KINETICS OF COLLOIDAL CHEMICAL SYNTHESIS OF
6.5 KINETICS OF THE HEAT-UP METHOD
are exactly the conditions required for size focusing. As a result, the focusing effect takes place and the value of sr(r) decreases with increasing mean size of the nanocrys-tals. To summarize, in the hot injection process, the high initial supersaturation level induces both burst nucleation and subsequent size focusing with the consumption of the monomers.
1-octadecene are frequently used as solvents. However, there is a clear difference between these two synthetic procedures. In the heat-up method, there is no operation that abruptly induces high supersaturation. The size distribution control mechanism of this method relies mainly on the reaction kinetics of the precursors and the heat procedure.
The precursors used for the iron oxide nanocrystal synthesis via the heat-up method are various iron carboxylate complexes, including the most widely used iron-oleate complex. Generally, when heated, metal carboxylate complexes thermally decompose at temperatures near 3008C or higher to produce metal oxide nanocrystals along with some byproducts, such as CO, CO2, H2, water, ketones, esters, and various hydro-carbons. It is thought that the decomposition reaction proceeds via the formation of thermal free radicals from metal carboxylate (26, 27):
M OOCR ! M†þ RCOO† (6:26)
M OOCR ! MO†þ RC†O (6:27)
In the synthesis of the nanocrystals, a homogeneous iron-oleate solution prepared at room temperature is heated to 3208C, which is the thermal decomposition temperature of iron-oleate complex, and held at that temperature (24). As shown in Figure 6.13, the curve for the reaction extent of the thermal decomposition of iron-oleate complex in the solution shows a sigmoidal shape, which is typical of autocatalytic reactions.
Interestingly, there is a time lag between the onset of the reaction extent curve and the initiation of the nanocrystal formation. As shown in the right of the figure, when the solution temperature just reaches 3208C, there is a trace amount of nanocrys-tals in the solution while about half of the iron-oleate complex has already been decomposed. This implies that iron oxide crystal is not a direct product of the thermal decomposition of iron-oleate complex. Rather, when iron-oleate complex is thermally
Figure 6.13 The temporal change of the solution temperature and the reaction extent of the thermal decomposition (left). The time when solution temperature just reached 3208C is set as zero (t¼ 0) and indicated by a vertical dotted line. The TEM images of the nanocrystals in the solution at different times of aging at 3208C are shown (right). All scale bars are 20 nm.
CHEMICAL SYNTHESIS OF MONODISPERSE SPHERICAL NANOCRYSTALS 146
decomposed in the solution, it seems to be converted into more labile species, suppo-sedly, polyiron oxo clusters, that can precipitate as iron oxide. In other words, the intermediate species produced by the decomposition of iron-oleate complex seems to act as the monomer for the iron oxide precipitation reaction (28).
As shown in Figure 6.13, the nanocrystals initially generated grow rapidly and become uniform in size within a few minutes. Further aging at 3208C induces a slow ripening process. During the heat process, the reduction of Fe3þions to Fe2þions occurs by in situ generated H2. As a result, the iron oxide nanocrystals that are produced are generally composed of g-Fe2O3 and Fe3O4. When the reaction tem-perature is higher than 3808C, extensive reduction occurs to produce nearly pure Fe nanocrystals (24, 29). The size of the nanocrystals can be controlled by varying the reaction conditions such as the temperature, aging time, surfactant, precursor con-centration, and the precursor to surfactant ratio. In general, it is very hard to obtain monodisperse iron oxide nanocrystals smaller than 5 nm using the heat-up method, whereas the hot injection method can produce nanocrystals as small as 1 to 2 nm.
The most attractive characteristics of the heat-up method are its simplicity and reliability. The synthetic procedure can be easily scaled up to yield nanocrystals in quantities as high as several tens of grams (24). In the following section, we will dis-cuss how this very simple heat-up method can produce monodisperse nanocrystals.
6.5.2 Size Distribution Control
The time evolutions of both the number concentration and the size distribution of the iron oxide nanocrystals are shown in Figure 6.14. Interestingly, although the cedures used to initiate the precipitation reaction of the heat-up and hot injection pro-cesses are very much different, the precipitation reactions themselves proceed in a similar way once they are started. Comparing Figure 6.11 and Figure 6.14, it can be seen that the nucleation and growth process of the iron oxide nanocrystals via the heat-up method is very similar to that observed in the hot injection process in that there is a sudden increase in the number concentration of the nanocrystals and a rapid narrowing of the size distribution accompanied by a high growth rate. In other words, burst nucleation and size focusing also take place in the heat-up process, as in the hot injection process. Considering this similarity in the nanocrystal formation kinetics in these two seemingly different synthetic processes, a high supersaturation level is critical for the nucleation and growth process to occur in the heat-up process.
