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Cite this: DOI: 10.1039/c5nr00028a

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Size control by rate control in colloidal PbSe quantum dot synthesis† Richard Karel Čapek,* Dianna Yanover and Efrat Lifshitz* A recently demonstrated approach to control the size of colloidal nanoparticles, “size control by rate control”, which was validated on the examples of colloidal CdSe- and CdS-quantum dot (CQD) synthesis, appears to be a general strategy for designing technically applicable CQD-syntheses. The “size control by

Received 3rd January 2015, Accepted 6th February 2015

rate control” concept allows full-yield syntheses of ensembles of CQDs with different sizes by tuning the solute formation rate. In this work, we extended this strategy to dialkylphosphine enhanced hot-injection

DOI: 10.1039/c5nr00028a

synthesis of PbSe-CQDs. Furthermore, we provide new insight into the reaction mechanism of dialkyl-

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phosphine enhancement in TOPSe based CQD-syntheses.

Introduction Colloidal semiconductor quantum dots (CQDs) are currently in the focus of scientific attention because the size quantisation effect1 allows adjusting their electronic properties (e.g., their band-gap energy) as required. Cadmium chalcogenide and lead chalcogenide CQDs are among the most extensively studied materials because of their electronic properties, which are almost ideal for application in solar cells, LEDs, and biolabeling.2–5 In addition, they can be easily obtained by hotinjection synthesis.6 In hot-injection synthesis, one precursor is usually injected into a reaction mixture containing the other precursor and the required ligands at elevated temperatures. In the last few decades, metal chalcogenides have become predominant in CQD synthesis due to a large variety of chalcogenide sources. These sources include solutions of elemental chalcogens in alkenes,7 trialkylphosphine and bis(trimethylsilyl) chalcogenides,6,8 as well as reactants produced by reactions between alkenes and chalcogens.9 Due to the sufficiently low reactivity of trialkylphosphine chalcogenides, a diffusion-controlled growth of CQDs can occur, which is driven by the formation reaction of the solute (“dissolved material”, section S1, ESI†).10 Thus, CQD size tuning can be readily achieved by changing the reaction time, while maintaining a sharp size distribution of the CQDs.6,10–12

Schulich Faculty of Chemistry, Russell Berrie Nanotechnology Institute, Solid State Institute, Technion, Haifa 32000, Israel. E-mail: [email protected], [email protected] † Electronic supplementary information (ESI) available: Additional data about the reaction and growth kinetics, NMR-data and exemplary TEM images of PbSeCQDs prepared by the procedure described in this publication. See DOI: 10.1039/c5nr00028a

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However, the intrinsic drawback of this method is the possibility of obtaining smaller particles only at the expense of a reduced chemical yield. Owen et al. have shown that the total number of nuclei, formed in trioctylphoshine selenide-(TOPSe) and cadmium phosphonate-based CdSe-CQD synthesis, depends on the CdSe-solute formation rate, which, ultimately, depends on the precursor concentrations. This observation is in agreement with the modelling results of Abé et al., which were based on classical precipitation kinetics;13 it was found that increasing the solute formation rate leads intrinsically to an increase of the total number of nuclei formed during a CQD synthesis. Furthermore, the authors demonstrated experimentally that the total number of nuclei formed is changed to a different extent compared to the absolute yield, when the concentration of the rate-determining precursors is changed.13 In their case, raising the rate-determining precursor concentrations always leads to a larger increase of the nuclei number as compared to the absolute yield increase, allowing reduction of the mean particle size at full yield by enhancing the reaction rate. This approach, namely to control the mean particle size at full yield by tuning the formation rate of the solute, will be referred to as “size control by rate control” in the following text.14,15 To transfer the “size control by rate control” concept to other CQD syntheses, a detailed understanding of the kinetics of their solute formation rate is necessary. In the case of using TOPSe in the synthesis of PbSe-CQDs, the solute formation rate of PbSe appears to be extremely low.16 As expected, this leads to the formation of a small number of nuclei.13 Moreover, a terminal strong defocussing at very low reaction yields precludes the opportunity of obtaining sharp size distributions at high reaction yields.10,16 Steckel et al. and Joo et al. have demonstrated that using secondary phosphines (diphenylphosphine; H(DPP)) in TOPSe-

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based synthesis of PbSe-CQDs leads to a solute formation rate increase, which allows preserving sharp size distributions up to reaction yields close to unity.10,16 Furthermore, Evans et al. showed that increasing the solute formation rate by using secondary phosphines and secondary phosphine chalcogenides, is suitable for producing relatively small PbSe-CQDs at high reaction yields.17,18 However, no systematic relationship between the “size control by rate control” concept and the solute formation rate tuning in PbSe-CQDs synthesis has been established yet.10,13,19 Considerable effort was made to identify the reactants, intermediates, and by-products of H(DPP)-enhanced PbSe- and CdSesynthesis by NMR spectroscopy.19,20 However, the solute formation rate dependence on the concentration of different precursors was not determined, nor was the influence of the Pb2+ and TOPSe concentrations assessed. Thus it appears important to conduct a detailed kinetic investigation of the solute formation rate dependences on the concentrations of individual precursors. In this paper, a kinetic investigation of the PbSe solute formation rate was conducted by means of UV-Vis spectroscopy and the results were correlated with those of NMR studies. This allowed suggesting the most probable reaction mechanism for the enhancement of the solute formation rate by secondary phosphines. Finally, the solute formation rate tuning by varying the precursor concentrations was used to demonstrate that the “size control by rate control” concept provides a facile route for controlling the mean PbSe-CQDs size. In addition, in the present work, we introduce and further develop the concept of “size control by temperature control”, based on the earlier observed dependence of the particle size on the growth temperature.16 As a result, we succeeded in obtaining PbSe-CQDs with a pronounced band-gap transition, which could be tuned in the range of 1050–2050 nm (∼1.2–0.6 eV, respectively) for reaction yields above 80%, calculated with regard to the initial lead amount.

