Design Rules for One-Step Seeded Growth of Nanocrystals

May 22, 2019 - Design Rules for One-Step Seeded Growth of Nanocrystals: Threading the Needle between Secondary Nucleation and Ripening ...
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Cite This: Chem. Mater. 2019, 31, 4173−4183

Design Rules for One-Step Seeded Growth of Nanocrystals: Threading the Needle between Secondary Nucleation and Ripening Haoran Yang,† Leslie S. Hamachi,‡ Iva Rreza,‡ Wesley Wang,§ and Emory M. Chan*,† †

The Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States Department of Chemistry, Columbia University, New York, New York 10027, United States § Department of Chemistry, University of California at Berkeley, Berkeley, California 94720, United States ‡

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S Supporting Information *

ABSTRACT: The heterogeneous growth of inorganic shells on seed nanocrystals is used to synthesize heterostructured nanocrystals such as core@shell quantum dots for applications ranging from biological imaging to solid-state lighting. Control over shelling reactions can be achieved through continuous or layer-by-layer growth methods that are tedious and time-consuming, particularly for the growth of complex, multishell heterostructures. Here, we leverage high-throughput synthesis along with a library of precursors with tunable reactivity to develop a comprehensive understanding of the role of precursor reactivity, ligands, and temperature in one-step, seeded growth reactions on CdSe quantum dots. These experiments reveal a narrow range of precursor reactivity and monomer solubility that fosters the uniform, purely heterogeneous growth of shell material on the seed particles. This narrow “ideal growth” regime in experimental parameter space is sandwiched between opposing regimes that lead to secondary nucleation or ripening during growth. We also report that, at high concentrations of tri-n-octylphosphine, shell growth reactions exhibit “digestive ripening”, in which size distributions focus while particles dissolve. Coupled with kinetic simulations, these experiments reveal that the precursor reaction rate and monomer solubility are highly interdependent shell growth parameters that determine the balance between secondary nucleation and ripening. In contrast, the surface energy determines the evolution of the size and polydispersity of the heterostructures over time.

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INTRODUCTION The “seeded” growth of secondary materials on existing colloidal nanocrystals (NCs) is a key unit operation in the fabrication of complex nanoscale heterostructures. For applications such as solid-state lighting, solar concentrators, and biological imaging,1 shells are grown on semiconductor quantum dots (QDs) to confine excitons, passivate surface states, and direct the flow of carriers across nanoparticles.2 To finely tune these operations, scientists synthesize more advanced heterostructures such as multishell nanoparticles,3 “giant” core−shell nanocrystals,4 graded alloy interfaces,5 and spherical quantum wells.6 These structures have demonstrated reduced Auger recombination rates, near-unity photoluminescence quantum yield (PLQY), low lasing thresholds, and longterm photostability.1,7,8 Shell growth reactions are typically implemented via techniques such as successive ion layer adsorption and reaction.9 These techniques typically utilize numerous or continuous injections of shell precursors to avoid secondary nucleation of nanoparticles of the shell material.4,10−12 Although they confer exquisite control over shell composition, these long, multistep workflows scale poorly. In principle, shell growth could be accelerated if performed in a single reaction step. Such one-step reactions would rely on precisely controlled reaction kinetics, rather than injection sequence, to supply monomers to the shell growth reactions.13 © 2019 American Chemical Society

A key challenge of such one-step reactions is that the overproduction of shell material (“monomer”) results in secondary nucleation. Limited success has been reported in this regard; for example, Hens et al. recently reduced secondary nucleation by elevating monomer solubility with high oleic acid concentration.14 However, increasing the solubility of monomers may also modulate the rates of the shell growth and competing processes.15 This is likely because nanocrystal synthesis is a complex network of simultaneous reactions that includes precursor conversion, homogeneous nucleation, heterogeneous surface reactions, and particle dissolution. The delicate balance between these competing processes means that tuning a single reaction parameter is unlikely to produce optimal shell growth over a wide range of core sizes and shell thicknesses. To elucidate a general set of design principles for the one-step growth of monodisperse core−shell nanoparticles, a more holistic and comprehensive investigation of key reaction parameters is needed. Here, we systematically evaluate the critical kinetic and thermodynamic factors in one-step nanocrystal shell growth reactions using high-throughput synthesis, a library of Received: March 9, 2019 Revised: May 18, 2019 Published: May 22, 2019 4173

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Figure 1. (a) Schematic of the four QD growth regimes observed in one-step seeded growth reactions. (b) Simulated final particle number n (represented by color) as a function of precursor reaction rate constant k and bulk monomer solubility M0 at a growth temperature of 300 °C.