In the hot injection process, the synthetic reaction is initiated intentionally in the high supersaturation condition. On the other hand, in the heat-up process for the syn-thesis of iron oxide nanocrystals, the actual monomer is not iron-oleate complex but the intermediate species produced by the thermal decomposition of iron-oleate complex, as mentioned above. As a result, in the heat-up process, the solution is not supersaturated at the start and the high supersaturation is induced in a manner different from the hot injection process.
The induction of the high supersaturation and the initiation of burst nucleation are explained by the theory of homogeneous nucleation. As discussed in Section 6.3.1, the interfacial free energy acts as an energy barrier for the nucleation reaction. Because the
6.5 KINETICS OF THE HEAT-UP METHOD 147
surface to volume ratio of a nucleus is very high, the energy barrier is high enough to prevent the nucleation reaction even at considerably high supersaturation levels. As a result, as the temperature increases, the monomers (the intermediate species) generated from the thermal decomposition of iron-oleate complex accumulate in the solution until the supersaturation is high enough to overcome the energy barrier. The nucleation process is initiated suddenly during the heat procedure as if a switch is turned on.
However, as in the case of the hot injection process, the monomer consumption of the nuclei lowers the supersaturation level and the nucleation is terminated soon.
We performed a numerical simulation to investigate the size distribution control mechanism in the heat-up process (28). As shown in the left-hand plots of Figure 6.15, the simulation results matched very well with the experimental results shown in Figure 6.14. In the right-hand plots of Figure 6.15, the formation process of the nanocrystals can be divided into three periods. In the first period, only the accumulation of the monomers in the solution takes place and the nucleation process is suppressed by the energy barrier for the nucleation reaction. In the second period, the nucleation process is initiated suddenly. The combination of the rapid nucleation and growth of the nanocrystals leads to the increase of the relative standard deviation of the size distribution of the nanoparticles in this period. In the third period, the nucleation process is terminated due to the decrease in the supersaturation level and only the growth process proceeds. In this period, the conditions required for size focus-ing, namely no additional nucleation and high supersaturation, are both satisfied and fast narrowing of the size distribution occurs.
Notably, the characteristics of the nucleation and growth periods in the heat-up process are the same as those in the hot injection process (Figs. 6.12 and 6.15). In both cases, burst nucleation and size focusing are kinetically driven by the high super-saturation level at the start of the nucleation period. With respect to the size distribution Figure 6.14 The temporal change of the number concentration of iron oxide nanocrystals (left). The time evolution of their mean size and the relative standard deviation are shown together (right). The time is set as zero when solution temperature just reached 3208C, just the same as in Figure 6.13.
CHEMICAL SYNTHESIS OF MONODISPERSE SPHERICAL NANOCRYSTALS 148
control, the essential difference between the two methods is the way in which the high supersaturation condition is achieved before the initiation of the precipitation process.
In the hot injection method, it is accomplished by an external operation, namely, the rapid injection of the reactive precursors. In the heat-up method, the accumulation of the intermediate species caused by the thermal decomposition of iron-oleate complex induces the high supersaturation level.
Figure 6.15 The computer simulation results of the heat-up process in Figure 6.14 (left). The temporal changes of various parameters near t¼ 0 are shown in the right plots. The symbols and notations are the same as those in Figure 6.12 except for the shaded area with the vertical stripes, which indicates the accumulation period.
Figure 6.16 The LaMer diagram. Scis the critical supersaturation, the minimum supersatura-tion level for the homogeneous nucleasupersatura-tion.
6.5 KINETICS OF THE HEAT-UP METHOD 149
It is very interesting that both the heat-up and hot injection methods can be well fitted to the LaMer model, a classical theory for the formation of uniform particles (2, 3). The LaMer diagram shows schematically how the rapid nucleation and the separation of nucleation and growth are achieved under the condition of continuous monomer supply (Fig. 6.16). In the diagram, the whole particle formation process is divided into three stages; the prenucleation stage (stage I), the nucleation stage (stage II), and the growth stage (stage III). These three stages coincide with the accumu-lation of the monomers in the first period, the burst nucleation in the second period, and the size focusing in the third period, respectively, in the current heat-up process, as depicted in Figure 6.15. Schematically, the hot injection process can be regarded as a special case of the LaMer model in which stage I is omitted. Consequently, the heat-up and hot injection processes share stages II and III in the LaMer diagram.