Experimental section Chemicals Lead oxide (PbO; 99.9%+), selenium (99.99%), n-hexadecane (99%), 1-octadecene (ODE; Tech.), oleic acid (H(OA); tech. and ≥99%), acetonitrile (≥99.9%), heptane ( p.a.), and toluene-D8 (99.6%) were purchased from Aldrich. Trioctylphosphine (TOP, 97%) and diphenylphosphine (H(DPP); 99%) were purchased from Strem. For NMR experiments, we used H(DPP) (10 wt%; purchased from Strem), after the removal of hexane by evaporation. Tetrachloroethylene (spectroscopic grade) was purchased from Merck. Ethanol (absolute) and toluene (analytical) were purchased from Frutarom. If not otherwise indicated, the highest-grade chemicals were used without further purification. Trioctylphosphine If not mentioned otherwise, TOP was purified before use similarly to the procedure described by Joo et al.;16 TOP was heated

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up to 160 °C under vacuum for at least 30 min to remove low boiling components like e.g. dialkylphosphines. Trioctylphosphineselenide 0.2 M and 0.4 M solutions of TOPSe in TOP were prepared by reacting selenium powder with non-purified trioctylphosphine (TOP) at room temperature (RT) under vigorous stirring in a nitrogen filled glove box. Pure TOPSe was typically prepared by stirring selenium in TOP at RT (2.5 mmol Se mL−1 TOP) for at least 16 h under nitrogen. The excess of selenium was separated by centrifugation and the clear yellowish solution was purified by fractional distillation via a 40 cm Vigreux column, producing completely colourless liquids. The purity of the fractions was checked by 1H- and 31P-NMR spectroscopy (Fig. S1, ESI†). Synthesis of PbSe-CQDs If not otherwise stated, 0.4 mmol PbO and 1.2 mmol H(OA) (≥99%) were mixed in a 25 mL flask and n-hexadecane was added to obtain the total mass of 8 g. Then the mixture was heated at 100 °C under vacuum for 1 hour. During this time the reaction mixture turned clear, indicating a quantitative formation of Pb(OA)2 from PbO and H(OA). Next, 4 mL of a mixture containing specific amounts of TOP, TOPSe and H(DPP), dissolved in n-hexadecane were injected into the Pb(OA)2 solution under nitrogen at the injection temperature. Then the temperature was reduced to the growth temperature, and aliquots were taken from the reaction mixture at definite time intervals. Each aliquot was injected into a mixture of toluene, ethanol, and acetonitrile (4 : 3 : 3), usually causing a quantitative precipitation. Finally, the precipitate was separated by centrifugation. The following procedures were performed under nitrogen: the precipitate was dissolved in 0.5 mL hexane and 0.5 mL acetonitrile were added at once. Then 1–2 mL ethanol were added drop-wise, resulting in a quantitative precipitation of the CQDs. Finally, the precipitate was separated by centrifugation, dried, and redissolved in tetrachloroethylene. PbSe-CQDs for the NMR experiments were prepared in a similar way: 1 mmol of PbO and 3 mmol of H(OA) (tech.) were mixed in a 25 mL flask and n-hexadecane was added to obtain a total mass of 20 g. The injection mixture consisted of 2 mmol H(DPP) and 2 mmol TOPSe ( pure), dissolved in n-hexadecane (total volume 8 mL). The injection was performed at 115 °C and the growth lasted for 14 min at 100 °C. Pb(OA)2-treatment of PbSe-CQDs for NMR-investigations 1 mmol of PbO and 3 mmol of H(OA) (tech.) were mixed with n-hexadecane, the total volume being 8 g. The mixture was heated to 100 °C under vacuum and allowed to remain at this temperature for 1 h. Then the temperature was reduced to 60 °C and PbSe-CQDs, dissolved in hexane, were injected under nitrogen. The mixture was heated to 100 °C under vacuum and maintained at this temperature for another hour. Then the setup was placed again under nitrogen and transferred to a nitrogen-filled glove box. The mixture was dissolved

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in toluene and the PbSe-CQDs were precipitated with ethanol and 2-propanol. The precipitate was separated by centrifugation, washed with ethanol, and dissolved in hexane. Then the CQDs were precipitated again with ethanol and separated by centrifugation. The precipitate was dried and dissolved in hexane.

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Preparation of H(DPPSe) 2 mmol of selenium were mixed with 2.5 mmol of H(DPP) in 4 mL of heptane. The mixture was heated until it became clear and then cooled to RT. The solid H(DPPSe) produced was separated by centrifugation. Then the solid was recrystallized 2 times from a mixture of heptane (4 mL) and toluene (0.5 mL), dried under vacuum, and redissolved in hexane. Sample preparation for NMR experiments Solutions of PbSe-CQDs in hexane were dried under vacuum and the material obtained was redissolved in toluene-D8. Determination of the PbSe reaction yield and of the PbSe-CQD diameter by UV/Vis-NIR spectroscopy The reaction yield was determined as described by Joo et al.16 The volume fraction of PbSe ϕPbSe in solution was calculated using the theoretical intrinsic absorption coefficient µi of colloidal PbSe in TCE at 400 nm according to Moreels et al.:20,21 ϕ = (A ln(10))/(µil), where A is absorbance and l is the mean path length of the light through the sample. ϕPbSe in the solution and the dilution relative to the reaction mixture being known, it was possible to determine the amount of PbSe in the reaction mixture. Since Pb(OA)2 was always the precursor, which was not used in excess, the PbSe yield was estimated according to: ηPbSe = [PbSe]/[Pb(OA)2]. It should be noted that n(PbSe) is assumed to be equal to the amount of Se2− formed from TOPSe in the course of the reaction. The diameter of the CQDs was estimated on the basis of the recorded absorption spectra, using the sizing-curve obtained by Dai et al.22 Determination of the reaction rate The reaction rate under particular conditions was determined using the plot of the reaction yield versus time. Since the precise rate dependence was unknown, it was fitted assuming a single exponential decay of the lead precursor. The plot of the reaction rate (in % min−1) was obtained by differentiating the fit function (see Fig. 1). Then the reaction rate for a particular yield (usually 50%) was determined. Using this procedure allowed the determination of the reaction rate taking all the data points into account. UV/Vis-NIR absorption spectroscopy Absorption spectra were recorded on a JascoV-570 absorption spectrometer using Rotilabo-Spectrosil semi-micro absorption cuvettes. TEM TEM images were obtained using a Technai F20 G2 system operated at 300 kV.

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Fig. 1 Dependence of the reaction rate on the TOP and H(DPP) concentrations. Reaction yield development: (a) injection and growth temperature was 180 and 160 °C, respectively. Black: 0.8 mmol pure TOPSe; red: 2 ml of a 0.4 M TOPSe solution in TOP as an anion precursor. (b) The same reaction conditions as in (a), but with 0.8 mmol H(DPP) added. Injection and growth temperatures were 140 and 125 °C, respectively. Solid lines: fitted to the data points assuming exponential decay of the lead precursor. (c) Relative reaction rates determined by differentiating the fits presented in (b).

