Nucleation and Growth Kinetics of CdSe Nanocrystals in Octadecene

Transcription

1 VOLUME 4, NUMBER 12, DECEMBER 2004 Copyright 2004 by the American Chemical Society Nucleation and Growth Kinetics of CdSe Nanocrystals in Octadecene Craig R. Bullen and Paul Mulvaney* Chemistry School, UniVersity of Melbourne, ParkVille, VIC, 3010, Australia Received March 1, 2004; Revised Manuscript Received September 12, 2004 ABSTRACT The growth kinetics of CdSe nanocrystals nucleated from TOPSe and cadmium oleate were investigated in octadecene, a non-coordinating solvent. The effects of temperature and the oleic acid concentration on the kinetics of both nucleation and particle growth were investigated. It was found that increasing oleic acid concentrations led to smaller numbers of nuclei, smaller initial nuclei size, and larger final particle sizes. The rate constant for steady-state CdSe deposition was found to be cm s -1 at 265 C, far slower than the diffusion limit. The number of growing particles remained constant following the initial nucleation step. The radius of the primary CdSe nuclei varied from 1.0 ± 0.1 nm down to 0.8 ± 0.2 nm at lower oleic acid concentrations. Between 2 and 8% of the available Cd was consumed during nucleation. From the residual TOPSe and cadmium oleate concentrations at the onset of Ostwald ripening, the solubility of 2.2 nm CdSe in octadecene is measured to be M 2 at 265 C. The surface free energy of CdSe in octadecene was found to be 0.17 J/cm 2, which leads to an estimate of a 9% size distribution in the nanocrystals at the moment of nucleation. Introduction. Spectroscopic monitoring of the growth of semiconductor nanocrystals provides a useful method for exploring the process of particle nucleation in solution. Provided that there is a concrete relationship between the optical spectrum and the particle size, initial conditions during nucleation can be inferred. Such data are essential for the reproducible preparation of monodisperse semiconductor nanocrystals. In the case of CdSe, several groups have carried out extensive analyses of the position of the first excited state (1S e -1S 3/2h ) as a function of the mean crystallite size, determined by electron microscopy. 1-4 The data by Banin and co-workers show a 1/R dependence of the exciton energy on particle radius, 2 and this provided the first extensive correlation between size and optical band edge. Peng and colleagues have recently carried out a more * Corresponding author. mulvaney@unimelb.edu.au; fax: systematic investigation of the extinction coefficient of CdSe, CdS, and CdTe nanocrystals over a wide range of sizes. 3 Their correlations also include the data from numerous former studies, including those of Banin et al. From their results, it is possible to measure key parameters associated with particle nucleation, such as the number of nucleation centers and the rate constants for monomer addition to the nascent crystallites. Several key issues can be resolved from such measurements. First, it is important to establish whether separate nucleation and growth time regimes operate in nanocrystal synthesis, i.e., whether there is a single burst of nucleation followed by a pure growth phase, during which the particle number is fixed. In many systems, such as the synthesis of nanocrystals in glasses, nucleation may continue to occur throughout the growth phase. 5 A second important question is the role of capping agents. As the nuclei grow, van der Waals interactions can cause rapid coalescence of /nl CCC: $27.50 Published on Web 11/10/ American Chemical Society

2 nuclei and unrestrained particle growth. Ligands such as oleate and TOP are chemically bonded to both the precursors and to the particles that form. Such bonds resist van der Waals forces. Capping agents may be added during synthesis to adsorb and limit particle-particle aggregation, though such molecules may, in principle, hinder monomer deposition too. Furthermore, it is possible that complexation of capping agents to the monomers and precursors may impede nucleation, which will then lead to larger, rather than smaller, particle sizes. In this report, we examine the actual nucleation conditions and the growth of CdSe in octadecene, a system that provides a comparatively simple, noncoordinating environment for particle nucleation and growth and an economical route to highly luminescent semiconductor particles. Yu and colleagues have already shown that CdSe with a narrow size distribution can be synthesized in this solvent. 