concentration of the particles from their absorption spectra. Although refining the growth of heterogeneous core−shell structures is the ultimate goal of this research, the coexistence of two or more materials complicates the determination of the reaction kinetics since the concentrations and dimensions of the nanostructures are not straightforward to extrapolate from optical properties. To simplify the quantification of the kinetics, we chose to perform seeded growth reactions, in which the seed and the shell materials are both CdSe since calibration curves exist for CdSe. CdSe QDs exhibit few absorption spectral features at 350 nm and so the optical density at 350 nm was used to estimate the concentration of the crystalline CdSe.22,23 Meanwhile, the average diameter of the CdSe QDs can be estimated from the first excitonic absorption peak according to an established empirical sizing formula,23 allowing us to calculate the number density of the particles and providing a quantitative picture of the seeded growth reactions. Data analysis methods and a discussion of the sources of errors are provided in the Supporting Information (SI). The spectral evolution of two representative reactions is shown in Figure S1. Using the method described above, we extracted the evolution of the particle size, the particle number density, and the concentration of CdSe molecular units in crystalline form, as shown in Figure S2. The yield of CdSe molecular units in crystalline form is fit to a firstorder rate equation (eq 2 in the Methods) to obtain the apparent rate constant (kobs) for the growth reaction (see Methods for additional details). According to the previous reports, the formation of CdSe monomers by a precursor conversion reaction is believed to be the rate-limiting step.18,24,25 Therefore, kobs is a probe of the precursor reactivity, which is a critical reaction parameter that determines the rate of monomer accumulation induced by the precursor conversion reaction. The Ideal Shell Growth Regime Lies between Secondary Nucleation and Ripening during Growth.

precursors with a tunable reactivity, and kinetic modeling. To understand the kinetics of the reactions, we used an automated nanocrystal synthesis robot16 to perform seeded growth reactions of CdSe QDs to investigate the effect of temperature, type of precursors, and concentration of ligands, e.g., oleic acid (OLAC) and tri-n-octylphosphine (TOP), on the reaction kinetics and the evolution of particle size distribution. We find that ideal seeded growth, i.e., the uniform coating of shell material onto the original seeds, lies within a narrow region of this multidimensional parameter space. Deviation from these finely balanced conditions leads to either secondary nucleation or ripening during growth (Figure 1a). Kinetic simulations of seeded growth reactions qualitatively reproduce these three types of reaction behaviors we observed (Figure 1b). In addition, our kinetic analysis revealed a unique “digestive ripening” process, in which the particle size distribution focuses while particle number decreases, in the presence of high concentrations of TOP. Simulations suggest the change in surface energy when the surface of the QDs is capped with TOP or TOPO may explain the digestive ripening phenomenon. This study demonstrates that the one-step growth of shells on colloidal nanoparticles is a complex process in which the kinetics of competing nucleation and ripening processes and the thermodynamic stability of the particles must be finely balanced to control the morphology of core@ shell heterostructures.

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RESULTS AND DISCUSSION Reaction kinetics play a crucial role in controlling the nucleation and growth in nanocrystal (NC) synthesis.14,17−21 To decouple the kinetic factors involved in seeded growth reactions, we first sought a means to track their reaction kinetics. We utilized a nanocrystal synthesis robot to perform reproducible reactions and to collect aliquots over time,16 and monitored particle growth by extracting the size and 4174

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Chemistry of Materials Scheme 1. Seeded Growth Reaction Schemea

a

R = C17H33; R1 = R2 = alkyl and aryl substituents enumerated in Table 1; TOP = tri-n-octylphosphine.

Figure 2. Summary of the absorption and photoluminescence spectra of the final products from the reactions, in which (a) precursor reactivity, (b) concentration of oleic acid, and (c) temperature are varied.

and sizes extracted from absorption spectra to classify the different regimes of shell growth. Effect of Precursor Reactivity. To vary the reaction rate independently from other reaction parameters, we leveraged a library of selenium precursors recently designed13 to span a wide range of reactivities with cadmium oleate during chalcogenide QD growth.19,26,27 We synthesized five distinct N,N′-disubstituted imidazolidine selones (Scheme 1), with the electron-withdrawing and steric nature of the substitutional group enabling fine control over the observed rate constant kobs for CdSe production (Table 1). The full details regarding the synthesis and reactivity of these compounds are reported by Hamachi et al.13 Under standard synthesis conditions, kobs can be tuned across 2 orders of magnitude from 1.2 × 10−3 to 7.5 × 10−2 s−1, as shown in Table S1. The final particle size and number density as a function of the rate constant are plotted in Figure 3a. When a relatively fast-reacting compound is used (kobs = 7.5 × 10−2 s−1), we observed extensive secondary nucleation, as illustrated by a 5-fold increase in the particle number density and an average diameter of 3.0 nm, which is significantly smaller than the “ideal size”. We note that the final particle size distributions do not appear to exhibit multiple populations (Figure 2a) despite the occurrence of secondary nucleation; this insensitivity is due to the fact that the secondary population of particles quickly grows to diameters similar to those of the seeds. To verify the existence of secondary nucleation, we performed a similar reaction using 4.1 nm CdSe seeds under otherwise identical conditions. In this case, two sets of spectral features are clearly visible (Figure S9), indicating the two particle populations of different average size. On the contrary, lowering the monomer generation rate