Results and discussion Estimation of the PbSe-solute formation based on the PbSe-CQD formation rate It is hardly possible to determine directly the solute concentration since it represents a fast-reacting intermediate. Two methods are commonly used to determine the solute formation: the quantitative determination of the reaction by-products by means of NMR spectroscopy19 or the measurement of the formed colloid concentration by UV/Vis-NIR spectroscopy.13,16,19,23 The latter method has a more wide-spread use because, in contrast to the former one, it is reliable even in the case of unknown reaction mechanisms or complex pathways of the by-product decomposition, as in the case of rate enhancement by H(DPP).18 Although an intrinsic error of the determination of the colloid formation by UV/Vis-NIR arises from disregarding the free solute concentration, a combined NMR–UV/Vis-NIR study19 showed that the formation of CdSeCQDs almost perfectly corresponded to the consumption of

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the precursors, i.e., the free solute concentration is usually negligible. A similar behaviour was observed for PbSe-CQDs (Fig. S2, ESI†). Therefore, in what follows, it is assumed that the PbSecolloid formation rate equals the PbSe solute formation rate.

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Trioctylphosphine and oleic acid reduce the reaction rate Understanding the reaction kinetics is essential for the application of the “size control by rate control” concept. Therefore, the experimental results of the PbSe-colloid formation rate were, first of all, related to the reaction mechanisms that are supposed to be responsible for enhancing the PbSe solute formation rate, in reactions of trioctylphosphine selenide (TOPSe), diphenylphosphine (H(DPP)), and lead oleate (Pb(OA)2). Steckel et al. observed that the formation of PbSe-CQDs from lead oleate, diphenylphosphine, and trioctylphosphine selenide resulted in the following by-products: diphenylphosphine oxide (DPPO), trioctylphosphine oxide (TOPO), trioctylphosphine (TOP), and oleic acid anhydride (OA2). The authors have suggested the following two reaction pathways, the first one involving only lead oleate and TOPSe, while the second one being enhanced by H(DPP): PbðOAÞ2 þ TOPSe ! ½PbSe þ OA2 þ TOPO

ð1Þ

PbðOAÞ2 þ TOPSe þ HðDPPÞ ! ½PbSe þ OA2 þ DPPO þ TOP ð2Þ where [PbSe] is the PbSe-solute (section S1, ESI†). The authors also supposed that, in the case of reducing Pb(OA)2 by surplus phosphine (in their case, H(DPP) or TOP), the rate-determining step was an in situ formation of Pb0, followed by a fast reaction of Pb0 with TOPSe: PbðOOCRÞ2 þ ðPR1 2 R2 Þ ! Pb0 þ OðPR1 2 R2 Þ þ OðOCRÞ2

ð3Þ

where R is oleyl, R1 is phenyl or n-octyl, and R2 is H or n-octyl. Later Evans et al.18 proposed two alternative reaction pathways (eqn (4)–(6)) for the rate enhancement due to H(DPP), namely: (1) the formation of diphenylphosphine selenide (H(DPPSe)), as a highly reactive selenium source, from TOPSe and H(DPP); and (2) the formation of activated lead-DPP complexes. It has to be noted that H(DPPSe) is able to perform tautomerization forming selenophosphinous acid, which later could form, under deprotonation, a Pb–Se bonding.24,25 TOPSe þ HðDPPÞ Ð TOP þ HðDPPSeÞ

ð4Þ

PbðOAÞ2 þ HðDPPÞ Ð ½PbðOAÞðDPPÞ þ HðOAÞ

ð5Þ

PbðOAÞ2 þ 2HðDPPÞ Ð ½PbðDPPÞ2  þ 2HðOAÞ

ð6Þ

TOP and H(OA), chemicals required for the preparation of the anion and cation precursor, TOPSe and Pb(OA)2, are usually used in excess. Furthermore, eqn (1) and (2) indicate that the TOP concentration rises during the reaction, while the H(OA) concentration stays constant.10 Thus, it is essential to understand the effect of TOP and H(OA) concentrations on the solute formation rate.

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The influence of the TOP concentration on the solute formation rate is difficult to determine since commercial TOP often contains secondary phosphines which are highly reactive impurities.16,18 For this reason, we first investigated the effect of free TOP, in the presence and in the absence of H(DPP), on the PbSe-colloid formation rate. The data presented in Fig. 1(A) relate to the yield developments of two reactions, where TOPSe was injected into a reaction mixture consisting of Pb(OA)2, oleic acid, and n-hexadecane. The injection and the growth temperature were 180 and 160 °C, respectively. For one reaction, the injection mixture (black points) was prepared from 0.8 mmol pure TOPSe (TOPSe free of TOP, see Fig. S1, ESI†) diluted with n-hexadecane to a total volume of 4 ml. For the second reaction, the injection mixture (red points) was prepared by diluting 2 ml 0.4 M TOPSe with n-hexadecane to a total volume of 4 ml. If the injection mixture was prepared from 0.4 M TOPSe, an initial steep rise of the reaction yield of colloidal PbSe ([PbSe]col ) appeared, which was followed by deceleration of the reaction rate. In contrast, when the TOP-free injection mixture was used under the same conditions, the initial yield development was slower, but more continuous. The initially higher reaction rate with 0.4 M TOPSe can be explained by the presence of impurities, such as secondary phosphines, in the TOP solution.16,18 Under similar reaction conditions, the addition of 0.8 mmol H(DPP) to the injection mixture resulted in a significantly enhanced reaction rate (see Fig. 1(B)). Therefore, the injection and the growth temperatures were lowered to 140 and 125 °C, respectively. The comparison of the reaction yield development with pure TOPSe and with a 0.4 M solution of TOPSe in TOP in the presence of H(DPP) shows that the reaction rate is lower if TOP is present. To get a better understanding of the influence of TOP, the relative reaction rates were evaluated. This was done by fitting the yield-development data (Fig. 1(B)) assuming an exponential decay of the Pb(OA)2 concentration (an exponential decay was chosen here, since it is one of the simplest consistently decreasing fit functions). The yield was calculated as the yield of lead since, in all reactions, it is the precursor that is not in excess. Next, the development of the relative PbSe-colloid formation rate (in % min−1, Fig. 1(C)) was evaluated by differentiating the fit functions shown in Fig. 1(B). For a reaction yield of 50%, the PbSe-colloid formation rate drops by a factor of about 5.9 (from 18.3 to 3.1% min−1) when using 0.4 M TOPSe instead of pure TOPSe (Fig. 1(C)). On the other hand, the concentration of TOP at a reaction yield of 50% for the colloid is, at least, 19 times higher (section S4, ESI†) when 0.4 M TOPSe is used, which indicates that the PbSe solute formation rate does not decrease linearly with increasing TOP concentration. In general, there could be three reasons for the rate reduction that occurs due to the presence of free TOP: (1) Free TOP may induce back reactions from the intermediates to the precursors (e.g., according to eqn (2)). (2) High TOP concentrations may significantly change the nature of the solvent, influencing the individual reaction rates