6 We will show that addition of oleate as a capping agent leads to a decrease in the nucleation rate. Experimental Section. All chemicals were used without further purification. Selenium shot (99.999%) and technical grade octadecene and tributylphosphine (TBP) were obtained from Aldrich. Technical grade oleic acid, cadmium oxide, and AR chloroform were sourced from BDH. A stock cadmium oleate solution was prepared by heating a mixture of 30 g oleic acid (106 mmol), 5.1 g cadmium oxide (40 mmol) to 180 C until a clear, gold-brown solution was obtained. The solution was made up to 100 g with ODE and passed through a 450 nm filter. A 10 g aliquot of the stock solution therefore contained 4 mmol cadmium and 10.6 mmol oleic acid. To prepare the stock selenium injection solution, g selenium shot (10 mmol) was reacted with 2.5 g tributylphosphine (12.4 mmol). The resulting colorless solution was dispersed in ODE to give a final stock solution volume of 75 ml. A 10 ml quantity of this solution was used for each quantum dot preparation (1.4 mmol Se per reaction). To prepare CdSe nanocrystals, a 60 g mixture of octadecene, 10 g cadmium stock solution, and variable amounts of oleic acid were transferred to a 250 ml threeneck round-bottom flask fitted with water cooled condenser and thermocouple and the synthesis was then conducted under a nitrogen atmosphere. The mixture was heated to 275 C, the heater was switched off, and the 10 ml of TBPSe solution swiftly injected. The growth temperature was held at 265 C. Typically rapid color changes from yellow to orange to red to dark red were observed in the first s after injection. Samples for absorbance and fluorescence spectroscopy were taken at regular time intervals up to 300 s after nucleation, and diluted 1:10 immediately into chloroform. A Cary 5E UV-vis-NIR spectrophotometer was used to collect absorbance spectra, while steady-state fluorescence spectra were measured on a Cary Eclipse instrument. Results. In Figure 1, we present absorption and emission spectra of CdSe nanocrystals as a function of the time after nucleation. The solution contained only cadmium oleate (4 mmol), TOPSe (1.4 mmol), and oleic acid (10.6 mmol). The injection temperature was 275 C. Reaction was almost Figure 1. (a) Absorption and (b) fluorescence spectra of CdSe nanocrystals as a function of time after injection of a solution of 10 ml octadecene containing 1.4 mmol TOPSe into 50 ml 60 mm cadmium oleate dissolved in octadecene and 0.4 mm oleic acid stirred under N 2 at 275 C. Figure 2. Radius vs time and full-wih-half-maximum curves (open circles) for CdSe nanocrystals, prepared as in Figure 1, for oleic acid concentrations of 120 mm (triangles); 160 mm (circles); 200 mm (squares). T inj ) 275 C. instantaneous and the solution quickly developed to a deep orange-red color following the 0.5 s injection. The first excited state absorption band narrowed during growth of the crystals, with an initially broad fwhm of 43 nm decreasing to 30 nm during the first 200 s of particle growth (Figure 2). In Figure 2, we show a plot of the particle radius as a function of time after injection at 275 C for solutions containing increasing oleic acid concentrations. The radii have been calculated from the exciton peak energy using eq 3 from Yu s calibration data. 3 Similar results were obtained from Banin s calibration curve. The ratio of oleic acid to 2304 Nano Lett., Vol. 4, No. 12, 2004

3 Figure 3. Calculated CdSe nanocrystal concentrations as a function of time for five oleic acid concentrations. The concentrations are calculated using calibration data from ref 3. From top to bottom the oleic acid concentrations are 120, 160, 200, 240, and 280 mm, respectively. cadmium was varied from 2.65:1 up to 5.3:1 in these experiments. It is immediately apparent that the average particle size at 5 s is smallest for solutions containing less oleic acid, but this leads to the fastest particle growth. Consequently, there is a crossover time when comparing different syntheses, which occurs at around 20 s. The smallest particle sizes we could reliably obtain correspond to samples about 5 s old and at low oleic acid concentrations; these had radii of about 0.8 ( 0.2 nm. The experiments were generally terminated after about 5 min growth. At this point, the fwhm of the emission spectra begins to broaden again. The broadening indicates the onset of conventional Ostwald ripening, which causes a slow defocusing of the size distribution. This aspect of the growth kinetics has been well studied, and the process is understood. 