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Control of particle size by pressure adjustment in cobalt nanoparticle synthesis
Colloids and Surfaces A: Physicochem. Eng. Aspects 330 (2008) 14–20
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Colloids and Surfaces A: Physicochemical and Engineering Aspects journal homepage: www.elsevier.com/locate/colsurfa
Control of particle size by pressure adjustment in cobalt nanoparticle synthesis Christoffer Johans a,∗ , Maija Pohjakallio a , Mari Ijäs a , Yanling Ge b , Kyösti Kontturi a a b
Department of Chemistry, Helsinki University of Technology, P.O. Box 6100, FIN-02015 TKK, Finland Department of Materials Science and Engineering, Helsinki University of Technology, P.O. Box 6200, FI-02015 TKK, Finland
a r t i c l e
i n f o
Article history: Received 9 May 2008 Received in revised form 4 July 2008 Accepted 7 July 2008 Available online 16 July 2008 Keywords: Cobalt nanoparticles Nucleation Growth Size control Supersaturation
a b s t r a c t Cobalt nanoparticles have been synthesized by a novel pressure drop-induced decomposition method, where Co2 (CO)8 is first heated under high CO pressure and then decomposed by applying a rapid pressure drop. The nucleation rate, and consequently the particle size, is a sensitive function of the supersaturation set by the decomposition pressure. The particle diameter, analyzed by TEM, can be changed between 6 and 140 nm by changing the decomposition pressure between 1 and 5 bar. The CO released during the decomposition was measured by following the pressure change in the reactor. A simplified model assuming instantaneous nucleation followed by kinetically constrained growth gave a rate constant of 6 × 10−5 cm4 mol−1 s−1 for the growth reaction. The relation between particle size and supersaturation was analyzed with the classical nucleation model. While an excellent qualitative correlation was found, the calculated critical size of the nuclei was between 1 and 3 atoms, which indicates that the classical nucleation model is not adequate for explaining the phenomena related to nucleation in this type of nanoparticle synthesis. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Control of nucleation and growth is a key factor in the preparation of solid colloidal particles. Already the early work by LaMer and Dinegar [1] showed that a short nucleation time followed by diffusion limited growth produced monodisperse sulfur particles. Due to the expansion of nanoscience and nanotechnology, the interest and importance of colloidal synthesis procedures have increased enormously during the past decade. Many of the numerous synthesis methods of nanoparticles are based on colloidal chemistry, and thus the formation mechanisms of dispersed particles are of crucial importance. While an immense number of preparation methods describing nanoparticle syntheses have been published [2–6] nucleation and growth mechanisms are still poorly understood. Experimental data on the initial stages of the synthesis is difficult to obtain and thus scarce. A better understanding of nucleation and growth is extremely important since it affects both the size and the size distribution of the resulting particles. Nanoparticle size can be affected by different experimental means, e.g. by reaction time, temperature, concentrations and nature of the protecting ligand. Many of these means are system specific and work only over narrow size ranges. The role of experimental parameters can be quite complex,
∗ Corresponding author. Tel.: +358 9 451 2586; fax: +358 9 451 2580. E-mail address: [email protected].fi (C. Johans). 0927-7757/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2008.07.013
and hence the response to a change in synthesis conditions may be quite opposite in different systems. For example, it is generally acknowledged that an increase in ligand concentration leads to smaller particle size [7,8], as has been found in the synthesis of cobalt particles from Co2 (CO)8 [4]. However, opposite trends have been observed when preparing iron particles from Fe(CO)5 [9]. Due to their numerous applications e.g. in the fields of electronics, catalysis and drug delivery, synthesis of magnetic nanoparticles has been a subject of intense research in recent years. Among magnetic materials cobalt ranks next to iron in the number of publications devoted to nanoparticles [10]. It has been recognized that in order to obtain good quality nanoparticles it is essential to separate the nucleation and growth stages [1,11]. This requires a high degree of control of supersaturation, which has for example been realized in the hot injection method [12]. Originally, Bawendi and Dinega [3] injected dicobalt octacarbonyl (Co2 (CO)8 ) into a hot solvent containing trioctylphosphane oxide (TOPO) as a coordinating ligand. When heated, Co2 (CO)8 decomposes into metallic cobalt and carbon monoxide, and very pure particles can be obtained since CO is the only by-product: nCo2 (CO)8 → nano-Co + 8nCO(g)
(I)
Puntes et al. [4] have shown that a remarkable range of monodisperse spherical cobalt nanoparticles and rods with defined dimensions can be obtained using the hot injection method with two surfactants that bind with different strengths to different crystal surfaces. Pericas and co-workers [13] have published a study on
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2. Experimental
Fig. 1. Schematic presentation of the autoclave and reactants for the pressure dropinduced decomposition synthesis of cobalt nanoparticles.
the mechanics and kinetics of the decomposition reaction under conditions typical in Puntes’ synthesis. They found that depletion of cobalt dicarbonyl occurs typically at time scales of 10 min, and that the surfactants actively participate in the reaction and to affect the decomposition kinetics. They also identified important intermediates such as Co(CO)4 and Co4 (CO)12 . Kumar and co-workers [14] have shown that the surfactants present in the synthesis interact not only with the cobalt carbonyl reactant, and but also with the metal surface of the particle. In their study, the alkyne-bridged dicobalt hexacarbonyl reacts with the surfactants already prior to nucleation, and consequently the reaction mechanism changes. The preparation of cobalt particles by the hot injection method is not limited to Co2 (CO)8 , e.g. Sun and Murray[15] prepared cobalt particles by injecting a reducing agent into a hot solution containing cobalt oleate. In addition to cobalt, the hot injection method has been successfully applied to the preparation of other metal and semiconductor nanoparticles. A good review on the physical chemistry of hot injection has been written by Vanmaekelbergh and co-workers [11]. In this paper we present a novel pressure drop-induced decomposition method in which the supersaturation during the thermal decomposition of Co2 (CO)8 is controlled via the carbon monoxide pressure (Fig. 1). Initially, Co2 (CO)8 and surfactants are heated in dodecane and under high CO pressure which prevents Co2 (CO)8 from decomposing. Then the pressure is rapidly dropped, which causes Co2 (CO)8 to decompose thus inducing nucleation and growth of cobalt nanoparticles. The growth reaction proceeds until all Co2 (CO)8 is consumed. Variation of the magnitude of the CO pressure drop gives a simple means to control the supersaturation and hence nucleation and growth, well comparable to that observed in electrochemical experiments with the variation of the applied potential. The particle diameter can be changed between 6 and 140 nm by changing the final decomposition pressure between 1 and 5 bar. Even though many aspects of our method are similar to the hot injection method, the quantitative control of the CO pressure provides a means to directly control the synthesis and to study how the supersaturation affects nucleation rates. This is rather unique in nanoparticle preparation.