To understand the effect of the reaction parameters on the kinetics and, in turn, on the behavior of the seeded growth process, we performed a series of reactions (Scheme 1), in which the reactivity of precursors, reaction temperature, and the concentration of ligands (oleic acid and tri-n-octylphosphine) were individually varied (Figures 2 and 3a,c,e). In each reaction, the size of the seeds, their number density, and the amounts of shell precursors are kept constant. In a typical seeded growth reaction of a scale of 10 mL, 80 nmol of 2.8 nm diameter CdSe QDs are used as seeds (see Figure S3 for the characterization of the seeds), and the molar ratio between the shelling material to the seed material is 5:1. A summary of the synthesis conditions studied is shown in Table S1, together with the calculated apparent reaction rate constants, the final yields, and the final particle sizes. The corresponding absorption and photoluminescence spectra of the final products are shown in Figure 2, while representative transmission electron microscope (TEM) images and size histograms are shown in Figures S4−S7. If all CdSe molecular units generated from precursor conversion are distributed uniformly onto the 2.8 nm seeds, a condition we hereafter refer to as “ideal growth”, such reactions should produce 5.1 nm diameter QDs when the reaction yield is 100%. The actual yield at reaction completion varies in the range of ca. 68−96%, which corresponds to “ideal” final sizes ranging from 4.6 to 5.0 nm. In this ideal case, the number of nanoparticles should be the same as the number of seed nanoparticles. Deviation of the experimental particle number or final particle size from the ideal growth regime would therefore indicate either the formation of new particles (e.g., secondary nucleation) or the dissolution of existing ones (e.g., ripening). Thus, we used the nanocrystal concentrations 4175

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Figure 3. Experimental final diameter and particle number density estimated based on absorption spectra when the observed precursor reaction rate constant kobs (a), concentration of oleic acid [OLAC] (c), and growth temperature T (e) are varied, and the corresponding simulated final diameter and particle number density when theoretical rate constant k (b), monomer solubility M0 (d), and T (f) are varied. The dashed line represents the number density of the seeds and therefore indicates whether the reaction is ideal. The error bars represent the estimated uncertainty based on the full width at half-maximum of the first absorption peak. The same set of experimental data estimated based on TEM study is plotted in Figure S8 for comparison.

reactivities that span orders of magnitude13,26,27 so that the optimal precursors can be selected for a given set of nanocrystal growth conditions. To understand the kinetic implications of the experimental parameters on the seeded growth reaction, we simulated the reaction trajectories of the growing nanoparticles using a numerical model based on that of Hens et al.14,28 In this model, the growth and dissolution of the particles, together with the possible homogeneous nucleation, are all considered in the mass balance differential equations. The temporal evolution of the size distribution function of the particles, c(r,t), is calculated by numerically solving the coupled differential equations; the solutions are then used to determine the average size and particle number density. The details of the modeling are presented in the Supporting Information, and the results of typical simulations are shown in Figure S10. The theoretical model qualitatively reproduces the experimental trend as the precursor reaction rate constant k is varied (Figure 3b). As k is increased from 10−4 to 10−1 s−1, three regions from ripening during growth (nfinal < nseed) to ideal growth (nfinal = nseed) to secondary nucleation (nfinal > nseed) are predicted, as shown in Figure 3b. Like the experimental observation, the simulation suggests that a narrow range of k

Table 1. Library of Imidazolidine Selones and Their Observed Rate Constants kobs kobs (s−1)

R1 = R2 a b c d e

phenyl t-butyl methyl ethyl i-propyl

(7.5 (4.7 (8.6 (4.0 (1.2

± ± ± ± ±

0.4) 0.1) 1.6) 0.2) 0.1)

× × × × ×

10−2 10−2 10−3 10−3 10−3

by utilizing the slower compound suppresses the secondary nucleation. However, our experiment shows that a precursor that reacts too slowly might allow the growth to fall into a ripening regime; when the compound of the lowest rate constant (1.2 × 10−3 s−1) was used, the final particle number density was estimated as 5 ± 2 mM by absorption spectrum (7.5 ± 0.2 mM by TEM), which is slightly smaller than the number density of the seeds. This indicates that, during growth, a small portion of the existing particles are either partially dissolved or fused into larger ones. The optimal rate constant seems to fall within a narrow range between 1.2 × 10−3 and 4.0 × 10−3 s−1. This narrow window for ideal growth highlights the value of developing precursor libraries that offer 4176