7 In Figure 3, we present data on the particle concentration vs time for different oleic acid concentrations. These numbers are calculated by using the exciton energy to determine the particle radius and then the extinction coefficient for each size to determine the particle concentration using the equations from ref 3. Within experimental error, we find that the particle concentration in these experiments is constant from the moment of initial growth until the reactions are terminated at around 5 min growth. This is the first verification of this assumption for nanocrystal growth in a non-coordinating solvent. Particularly striking is the fact that the concentration of nuclei is consistently decreased by the increase in capping agent concentration. In Figure 4, we show the nuclei concentration vs [oleic acid]/[cadmium] ratio. At high ratios we see that only a few large particles form since the rate of nucleation approaches zero at [oleic acid]/ [cadmium] > 5.0. This is borne out qualitatively by experiments. Under such conditions, very large particles are observed by HRTEM, despite the very high capping agent concentration. When there is a large excess of capping agent, the few nuclei that are formed grow very rapidly but nonuniformly. The data also allow us to extrapolate to the condition of nucleation in the absence of a stabilizer ([oleic acid]/[cd] f 0). This is not useful in practical terms because particle aggregation is unhindered as pointed out in the Introduction. However, we can predict that pure nucleation Figure 4. Concentration of CdSe nuclei at 275 C in octadecene as a function of the added oleic acid. A linear fit gives 0.10 mm at [oleic acid] ) 0, and zero particles at [oleic acid]/cd] ) 5.0 (0.33 M). in octadecene will produce around 1 mm CdSe nuclei under these conditions. This corresponds to around 2-3% of the available precursor molecules under the nucleation conditions employed. It was observed that the initial nuclei sizes after 5 s are smaller at higher temperatures. The final particle sizes are also smaller. Hence at all times, the particles nucleated at higher temperatures have smaller radii than those nucleated at lower temperatures. This indicates that nucleation is substantially faster as the temperature is increased, and that the growth kinetics are less strongly dependent on temperature, i.e., the activation temperature for nucleation is higher than the activation process for monomer addition. Consequently, higher temperatures produce more nuclei, though of a smaller size, which results in overall smaller particles. Discussion. The nucleation of CdSe in hot octadecene provides an ideal model system to verify kinetic models of particle growth in solution. Our aim in this study was to measure the number of nuclei formed during the nanocrystal synthesis and to estimate the initial size of these nuclei prior to growth. No such measurements have appeared for this system, despite its technological relevance to the controlled synthesis of tunable, luminescent materials. The data in Figure 3 clearly indicate that the nuclei concentrations are constant throughout the reaction within experimental error; furthermore nucleation is a very fast process that ceases almost immediately after monomer injection. This considerably simplifies the analysis of the data. However, to estimate the initial size of these nuclei, we need to extrapolate the radius-time data back to the moment of injection. To do so requires some sort of kinetic model for the particle growth. We will assume that the growth is much slower than the mass transfer limit, i.e., deposition is activation-controlled. This will be justified a posteriori. Then the rate must obey an equation of the form d[cd] t )-ka(t)[cd] t N(t) (1) where [Cd] t is the concentration of available Cd at time t, A(t) is the surface area of each particle at time t, N(t) isthe Nano Lett., Vol. 4, No. 12,