Dodecane (Fluka, purum), dicobalt octacarbonyl (Fluka, purum), oleic acid (Merck, Ph Helv, NF) and trioctylamine (Aldrich, 97%) were used as-received without further purification. First we examined how the pressure affects the decomposition of cobalt carbonyl by heating Co2 (CO)8 in dodecane in a closed autoclave (Parr 4843) under different initial CO pressures. The initial CO pressure was set at a temperature of 40 ◦ C, after which the autoclave was closed. The sample was then heated at a rate of 1 ◦ C/min, and the pressure was measured as a function of temperature. In the nanoparticle synthesis 20 ml dodecane, 0.5 g Co2 (CO)8 , 1.07 ml trioctylamine and 0.1 ml oleic acid were loaded into the 100 ml reactor (Parr) and flushed with CO (Fig. 1). Then the initial pressure was set to 58 bar at 25 ◦ C and the system was heated to 170 ◦ C at a rate of 3 ◦ C/min. The pressure increased to 86 bar during the heating, which corresponds well to that predicted by the ideal gas law if no decomposition occurs. After 170 ◦ C had been reached, the pressure was dropped to the desired pressure (1.3, 2.3, 3.2, 4.5 and 5.5 bar) by opening the gas release valve (Fig. 1). The pressure drop was completed in less than 2 s. When the desired pressure, hereafter referred as the decomposition pressure, had been reached, the valve was closed and the decomposition reaction was monitored by measuring the pressure change in the autoclave. Transmission electron microscope (TEM) measurements were performed with a Tecnai 12 instrument operated at 120 kV accelerating voltage. The samples were prepared by drop casting the nanoparticle dodecane solution obtained from the synthesis on formvar/carbon-coated copper grids and dried in air. The solutions were vigorously shaken to break possible aggregates. The particle size was obtained from the TEM micrographs by manually measuring the diameter. High resolution transmission electron microscope measurements were performed on a Tecnai G2 F20 Stwin GIF Tridiem instrument operated at 200 kV. The samples for HRTEM were prepared by drop casting from a synthesis solution diluted 1:100 with chloroform on formvar/carbon-coated copper grids. 3. Results and discussion 3.1. Decomposition of Co2 (CO)8 and synthesis of cobalt nanoparticles Since Co2 (CO)8 decomposes into metallic cobalt and carbon monoxide when heated, it is evident that the reaction must be affected by the carbon monoxide pressure. In the first measurements, Co2 (CO)8 was heated at 1 ◦ C/min in a closed autoclave under different initial pressures set at 40 ◦ C. During heating, the pressure inside the autoclave increased due to both the increased thermal motion of the gas molecules and the release of additional CO from Co2 (CO)8 . The amount of CO released was calculated from the pressure increase using the ideal gas law. Although a thorough thermodynamic treatment would require a more elaborate equation of state, parameters for the temperature dependence of CO solubility in dodecane, and deviations from equilibrium due to non-zero heating rate, this simplified approach is sufficient for our purposes.
Table 1 Particle diameter obtained from TEM and calculated values for the critical radius and the number of atoms in the critical nucleus at different decomposition pressures Decomposition pressure (bar)
TEM diameter (nm)
Critical radius (Å)
Number of atoms in a cluster of critical size
1.3 2.3 3.2 4.5 5.5
6 20 31 81 139
1.29 1.49 1.64 1.83 1.97
0.8 1.3 1.7 2.4 2.9
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3.2. TEM analysis of size and structure of as-synthesized cobalt nanoparticles
Fig. 2. The percentage of CO released during the heating of Co2 (CO)8 in dodecane as a function of temperature at different initial pressures. The heating rate was 1 ◦ C/min and the initial pressures indicated were set at 40 ◦ C.
Fig. 2 presents the amount of released CO gas a function of temperature. At low initial pressures, 1–2 bar, the curves show two rising parts separated by a clear plateau. This is an indication that two separate reactions take place. During the first rising part, thus during the first reaction at approximately 75–100 ◦ C, about 25% of the CO ligands are released. This suggests that the first reaction is the well known dimerization of Co2 (CO)8 according to 2Co2 (CO)8 → Co4 (CO)12 + 4CO(g)
(II)
The second rising part, at temperatures above 130 ◦ C, corresponds to the decomposition of Co2 (CO)8 (and Co4 (CO)12 ) into metallic cobalt according to reaction (I). Fig. 2 shows that an increase in the CO pressure suppresses both reactions (I) and (II), and that the increase in temperature at which the reaction starts is greater for reaction (II) than for reaction (I). When the initial pressure is 40 bar, the first rising part and the plateau disappear completely indicating that the decomposition proceeds directly from Co2 (CO)8 to metal. This is an interesting result as decomposition of cobalt carbonyl has previously been carried out at lower temperatures to avoid undesired byproducts, such as Co4 (CO)12 complexes [16]. If the initial pressure is further increased to 50 bar neither dimerization nor decomposition occurs in the temperature range studied. Thus, at pressures above this, decomposition can be completely suppressed. The data presented in Fig. 2 were measured in the absence of surfactants. Several surfactants were found to influence the decomposition process, indicating that they react with the cobalt carbonyl, as has been observed previously [14]. For example, if trioctylphosphine oxide or oleic acid in high concentrations was used as surfactants, a significant release of CO and a shift of the decomposition to lower temperatures were observed at low pressures. Thus there was a change in the shape of the curves, i.e. in the reaction mechanism. Therefore, attention must be paid in choosing such surfactants and concentrations, which do not react with Co2 (CO)8 during the heating to the synthesis temperature. In the nanoparticle synthesis we used a mixture of trioctylamine and oleic acid. These surfactants were not observed to affect the decomposition reactions in the concentration range used. The principle of our method in synthesizing cobalt nanoparticles was to first heat Co2 (CO)8 and surfactants in dodecane under a high CO pressure and then quickly drop the pressure to a level where decomposition of Co2 (CO)8 occurs directly into metallic cobalt. The idea is to control supersaturation, and hence nucleation rates, by adjusting the carbon monoxide pressure during the decomposition step. Several different decomposition pressures were used, as we wanted to study how the magnitude of the pressure drop affects the size of the nanoparticles produced.