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Chemistry of Materials (0.5 × 10−3 to 1.0 × 10−3 s−1) is required if ideal growth is desired. This model supports a ripening mechanism in which smaller particles dissolve and larger particles grow under the low monomer supersaturation that results from slow precursor conversion. This ripening phenomenon is similar to the wellknown Ostwald ripening, which usually happens after the depletion of the precursors. Here, we show that ripening may also happen during the growth if the precursor conversion is too slow. While these modeling and spectral data cannot be used to rule out an alternate ripening mechanism involving the aggregation of particles, our subsequent investigation into ligand effects suggests that this pathway is unlikely. Effect of Oleic Acid. In addition to precursor reactivity, surface ligands also have profound impacts on nanoparticle nucleation and growth.29−31 Recently, Hens et al. reported that higher concentrations of oleic acid in seeded growth reactions of CdSe/CdS QDs favor heterogeneous growth over homogeneous nucleation.32 To better understand the role of oleic acid in reaction kinetics and particle growth, we systematically varied the concentration of oleic acid, [OLAC], from 24 to 2355 mM, while keeping the reaction temperature constant at 300 °C and using 1,3-diethylimidazolidine-2-selone as the Se precursor. The effect of oleic acid on particle growth is not significant but observable, evidenced by a ca. 1 nm change in the final average particle size. The size distribution broadens at intermediate [OLAC] but then focuses at high [OLAC]; this nonmonotonic behavior may arise from ligand-dependent surface thermodynamics discussed in a later section. Similar to the report from Hens et al., which used TOP-S as a sulfur precursor for the growth of the CdS shell, we also observed reduced secondary nucleation at high [OLAC] with our 1,3-diethylimidazolidine-2-selone precursor for the seeded growth of CdSe (Figure 3c). However, we note that increasing [OLAC] to high levels also moves the reaction away from ideal growth; a careful analysis of the size and particle number density reveals an enhanced ripening effect under high [OLAC] above 768 mM. This effect might have been overlooked in many of the previous studies on CdSe@CdS core/shell structures since the amount of CdSe dissolved from the seeds is relatively low compared to that of the CdS in the shell. Avoiding kinetic regimes that favor ripening is critical when growing heterostructures like CdSe@CdS since the dissolution of seed nanoparticles will modify the composition of shells, e.g., resulting in alloyed shells, and will also modify the dimensions of the seeds. Unlike the precursor reactivity, which directly links to the accumulation rate of the monomers, the role of oleic acid here is not well defined since the ligand may serve multiple roles. Consistent with Hens et al., we found that [OLAC] exhibits minimal influence on the formation rate of CdSe, as the rate constant remains almost unchanged at all [OLAC] tested (Figure S11). It was proposed that oleic acid may increase the monomer solubility, which suppresses monomer supersaturation and therefore reduces secondary nucleation.14 Given that the effect of oleic acid is universal regardless of the precursor selection (TOP-S, ref 11, or imidazolidine selones, this study), it is likely that the concentration of oleic acid does affect the solubility of CdSe monomers. Our simulation demonstrates that, when monomer solubility is varied from 0.1 to 16 × 10−8 mol/m3, ideal growth, secondary nucleation, and ripening during growth are again predicted (Figure 3d). The qualitative agreement between the simulation and the experiment suggests

a highly plausible correlation between [OLAC] and the monomer solubility, i.e., a ca. 10-fold increase in monomer solubility as [OLAC] increases from 24 to 2355 mM. Again, the simulation highlights that a narrow range of monomer solubility (0.75−2 × 10−8 mol/m3) is required for achieving the ideal growth. These simulations also suggest that the ripening under high [OLAC] is due to the enhanced dissolution of smaller particles. Conversely, the alternate ripening mechanism involving particle fusing cannot explain the experimental observation that ripening is more significant under high [OLAC]; as a ligand, oleic acid should have the opposite effect of stabilizing the particles. Effect of Growth Temperature. Finally, we investigated the effect of temperature on QD growth behavior while keeping [OLAC] constant at 288 mM and using 1,3-diethylimidazolidine-2-selone as the Se precursor (Figure 3e). At 300 °C, we observe minor secondary nucleation; however, below 280 °C, we observe ripening instead. The effect of temperature may be multifold, as it changes not only the reaction rate of the precursors but also the relative nucleation/growth rate and monomer solubility.33 As the temperature decreases from 300 to 240 °C, the measured rate constant of the precursor decreases by 1 order of magnitude (from 4.0 to 0.4 × 10−3 s −1 ), which is shown in Figure S12. Applying our experimentally determined rate constant to our simulations, we obtain the results shown in Figure 2f, which qualitatively reproduces the experimental trend. The ripening experimentally observed at low temperature is more severe than that predicted by the model, which could be attributed to factors not included in the simulation, such as the change in surface energy, monomer adsorption rate, etc. Nevertheless, the qualitative agreement of the simulation to experiment indicates that temperature influences seeded growth reactions mainly by modifying the reactivity of the precursors. Ideal Growth Is Achieved by Balancing Multiple Reaction Parameters in Synthetic Parameter Space. Since precursor reactivity, ligand concentration, and temperature all influence shell growth, we sought to understand how these experimental parameters affect nanocrystal shell growth when they are changed simultaneously. Mapping multidimensional parameter space is essential for studying complex networks since the optimization of one physical property (particle concentration) often occurs to the detriment of others (reaction rates, size distribution). By modeling reactions over 72 binary combinations of k (nine values from 3.3 × 10−5 to 3.3 × 10−1 s−1) and M0 (eight values from 1.0 × 10−9 to 2.5 × 10−7 mol/m3) at a growth temperature of 300 °C, we successfully reproduced the three growth scenarios that we had observed experimentally. These data were used to generate a two-dimensional phase diagram (Figure 1b) showing the final particle number (nfinal) as a function of k and M0. As with the one-dimensional series shown in Figure 3, three distinct growth regimes in this diagram (Figure 1b) are delineated by the conditions: nfinal > nseed (secondary nucleation), nfinal ≈ nseed (ideal growth), and nfinal < nseed (ripening during growth). Notably, the regime favoring ideal growth does not always occur at the same values of k or at consistent values of M0; rather, the phase diagram in Figure 1b indicates that the ideal monomer solubility scales approximately linearly with the precursor reactivity. Conceptually, the linear boundaries of the three growth regions in Figure 1b originate from the difference in the rates of three competing processes, namely, nucleation, growth, and dissolution, which are determined by super4177

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Figure 4. Effect of TOP in the seeded growth reactions. (a) Final diameter and particle number density and (b) precursor rate constant as a function of [TOP]. (c, d) UV−vis absorption and photoluminescence spectra and (e, f) TEM images of the final products without (c, e) and with (d, f) TOP. Both reactions were performed at [OLAC] of 288 mM and a temperature of 300 °C using 1,3-diethylimidazolidine-2-selone as precursor.

