, as verified by X-ray diffraction (XRD). The final nanocrystals are in the orthorhombic Ag2Se/monoclinic Ag2S phase. No remnant CdSe/CdS is seen in XRD or in the excitonic absorption spectrum. There also appears to be no prevalence of partial exchange leading to mixed CdSe/Ag2Se heterostructures. If such heterostructures were prevalent, the excitonic absorption would have exhibited considerable peak shifts, which was not our observation. A kinetics study9 employing X-ray absorption had also showed in the past that there is no significant population of mixed heterostructures during the exchange of CdSe nanocrystals. Such intermediates in the exchange process are too short-lived to be detected with a technique of limited sampling rate or time resolution.

The sigmoidally decreasing wide-field trajectory (black curve in Figure 2 top, right panel) simply reflects the ensembleaveraged kinetics of cation exchange.27 However, inspection on the level of single nanocrystals reveals that the cation exchange reaction progresses via individual nanocrystals turning OFF oneat-a-time. Each individual nanocrystal is observed, from its photoluminescence intensity trajectory (Figure 2 top, right panel), to make a rather abrupt transition from having an ON emission intensity level (albeit convoluted with blinking behavior) to being permanently OFF (i.e., the Ag2Se nanocrystal state). The gradual ensemble kinetics is thus comprised of several of these discrete single-nanocrystal switching events. This finding leads us to a dynamic picture of the cation exchange process where entire nanocrystals switch one-at-a-time from CdSe to Ag2Se on a time scale much faster than the overall reaction 989


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Figure 3. Statistical analysis of single-nanocrystal switching events: Single-nanocrystal waiting times (left panel) exhibit a peaked distribution. A peaked distribution indicates that the exchange reaction is not diffusion-limited or memoryless; rather it involves a critical or activation event, following which exchange is rapid and spontaneous. Distributions are shown for four different Ag+ concentrations. Waiting times were determined as described in the SI. To account for experiment-to-experiment variations, multiple (between one and six) trials were performed at a given concentration until enough particle statistics were obtained. Waiting time distributions from different trials were combined together after centering their maxima at t = 0. The width of the distribution, obtained by Gaussian fitting, is inversely proportional to the ensemble reaction speed. The red curve (right panel) shows that the higher the Ag+ concentration, the narrower this distribution. On the other hand, the average single-nanocrystal switching time is independent of the concentration, as shown by the black curve (right panel). For single-nanocrystal switching times, average (τ) and standard deviation (error bars) were determined at each concentration from at least 70+ nanocrystals. The SI outlines the procedure for the determination of switching times from individual nanocrystal trajectories.

Figure 4. Stochastic cooperative model reproduces observed dynamics of nanocrystal transitions: A stochastic model that incorporates positive cooperativity between Ag+ incorporation events (left panel) reproduces the experimental observations. The ensemble kinetics of ion incorporation (left, top panel) follows a sigmoidal trajectory as seen in experiment. However, this ensemble trajectory is comprised of several sharp single-nanocrystal transitions, as shown by 10 representative single nanocrystal trajectories (left, bottom panel). Each one of the 200 nanocrystals undergoes a sharp transition at a distinct time. The distribution of waiting times (left, inset) shows a peaked distribution, similar to the experimental observation. On the other hand, a diffusion limited-model of cation exchange (right), lacking any cooperativity, follows a hyperbolic curve both at the ensemble level (right, top panel) and on the level of single nanocrystals (right, bottom panel). No sharp single-nanocrystal transitions are seen. Details of the model are described in the SI. Each unit of time on the x-axis corresponds to the period between successive Ag+ ions becoming available to the ensemble.

panel). A typical transition occurs over few 100 ms (albeit with large variation), during which the nanocrystal likely incorporates several Ag+ ions, until it reaches the Ag2Se state and turns

kinetics. It must be noted that single-nanocrystal transitions, while rapid compared to the more gradual ensemble-scale conversion, are certainly not instantaneous (Figure 2 bottom 990