6.6 SUMMARY
In this chapter, we described the basic concepts of the control of the size distribution and the theory of the nucleation and growth reactions of two representative synthetic methods for monodisperse nanocrystals, the hot injection and heat-up methods.
Mechanistic studies reveal that the size distribution control processes of these two methods are virtually the same, even though the synthetic procedures are quite differ-ent. The size distribution control mechanisms of these two synthetic methods are summarized schematically in Figure 6.17. Given that the nucleation and growth models are governed by Equations (6.6) and (6.22) to (6.25), the two different monomer supply modes induce very similar size distribution control mechanisms, which comprise burst nucleation followed by a size focusing growth process.
Figure 6.17 Schematic of the size distribution control mechanism of the hot injection and heat-up methods. In the left boxes, the monomer supply modes are shown as the plots of supersaturation vs. time. In the right boxes, the resulting time evolutions of the nucleation rate, the mean size, and the relative standard deviation are shown. The injection time and the start of the heat procedure are set as t¼ 0 in the hot injection and the heat-up processes, respectively.
CHEMICAL SYNTHESIS OF MONODISPERSE SPHERICAL NANOCRYSTALS 150
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PROBLEMS
1. Using the graphical method depicted in Figure 6.4, verify that the steeper the graph, the faster the size focusing process occurs.
PROBLEMS 151
2. Assuming Cband Csare constants, from Equation (6.11) derive that;
d(sr2)
dt ¼ 2VmD(Cb Cs) 1r 1 r
" #
where
r ¼ 1 N
XN
i¼1
ri
and
1 r
¼1 N
XN
i¼1
1 ri
N is the number of particles in the system. According to the arithmetic-geometric-harmonic mean inequalities, (1=r) is always greater than 1=r and, thus, the right-hand side of the above equation is negative. This shows that the size distribution is always narrowed when the growth rate is proportional to 1/r and Cband Cs are constants. (Hint: use the relation sr2 ¼ r2 (r)2.)
3. Using the relations dG/dn ¼ Dm and dG ¼ gdA, derive Equation (6.17). (Hint: for a spherical particle, dA¼ 8prdr.)
4. What are the roles of the surfactants in the colloidal chemical synthesis of nanocrystals?
5. What are the two most important requirements (or conditions) for the formation of monodisperse nanocrystals?
6. Referring to the LaMer plot in Figure 6.16, explain what happens in each of the three stages.
ANSWERS
2. From the definition of sr, we have d(sr2)
dt ¼ d dt
1 N
XN
i¼1
ri2 1 N
XN
j¼1
rj
!2
2 4
3 5
¼1 N
XN
i¼1
2ri
dri
dt 2 N2
XN
j¼1
rj
XN
k¼1
drk
dt
CHEMICAL SYNTHESIS OF MONODISPERSE SPHERICAL NANOCRYSTALS 152
Inserting Equation (6.11), we can get d(sr2)
dt ¼VmD
N (Cb Cs)XN
i¼1
2ri1 ri
2VmD
N2 (Cb Cs)XN
j¼1
rjXN
k¼1
1 rk
Rearranging leads to d(sr2)
dt ¼ 2VmD(Cb Cs) 11 N
XN
j¼1
rj 1 N
XN
k¼1
1 rk
" #
By the definition of r¯ and (1=r), this equation can be rewritten as the form given in the problem.
3. From the definition, we know that
dG¼ Dm dn ¼ g dA For a spherical particle, the following relation is valid.
dn¼4pr2 Vm dr Combining the equations presented so far, we have
Dm dn¼ Dm4pr2 Vm
dr and
Dm dn¼ 8prg dr By equating those two equations, we get the result.
4. (1) To prevent the aggregation of the nanocrystals; (2) control of the size and shape of the nanocrystals; (3) to provide their solubility in a wide range of solvents; (4) exchanged with another coating of organic molecules having different functional groups or polarity.
5. (1) Burst nucleation: inhibition of additional nucleation during growth; complete separation of nucleation and growth.
(2) Diffusion-controlled growth: size focusing works.
6. The three stages coincide with the accumulation of the monomers in the first period, the burst nucleation in the second period, and the size focusing growth in the third period, respectively.
ANSWERS 153