(Figure S13), albeit with a shift in the balance of k and M0 to higher reactivity and lower solubility. This analysis highlights the fact that shell growth parameters are highly interdependent, and varying one parameter requires reoptimization of all other parameters to achieve ideal shell growth. Evaluation of the Uncertainty in the Size Analysis. Compared to the CdSe QDs synthesized with the frequently used tri-n-octylphosphine selenide (TOP-Se) precursor, the particles grown in this study with substituted selenone precursors generally exhibit slightly larger relative size distributions, between 10 and 18%, as determined by TEM. The relatively broad size distributions are not surprising for reactions that exhibit secondary nucleation or ripening and are expected when utilizing new precursors and when varying reaction conditions far from their optimized values. Broad absorption features, however, can lead to uncertainty in the particle sizes and concentrations extracted from those spectra. For the reactions discussed here, the half-width at halfmaximum (HWHM) of the first excitonic absorption peak ranges from 14 to 35 nm (Table S1), which corresponds to uncertainties of ±0.2 to 0.5 nm in the average size, respectively (see SI for the explanation of calculations). To demonstrate that the nanocrystal parameters extracted from these spectra are valid, we performed a careful TEM size study on selected samples, including those with large HWHM. As shown in Table S1, the differences in the average sizes estimated from these two methods, regardless of the polydispersity, are within 0.3 nm (less than 6% relative to the average size) for the majority of the samples. As shown in Figure 3 and discussed above, the nanoparticle diameters investigated here span a range of 2.6 nm. Since this range is significantly larger than the 0.3 nm uncertainty, we believe that the observed trends discussed in the previous sections contain statistically meaningful information regarding the particle growth pathways (see the Supporting Information for an extended error analysis). Trioctylphosphine Narrow Size Distributions via Digestive Ripening. Even for the conditions that are close to the ideal seeded growth (samples 1d, 2e, and 3a in Table S1), the size distributions of the particles grown in this study

saturation (S), i.e., the ratio of the monomer concentration to its solubility M0 (refer to SI for the governing equations). There exists an intermediate supersaturation range where both nucleation (which occurs at high supersaturation) and dissolution (low supersaturation) are negligible. In this intermediate regime, conformal growth is dominant. Therefore, the trajectory of S versus time t throughout the span of the reaction dictates the growth regime. The temporal evolution of S is determined by the difference between the monomer generation rate (precursor conversion and particle dissolution) and monomer consumption rate (nucleation and particle growth). These rates are functions of S, and dS/dt is highly dependent on S (see governing eqs S2−S4 in the SI). Therefore, the most important term predicting the growth regime is the initial slope of S versus t, which is determined by the equation dS dt

= t=0

k[P ]0 M0

(1)

where [P]0 is the initial precursor concentration. This analysis assumes that in the initial stage of the reaction, the change in monomer concentration is solely determined by the first-order conversion reaction of precursors, i.e., both the growth term and nucleation term are zero at t = 0 in eq S2. As the ratio between k and M0 is fixed, the initial supersaturation will be the same, which will lead to a similar growth trajectory. This explains the approximately linear relationship between k and M0 of the ideal growth region revealed in Figure 1b. According to the phase diagram in Figure 1b, a matching pair of k and M0 is required for achieving the ideal growth, which emphasizes the importance of balancing the kinetic factors in the seeded growth reactions in multidimensional parameter space. This design rule suggests that if maximizing the shell deposition rate (k) is an objective, e.g., to shorten reaction times, then the solubility of the monomer also must be increased to a precise level to ensure uniform shell growth without secondary nucleation or ripening. We also simulated seeded growth at lower growth temperature; seeded shell growth simulated at 240 °C produced a similar phase diagram 4178

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Figure 5. Simulation results under different surface energy profiles, γ(r). (a) Evolution of the size distribution functions; the insets show the γ(r) functions implemented in each simulation; (b) comparison of the particle size distribution function at the end of the reactions, i.e., when the yield is 99%.