The effect of the decomposition pressure on the size of the synthesized cobalt nanoparticles can be seen in the TEM micrographs shown in Fig. 3. At a decomposition pressure of 1.3 bar small particles with a diameter of approximately 6 nm were produced. These particles do not interact strongly with each other, and hence no superstructures or aggregates were formed on the TEM grid. When the synthesis was carried out at 2.3 bar particles with a diameter of approximately 20 nm were obtained. The interparticle forces between these bigger particles are stronger than those between the smaller particles, and thus the particles form ordered structures on the TEM grid. At a decomposition pressure of 3.2 bar the synthesis produced even bigger particles, with a diameter of approximately 31 nm, which cluster readily on the grid. Particles of 81 and 139 nm were obtained at decompostion pressures of 4.5 and 5.5 bar, respectively. It is also interesting to note that the shape of the particles becomes more elusive with increasing particle size. A possible explanation is that the transition results from the growth of multicrystalline particles counterbalanced by the surface energy. Multicrystalline cobalt nanoparticles have previously been observed by others [8] and may result from the growth of particles aggregated from nanocrystalline subunits or from the internal reorganization of atoms after their attachment to the particle surface [17–19]. Without such restructuring, the clusters would grow according to diffusion-limited aggregation or other similar processes and could be fractal. The multicrystalline nature of the particles can be observed in the TEM micrographs as dark spots on the particles [8]. A HRTEM micrograph of our cobalt nanoparticle shown in Fig.3f clearly indicates the multicrystalline nature of the particle. It should be noted that tridodecylamine was used as the stabilizing surfactant in this case. 3.3. Gas release transients during particle growth The gas release transients measured during the particle synthesis are shown in Fig. 4. In a typical particle synthesis, the gas release rate initially increases, after which the reaction proceeds at an almost constant rate until all the reactants have been consumed. Interestingly, the lower the decomposition pressure was, the higher was the decomposition rate of Co2 (CO)8 . These differences in reaction rates reflect the different number densities of growing particles that result from the variation in supersaturation. The final amount of gas released was independent of the decomposition pressure, indicating that the reaction proceeds until all reactants have been consumed, which indicates that the growth reaction deviates considerably from equilibrium. Let us consider the growth of a particle by addition of monomers to its surface under kinetic control, then dR = kc (t) dt
(1)
where k is the rate constant for the deposition reaction, t is time, R is the radius of the particle and c(t) is the concentration of reactant. The dissolution reaction has been omitted since the deviation from equilibrium is large. We assume here that kinetic control is more likely than diffusion control since the mass transfer to nanometer sized particles is rather fast. This assumption is justified by the obtained results as shown below. If we assume that the nucleation process is instantaneous, i.e. all particles are formed immediately after the pressure drop, the following expression for the remaining
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Fig. 3. TEM micrographs of the cobalt particles synthesized in dodecane–trioctylamine–oleic acid mixture at different decomposition pressures: (a) 1.3 bar, (b) 2.3 bar, (c) 3.2 bar, (d) 4.5 bar and (e) 5.5 bar. (f) HRTEM micrograph of a tridodecylamine protected particle prepared at a decomposition pressure of 1.3 bar showing the multicrystalline structure of the as-synthesized particles.
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3.4. Analysis of the relation between the particle size and supersaturation set by the decomposition pressure
precursor in Fig. 4. (a) Decomposition of the Co2 (CO)8 dodecane–trioctylamine–oleic acid mixture after the pressure drop. The ini◦ tial pressure p0 before the drop was 86 bar (170 C). The value to which the pressure was dropped, i.e. the decomposition pressure p1 , affected the rate of decomposition: p1 = 1.3 bar (solid line), p1 = 2.3 bar (dots), p1 = 3.2 bar (dash), p1 = 4.5 bar (dash-dot-dot) and p1 = 5.5 bar (long dash). The horizontal curve (dash-dot) is a blank measurement in absence of Co2 (CO)8 at p1 = 1 bar. (b) Calculated gas release transients (Eq. (3)) for kinetic growth following instantaneous nucleation k = 6 × 10−5 cm4 mol−1 s−1 and particle radii as obtained from TEM analysis of p1 = 1.3 bar (solid line), p1 = 2.3 bar (dots), p1 = 3.2 bar (dash), p1 = 4.5 bar (dash-dot-dot) and p1 = 5.5 bar (long dash).
concentration is obtained from the mass balance:
c(t) = c
0
1−
R(t) 3 Rfinal
(2)
1−
R(t) 3 Rfinal
G C
A ∝ c exp −
and consequently for the particle radius dR = kc 0 dt
Surprisingly few studies that quantitatively link experimentally obtained nanoparticle size to nucleation and growth models exist in the literature. Privman et al. have in a series of papers treated burst nucleation followed by aggregational growth of nanosize precursors [17] and recently by diffusional growth [18] following the LaMer model [1,19]. LaMer and Dinegar proposed that, from a strong initial supersaturation, a rapid nucleation burst of particles would initially occur, followed by the adsorption of diffusing atomic matter onto the nucleated particles [20]. While these models can predict several experimentally observed features, quantitative comparison to experiments is still very scarce due to the limited amount of available data. Here we take a simplified approach using the classical nucleation model to analyze the relation between particle size and decomposition pressure. Just after the pressure drop a supersaturated state occurs, which leads to a rapid nucleation burst. Similarly, to the assumptions in the hot injection method and LaMer model, the nucleation burst is quenched by the decrease in temperature caused by the pressure drop, the presumably endothermic formation of a new phase, the decrease in reactant concentration and the rise in pressure due to released CO. All these factors contribute to an instantaneous nucleation burst. This is also supported by the experimental gas release transients. Thus, we can assume that nucleation takes place in a defined short period of time after the pressure drop. In this approach it is assumed that, without further consideration of the growth mechanism, the number density of nuclei is reflected in the particle size obtained, i.e. the aggregation or dissolution of nucleated particles is not considered. While aggregation could not be observed in the gas release transients, it is difficult to rule out aggregation during the initial stages. Dissolution is considered to be irrelevant since growth occurs at a high level of supersaturation. In addition, Ostwald ripening has not been observed for magnetic alloy particles despite long-term heating [21]. If the formation of a critical nucleus is necessary for the phase growth to occur, the rate of nucleation may be estimated by the frequency with which new growth centers appear. The nucleation rate is thus
(3)
Rfinal is the particle radius at the end of the synthesis obtained from the TEM analysis and c0 equals the amount of Co2 (CO)8 initially present in the reactor. Thus, k is the only unknown parameter in Eq. (3). Eq. (3) was numerically solved using standard Runge–Kutta scheme. Plots of c(t)/c0 using k = 6 × 10−5 cm4 mol−1 s−1 are shown in Fig. 4b. Interestingly, the CO release rates observed experimentally can be well described using the same value for k for all decomposition pressures, despite the crude model. This leads to the following conclusions. The overall reaction rate scales with the area of the particle ensemble, and hence the particles grow primarily by the addition of monomeric species to the particle. The observed rate constant is much smaller than expected for an unhindered diffusion controlled reaction, k DVM /R, showing that the particles grow under kinetic control. VM is the molar volume of the deposited phase. Furthermore, the nucleation burst can be considered short compared to the growth time, i.e. instantaneous nucleation can be assumed. Aggregation of particles seems to be negligible, since it would change the effective surface area, which is not observed.