4 number of particles at time t, and k is an interfacial rate constant with units (length/time) that reflects the ratedetermining steps during deposition. Under steady-state growth conditions both Se and Cd should deposit at equal rates, so we may describe the particle growth in terms of either species. From the results in Figure 3, the number of particles remains constant following nucleation, N(t) ) N o ; furthermore, we assume spherical symmetry so that A(t) ) 4πr(t) 2. Then the rate of increase in the volume of precipitated CdSe in the entire solution is dv ) V m d[cdse] t )- V m d[cd] t where V m is the molar volume of CdSe. The effective concentration of free Cd, [Cd] t, is equal to the initial concentration injected [Cd] o, less the amount already deposited, [Cd] dep, less the amount remaining at equilibrium, [Cd] eq. Hence: with A ) V m ([Cd] o -[Cd] eq ) and B ) N o 4π/3. Suitable values are V m (CdSe) ) cm 3 /mol and N o from Figure 3 is /cm 3. Two terms contribute to the changing rate of growth of the nanocrystals. The surface area of each NC is increasing over time, which tends to make the reaction rate actually accelerate, but there is a decreasing concentration of Cd and Se monomers, which ultimately causes the growth rate to slow. Consequently, at very early times, the radius grows almost linearly, but then asymptotes toward its maximum value, given by r max ) (A/B) 1/3, at which point all the excess Cd in solution will have been consumed. Integration of eq 3 yields time as a function of r, (i.e., t ) f(r) + C) Unfortunately, this equation is not readily inverted to give r(t) explicitly. From the boundary condition that r ) r o at t ) 0, we find C )-f(r o ). Despite the simplicity of the rate eq 3, the integrated form is complex, and fitting the data to eq 4 is not trivial. Using the experimental values for A and B (see main text), we calculated growth curves and adjusted the rate constant k to give agreement with the experimental data. The results of a typical fit to the data are shown in Figure 5, and yield r o ) 1.0 ( 0.1 nm for low oleic acid concentrations and r o ) 0.8 ( 0.2 nm for the highest oleic acid concentrations. Note that the errors here refer to the estimated error in the conversion from spectral peak to particle size. The best fits for the rate constant for monomer deposition, k, were cm/s, at least 8 orders of magnitude below the diffusion limited rate constant. The rate constant for growth did not change significantly with added (2) dr ) k (V m ([Cd] o - [Cd] eq ) - N o 4πr3 3 ) ) k(a - Br 3 ) (3) t ) 2B 1/3 ] r + A 2 3arc tan[1 1/3 + 3 Log[ A2/3 + B 1/3 A 1/3 r + B 2/3 r 2 (A 1/3 - B 1/3 r) ] 2 6B 1/3 ka 2/3 + C (4) Figure 5. Fit to the radius-time curves using eq 5 and [oleic acid] ) 120 mm, [Se] ) 18 mm, [TOP] ) 25 mm, [Cd] o ) 50 mm, V m ) cm 3 /mol, N o ) cm -3 from Figure 3, and with k ) cm/s. The values of r o, the radii of the actual nuclei that grow into CdSe NCs was found to be 1.0 ( 0.1 nm. oleic acid. We point out again that the much slower process of Ostwald ripening is not included in the kinetic model here, which focuses on proving whether well-separated nucleation and growth processes occur in these systems by analysis of the particle size-time curves in the early growth stages. The results presented here indicate that the oleic acid is not only an efficacious capping agent for CdSe QDs in octadecene but it markedly influences the primary nucleation steps in two distinct ways. First, the number of nuclei is reduced almost linearly as oleic acid is added. This is not so surprising. Nucleation is more difficult in the presence of oleic acid due to its complexation to Cd. However, the results also show that the initial nuclei in the presence of oleic acid are smaller than in its absence. This is counter-intuitive, since the lower degree of supersaturation in the presence of the ligand should lead to larger nuclei. Hence, the complexing agent reduces the rate of nucleation by reducing the active monomer concentration, but it also rapidly caps the nuclei as they form. These two effects compete with each other. If there is too much capping agent, nucleation can be completely hindered, ultimately leading to indiscriminate growth of a small population of nuclei. However, because there are fewer nuclei formed in the presence of the ligand, we