ligands encourage the dissolution of the smaller particles; the increased solute stimulates the growth of the rest of the particles, thereby narrowing the size distribution. Such digestive ripening has been reported for the synthesis of metal nanoparticles34 and lanthanide-doped nanoparticles;35 however, the digestive ripening of semiconductor compound nanocrystals is only beginning to be investigated.36 Digestive ripening behavior is not predicted by our previously described numerical simulations when kinetic factors such as precursor rate constant, monomer solubility, and temperature are varied. To rationalize this behavior, we consider the influence of ligand binding to the particle surface. Unlike oleate, which is a negatively charged X-type ligand and preferentially binds to the exposed cation-rich facets of the CdSe QDs, neutral L-type TOP or TOPO (generated in the QD growth reaction in situ from TOP) is more likely to bind to neutral facets. Therefore, in a binary-ligand synthesis with both OLAC and TOP, the surface properties of the QDs may be significantly different from those of the OLAC-based synthesis. Comparing the morphology of the QDs synthesized with and without TOP under TEM, we notice that particles grown without TOP are faceted (Figure 4e), whereas those grown with TOP are spherical (Figure 4f). In addition, we observe that CdSe QDs synthesized under high [TOP] adopt a wurtzite phase, whereas those synthesized without TOP always exhibit a zinc-blende phase, as shown in Figure S14. The difference in crystal structure possibly originates from the different binding energies of TOP or TOPO and OLAC on the QD surface.37 Gao et al.38 observed a similar ligand-induced phase transition with CdSe QDs. This evidence suggests that TOP induces digestive ripening by modifying the surface energy of the QDs, which we did not consider in the kinetic simulations presented above. Size Dependence of the Per-Atom Surface Energy Influences the Evolution of Size Distribution over Time. To test this hypothesis, we varied the γ parameter in our numerical model, which represents the surface energy per unit area. In the simulations presented thus far (which are based on models routinely used in the literature14,28,31), γ is assumed to be independent with particle diameter. In reality, γ should vary with factors such as crystal structure of the nanocrystals, the orientation of the exposed facets, the curvature of the particle surface, the number of surface dangling bonds, ligand type, and ligand coverage. Therefore, γ should exhibit a dependence on size, a phenomenon that has been reported both experimentally and theoretically.39,40 However, to our knowledge, the effect of the size dependence of γ on the size distributions of growing nanoparticles has not been investigated yet via

with substituted selenone precursors are ca. 13%, which is broader than the best results from syntheses that use TOP-Se. These distributions are also considerably more polydisperse than predicted by our numerical simulation (as low as 5%). To generate a more complete understanding of the role of TOP in narrowing size distributions, we added various amounts of TOP to the 1,3-diethylimidazolidine-2-selone reactions. As [TOP] is increased, we observed a nonmonotonic trend in the QD seeded growth pathway (Figure 4a), along with a nonmonotonic change in the precursor reaction rate (Figure 4b). At low [TOP], increasing [TOP] from 0 to 18 mM leads to a rapid, 8-fold increase in kobs from 0.004 to 0.031 s−1. Consistent with our model, the increase in precursor reactivity promotes secondary nucleation, which results in a decrease in the final particle size and an increase in the particle number density. Above 18 mM TOP, further increasing [TOP] to 192 mM results in a slow decrease of the rate constant to 0.014. We note that the reaction rate in these reactions is at least three times higher than the reaction rate without TOP. The modification of the reaction rate in the presence of TOP may be due to its possible reaction with the selone precursor or with intermediate Se-containing species. The sharp increase in the reaction rate as [TOP] is increased above 18 mM (Figure 4a) is consistent with the fact that the reactivity of TOP-Se is approximately 6-fold higher (0.024 s−1) than that of 1,3diethylimidazolidine-2-selone under the standard synthesis conditions. However, further investigation is needed to confirm any side reactions that involve selone precursors. Interestingly, the increased precursor reactivity at high [TOP] does not result in enhanced secondary nucleation as expected. This is distinctly different from the reactions without TOP, in which secondary nucleation and precursor reactivity are always positively correlated. Instead, we observed a decrease in the particle number density to ca. 6 mM, which is 25% less than the seed particle density, as shown in Figure 4a. As a result, the final average size grows into 5.6 nm estimated by the first excitonic peak of the absorption spectrum (5.4 ± 0.4 nm by TEM), a diameter that is considerably larger than the ideal size of 4.7 nm. The decrease in the particle number density is also observed with Ostwald ripening. However, in stark contrast to the increasing size distributions observed with Ostwald ripening, we observed size focusing at high [TOP]. A size dispersity as low as 8% and a narrow emission line width of 88 meV (28 nm centered at 630 nm) are obtained at [TOP] = 192 mM (Figure 4d). In comparison, synthesis without TOP yields relatively broader size distribution and emission line width (Figure 4c). We rationalize this behavior with a mechanism in which TOP 4179

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injection shell growth reactions, undesirable side processes such as secondary nucleation and ripening can be avoided if monomer production and consumption rates are carefully balanced by simultaneously tuning the precursor reaction rate, monomer solubility, and temperature. These parameters dictate the degree of supersaturation and therefore define the growth regime (i.e., ideal growth, secondary nucleation, or Ostwald ripening). These findings highlight the importance of controlling precursor reactivity within a narrow range optimized for ideal shell growth. Furthermore, they highlight that tuning one shell growth parameter (e.g., increasing precursor reactivity to accelerate shell growth) requires the corresponding optimization of other parameters (e.g., increasing monomer solubility) since their effects on nucleation and growth kinetics are coupled. Understanding these interdependencies will enable the design of fast shell growth reactions with quantitative yield and precise control over shell composition.13 Moreover, we find that the kinetic factors alone cannot guarantee uniform final sizes, as the evolution of the particle size distribution is strongly influenced by the size-dependent, per-atom surface energy, which describes the thermodynamic stability of a particle. By adjusting the surface energy through ligand coordination, we show that nonclassical growth regimes can be achieved, such as the digestive ripening shown here. Our simulation with size-dependent surface energy may also shed light on nanocrystal synthesis involving magic-sized clusters (MSCs), which have been reported for a variety of materials, including metals, semiconductors, and oxides.42 MSCs are often obtained alongside NCs in III−IV material synthesis, which is consistent with our model’s prediction of multimodal size distribution under the γ profile 2, as there might exist multiple surface energy minima for nanoparticles of different sizes.43 In comparison, a single thermodynamically stable size will effectively help the size focus, as discussed for γ profile 3. These results indicate that designing a ligand environment that preferentially stabilizes NCs of a certain size is highly desirable when targeting narrow size distributions.