kT
(4)
where GC is the work for critical nucleus formation and c is the concentration of monomers. A particle of critical radius, rC , has an equal probability of growing and dissolving. According to the classical model the energy of formation is given by the sum of the free energy associated with the formation of bulk and the surface energy, GNet = A GSurf + V GBulk , where A and V are the area and volume of the cluster. For a spherical nucleus the maximum energy and the corresponding critical radius are given by GC =
2 3 16VM 2 3 GBulk
rC = −
2VM GBulk
(5)
(6)
where VM is the molar volume of the growing phase, here assumed to equal that of bulk cobalt. is the effective surface energy of the cluster. LaMer and Pound [22] noted that the classical nucleation theory requires the use of the macroscopic interfacial energies. To be accurate the surface energy depends on the curvature, i.e. on the radius of the particles. It can, however be assumed that for most materials the surface energy does not vary strongly with size. For
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example, Benson and Shuttleworth [23] found that even for a crystallite containing 13 molecules the surface energy was only 15% less than for a planar surface and Walton [24] describes a 35% increase in the surface energy of a KCl crystal of four ions in radius. It should be noted that the nucleation rate depends exponentially on the surface energy, and that small errors can have very significant effects on the nucleation rate [23]. In this study, the value of the surface energy of the presumed surfactant-covered nucleus is not known a priori. GBulk is the thermodynamic supersaturation of the deposition reaction referred to bulk. This quantity changes with Co2 (CO)8 concentration and CO pressure. The dependence of GBulk on the CO pressure provides a very convenient means, comparable to the applied potential in electrochemical experiments, to vary the level of supersaturation. If we assume that equilibrium prevails prior to the pressure drop, and further, that the change in monomer reactant concentration and pressure is negligible during nucleation burst, then the driving force for the deposition reaction is GBulk = 4RT ln
p 1
(7)
p0
where R gas constant, p0 is the pressure before the pressure drop (initial pressure) and p1 is the pressure after the drop (decomposition pressure). The factor 4 follows since 4CO molecules are released from Co2 (CO)8 for every deposited cobalt atom. It is pointed out here that the finite reaction rates observed in this study support the assumption of equilibrium, since pressure is not expected to affect reaction kinetics. Combining (Eqs. (5) and (7)) gives GC =
2 3 VM
2
(8)
3R2 T 2 ln(p1 /p0 )
From Eq. (8) it can be seen that the nucleation rate decreases increasing decomposition pressure, i.e. size increases with increasing pressure (see Fig. 5a). An important experimental observation is the extreme sensitivity of the nucleation rate to supersaturation. A change from 1.3 to 5.5 bar, corresponding to a change in supersaturation energy from 62 to 41 kJ/mol, changes the particle diameter from 6 to 140 nm (see Fig. 5a). If we assume that all the nuclei are formed within a short defined time t after the pressure drop, the nucleation rate should be proportional to the number density of nuclei, which in turn is proportional to the inverse of the cube of the radius of the particles obtained. Thus we can say that 3
ln A ∝ ln
d0 NA VM 2 3 ∝− 3 3 d 3R T 3 (ln(p1 /p0 ))2
(9)
where d is the particle diameter and d0 is a scaling parameter equal to 1 nm. Thus, a plot of ln(d03 /d3 ) vs. 1/[ln(p1 /p0 )]2 should yield a straight line if the classical nucleation model and the assumptions made here apply. A plot based on our experimental results is shown in Fig. 5b. It should be emphasized that we do not know in detail how the length of the nucleation burst varies with pressure, and thus the assumption of instantaneous nucleation may not be accurate.1 However, the experimental points shown in Fig. 5b fit excellently to a straight line, indicating that despite the simplifying assumptions the classical nucleation model seems to qualitatively predict the nucleation process very well. While the TEM pictures show multicrystalline particles that may have resulted from aggregation of smaller subunits, the good agreement of the experimental
1 The length of the nucleation burst can also be estimated from Fig. 2, for example, by assuming that the significant part of the nuclei has been formed when 25% of the CO has been released. This has, however, only a minor effect on the slope in Fig. 5b, yielding a surface tension of 650 mN/m and critical sizes between 1.0 and 3.7 atoms.
Fig. 5. (a) The average diameter of trioctylamine/oleic acid stabilized cobalt nanoparticles calculated from TEM images as a function of the decomposition pressure at which the particles were synthesized. (b) Dependence of the particle nucleation rate on the supersaturation (p1 /p0 ).
data with both the calculated gas release transients and the classical nucleation model suggests a particle number density conserving mechanism, such as growth through adsorption of diffusing atomic matter. The surface energy of the cobalt nanoparticles can be obtained from the slope in Fig. 5b and equals to 603 mN/m. This value seems physically plausible, considering that the surface energy of the metal core is significantly lowered by the adsorbed surfactants and carbon monoxide, although it is difficult to verify. If we calculate the critical size of the nuclei using this value for the surface energy the critical size is 0.8 atoms (rc = 1.29 Å) at 1 bar and increases to 2.9 atoms (rc = 1.97 Å) at 5.5 bar, see Table 1. These sizes are too small for the macroscopic classical nucleation model to be physically realistic, however, our results agree with previous nucleation studies in which the critical nucleus size obtained with both classical and atomistic models indicate that a small or very small critical nucleus is formed [25]. The plot in Fig. 5b is analogous to the ln A vs. 1/2 plot commonly shown in electrochemical nucleation studies, in which the overpotential corresponds to RT ln(p1 /p0 ) in Eq. (9). The applicability of this type of nucleation models has been discussed in detail in electrochemical context [25–28], where similar critical sizes of less than a few atoms have frequently been found. These results were explained by the poor approximations involved in the classical nucleation theory for the complex sequence of reactions leading to the formation of a critical nucleus [27] and by the use of macroscopic concepts having no physical meaning for very small clusters [26–28]. Comparison of these results with ours highlights the fact
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that even though nucleation in nanoparticle synthesis may quantitatively be described by the classical nucleation theory, this theory cannot give physical explanations to the phenomena occuring during the nucleation burst. 4. Conclusion In this paper we have presented a novel method for the synthesis of cobalt nanoparticles. In our pressure drop-induced decomposition method the supersaturation during the thermal decomposition of Co2 (CO)8 is directly controlled via the carbon monoxide pressure. The supersaturation affects the nucleation rate, and hence the number density of the particles formed, which is inversely proportional to the final size of the particles obtained. When the pressure before the decomposition was 86 bar (at 170 ◦ C) the particle diameter could be changed between 6 and 140 nm by changing the final decomposition pressure between 1.3 and 5.5 bar. The growth rates of the particles were analyzed by correlating the CO released in the synthesis to a model based on kinetically controlled growth following instantaneous nucleation. The particle size dependence on the supersaturation was analyzed with the classical nucleation model and a qualitative agreement was found. However, the calculated critical sizes between 1 and 3 atoms indicate that the macroscopic assumptions of classical nucleation model are not adequate for explaining the phenomena related to nucleation in this type of nanoparticle synthesis. Acknowledgements We thank the Academy of Finland, Tekes, OMG, Outotec and Magnasense for financial support.