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(the injection mixture contained about 1360 mg of TOP if 0.4 M TOPSe was used, which corresponds to more than 10 wt% of the total reaction mixture). (3) TOP is a ligand, which may block reactive sites of the lead complex.26 The formation of cadmium-oleate/TOP complexes was discussed by Yu et al.26 If TOP binds to Pb(OA)2, a significant concentration of the lead-TOP complex should be apparent in the 31 P-NMR spectra. If the phosphorus of TOP would bind to lead, a characteristic phosphorus-signal should appear, which possesses two satellites, each satellite’s intensity being ∼14% of the main peak intensity (207Pb has a natural abundance of 22.1% and a nuclear spin of 1/2), showing a coupling constant of about 2000 Hz ( JPb–P).27 However, in the 31P-NMR spectrum of a mixture of Pb(OA)2 and TOP (both 0.5 M), there was no indication of TOP being bound to lead (for detailed discussion of the NMR results see ESI, section S5 and Fig. S3†). Yu et al. observed H(DPPSe) in 31P-NMR spectra of TOP-free TOPSe and H(DPP) mixtures, while no H(DPPSe) was observed in the presence of TOP.26 It was concluded that the rate of reduction in the presence of TOP takes place, since the DPPSe concentration is reduced in the presence of TOP according to the equilibrium in eqn (4). Under TOP-free conditions, we also observed a signal in the 31P-NMR spectra that may be attributed to H(DPPSe) (Fig. S4, ESI†) in mixtures of H(DPP) and TOPSe. Furthermore, we observed that selenium can be transferred from H(DPPSe) to TOP (Fig. S5, ESI†). Although our results confirm the equilibrium described by eqn (4), studying the reaction kinetics is necessary to decide: (1) If the PbSe-colloid formation rate is determined by the H(DPPSe) formation. (2) If eqn (4) describes a pre-equilibrium, which is much faster than the subsequent steps. In summary, we conclude that the rate reduction due to the presence of TOP, cannot be attributed to the formation of a lead-TOP complex, but rather to the reduction of the H(DPPSe) concentration according the equilibrium in eqn (4) or to the deviations from the ideal solution behaviour. Similarly, the reaction rate is reduced when more H(OA) is added to the reaction mixture (ESI, Fig. S6, Table S1†).16 The values for the colloid formation rate at 20% reaction yield, which are presented in Fig. S6 (ESI, cf. Table S1†), indicate that the reaction rate is reduced by a factor of 2.7 if the concentration of free oleic acid is increased by a factor of 10. Thus it can be concluded that the effect is not linear with respect to the oleic acid concentration. In the same way, like in the case of the rate reduction by TOP, the rate reduction by H(OA) may be explained by the equilibria between Pb(OA)2 and different lead-DPP complexes (eqn (5) and (6)), a deviation from ideal solution behaviour or by the binding of free oleic acid to Pb(OA)2. Yu et al. observed a peak at 7.8 ppm in 31P-NMR spectra of Pb(OA)2–H(DPP) mixtures, and supposed that this species might be a lead-DPP complex,17 supporting the idea of a reaction pathway via the equilibria shown in eqn (5) or (6). Reproducing this experiment, we did not observe the above mentioned NMR peak

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and, therefore, attribute it to some impurity, which was absent in our chemicals. Moreover, we have not found any indication of J31P-207Pb couplings in hydrogen decoupled 31P-NMR spectra (section S8 and Fig. S7, ESI†). In view of the above, we can assert that NMR-spectroscopy provides no indication of any lead-DPP complex formation. In summary, it has been found that the PbSe solute formation rate is lowered by TOP and H(OA). In a mixture of pure TOPSe and H(DPP), H(DPPSe) was detected, which supports the hypothesis of a reaction rate enhancement according to eqn (4). However, the reaction rate is also enhanced in the presence of TOP, when the H(DPPSe) concentration is below the detection limit. Although there is no indication of the presence of lead-DPP complexes by NMR-spectroscopy, a reaction pathway via the supposed (eqn (5) and (6)) cannot be excluded, since the concentration of these complexes might be simply below the detection limits. However, the effect of TOP and H(OA) on the reaction rate may have other reasons, e.g., deviation from the ideal solution behaviour. Therefore, only a kinetic study might allow drawing an unambiguous conclusion with regard to the proposed reaction mechanisms (eqn (4)–(6)). The reaction rate linearly depends on the DPP concentration To investigate the PbSe-colloid formation rate dependence on the H(DPP) concentration, pure TOPSe was used in an 8 : 1 excess to lead and at H(DPP) : lead ratios varying from 1 : 1 to 8 : 1. The second set of experiments was conducted under the same conditions, but in the presence of additional TOP (the TOP to lead concentration ratio was 8 : 1). The [PbSe]col yield development is shown in Fig. 2(A) and (B). Similar to Fig. 1(B), the solid lines represent a fit obtained under the assumption of a first-order decay of the Pb(OA)2-concentration. Although the fits do not seem to be very accurate in all cases, it is possible to estimate the relative reaction rates for reaction yields of 50% for various H(DPP) concentrations (the (H(DPP) amount reaction yields of 50% were estimated assuming a stoichiometric consumption of H(DPP) per PbSe unit). It can be seen in Fig. 2(C) that the reaction rate increases almost linearly with the H(DPP) concentration, which indicates a first-order rate dependence. Thus it can be concluded that H(DPP) is a ratedetermining precursor. Furthermore, the linear rate dependence on the H(DPP)-concentration allows ruling out the reaction pathway described by eqn (6). This pathway would lead to a parabolic increase of the reaction rate with increasing H(DPP) concentration. The reaction pathway via H(DPPSe) is the most probable Although the NMR investigation indicates that the enhancement of the reaction rate may be due to the formation of H(DPPSe), still other enhancement mechanisms cannot be excluded. For this reason, we investigated the PbSe-colloid formation rate dependence on TOPSe and Pb(OA)2. Fig. 3(A)–(C) show experiments similar to those shown in Fig. 2, but by varying the TOPSe concentration instead of the H(DPP) concentration. Similar to H(DPP), the relative PbSe-colloid for-