find the somewhat unexpected result that larger clusters form as we increase the concentration of oleic acid. It should be pointed out that at low ligand concentrations, the main effect is the capping action. Under these conditions, the ligand may act to stabilize small nanocrystals and prevent growth through coalescence or ripening, as one normally expects. At longer times, the particle size distribution has focused, the emission from the luminescent crystals has narrowed (Figure 2), and the mean particle size is well-defined. We can determine the degree of supersaturation during nucleation if we can measure the residual concentration of monomers at this time. From the extinction coefficient and the particle number concentration, we typically find that the total amount of Cd and Se deposited is about 85% of the 50 mm analytical monomer concentration. Hence the solubility product is 2306 Nano Lett., Vol. 4, No. 12, 2004

5 K(r ) 2.2 nm) ) [Cd][Se] M 2 at 265 C. This is related to the bulk solubility of CdSe through K(r) ) K exp(-4γv m /rkt) (5) where K is the (unknown) bulk solubility of CdSe in octadecene, and γ is the effective surface free energy per unit area. Armed with these equilibrium concentrations, and nuclei size we can estimate the effective surface free energy of the clusters during nucleation: γ ) RT lnsr nuc /4V m (6) which for S (50 mm/4 mm) 2 150, r nuc ) 1 nm, T ) 540 K, V m ) m 3 /mol yields γ ) 170 mj/m 2, which seems reasonable. This in turn yields a value for the initial size distribution of nuclei: 5 N(r) ) N(r nuc ) exp(-4πn a γ (r-r nuc ) 2 /3RT) (7) The fwhm of the size distribution at time zero is then fwhm ) (3RT/4πN a γ ln(2)) 1/2, and we obtain 9% in very good agreement with current HRTEM data. This dispersity value matches well experimental and theoretical models of the narrowing or focusing of the size distribution found during CdSe growth. 7,8 Since there are about 75 CdSe molecules per nucleus at r nuc ) 1 nm, and the concentration of nuclei found in Figure 3 is about µm in a solution containing 60 mm Cd, the total amount of monomer consumed during nucleation varies from 2 to 8%, depending on the ratio of oleic acid to cadmium monomer concentration. Nucleation is consequently very facile at 550 K. Finally, we note that since the two processes, nucleation and particle growth, are decoupled in this system, there are two, well-defined activation energies. The activation enthalpy for nucleation, H nuc, will generally be much higher than the activation enthalpy for deposition, H dep. As a result, higher temperatures should generally favor smaller particles. This is true provided that both coagulation and Ostwald ripening are also not accelerated at higher temperatures. Conclusions. Octadecene provides a useful medium for studying the growth of CdSe QDs. We have found preliminary values of the radius and concentration of the CdSe nuclei and verified that the growth phase proceeds independently of the nucleation phase and that the growth kinetics obey eq 4. Nucleation consumes about 2-8% of the free Cd. The monodispersity and separated nucleation and growth simplify the assumptions needed to arrive at these values. Finally, we have shown unambiguously that the capping agents not only determine the rate of growth but also play a major role in determining the number and size of the nuclei formed during injection. The presence of a vast excess of capping agent may lead to larger, not smaller, particle sizes. Acknowledgment. C.B. acknowledges receipt of an MRS scholarship and the authors thank the ARC for a SPIRT Grant (C ) and Quantum Dot Corporation for supporting this research. Useful discussions with Daniel Gomez are acknowledged. References (1) Murray, C. B.; Norris, D. J.; Bawendi, M. G. J. Am. Chem. Soc. 1993, 115, (2) Soloviev, V. N.; Eichhofer, A.; Fenske, D.; Banin, U. J. Am. Chem. Soc. 2000, 122, (3) Yu, W. W.; Qu, L.; Guo, W.; Peng, X. Chem. Mater. 2003, 15, (4) Leatherdale, C. A.; Woo, W.-K.; Mikulec, F. V.; Bawendi, M. G. J. Phys. Chem. B 2002, 106, (5) Liu, L. C.; Risbud, S. H. J. Appl. Phys. 1990, 68, (6) Yu, W.; Peng, X. Angew. Chem., Int. Ed. 2002, 41, (7) Peng, X.; Wickham, J.; Alivisatos, A. P. J. Am. Chem. Soc. 1998, 120, (8) Talapin, D.; Rogach, A.; Haase, M.; Weller, D. J. Phys. Chem. B 2001, 105, NL Nano Lett., Vol. 4, No. 12,