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Colloids and Surfaces A: Physicochemical and Engineering Aspects journal homepage: www.elsevier.com/locate/colsurfa
Control of particle size by pressure adjustment in cobalt nanoparticle synthesis Christoffer Johans a,∗ , Maija Pohjakallio a , Mari Ijäs a , Yanling Ge b , Kyösti Kontturi a a b
Department of Chemistry, Helsinki University of Technology, P.O. Box 6100, FIN-02015 TKK, Finland Department of Materials Science and Engineering, Helsinki University of Technology, P.O. Box 6200, FI-02015 TKK, Finland
a r t i c l e
i n f o
Article history: Received 9 May 2008 Received in revised form 4 July 2008 Accepted 7 July 2008 Available online 16 July 2008 Keywords: Cobalt nanoparticles Nucleation Growth Size control Supersaturation
a b s t r a c t Cobalt nanoparticles have been synthesized by a novel pressure drop-induced decomposition method, where Co2 (CO)8 is first heated under high CO pressure and then decomposed by applying a rapid pressure drop. The nucleation rate, and consequently the particle size, is a sensitive function of the supersaturation set by the decomposition pressure. The particle diameter, analyzed by TEM, can be changed between 6 and 140 nm by changing the decomposition pressure between 1 and 5 bar. The CO released during the decomposition was measured by following the pressure change in the reactor. A simplified model assuming instantaneous nucleation followed by kinetically constrained growth gave a rate constant of 6 × 10−5 cm4 mol−1 s−1 for the growth reaction. The relation between particle size and supersaturation was analyzed with the classical nucleation model. While an excellent qualitative correlation was found, the calculated critical size of the nuclei was between 1 and 3 atoms, which indicates that the classical nucleation model is not adequate for explaining the phenomena related to nucleation in this type of nanoparticle synthesis. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Control of nucleation and growth is a key factor in the preparation of solid colloidal particles. Already the early work by LaMer and Dinegar [1] showed that a short nucleation time followed by diffusion limited growth produced monodisperse sulfur particles. Due to the expansion of nanoscience and nanotechnology, the interest and importance of colloidal synthesis procedures have increased enormously during the past decade. Many of the numerous synthesis methods of nanoparticles are based on colloidal chemistry, and thus the formation mechanisms of dispersed particles are of crucial importance. While an immense number of preparation methods describing nanoparticle syntheses have been published [2–6] nucleation and growth mechanisms are still poorly understood. Experimental data on the initial stages of the synthesis is difficult to obtain and thus scarce. A better understanding of nucleation and growth is extremely important since it affects both the size and the size distribution of the resulting particles. Nanoparticle size can be affected by different experimental means, e.g. by reaction time, temperature, concentrations and nature of the protecting ligand. Many of these means are system specific and work only over narrow size ranges. The role of experimental parameters can be quite complex,
∗ Corresponding author. Tel.: +358 9 451 2586; fax: +358 9 451 2580. E-mail address: [email protected].fi (C. Johans). 0927-7757/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2008.07.013
and hence the response to a change in synthesis conditions may be quite opposite in different systems. For example, it is generally acknowledged that an increase in ligand concentration leads to smaller particle size [7,8], as has been found in the synthesis of cobalt particles from Co2 (CO)8 [4]. However, opposite trends have been observed when preparing iron particles from Fe(CO)5 [9]. Due to their numerous applications e.g. in the fields of electronics, catalysis and drug delivery, synthesis of magnetic nanoparticles has been a subject of intense research in recent years. Among magnetic materials cobalt ranks next to iron in the number of publications devoted to nanoparticles [10]. It has been recognized that in order to obtain good quality nanoparticles it is essential to separate the nucleation and growth stages [1,11]. This requires a high degree of control of supersaturation, which has for example been realized in the hot injection method [12]. Originally, Bawendi and Dinega [3] injected dicobalt octacarbonyl (Co2 (CO)8 ) into a hot solvent containing trioctylphosphane oxide (TOPO) as a coordinating ligand. When heated, Co2 (CO)8 decomposes into metallic cobalt and carbon monoxide, and very pure particles can be obtained since CO is the only by-product: nCo2 (CO)8 → nano-Co + 8nCO(g)
(I)
Puntes et al. [4] have shown that a remarkable range of monodisperse spherical cobalt nanoparticles and rods with defined dimensions can be obtained using the hot injection method with two surfactants that bind with different strengths to different crystal surfaces. Pericas and co-workers [13] have published a study on
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2. Experimental
Fig. 1. Schematic presentation of the autoclave and reactants for the pressure dropinduced decomposition synthesis of cobalt nanoparticles.
the mechanics and kinetics of the decomposition reaction under conditions typical in Puntes’ synthesis. They found that depletion of cobalt dicarbonyl occurs typically at time scales of 10 min, and that the surfactants actively participate in the reaction and to affect the decomposition kinetics. They also identified important intermediates such as Co(CO)4 and Co4 (CO)12 . Kumar and co-workers [14] have shown that the surfactants present in the synthesis interact not only with the cobalt carbonyl reactant, and but also with the metal surface of the particle. In their study, the alkyne-bridged dicobalt hexacarbonyl reacts with the surfactants already prior to nucleation, and consequently the reaction mechanism changes. The preparation of cobalt particles by the hot injection method is not limited to Co2 (CO)8 , e.g. Sun and Murray[15] prepared cobalt particles by injecting a reducing agent into a hot solution containing cobalt oleate. In addition to cobalt, the hot injection method has been successfully applied to the preparation of other metal and semiconductor nanoparticles. A good review on the physical chemistry of hot injection has been written by Vanmaekelbergh and co-workers [11]. In this paper we present a novel pressure drop-induced decomposition method in which the supersaturation during the thermal decomposition of Co2 (CO)8 is controlled via the carbon monoxide pressure (Fig. 1). Initially, Co2 (CO)8 and surfactants are heated in dodecane and under high CO pressure which prevents Co2 (CO)8 from decomposing. Then the pressure is rapidly dropped, which causes Co2 (CO)8 to decompose thus inducing nucleation and growth of cobalt nanoparticles. The growth reaction proceeds until all Co2 (CO)8 is consumed. Variation of the magnitude of the CO pressure drop gives a simple means to control the supersaturation and hence nucleation and growth, well comparable to that observed in electrochemical experiments with the variation of the applied potential. The particle diameter can be changed between 6 and 140 nm by changing the final decomposition pressure between 1 and 5 bar. Even though many aspects of our method are similar to the hot injection method, the quantitative control of the CO pressure provides a means to directly control the synthesis and to study how the supersaturation affects nucleation rates. This is rather unique in nanoparticle preparation.