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Fig. 3 Reaction rate dependence on the TOPSe-concentration. (a) Yield-developments for an injection and growth temperature of 80 °C/ 70 °C, a H(DPP) to lead ratio of 8 : 1 and different TOPSe to lead ratios. Solid lines: fit to data points assuming an exponential decay of the lead precursor. Open/closed circles: independent reactions. (b) The same reaction conditions as in (a), but additional TOP added (TOP to lead ratio 8 : 1). (c) Relative reaction rates at a reaction yield of 50% versus the amount of TOPSe, estimated by the fits assuming an exponential decay of the lead precursor for the reactions shown in (a) and (b). (d) Relative reaction rates at a reaction yield of 50% for reactions shown in Fig. 2(b) and (b). Error bars give a combination of the standard deviation of the fit-functions and the standard deviation between the individual measurements performed at particular H(DPP)- or TOPSeconcentrations.

Fig. 2 Development of PbSe yield at different H(DPP) : Pb(OA)2 ratios. The injection and growth temperature was 80 and 70 °C, respectively; the TOPSe : Pb(OA)2 was 8 : 1. (a) In the absence of additional TOP; (b) with TOP added (TOP : Pb(OA)2 concentration ratio 8 : 1). Solid lines: fitted to the data points assuming an exponential decay of the lead precursor concentration. Open/closed circles: independent reactions. (c) Dependence of the relative reaction rate at 50% reaction yield on H(DPP)-concentration, estimated according to the fits shown in panels (a) and (b). Error bars: a combination of the standard deviation of the fitfunctions and the standard deviation between the individual measurements performed at particular H(DPP) concentrations.

mation rate at reaction yield of 50% rises almost linearly with the TOPSe concentration (Fig. 3(C)), indicating a reaction order of 1, relative to TOPSe. In Fig. 3(D), the rate dependences on TOPSe and H(DPP) are compared (reactions with additional TOP from Fig. 2(C) and 3(C)). We see that the behaviour is very similar, but it appears that the solute formation rate seems to be slightly more sensitive to the H(DPP) concentration. To investigate the rate dependence on lead, we kept the TOP, TOPSe and H(DPP) amounts constant (always 3.2 mmol) and varied the Pb(OA)2 concentration (lead to oleic acid ratio 1 : 3). Fig. 4 shows the absolute yield developments for Pb(OA)2 amounts between 0.2 mmol and 1.6 mmol. Initially the yield developments are very similar and can be described by linear behaviour (fit was made using the first 3 data points – 15 s, 30 s and 1 min – of the reaction with the

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highest Pb(OA)2 concentration). We see a weak trend only for high reaction yields; that is, the absolute reaction yield rises slightly faster with a higher Pb(OA)2 concentration. In addition, we see a reduction of the PbSe-colloid formation rate with increasing reaction time. Interestingly, the linear behaviour and matching of the reaction rate persist for all reactions until yields of about 50% are obtained (Fig. S8, ESI†). Since the H(OA) concentration increases with the lead concentration, the observed behaviour might be partially explained by the reduction of the reaction rate due to H(OA). However, the influence of the H(OA) concentration on the reaction rate would be far too weak to explain why the initial reaction rate is independent of the Pb(OA)2-concentration. Finally, the linear increase of the reaction yield indicates a reaction order of zero relative to lead. In summary, the kinetic investigations indicate an initial reaction order of one relative to the TOPSe and H(DPP) concentrations, and a reaction order of zero relative to the Pb(OA)2 concentration. This can be explained only by assuming a reaction pathway via H(DPPSe), where the H(DPPSe) formation is the rate determining step. Furthermore, the initial reaction rate is independent of lead concentration. Thus, we conclude that the formation of the DPPSe-lead complex is much faster than the back reaction from H(DPPSe) and TOP to H(DPP) and TOPSe. Therefore, the assumption of a fast pre-equilibrium according to eqn (4) does not hold, and we conclude that only the H(DPPSe) formation reaction determines the initial solute

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Fig. 4 Reaction rate dependence on lead. (a) Development of the absolute reaction yields for an injection and growth temperature of 80 °C/70 °C. H(DPP), TOPSe and TOP amounts: each 3.2 mmol, lead to oleic acid ratios of 1 : 3 and different amounts of lead within the reaction mixture. (b) Results from (a), magnified.

formation rate of PbSe. In addition we have to conclude that high concentrations of TOP and H(OA) lead to a deviation of the behaviour in ideal solution. Rate reduction at higher yields might appear due to H(DPPSe) adsorption at the CQDs surface The drop of the reaction rate for reaction yields above 50% (Fig. S7, ESI†) indicates that a reaction mechanism takes place, where a reactant performs a side reaction with a product (main- or byproduct) of the reaction, reducing the amount of this reactant and finally the PbSe-colloid formation rate. Obviously, a reaction of a reactant with the main product is highly probable in this case, like e.g. a chemisorption of H(DPPSe) at the surface of the PbSe-CQDs, which possess excess lead on their surfaces.20 To explain the rate reduction at high yields, the chemisorption of H(DPPSe) at the PbSe-CQDs would have to be followed by a slow decomposition of DPPSe− on the surface of the CQDs. A similar mechanism was observed for CdS-CQDs when coated with CdS using H(DPPS) (diphenylphosphine sulfide) as the anion precursor.28

