3262
I n d . Eng. Chem. Res. 1994,33,3262-3266
Mechanism of Formation of CdS and ZnS Ultrafine Particles in Reverse Micelles Takayuki Hirai,' Hiroshi Sato, and Isao Komasawa Department of Chemical Engineering, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka 560, Japan
The mechanism of formation of cadmium sulfide and zinc sulfide ultrafine particles in reverse micelles has been studied, using sodium bis(2-ethylhexyl) sulfosuccinate (AOTYisooctane as a reverse micellar solution. The particle formation process was followed by the change in Wvisible absorption spectra. The effects of reactant concentration and water content on the particle diameter were also investigated. Particle formation by nucleation and growth occurred very rapidly and was complete within 0.02 s, followed by particle coagulation. The particle coagulation rate constant was found to be controlled only by the intermicellar exchange rate, in the initial stage. With increasing particle diameter, the coagulation was dominated by the statistical distribution of particles among the reverse micelles. As the diameter of particle approached t h a t of the water core in reverse micelle, the coagulation became restricted by the micellar size.
Introduction There has been much recent interest both in ultrafine particles and in the procedures required to prepare and stabilize uniform ultrafine particles. Reverse micelles consist of nanometer-sized water cores dispersed in an apolar solvent. Various water-soluble molecules can be solubilized in the water cores. Reverse micelles can exchange their contents in the water cores via both fusion and redispersion processes. The rate of reaction in reverse micellar system competes with that of intermicellar exchange process. For the fast reaction, the reaction proceeds via intermicellar exchange and the reaction rate is controlled by the exchange rate (Fletcher et al., 1987). On the other hand, the rate of the reaction slower than the exchange is not affected by the exchange rate and depends on the statistical distribution of reactants among the reverse micelles (Oldfield, 1991; Mufioz et al., 1991). Since this applies to the process of formation of ultrafine particles in reverse micelles, studies of the rate of formation of differing particles for both fast and slow reaction cases are necessary to understand the mechanism of the process. In a previous work, the mechanism of formation of titanium dioxide particles by hydrolysis of titanium tetrabutoxide (TTB) in AOT reverse micelles was studied, as a case of slow reaction (Hirai et al., 1993). The W-visible absorption spectra of the reverse micellar solution showed that the 'M'B was converted slowly into the particles via hydrolysis and particle formation processes and that the particle formation process was controlled by the statistical distribution of hydrolyzed TTB molecules among the reverse micelles. Studies of particle formation processes by chemical reactions faster than the exchange process have been reported. Towey et al. (1990) proposed the model for these processes by replacing the diffusion controlled coagulation rate constant of the Smoluchowski rapid coagulation model (1916) by the intermicellar exchange rate constant. The particle formation processes of cadmium sulfide particles (Towey et al., 1990) and silver particles (Petit et al., 1993) have been analyzed by this model. In the case of CdS, a W absorbance change at 280 nm in the initial period of up to 80-500 ms was explained by this model. The spectrum, however, continued to change after 500 ms, and a study for a longer period is thus needed to obtain a complete picture
of the particle formation process. Another question is how the particle material affects the particle coagulation process. While the coagulation rate is expected to be independent of the material, this has not been confirmed experimentally. The mechanism of formation of cadmium sulfide and zinc sulfide ultrafine semiconductorparticles in reverse micelles by fast reaction has now been studied. In this, the particle formation process from 10 ms to 60 min was followed by the change of W-visible absorption spectra, using the stopped-flowtechnique. This showed that the coagulation slowed down and became dependent on the material of particles with increasing particle diameter. A model for the reduced rate of coagulation will be proposed.