Dodecane (Fluka, purum), dicobalt octacarbonyl (Fluka, purum), oleic acid (Merck, Ph Helv, NF) and trioctylamine (Aldrich, 97%) were used as-received without further purification. First we examined how the pressure affects the decomposition of cobalt carbonyl by heating Co2 (CO)8 in dodecane in a closed autoclave (Parr 4843) under different initial CO pressures. The initial CO pressure was set at a temperature of 40 ◦ C, after which the autoclave was closed. The sample was then heated at a rate of 1 ◦ C/min, and the pressure was measured as a function of temperature. In the nanoparticle synthesis 20 ml dodecane, 0.5 g Co2 (CO)8 , 1.07 ml trioctylamine and 0.1 ml oleic acid were loaded into the 100 ml reactor (Parr) and flushed with CO (Fig. 1). Then the initial pressure was set to 58 bar at 25 ◦ C and the system was heated to 170 ◦ C at a rate of 3 ◦ C/min. The pressure increased to 86 bar during the heating, which corresponds well to that predicted by the ideal gas law if no decomposition occurs. After 170 ◦ C had been reached, the pressure was dropped to the desired pressure (1.3, 2.3, 3.2, 4.5 and 5.5 bar) by opening the gas release valve (Fig. 1). The pressure drop was completed in less than 2 s. When the desired pressure, hereafter referred as the decomposition pressure, had been reached, the valve was closed and the decomposition reaction was monitored by measuring the pressure change in the autoclave. Transmission electron microscope (TEM) measurements were performed with a Tecnai 12 instrument operated at 120 kV accelerating voltage. The samples were prepared by drop casting the nanoparticle dodecane solution obtained from the synthesis on formvar/carbon-coated copper grids and dried in air. The solutions were vigorously shaken to break possible aggregates. The particle size was obtained from the TEM micrographs by manually measuring the diameter. High resolution transmission electron microscope measurements were performed on a Tecnai G2 F20 Stwin GIF Tridiem instrument operated at 200 kV. The samples for HRTEM were prepared by drop casting from a synthesis solution diluted 1:100 with chloroform on formvar/carbon-coated copper grids. 3. Results and discussion 3.1. Decomposition of Co2 (CO)8 and synthesis of cobalt nanoparticles Since Co2 (CO)8 decomposes into metallic cobalt and carbon monoxide when heated, it is evident that the reaction must be affected by the carbon monoxide pressure. In the first measurements, Co2 (CO)8 was heated at 1 ◦ C/min in a closed autoclave under different initial pressures set at 40 ◦ C. During heating, the pressure inside the autoclave increased due to both the increased thermal motion of the gas molecules and the release of additional CO from Co2 (CO)8 . The amount of CO released was calculated from the pressure increase using the ideal gas law. Although a thorough thermodynamic treatment would require a more elaborate equation of state, parameters for the temperature dependence of CO solubility in dodecane, and deviations from equilibrium due to non-zero heating rate, this simplified approach is sufficient for our purposes.
Table 1 Particle diameter obtained from TEM and calculated values for the critical radius and the number of atoms in the critical nucleus at different decomposition pressures Decomposition pressure (bar)
TEM diameter (nm)
Critical radius (Å)
Number of atoms in a cluster of critical size
1.3 2.3 3.2 4.5 5.5
6 20 31 81 139
1.29 1.49 1.64 1.83 1.97
0.8 1.3 1.7 2.4 2.9
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3.2. TEM analysis of size and structure of as-synthesized cobalt nanoparticles
Fig. 2. The percentage of CO released during the heating of Co2 (CO)8 in dodecane as a function of temperature at different initial pressures. The heating rate was 1 ◦ C/min and the initial pressures indicated were set at 40 ◦ C.
Fig. 2 presents the amount of released CO gas a function of temperature. At low initial pressures, 1–2 bar, the curves show two rising parts separated by a clear plateau. This is an indication that two separate reactions take place. During the first rising part, thus during the first reaction at approximately 75–100 ◦ C, about 25% of the CO ligands are released. This suggests that the first reaction is the well known dimerization of Co2 (CO)8 according to 2Co2 (CO)8 → Co4 (CO)12 + 4CO(g)
(II)
The second rising part, at temperatures above 130 ◦ C, corresponds to the decomposition of Co2 (CO)8 (and Co4 (CO)12 ) into metallic cobalt according to reaction (I). Fig. 2 shows that an increase in the CO pressure suppresses both reactions (I) and (II), and that the increase in temperature at which the reaction starts is greater for reaction (II) than for reaction (I). When the initial pressure is 40 bar, the first rising part and the plateau disappear completely indicating that the decomposition proceeds directly from Co2 (CO)8 to metal. This is an interesting result as decomposition of cobalt carbonyl has previously been carried out at lower temperatures to avoid undesired byproducts, such as Co4 (CO)12 complexes [16]. If the initial pressure is further increased to 50 bar neither dimerization nor decomposition occurs in the temperature range studied. Thus, at pressures above this, decomposition can be completely suppressed. The data presented in Fig. 2 were measured in the absence of surfactants. Several surfactants were found to influence the decomposition process, indicating that they react with the cobalt carbonyl, as has been observed previously [14]. For example, if trioctylphosphine oxide or oleic acid in high concentrations was used as surfactants, a significant release of CO and a shift of the decomposition to lower temperatures were observed at low pressures. Thus there was a change in the shape of the curves, i.e. in the reaction mechanism. Therefore, attention must be paid in choosing such surfactants and concentrations, which do not react with Co2 (CO)8 during the heating to the synthesis temperature. In the nanoparticle synthesis we used a mixture of trioctylamine and oleic acid. These surfactants were not observed to affect the decomposition reactions in the concentration range used. The principle of our method in synthesizing cobalt nanoparticles was to first heat Co2 (CO)8 and surfactants in dodecane under a high CO pressure and then quickly drop the pressure to a level where decomposition of Co2 (CO)8 occurs directly into metallic cobalt. The idea is to control supersaturation, and hence nucleation rates, by adjusting the carbon monoxide pressure during the decomposition step. Several different decomposition pressures were used, as we wanted to study how the magnitude of the pressure drop affects the size of the nanoparticles produced.