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Fig. 5(A) presents a 1H-NMR spectrum of as-prepared PbSeCQDs. Besides the strong solvent peaks (toluene-D8) at ∼7 ppm, a broadened alkene peak of the oleate-ligands which are bound to the CQDs, appears at 5.8 ppm. The broadening can be attributed to an enhanced transversal inter-proton relaxation mechanism, which occurs due to the reduced rotational freedom of the ligands bound to the CDQsurface.29–31 Furthermore, two broad peaks at 8.4 and 7.6 ppm are observed, which cannot be directly identified, but vanish if the PbSe-CQDs are treated with lead oleate at 100 °C for one hour (Fig. 5(B)). When H(DPPSe) is added, again the peak at δ = 8.4 ppm and other peaks appear in this region (e.g. at 8.6, 8 and 7.6 ppm; Fig. 5(C) and S9, ESI†). In addition, we see free oleic acid (sharp alkene peaks), indicating that the oleate ligands were replaced by another ligand.30 In 31P-NMR spectra of mixtures of H(DPPSe) and Pb(OA)2-treated PbSe-CQDs, we see no indication of H(DPPSe) (cf. Fig. 5(D) and (E)). This can be explained by an adsorption of H(DPPSe) at the surface of the CQDs: in this case the phosphorus of DPPSe− would be directly bound to a CQD (by one chemical bond), having no rotational freedom relative to the CQD, so that the peak broadening would make it, most likely, impossible to distinguish the peak from the baseline. Finally, we conclude that the oleate ligand is exchanged by H(DPPSe), and that DPPSe− is chemisorbed at the surface of the PbSeCQDs. When mixing Pb(OA)-treated PbSe-CQDs with H(DPP) (amount corresponding to 0.25 ML) and TOPSe (8 : 1 relative to H(DPP)), we see after about 2 days 1H-NMR peaks, which can be related to DPPSe− adsorption at the PbSe-CQD surface, a slight broadening of the oleate-peak (indicating an OA−/ DPPSe− exchange) and free H(DPP)-peaks (Fig. 5(F)). Furthermore, we see peaks for TOPSe, TOP and H(DPP) in the 31 P-NMR spectrum, and also other peaks that are partially described in the literature and attributed to the decomposition products of DPPSe− (Fig. 5(G)).18 We note that no formation of TOP could be directly detected after mixing the PbSe-CQDs and H(DPP)Se/TOP (Fig. S10, ESI†). In the end, our investigation shows that H(DPPSe) can be chemisorbed by PbSe-CQDs, and that the DPPSe− which is chemisorbed by the CQDs decomposes to Se2− (which is bound to the CQDs) and other by-products. However, from the point of view of reaction kinetics, the more relevant question is, in how far this mechanism affects the PbSe-colloid formation rate of PbSe: according to the NMR-investigation, the 2 peaks at 7.6 ppm and 8.4 ppm, which are observed in 1H-NMR of as-prepared CQDs (Fig. 5(A), can be related to DPPSe−-ligands which are bound to the CQDs. Their detection proves that the decomposition of the DPPSe−-ligands on the surface of CQDs is slow in comparison with the other mechanisms. Furthermore, their disappearance due to the Pb(OA)2-treatment shows that the DPPSe−-ligands can be decomposed in the presence of lead (Fig. 5(B)). Thus it is reasonable that the PbSe-colloid formation rate will drop, when the CQD-surface area becomes large and the Pb(OA)2 concentration low.

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Fig. 5 NMR-spectra in toluene-D8 (a) 1H-NMR-spectrum of as-prepared PbSe-CQDs, (b) 1H-NMR spectrum of Pb(OA)2 treated PbSe-CQDs, (c) 1 H-NMR-spectrum of Pb(OA)2-treated PbSe-CQDs after addition of H(DPPSe) for 0.25 ML of PbSe, (d) 31P-NMR-spectrum of H(DPPSe), (e) 31P-NMR spectrum of Pb(OA)-treated PbSe-CQDs after addition of H(DPPSe) for 0.25 ML of PbSe, (f ) 1H-NMR-spectrum of Pb(OA)2-treated PbSe-CQDs two days after addition of H(DPP) for 0.25 ML of PbSe and TOPSe (H(DPP):TOPSe ratio 1 : 8) and (g) 31P-NMR-spectrum of Pb(OA)2 treated PbSe-CQDs three days after addition of H(DPP) for 0.25 ML of PbSe and TOPSe (H(DPP): TOPSe ratio 1 : 8).

Summary of the kinetics of the PbSe-solute formation rate Since the back-reaction from H(DPPSe) and TOP to H(DPP) and TOPSe is much slower than the consumption reaction of H(DPPSe) by Pb(OA)2, eqn (4) can be simplified from the viewpoint of kinetics: TOPSe þ HðDPPÞ ! TOP þ HðDPPSeÞ

ðslowÞ

ð7Þ

The following solute formation and precipitation is fast; we can summarise the non-rate determining steps: PbðOAÞ2 þ DPPSe ! ½PbSecol þ byproducts ðfastÞ

ð8Þ

The additional colloidal formation mechanism by the chemisorption of H(DPPSe) on the surface of the CQDs can be summarised as follows: ðPbX Sey ÞðOA2ðXY Þ Þ þ HðDPPSeÞ ! ðPbX SeY ÞðOA2ðXY Þ1 ÞðDPPSeÞ þ HðOAÞ ðfastÞ

ð9Þ

ðPbX SeY ÞðOAÞ2ðXYÞ1 ðDPPSeÞ ! ðPbX SeY þ1 ÞðOAÞXY 1 þ byproducts

ðslowÞ

ð10Þ

This explains why the reaction rate drops for higher reaction yields. In the beginning, no PbSe-CQDs are present in the reaction mixture, so that all H(DPPSe) is consumed according the solute formation mechanism (eqn (7) and (8)). During the synthesis the concentration of Pb(OA)2 decreases, while the surface area of the CQDs increases due to their growth. Thus, the H(DPPSe) consumption-rate by the PbSe-CQDs increases, while the H(DDPSe) consumption-rate by Pb(OA)2 decreases during the reaction. Since the decomposition of DPPSe− on the surface of the CQDs is slower than the decomposition of DPPSe− in the [Pb(OA)(DPPSe)]-complex, the PbSe-colloid formation rate drops when the amount of Pb2+-ions on the

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surface of the PbSe-CQDs becomes significantly high, compared to the amount of the Pb2+-ions in solution. Therefore, the occurrence of this alternative reaction mechanism reduces the PbSe-colloid formation rate at high reaction yields (Fig. 4 and Fig. S8, ESI†). In the kinetic investigation presented, the formation of byproducts was not taken into account. Therefore, the mentioned conclusion is only valid in a first approximation, since the formation of Ph2PPPh2, which is observed in 31P-NMRspectra (Fig. 5(G)), requires two equivalents of H(DPP) for the formation of one equivalent [PbSe]. The appearance of Ph2PPPh2 can be related to a cleavage mechanism of the [Pb (OOCR)(DPPSe)]-complex, where H(DPP) acts as a protic nucleophile: ½PbðOOCRÞðSePPh2 Þ þ EH ! ½PbSe þ EPPh2 þ HOOCR ð11Þ where EH represents a protic nucleophile, which can be e.g. H(DPP) or H(COOR), and HOOCR represents oleic acid. Following the observations of Steckel et al.,10 namely H(DPPO) and oleic acid anhydride (O(OA)2) are observed as final products, a decomposition pathway as indicated by Evans et al. (R = oleyl) can be assumed:18 Ph2 PPPh2 þ HðOOCRÞ ! HðDPPÞ þ ðRCOOÞPPh2