Experimental Section Sodium bis(2-ethylhexyl) sulfosuccinate (AOT), sodium sulfide, cadmium nitrate, and zinc nitrate were supplied by Wako Pure Chemical Industries, Ltd., and isooctane (2,2,4-trimethylpentane) was supplied by Ishizu Seiyaku, Ltd. All reagents were used without further purification. Distilled water was filtered with a 0.2-pm membrane filter and dissolved oxygen was purged by bubbling argon, prior to use. The reverse micellar solution was prepared by dissolving AOT in isooctane, followed by filtration using a membrane filter. The concentration of surfactant, [AOTI, was 0.1 M (M = mol/L). The water content (water t o surfactant molar ratio, W O= [HzOI/[AOTI) was varied in the range of 3- 10. Aqueous solutions containing cadmium nitrate, zinc nitrate, or sodium sulfide were prepared daily. The reverse micellar solutions containing the reactants were prepared by injecting required amounts of aqueous solution and were used within a few minutes. The reaction was initiated by rapid mixing of the reverse micellar solution (1.2 mL) containing cadmium nitrate or zinc nitrate and an equal volume of a reverse micellar solution containing sodium sulfide at 25 "C, using the mixer part of a stopped-flow equipment. The water content and surfactant concentration of both solutions were identical. For the measurement of the W-visible absorption spectra, for the period up to 1s, a stopped-flow spectrophotometer (Otsuka Electronics RA-401)and a diode array detector (Otsuka Electronics
0888-5885/94/2633-3262$04.50/00 1994 American Chemical Society
Ind. Eng. Chem. Res., Vol. 33,No. 12, 1994 3263 Table 1. Reverse Micellar Systems Used for Preparation of Particles ([AOT] = 0.1 M)
WO 3 6 10
d, (nm)
3.62 5.45 7.07
a,
0.154 0.165 0.175
N,/1OZo(L-l) 35.5 5.58 2.59
CJ10-4 (M) 58.9 9.27 4.31
0.2
0.1 M AOT/isooctan
h
I
Y
a, 0 C
RA-415)were used. For the measurement for the period from 1 s to 1min, the reverse micellar solutions were injected into a quartz flow cell (0.4 mL) by using the mixer and the resulting spectrum change following injection was recorded on a Hewlett-Packard HP8452A diode array spectrophotometer. When the reaction time was greater than 10 min, the mixed reverse micellar solution was injected into a beaker-type glass reactor (10 mL) and was kept in the dark with mild stirring (300 min-') generated by a magnetic stirrer. The solution was transferred to a cell to measure the Wvisible spectra when necessary. The size distribution of the reverse micelles was measured via a dynamic light scattering spectrophotometer (DLS, Otsuka Electronics DLS-700Ar). The number of micelles, N,, was calculated by the average diameter (d,) and the standard deviation (0,) as described previously (Kuboi et al., 1990). The results for the present micellar systems are shown in Table 1. The size of AOT reverse micelles has been reported to be independent of salt concentration (Aveyard et al., 1986) and of the change in countercation of AOT (Dunn and Robinson, 1990). Therefore, the size of micelles seems not to vary as a function of reactant concentration in the present study.
Results and Discussion Change in Absorption Spectrum of Solution during Formation of Particles. The formation of metal sulfide particles from metal ion and sulfide ion involves a chemical reaction stage, a nucleation stage, and a particle growth stage. The first stage is the reaction between metal ion and sulfide ion, resulting the formation of a metal sulfide molecule. The overall reactions are described by Cd(NO,), Zn(NO,),
+ Na,S - CdS + 2NaN03 + Na,S - ZnS + 2NaN0,
(1) (2)
Nuclei are formed in the nucleation stage from the oversaturated solute molecules. In the growth stage, larger particles are formed by particle growth, particle coagulation, and Ostwald ripening. Particle growth occurs by the addition of the solute molecules or ions to the particles. Particle coagulation is the result of the combination of the particles, making contact as a result of Brownian motion. Ostwald ripening occurs via the growth of larger particles accompanied by the dissolution of smaller particles. Semiconductor particles absorb the W-visible light having greater energy than the band gap. With a reduction in particle size, the band gap of the semiconductor particles becomes larger and there is a concomitant blue shift in the absorption spectrum (Brus, 1984). This size-dependent optical property provides a very convenient and useful way to monitor the growth of these semiconductorparticles. Figure 1shows the Wvisible absorption spectra obtained during the reaction M Cd(N0312or Zn(NO3)z and 1 x between 1 x M Na2S in the W O= 6 reverse micellar system. Since Cd(N03)2,Zn(NO3)2,and Na2S have very weak absorption characteristics, the observed absorption can be
m
e
s: n
0.1
a
350 400 450 250 300 Wavelength (nm) Wavelength (nm) Figure 1. Absorption spectra taken from 0.02 to 3600 s after mixing of reactants. (a) CdS; (b) ZnS.