The effect of the decomposition pressure on the size of the synthesized cobalt nanoparticles can be seen in the TEM micrographs shown in Fig. 3. At a decomposition pressure of 1.3 bar small particles with a diameter of approximately 6 nm were produced. These particles do not interact strongly with each other, and hence no superstructures or aggregates were formed on the TEM grid. When the synthesis was carried out at 2.3 bar particles with a diameter of approximately 20 nm were obtained. The interparticle forces between these bigger particles are stronger than those between the smaller particles, and thus the particles form ordered structures on the TEM grid. At a decomposition pressure of 3.2 bar the synthesis produced even bigger particles, with a diameter of approximately 31 nm, which cluster readily on the grid. Particles of 81 and 139 nm were obtained at decompostion pressures of 4.5 and 5.5 bar, respectively. It is also interesting to note that the shape of the particles becomes more elusive with increasing particle size. A possible explanation is that the transition results from the growth of multicrystalline particles counterbalanced by the surface energy. Multicrystalline cobalt nanoparticles have previously been observed by others [8] and may result from the growth of particles aggregated from nanocrystalline subunits or from the internal reorganization of atoms after their attachment to the particle surface [17–19]. Without such restructuring, the clusters would grow according to diffusion-limited aggregation or other similar processes and could be fractal. The multicrystalline nature of the particles can be observed in the TEM micrographs as dark spots on the particles [8]. A HRTEM micrograph of our cobalt nanoparticle shown in Fig.3f clearly indicates the multicrystalline nature of the particle. It should be noted that tridodecylamine was used as the stabilizing surfactant in this case. 3.3. Gas release transients during particle growth The gas release transients measured during the particle synthesis are shown in Fig. 4. In a typical particle synthesis, the gas release rate initially increases, after which the reaction proceeds at an almost constant rate until all the reactants have been consumed. Interestingly, the lower the decomposition pressure was, the higher was the decomposition rate of Co2 (CO)8 . These differences in reaction rates reflect the different number densities of growing particles that result from the variation in supersaturation. The final amount of gas released was independent of the decomposition pressure, indicating that the reaction proceeds until all reactants have been consumed, which indicates that the growth reaction deviates considerably from equilibrium. Let us consider the growth of a particle by addition of monomers to its surface under kinetic control, then dR = kc (t) dt
(1)
where k is the rate constant for the deposition reaction, t is time, R is the radius of the particle and c(t) is the concentration of reactant. The dissolution reaction has been omitted since the deviation from equilibrium is large. We assume here that kinetic control is more likely than diffusion control since the mass transfer to nanometer sized particles is rather fast. This assumption is justified by the obtained results as shown below. If we assume that the nucleation process is instantaneous, i.e. all particles are formed immediately after the pressure drop, the following expression for the remaining
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Fig. 3. TEM micrographs of the cobalt particles synthesized in dodecane–trioctylamine–oleic acid mixture at different decomposition pressures: (a) 1.3 bar, (b) 2.3 bar, (c) 3.2 bar, (d) 4.5 bar and (e) 5.5 bar. (f) HRTEM micrograph of a tridodecylamine protected particle prepared at a decomposition pressure of 1.3 bar showing the multicrystalline structure of the as-synthesized particles.
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3.4. Analysis of the relation between the particle size and supersaturation set by the decomposition pressure
precursor in Fig. 4. (a) Decomposition of the Co2 (CO)8 dodecane–trioctylamine–oleic acid mixture after the pressure drop. The ini◦ tial pressure p0 before the drop was 86 bar (170 C). The value to which the pressure was dropped, i.e. the decomposition pressure p1 , affected the rate of decomposition: p1 = 1.3 bar (solid line), p1 = 2.3 bar (dots), p1 = 3.2 bar (dash), p1 = 4.5 bar (dash-dot-dot) and p1 = 5.5 bar (long dash). The horizontal curve (dash-dot) is a blank measurement in absence of Co2 (CO)8 at p1 = 1 bar. (b) Calculated gas release transients (Eq. (3)) for kinetic growth following instantaneous nucleation k = 6 × 10−5 cm4 mol−1 s−1 and particle radii as obtained from TEM analysis of p1 = 1.3 bar (solid line), p1 = 2.3 bar (dots), p1 = 3.2 bar (dash), p1 = 4.5 bar (dash-dot-dot) and p1 = 5.5 bar (long dash).
concentration is obtained from the mass balance:
c(t) = c
0
1−
R(t) 3 Rfinal
(2)
1−
R(t) 3 Rfinal
G C
A ∝ c exp −
and consequently for the particle radius dR = kc 0 dt
Surprisingly few studies that quantitatively link experimentally obtained nanoparticle size to nucleation and growth models exist in the literature. Privman et al. have in a series of papers treated burst nucleation followed by aggregational growth of nanosize precursors [17] and recently by diffusional growth [18] following the LaMer model [1,19]. LaMer and Dinegar proposed that, from a strong initial supersaturation, a rapid nucleation burst of particles would initially occur, followed by the adsorption of diffusing atomic matter onto the nucleated particles [20]. While these models can predict several experimentally observed features, quantitative comparison to experiments is still very scarce due to the limited amount of available data. Here we take a simplified approach using the classical nucleation model to analyze the relation between particle size and decomposition pressure. Just after the pressure drop a supersaturated state occurs, which leads to a rapid nucleation burst. Similarly, to the assumptions in the hot injection method and LaMer model, the nucleation burst is quenched by the decrease in temperature caused by the pressure drop, the presumably endothermic formation of a new phase, the decrease in reactant concentration and the rise in pressure due to released CO. All these factors contribute to an instantaneous nucleation burst. This is also supported by the experimental gas release transients. Thus, we can assume that nucleation takes place in a defined short period of time after the pressure drop. In this approach it is assumed that, without further consideration of the growth mechanism, the number density of nuclei is reflected in the particle size obtained, i.e. the aggregation or dissolution of nucleated particles is not considered. While aggregation could not be observed in the gas release transients, it is difficult to rule out aggregation during the initial stages. Dissolution is considered to be irrelevant since growth occurs at a high level of supersaturation. In addition, Ostwald ripening has not been observed for magnetic alloy particles despite long-term heating [21]. If the formation of a critical nucleus is necessary for the phase growth to occur, the rate of nucleation may be estimated by the frequency with which new growth centers appear. The nucleation rate is thus
(3)
Rfinal is the particle radius at the end of the synthesis obtained from the TEM analysis and c0 equals the amount of Co2 (CO)8 initially present in the reactor. Thus, k is the only unknown parameter in Eq. (3). Eq. (3) was numerically solved using standard Runge–Kutta scheme. Plots of c(t)/c0 using k = 6 × 10−5 cm4 mol−1 s−1 are shown in Fig. 4b. Interestingly, the CO release rates observed experimentally can be well described using the same value for k for all decomposition pressures, despite the crude model. This leads to the following conclusions. The overall reaction rate scales with the area of the particle ensemble, and hence the particles grow primarily by the addition of monomeric species to the particle. The observed rate constant is much smaller than expected for an unhindered diffusion controlled reaction, k DVM /R, showing that the particles grow under kinetic control. VM is the molar volume of the deposited phase. Furthermore, the nucleation burst can be considered short compared to the growth time, i.e. instantaneous nucleation can be assumed. Aggregation of particles seems to be negligible, since it would change the effective surface area, which is not observed.