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time τ required for a single nanocrystal to complete a transition, once an activation event has occurred, is not influenced by the Ag+ concentration. Thus, the ensemble conversion rate is not dictated by this intrinsic single-nanocrystal switching time, but rather it is dictated by the time dispersion of single-nanocrystal transitions. In the high-concentration limit, when the frequency of nanocrystal activation events is no longer limiting, all nanocrystals make a transition in a very narrow window of time, and the ensemble conversion rate is limited only by the intrinsic switching rate of a nanocrystal rather than by the dispersion in single-nanocrystal transitions. It is likely that the cooperative nature of the process is responsible for the experimentally observed fast kinetics of Ag+ exchange and the low populations of intermediate heterostructures in the course of exchange. It is worth contrasting cation exchange of CdSe with Ag+ against cation exchange with Hg2+. Cation exchange of CdSe with Hg2+ is known to be kinetically slow and requires elevated temperatures.31 Exchange proceeds through a gradual progression through various stoichiometries of HgxCd1−xSe, seen from a gradual red-shift in the excitonic photoluminescence spectrum.31 These characteristics are quite unlike the Ag+ system. It is possible that these differences in behavior arise from the fact that exchange of Cd2+ by Ag+ (or Cu+) involves a change in cation valency, whereas exchange with Hg2+ does not. In the Ag+ (or Cu+) system, the change in valency of the cation needs to be charge compensated by the formation of Cd2+ vacancies in the lattice. Such vacancy formation may be at the origin of the cooperative dynamics.32 While the stochastic nature of chemical processes is wellknown, single-domain microscopy is only now enabling direct visualization of this stochasticity.15 Statistical information obtained from the single-particle trajectories is free of ensemble-averaging and therefore rich in mechanistic insight. Biophysicists have successfully exploited single-molecule studies16 to uncover structural dynamics in complex biomolecular processes. Single-nanocrystal studies have the potential for analogous advances in understanding of complex materials, heterogeneous catalysis, and emergent phenomena. For instance, the finding of positive cooperative dynamics may not be limited to ion exchange. Cooperativity may be ubiquitous to the solidstate, where transformations often involve complex interactions between atomic sites, such as those involving epitaxial matching, strain, or lattice defects. Cooperative dynamics may also bear a close relationship to critical nucleation phenomena33 and phase transitions that are so widely common in materials science.

permanently OFF. Note that if the photoluminescence turn OFF was a result of photooxidation or quenching by a single Ag+ dopant, the event would appear instantaneous relative to the 50 ms time resolution of the experiment, which we did not find to be the case. Each nanocrystal makes a transition at a distinct time t. The amount of time t a nanocrystal “waits” before making the transition is termed as the waiting time. A distribution N(t) of waiting times for hundreds of individual nanocrystals is shown in Figure 3. This distribution gives insight into the reaction dynamics. Single-step diffusion-limited reactions are memoryless: the probability of a transition occurring is the same irrespective of time, and therefore an exponential distribution of waiting times, N(t) ∝ e−kt is expected. Instead, we observed a peaked distribution of waiting times, which implies that the probability of a transition is not constant in time, but rather it is enhanced by the success of past reaction events. A memoryless process involving diffusion-limited ion exchange explains neither the sharp transitions of single nanocrystals nor the peaked distribution of waiting times. However, both observations can be explained by considering ion exchange to be positive cooperative, where a nanocrystal that has already undergone one or few Ag+ incorporation events has a far higher propensity for additional Ag+, as compared to another nanocrystal that has not incorporated any Ag+. For each nanocrystal, the first one or few Ag+ doping events serve as a form of activation,28,29 following which the nanocrystal undergoes a cascade of Ag+ incorporation events and makes a relatively abrupt transition to Ag2Se. A stochastic reaction model that incorporates positive cooperativity between exchange events on the same nanocrystal reproduces all of the experimentally observed features (Figure 4, left). The simulated time-trajectory of ion exchange for an ensemble of 200 nanocrystals showed similar to the experiment, sigmoidal kinetics with slow induction at early times. Singlenanocrystal trajectories revealed sharp transitions that are much more rapid compared to the gradual ensemble kinetics. In these simulations, incorporation of Ag+ into an already “activated” nanocrystal was assumed to be more favorable by 0.1 eV compared to a nanocrystal that has not undergone any Ag+ incorporation (see SI). When this positive cooperative bias is removed in simulations, diffusion-limited behavior is observed (Figure 4, right): the ensemble and all individual nanocrystals follow similar hyperbolic growth trajectories, with no sharp single-nanocrystal transitions. Thus, positive cooperativity30 is necessary for simulating the experimentally observed behavior. Simulations also confirm the peaked distribution of singlenanocrystal waiting times measured experimentally (see the inset in Figure 4). At early times, that is, in the induction period, the probability of a nanocrystal transition occurring is low. With elapsing time, as increasing opportunities for activation events are provided, the transition probability rises and so does N(t). Once the probability reaches a maximum (near the peak of the distribution), a large number of nanocrystals make a transition. Beyond this point, the overall population of nanocrystals decreases resulting in a fall in the distribution. The cooperative nature of the reaction is also manifested in the dependence of the kinetics on the Ag+ concentration (Figure 3). As the Ag+ concentration is increased, potential activation events can occur more frequently. As a consequence, there is a narrowing of the time-dispersion of single-nanocrystal transitions (indicated by the fwhm of the waiting-time distribution) and an increase in the ensemble reaction rate. In contrast, the