kinetic modeling. Here, in addition to modeling growth kinetics with constant γ (profile 1), we performed simulations under two other types of γ profiles. To mimic variations in the surface energy as the nanoparticle passes through closed-shell configurations, we used an alternate γ(r) function (profile 2) that oscillates with nanoparticle radius r. The third γ(r) function we considered (profile 3) was drawn from experimental surface energies measured for TOPO-capped CdSe QDs. The shapes of the three γ profiles are shown as insets in Figure 5a, and quantitative comparison of them is shown in Figure S15. Simulated nanoparticle growth with constant γ exhibited the typical reaction-driven size focusing, in which the reaction of precursors supplies monomers efficiently fast and drives the conformal growth of the particles and focuses the particle size (Figure 5a).28 The average radius of the QDs increased from 1.2 to 2.5 nm, while the particle number density remained constant. The relative size distribution decreased from 10 to 3%. In comparison, oscillating γ (profile 2) resulted in a multimodal size distribution (Figure 5b). Note that although this reaction is also “kinetically ideal” (i.e., the particle number stays constant throughout the reaction, as shown in Figure S15), a divergent size distribution is obtained. The simulation result agrees well with our experimental data that relatively broad size distributions are obtained even for reactions that approach the kinetically ideal growth regime when oleic acid is the only ligand. Considering the strong oleate−cadmium binding on the QD surface,41 QDs of closed-shell configurations and properly passivated surfaces may be more stable,39 i.e., local minima of γ may exist. The intermediate sizes in between these closed-shell configurations likely exhibit atomic step edges or adatoms with unpassivated surface dangling bonds, which will increase γ (refer to SI for more discussion). Therefore, it is reasonable to assume that γ exhibits an oscillating size dependence with multiple energy minima at different sizes. Indeed, the simulation under an oscillating γ profile suggests that, even if the growth is kinetically ideal, size focusing is not achieved due to thermodynamic obstacles. A third γ(r) profile (profile 3) is extrapolated from experimental data on TOPO-capped CdSe QDs, which shows a minimum at a radius of 1.4 nm.40 We find that this γ profile not only suppresses the nucleation rate but also yields a critical nucleus size that is larger than 1 nm even at a relatively high supersaturation S of 400 (Figure S15). This leads to the fast dissolution of particles smaller than the critical size, which, together with the precursor reaction, provides supersaturated monomers to drive the growth of the rest of the particles. Therefore, digestive ripening is predicted; although the particle number decreases, the size distribution becomes narrower (Figure 5c). These simulation results are qualitatively consistent with our experimental observations when TOP is used. This agreement supports our hypothesis that the digestive ripening process is a consequence of size-dependent variations in the surface energy due to TOP surface coordination. A comparison of the final particle size distributions simulated under the three γ profiles (Figure 5d) clearly highlights that these thermodynamic factors strongly influence the shell growth trajectories of QDs and, ultimately, their final size distributions. Discussion. Our results demonstrate the feasibility of a one-step shell growth method that does not rely on continuous or multiple injections of shelling precursors. For single-

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CONCLUSIONS Nanoparticle growth is a complex process that involves the simultaneous growth and dissolution of the existing particles and, in unfortunate cases, the generation of new nuclei. To achieve the ideal growth of conformal shells on seed nanoparticles, both kinetic and thermodynamic parameters must be precisely controlled. Using CdSe QD seeded growth as a model system, we have shown that kinetically ideal growth of shells on QDs requires precursors whose reactivities lie in a narrow range. These reactivities must be matched precisely with other reaction parameters such as monomer solubility and temperature, due to their interdependence. The narrow sliver of parameter space that is ideal for shell growth is sandwiched between large regimes that host ripening and secondary nucleation. In addition to these kinetic factors, surface energy, a thermodynamic factor, significantly influences the evolution of nanoparticle size distributions. Even in the kinetically ideal growth regime, multimodal size distributions may develop if multiple quasi-stable sizes exist. In contrast, when the per-atom surface energy profile exhibits a single minimum energy, as observed with high concentrations of TOP, digestive ripening occurs, which focuses on the size distribution. The kinetic and thermodynamic factors investigated and the reaction design principles developed here may be generalized to most colloidal 4180

DOI: 10.1021/acs.chemmater.9b00971 Chem. Mater. 2019, 31, 4173−4183

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Chemistry of Materials

isopropanol, ethanol, and methanol, followed by centrifugation and three additional precipitation/centrifugation cycles using a hexane/ isopropanol/ethanol mixture. Statistics of the particle size is obtained by measuring 200−300 particles for each sample. Calculation of Rate Constant (kobs). Consistent with previous reports,24,25 the production of CdSe can be fit to a first-order rate equation written as

nanocrystal reactions, including but not limited to metal, semiconductor, upconverting, transparent conductive oxide nanocrystals, and their core−shell heterostructures.