kT
(4)
where GC is the work for critical nucleus formation and c is the concentration of monomers. A particle of critical radius, rC , has an equal probability of growing and dissolving. According to the classical model the energy of formation is given by the sum of the free energy associated with the formation of bulk and the surface energy, GNet = A GSurf + V GBulk , where A and V are the area and volume of the cluster. For a spherical nucleus the maximum energy and the corresponding critical radius are given by GC =
2 3 16VM 2 3 GBulk
rC = −
2VM GBulk
(5)
(6)
where VM is the molar volume of the growing phase, here assumed to equal that of bulk cobalt. is the effective surface energy of the cluster. LaMer and Pound [22] noted that the classical nucleation theory requires the use of the macroscopic interfacial energies. To be accurate the surface energy depends on the curvature, i.e. on the radius of the particles. It can, however be assumed that for most materials the surface energy does not vary strongly with size. For
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example, Benson and Shuttleworth [23] found that even for a crystallite containing 13 molecules the surface energy was only 15% less than for a planar surface and Walton [24] describes a 35% increase in the surface energy of a KCl crystal of four ions in radius. It should be noted that the nucleation rate depends exponentially on the surface energy, and that small errors can have very significant effects on the nucleation rate [23]. In this study, the value of the surface energy of the presumed surfactant-covered nucleus is not known a priori. GBulk is the thermodynamic supersaturation of the deposition reaction referred to bulk. This quantity changes with Co2 (CO)8 concentration and CO pressure. The dependence of GBulk on the CO pressure provides a very convenient means, comparable to the applied potential in electrochemical experiments, to vary the level of supersaturation. If we assume that equilibrium prevails prior to the pressure drop, and further, that the change in monomer reactant concentration and pressure is negligible during nucleation burst, then the driving force for the deposition reaction is GBulk = 4RT ln
p 1
(7)
p0
where R gas constant, p0 is the pressure before the pressure drop (initial pressure) and p1 is the pressure after the drop (decomposition pressure). The factor 4 follows since 4CO molecules are released from Co2 (CO)8 for every deposited cobalt atom. It is pointed out here that the finite reaction rates observed in this study support the assumption of equilibrium, since pressure is not expected to affect reaction kinetics. Combining (Eqs. (5) and (7)) gives GC =
2 3 VM
2
(8)
3R2 T 2 ln(p1 /p0 )
From Eq. (8) it can be seen that the nucleation rate decreases increasing decomposition pressure, i.e. size increases with increasing pressure (see Fig. 5a). An important experimental observation is the extreme sensitivity of the nucleation rate to supersaturation. A change from 1.3 to 5.5 bar, corresponding to a change in supersaturation energy from 62 to 41 kJ/mol, changes the particle diameter from 6 to 140 nm (see Fig. 5a). If we assume that all the nuclei are formed within a short defined time t after the pressure drop, the nucleation rate should be proportional to the number density of nuclei, which in turn is proportional to the inverse of the cube of the radius of the particles obtained. Thus we can say that 3
ln A ∝ ln
d0 NA VM 2 3 ∝− 3 3 d 3R T 3 (ln(p1 /p0 ))2
(9)
where d is the particle diameter and d0 is a scaling parameter equal to 1 nm. Thus, a plot of ln(d03 /d3 ) vs. 1/[ln(p1 /p0 )]2 should yield a straight line if the classical nucleation model and the assumptions made here apply. A plot based on our experimental results is shown in Fig. 5b. It should be emphasized that we do not know in detail how the length of the nucleation burst varies with pressure, and thus the assumption of instantaneous nucleation may not be accurate.1 However, the experimental points shown in Fig. 5b fit excellently to a straight line, indicating that despite the simplifying assumptions the classical nucleation model seems to qualitatively predict the nucleation process very well. While the TEM pictures show multicrystalline particles that may have resulted from aggregation of smaller subunits, the good agreement of the experimental
1 The length of the nucleation burst can also be estimated from Fig. 2, for example, by assuming that the significant part of the nuclei has been formed when 25% of the CO has been released. This has, however, only a minor effect on the slope in Fig. 5b, yielding a surface tension of 650 mN/m and critical sizes between 1.0 and 3.7 atoms.
Fig. 5. (a) The average diameter of trioctylamine/oleic acid stabilized cobalt nanoparticles calculated from TEM images as a function of the decomposition pressure at which the particles were synthesized. (b) Dependence of the particle nucleation rate on the supersaturation (p1 /p0 ).
data with both the calculated gas release transients and the classical nucleation model suggests a particle number density conserving mechanism, such as growth through adsorption of diffusing atomic matter. The surface energy of the cobalt nanoparticles can be obtained from the slope in Fig. 5b and equals to 603 mN/m. This value seems physically plausible, considering that the surface energy of the metal core is significantly lowered by the adsorbed surfactants and carbon monoxide, although it is difficult to verify. If we calculate the critical size of the nuclei using this value for the surface energy the critical size is 0.8 atoms (rc = 1.29 Å) at 1 bar and increases to 2.9 atoms (rc = 1.97 Å) at 5.5 bar, see Table 1. These sizes are too small for the macroscopic classical nucleation model to be physically realistic, however, our results agree with previous nucleation studies in which the critical nucleus size obtained with both classical and atomistic models indicate that a small or very small critical nucleus is formed [25]. The plot in Fig. 5b is analogous to the ln A vs. 1/2 plot commonly shown in electrochemical nucleation studies, in which the overpotential corresponds to RT ln(p1 /p0 ) in Eq. (9). The applicability of this type of nucleation models has been discussed in detail in electrochemical context [25–28], where similar critical sizes of less than a few atoms have frequently been found. These results were explained by the poor approximations involved in the classical nucleation theory for the complex sequence of reactions leading to the formation of a critical nucleus [27] and by the use of macroscopic concepts having no physical meaning for very small clusters [26–28]. Comparison of these results with ours highlights the fact
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that even though nucleation in nanoparticle synthesis may quantitatively be described by the classical nucleation theory, this theory cannot give physical explanations to the phenomena occuring during the nucleation burst. 4. Conclusion In this paper we have presented a novel method for the synthesis of cobalt nanoparticles. In our pressure drop-induced decomposition method the supersaturation during the thermal decomposition of Co2 (CO)8 is directly controlled via the carbon monoxide pressure. The supersaturation affects the nucleation rate, and hence the number density of the particles formed, which is inversely proportional to the final size of the particles obtained. When the pressure before the decomposition was 86 bar (at 170 ◦ C) the particle diameter could be changed between 6 and 140 nm by changing the final decomposition pressure between 1.3 and 5.5 bar. The growth rates of the particles were analyzed by correlating the CO released in the synthesis to a model based on kinetically controlled growth following instantaneous nucleation. The particle size dependence on the supersaturation was analyzed with the classical nucleation model and a qualitative agreement was found. However, the calculated critical sizes between 1 and 3 atoms indicate that the macroscopic assumptions of classical nucleation model are not adequate for explaining the phenomena related to nucleation in this type of nanoparticle synthesis. Acknowledgements We thank the Academy of Finland, Tekes, OMG, Outotec and Magnasense for financial support.
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