ð12Þ

ðRCOOÞPPh2 þ HðOOCRÞ ! HðDPPOÞ þ OðOCRÞ2

ð13Þ

After the completion of this decomposition pathway, exactly one equivalent H(DPP) is consumed per equivalent [PbSe], explaining why the reaction yields close to unity are reached, when a 1 : 1 ratio of H(DPP) : Pb is used. However, for the application of the “size control by rate control” concept we only have to consider the reactions which determine the initial solute formation rate. Both, the chemisorption of H(DPPSe) on the surface of the PbSe-CQDs (eqn (9)

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and (10)) and the reduction of the H(DPP) concentration, which can appear due to an incomplete by-product decomposition (eqn (11)–(13)), does not play a significant role for the solute formation rate at low reaction yields. Only the DPPSeformation will influence the initial solute formation rate (eqn (7)), and thus the nucleation.13 Moreover, the reduction of the PbSe solute formation rate by free TOP and free H(OA) cannot be explained by the reaction kinetics, since the initial solute formation rate appears to be independent of Pb(OA)2 concentration (cf. eqn (8) and (9)). Thus, this rate-reduction has to be related to a deviation from the ideal solution behaviour. Increasing the TOPSe- and DPP-concentration leads to smaller particles, increasing the TOP concentration leads to larger particles Considering the “size control by rate control” concept, precursors which significantly influence the solute formation rate are the best choice for size control. Thus varying the concentration of the chemicals in the injection-mixture appears to be favourable for size-tuning, since the kinetic investigations revealed a first order rate dependence of the solute formation rate on TOPSe and DPP, and a reduction of the solute formation rate when adding TOP. Increasing the H(DPP) to Pb ratio leads to a slower growth of the particles relative to the reaction yield (Fig. 6(A), (B), and S11, ESI†). This circumstance originates from the fact that a larger number of nuclei are formed, if the concentration of H (DPP) is increased (Fig. 6(C) and (D)). This is in perfect agreement with the “size control by rate control” concept, where it is expected that the total number of nuclei increases if the initial solute formation rate is raised.13,19 Since TOP reduces the solute formation rate, the CQD-size increases faster relative to the reaction yield of [PbSe]col, when TOP is added to the injection-mixture (Fig. 6(A)–(D)). Almost the same behaviour is seen when varying the TOPSe amounts (Fig. S12, ESI†). Sharp size dispersions of CQD-samples are an essential requirement for their application. In Fig. 6(E), the development of the half width at half maximum (hwhm), which is a common quantity to describe the quality of a CQD-sample in terms of its size dispersion, is shown for different H(DPP) amounts without using TOP. For all the samples the hwhm drops with increasing wavelength. Furthermore, the development of the hwhm is very similar among the different samples. In detail, for high reaction yields, the hwhms show similar values for all the reaction mixtures. As a result, the described “size control by rate control”-approach allows one to obtain colloids with a comparable quality at high yields over a broad size range. The full capability of this approach is represented in Table S2 (ESI†). Size-control by the lead precursor and by the oleic acid concentration When the Pb(OA)2 concentration is changed and the anion precursor concentrations are kept constant, the diameter versus absolute yield development is only weakly influenced,

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Fig. 6 Size-control by rate-control based on the variations of the H (DPP) concentration. (a) Development of the diameter relative to the reaction yield for an injection and growth temperature of 80 °C/70 °C, a TOPSe to lead ratio of 8 : 1 and different H(DPP) to lead ratios. (b) The same reaction conditions as in (a), but additional TOP added (TOP to lead ratio 8 : 1). (c) Development of the number of CQDs inside the reaction mixture versus the chemical yield for the reaction shown in (a). (d) Development of the number of CQDs inside the reaction mixture versus the chemical yield for the reaction shown in (b). (e) Half width at full maximum (in meV) relative to λ1s–1s for the reactions shown in (a) and (b).

since the initial reaction kinetics does not depend on the Pb (OA)2-concentration (Fig. 4 and 7(A), Table S3, ESI†). Since the Pb(OA)2 is in all exemplary reactions the precursor is not in excess, raising the Pb(OA)2 concentration leads to an higher absolute yield, and, thus, to larger particles at yields close to unity. However, we still see a slight increase of the CQD-concentration while raising the Pb(OA)2-concentration (Fig. 7(B)). This CQD-concentration increase cannot be connected to a change of the reaction rate, since the initial reaction rate appears to be independent of lead concentration (cf. Fig. 4). An explanation can be given by taking the nature of the PbSe-solute into

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number of nuclei (Fig. 8(B)). This result is expected, since the PbSe-solute formation rate slows down and the [PbSe]-solubility increases with increasing OA-concentration (Fig. S5†).13,23

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Highly concentrated reaction mixtures

Fig. 7 Influence of the Pb(OA)2-concentration on the CQDs size. (a) Development of the diameter relative to the absolute yield for injection and growth temperatures of 80 °C/70 °C, respectively. TOPSe and TOP amount: each 3.2 mmol, lead to oleic acid ratios of 1 : 3 and different amounts of lead within the reaction mixture. (c) Development of the number of CQDs inside the reaction mixture versus time.

account. Abé et al. demonstrated that fewer nuclei are formed in a colloidal synthesis, if the solubility of the solute is enhanced.23 Here, the solubility of [PbSe], which is a binary salt, is determined by its solubility product: K s ¼ cðPb2þ ÞcðSe2 Þ

ð14Þ

with Ks as the solubility product and c as the activity of the particular ions. Since Pb(OA)2 is a salt, the Pb2+ concentration, and the concentration product in eqn (14), will scale, in the beginning of the reaction, almost linearly with the initial Pb(OA)2-concentration. Although the [PbSe]-solubility depends on the oleic acid concentration, which is in this case linearly connected to the Pb2+-concentration, the solubility will be determined by other ligands as well (e.g. TOP). Therefore, raising the Pb(OA)2concentration increases the concentration product more than the [PbSe]-solubility, leading to initially higher supersaturation and, thus, to the formation of a larger number of nuclei.13 In Fig. 8(A), the diameter to yield development for different oleic acid concentrations is shown. We see that the CQDs grow faster relative to the chemical yield if the oleic acid concentration is increased, resulting from the formation of a smaller

Fig. 8 Size-control by the oleic acid concentration. (a) Development of the diameter relative to the reaction yield for an injection and growth temperature of 80 °C/70 °C, H(DPP), TOPSe and TOP amounts of 3.2 mmol, 0.4 mmol of lead and different lead to oleic acid ratios. (b) Development of the number of CQDs relative to the reaction time for the reactions shown in (a).