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METHODS

Chemicals and Materials. Hexanes (98.5%), methanol (99.8%), ethanol (≥99.8%), and isopropanol (99.5%) were obtained from VWR. Acetonitrile (anhydrous, 99.8%), dichloromethane (≥99.5%), dodecane (≥99%), cadmium oxide (98%), trifluoroacetic acid (99%), trifluoroacetic anhydride (99%), triethylamine (≥99%), oleic acid (99%), oleic acid (90%), tetraethylene glycol dimethyl ether (“tetraglyme”, ≥99%), and 1-octadecene (90%) were obtained from Sigma-Aldrich and used without further purification except for tetraglyme, which was stirred with calcium hydride overnight and distilled prior to use. Tri-n-octylphosphine (TOP, 97%) was obtained from Strem Chemicals. Cadmium oleate was synthesized on a 30 mmol scale using the procedure reported by Hamachi et al.13 to make lead oleate,26 but substituting cadmium oxide for lead oxide. N,N′Disubstituted imidazolidine selones were synthesized using the procedures reported by Hamachi et al.13 Synthesis of 2.8 nm CdSe Seeds. Nanoparticle seeds were synthesized on the Workstation for Automated Nanomaterial Discovery and Analysis (WANDA),16 a robot housed in a nitrogen glovebox. In a typical procedure, a 40 mL vial was loaded with cadmium oleate (0.24 mmol, 0.162 g), oleic acid (90%, 0.48 mmol, 0.136 g), and 1-octadecene (18.85 mL, 14.870 g). Meanwhile, a selenium precursor solution of 0.2 M was prepared by dissolving N,N′-diphenyl imidazolidine selenone in tetraglyme in a separate vial at 100 °C. The cadmium oleate solution was loaded into the robot reactor where it was heated to 300 °C at a rate of 30 °C/min under a magnetic stirring rate of 500 rpm. The temperature was allowed to stabilize for 5 min once 300 °C was reached. Then, 1 mL of the selenium precursor was injected at a rate of 1.5 mL/s to the cadmium oleate solution and left to react for 2 min. The reaction was then quenched by a nitrogen gas flow around the vial. The reaction solution was used as seed stock solution without further purification. Seeded Growth Reactions. In a typical seeded growth reaction, a 40 mL vial was loaded with cadmium oleate (0.12 mmol, 0.081 g), nanoparticle seed solution (2 mL), and designed amounts of 1octadecene, oleic acid, and tri-n-octylphosphine; the total volume of 9.5 mL was maintained by adjusting the amount of 1-octadecene. Meanwhile, selenium precursor solutions of 0.2 M were prepared by dissolving the imidazolidine selenones in tetraglyme at 100 °C. Seeded growth solutions were loaded into the robot reactor where they were heated to the desired temperature at a rate of 30 °C/min under a magnetic stirring rate of 500 rpm. Then, 0.5 mL of the selenium precursor was injected at a rate of 1.5 mL/s into each seeded growth solution and left to react for the appropriate time before quenching with nitrogen flow. Nanocrystal Growth Kinetics. To track the evolution of the nanocrystal growth, aliquots of 60 μL each were taken during the reactions and were dispensed into preweighed 2 mL vials. The vials were weighed after loading with aliquots to determine their mass. The aliquots were diluted with 1440 μL of dodecane, and 200 μL of the diluted solutions were loaded into a quartz 96-well microplate (Hellma). UV−vis absorption and PL spectra were acquired using a Biotek Synergy2 multifunction microplate reader. The size and number density of CdSe QDs were estimated from the size-dependent extinction coefficient at the first excitonic absorption maximum reported in the literature.23 (See SI for more details on error analysis.) To determine the conversion kinetics of CdSe, the absorbance at 350 nm was monitored, which is less affected by the quantum size effect, and the concentration of crystallized CdSe in the reaction solution, [CdSe], was calculated based on the size-independent molar extinction coefficient reported in the literature.22 To verify the optically estimated sizes, we also verified the morphologies of selected samples using a JEOL JEM-2100F transmission electron microscope (TEM). For the TEM study, the as-synthesized nanocrystals were purified from the reaction mixture by precipitation with a mixture of

[Cdse] = [Cdse]seed + A ·(1 − e−kobst )

(2)

where [CdSe] is the molar concentration of crystallized CdSe, [CdSe]seed is the molar concentration of the initial seeds, A is the final concentration of CdSe formed by the shelling reaction, and kobs is the first-order rate constant. If the reaction reaches a final yield of 100%, A should be equal to the initial concentration of the limiting (Se) precursor, which is 10 mM in our experiments. The actual yield at reaction termination is usually less than 100% and varies depending on the reaction conditions. Therefore, we fit both A and kobs to the experimental data to quantify the kinetics of these reactions.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.9b00971.

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Reaction conditions, representative absorption and emission spectra for one-step seeded growth reactions, measured rate constants, representative electron micrographs and nanoparticle sizing, X-ray diffraction patterns, simulation data, simulation methods, and error analysis (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Haoran Yang: 0000-0002-9709-1062 Leslie S. Hamachi: 0000-0001-6299-8695 Emory M. Chan: 0000-0002-5655-0146 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Prof. J. S. Owen for discussions and comments. This work was supported by the Department of Energy, Office of Energy Efficiency and Renewable Energy (EERE), under Award Number DE-EE0007628. Work at the Molecular Foundry was supported by the Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

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REFERENCES

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