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ASSOCIATED CONTENT

S Supporting Information *

Details of CdSe nanocrystal, CdSe/CdS core−shell nanocrystal, and CdSe/CdS seeded rod synthesis and purification; flow-cell preparation; single-particle microscopy experiments and data processing; transmission electron micrographs of CdSe/CdS nanocrystals; details of ensemble-scale cation exchange and uncorrected absorbance spectra; comparison of Ag+ diffusion speed and flow rate; independence of waiting times from nanocrystal spatial positions; wide-field intensity trajectories as a function of AgNO3 flow rate; results from a single-particle experiment involving seeded rods; consistency of analysis using wide-field intensities and that using particle counts; control experiment with pure methanol; description of the stochastic reaction model; caption of supporting movie. This material is available free of charge via the Internet at http://pubs.acs.org. 991


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(22) Empedocles, S. A.; Norris, D. J.; Bawendi, M. G. Phys. Rev. Lett. 1996, 77, 3873−3876. (23) Talapin, D. V.; Koeppe, R.; Götzinger, S.; Kornowski, A.; Lupton, J. M.; Rogach, A. L.; Benson, O.; Feldmann, J.; Weller, H. Nano Lett. 2003, 3, 1677−1681. (24) Sahu, A.; Kang, M. S.; Kompch, A.; Notthoff, C.; Wills, A. W.; Deng, D.; Winterer, M.; Frisbie, C. D.; Norris, D. J. Nano Lett. 2012, 12, 2587−2594. (25) Sahu, A.; Khare, A.; Deng, D. D.; Norris, D. J. Chem. Commun. 2012, 48, 5458−5460. (26) Dong, B.; Li, C.; Chen, G.; Zhang, Y.; Zhang, Y.; Deng, M.; Wang, Q. Chem. Mater. 2013, 25, 2503−2509. (27) Dorn, A.; Allen, P. M.; Harris, D. K.; Bawendi, M. G. Nano Lett. 2010, 10, 3948−3951. (28) Fayet, P.; Granzer, F.; Hegenbart, G.; Moisar, E.; Pischel, B.; Wöste, L. In Metal Clusters; Träger, F., Putlitz, G., Eds.; Springer: Berlin, 1986; pp 199−202. (29) Mott, N. F. Nature 1955, 175, 234−236. (30) Hill, A. V. J. Physiol. 1910, 40, iv−vii. (31) Smith, A. M.; Nie, S. J. Am. Chem. Soc. 2010, 133, 24−26. (32) Hainovsky, N.; Maier, J. Solid State Ionics 1995, 76, 199−205. (33) LaMer, V. K. Ind. Eng. Chem. 1952, 44, 1270−1277.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS A.L.R. performed the experiments. A.L.R. and P.K.J. analyzed the data, discussed the results and prepared the manuscript. PKJ conceived the project, designed experiments, performed preliminary studies, and developed the model. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. (DGE1144245). P.K.J. acknowledges support from the DuPont Young Professor Award and Frederick Seitz Materials Research Laboratory. The above work was carried out in part at the Frederick Seitz Materials Research Laboratory Central Facilities, University of Illinois.

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Single-Nanocrystal Reaction Trajectories Reveal Sharp Cooperative

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