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In this section, we investigate how the size development is influenced if all precursors are increased. In Fig. 9(A) the yield development between a reaction using 0.4 mmol Pb(OA)2 and a reaction using 3.2 mmol Pb(OA)2 is compared (Pb : OA = 1 : 3, Pb : TOPSe = 1 : 2, Pb : H(DPP) = 1 : 2). As expected, the yield development is faster for the higher concentration reaction mixture, since the concentration of both rate determining precursors, TOPSe and H(DPP), is increased linearly with respect to the lead concentration (Fig. 9(B)). Interestingly, when the concentration is increased, the wavelength (size) increases slowly compared to the relative reaction yield. Thus, for yields around 80%, λ1s–1s reduces from 1377 nm to 1209 nm, when the concentration of the precursors is raised by a factor of 8 (Fig. 9(B) and S12, ESI†). Size control by the temperature The “size control by rate control” approach, which is presented here, allows size-tuning at high yields in a diameter-range between 3.2 and 4.8 nm, and is easily applicable, but becomes practically problematic for larger sizes. A typical synthesisscheme, which allows synthesizing PbSe-CQDs with diameters of about 4.8 nm (λ1s–1s ∼ 1500 nm) at a reaction yield around 80%, leads to a reaction time of ∼128 minutes (Fig. 10(A)). A further reduction of the H(DPP) : Pb(OA)2 and the TOPSe : Pb (OA)2 ratio, which would allow us to prepare larger PbSe-CQDs, would strongly reduce the solute formation rate, thus leading

Fig. 9 (a). Development of the reaction yield relative to the reaction time for a H(DPP) to lead and a TOPSe to lead ratio of 2 : 1 and different amounts of Pb(OA)2. (b) Development of the reaction yield relative to the wavelength of the first electronic transition (λ1s–1s) for the same reactions as presented in (a).

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Fig. 11 Absorption spectra of exemplary colloidal PbSe-CQDs samples. All samples obtained at reaction yields above 80%. Size control achieved by the variation of the reaction conditions.

Fig. 10 Size-control by the reaction temperature (a). Development of the reaction yield relative to the reaction time for a H(DPP) to lead and a TOPSe to lead ratio of 2 : 1, a TOP to lead ratio of 8 : 1 and different injection and growth temperatures. (b) Development of the reaction yield relative to the wavelength of the first electronic transition (λ1s–1s) for the same reactions as presented in (a). (c) Development of the number of CQDs relative to the reaction yield for the same reactions as shown in (a).

to even longer reaction times. To overcome this problem, the solute formation rate can be in raised by increasing the injection and growth temperatures. Joo et al. demonstrated that the size to yield development of PbSe-CQDs, different from CdSe-CQDs synthesis, is strongly temperature dependent.13,16 Higher temperatures lead to larger particle sizes. Accordingly, we increased the injection and growth temperatures to 110 °C/100 °C and 145 °C/130 °C, respectively. As seen in Fig. 10(A), this leads to a strong enhancement of the solute formation rate, and, as expected, to an increase of the nanoparticle size, meaning that the number of nuclei decreases with increasing temperature (Fig. 10(B) and (C), Table S3, ESI†). Interestingly, the number of CQDs does not drop during the course of the reaction for any temperature (Fig. 10(C)). Thus the reduction of the number of CQDs

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has to be related to a weaker nucleation, and not to a reduction of the number of nuclei due to the dissolution of smaller particles on behalf of the larger ones (Ostwald ripening). Finally, raising the injection and growth temperature from 80 °C/70 °C to 145 °C/130 °C, the diameter of the CQDs increases from 4.8 nm (λ1s–1s ∼ 1500 nm) to 5.9 nm (λ1s–1s ∼ 1800 nm) for yields above 80%. Fig. 11 demonstrates the potential of the combination of “size control by rate control” concept and “size control by temperature control” (cf. Tables S2 and S3, ESI†). By varying the composition of the injection mixture and the reaction temperature, we were easily able to prepare colloids of PbSe CQDs with sharp size dispersions (Fig. 12) and yields above 80% in a diameter range from 3.2 nm (λ1s–1s ∼ 1050 nm) to 6.8 nm (λ1s–1s ∼ 2050 nm; Fig. 11).

Fig. 12 Exemplary TEM images of PbSe-QDs and their corresponding histograms.

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Conclusion In conclusion, we demonstrate that the concept of size control by rate control, which was first demonstrated in CdSe CQDs synthesis, also applies in PbSe-CQDs synthesis. We initially investigated the reaction order of the PbSesolute formation rate. For low chemical yields, we observe a first order rate dependence of the PbSe-solute formation rate relative to the TOPSe- and H(DPP)-concentration, indicating a reaction pathway via H(DPPSe) and Pb(OA)2. Furthermore, we see that the solute formation rate is independent of the Pb(OA)2-concentration, while the addition of excess TOP and oleic acid leads to a reduction of the PbSe-solute formation rate. In addition to the reaction of Pb(OA)2 and H(DPPSe), H(DPPSe) can be adsorbed at the surface of the PbSe-CQDs, followed by a slow cleavage-reaction of the DPPSe−, reducing the formation rate of colloidal PbSe at high yields. Finally, tuning the formation rate of the PbSe-solute by varying the amounts of H(DPP), TOPSe and TOP allowed us to tune the mean particle diameter for colloids obtained at yields above 80% between 3.2 nm and 4.8 nm (for an injection and growth temperature of 80 °C/70 °C). In addition, by raising the injection and growth temperature, we were able to increase the mean diameter to 6.8 nm for yields above 80%.

Acknowledgements The research leading to these results has received funding from the European Community’s Seventh Framework Programme (FP7/2007–2013) under grant agreement no. 246200 and from the Schulich Faculty of Chemistry. Furthermore, we dedicate this work to Prof. Fenske on the occasion of his 70th birthday.

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