attributed to the formed CdS or ZnS semiconductor particles. The absorption of ZnS particles was observed a t a wavelength shorter than that for CdS. A continuous red shift in the absorption threshold was observed in both solutions. This indicates the decrease in band gap caused by the continuous increase in particle diameter. The magnitude of the absorption indicates the quantity of formed particles. After a time period of 0.02 s, the absorbance at the absorption peak is almost constant. This indicates that the conversion of the ions to the particles via both nucleation and particle growth is complete within this short period. This is caused by the fast formation reaction (eq 1)and by the low solubility of CdS (Towey et al., 1990). The increase in particle diameter after a time period of 0.02 s, without consumption of ions, can occur by coagulation or by Ostwald ripening. Ostwald ripening, however, may be considered to proceed over a much longer time scale in this case, since CdS has a very low solubility. The observed increase in particle diameter following the time of 0.02 s can, therefore, be attributed to a result of coagulation. In the case of ZnS, similar results were also observed. Size of Formed Particles. The size of the formed particles was estimated as follows. Since both CdS and ZnS are the direct gap semiconductors, the absorption data were fitted to the following equation to determine the direct band gap (Wang et al., 1987). O ~ = V A(hv
- E,)"2
(3)
where (T is the molar absorption coefficient, A is the proportional factor, hv is the photon energy, and E, is the direct band gap. The diameter was estimated by the band gap using Brus's equation (Brus, 1984)
where Eg,b"& is the bulk band gap, h is the Planck constant, d, is the particle diameter, me is the effective mass of an electron, mh is the effective mass of a hole, e is the charge of an electron, and E is the dielectric constant of the semiconductor. The electric parameters for CdS and ZnS are shown in Table 2. The estimated diameters of the particles a t various reaction times are shown in Figure 2. Particle diameter increased with time and with increase in reactant concentration. The diameter of CdS particles was greater than that of ZnS at the same conditions. To
3264 Ind. Eng. Chem. Res., Vol. 33,No. 12,1994 Table 2. Parameters for CdS and ZnS Eg,buk(eV)
m$mo
2.5 3.7
0.19 0.25
CdS ZnS
4r
I
-
mdmo 0.8 0.59 I
1
E/EQ
d (g/cm3)
5.7 5.2
4.58 4.08
I
I
0.1M AOTIisooctane Wo=6
n
A v
3-
~ x ~ o - ~ M
A
I
ma
-
Key [CdS]([ZnS]t 0 5 ~ 1 0M -~ ~ x ~ o - ~ M A 2x10-4M
A
r3
2
I"
4
1
I
I
I
0.01
0.1
1
10
I
I
I
I
~
2.5
A 0
I
,
I
3
I
I
J
~
J
,
3.5
dp (nm) Figure 4. Second-order coagulation rate constant as a function of particle diameter. Open symbols, CdS; Closed symbols, ZnS.
I
100
l
108
0
f
A
'
'
-
I
~
'
~
[CdS]((ZnS]) = ~ x I O - ~ M n
-
A
A
-
Figure 2. Change in particle diameter during preparation of particles. Open symbols, CdS; Closed symbols, ZnS.
-
%A
A
1
A 0
A
10 l ,
2.5
1-
, , , l , , + , l , , ,
3
A
3.5
d, (nm) 1
Figure 5. Effect of water content on second-order coagulation rate constant. Open symbols, CdS; Closed symbols, ZnS.
~" )
I
I
0.01
I
0.1
1
10
100
t (s) Figure 3. Change in particle number during preparation of particles. Open symbols, CdS; Closed symbols, ZnS.
study the mechanism of coagulation, the number of formed particles was calculated from the particle size data by assuming that all the precursor ions converted to particles. In addition, it was assumed that the particle density was independent of the particle size and that the formed particles were spherical and monodispersed. The results are shown in Figure 3. The number of particles was less than that of the micelles (Table 11, decreased with time, and increased with increasing reactant concentration. This shows that the coagulation proceeds via an intermicellar process and that it is therefore necessary to consider the rate for the intermicellar exchange process. Analysis of Particle Coagulation Kinetics by Rapid Coagulation Model. The exchange rate constant is reported to be lo6-los M-' s-l for the AOT/ isooctane reverse micellar system (Fletcher et al., 1987; Lang et al., 1988). Thus, the rearrangement of the micelles in the present system occurs on a sub-millisecond time scale, since the concentration of micelles was in the range of 10-4-10-3 M (Table 1). The colloidal particles coagulate via the collision of particles. In the homogeneous system, when no barrier exists in the collision, the particles coagulate via second-order kinetics and the rate constant is identical to that of the diffusion controlled rate constant (Smoluchowski, 1916). When a barrier exists, the coagulation rate constant is restricted.
If the particle coagulation is rapid in the reverse micellar system and the number of particles is less than that of the micelles, particle coagulation occurs via the fusion of two micelles containing particles. The coagulation, therefore, proceeds via second-order kinetics and the rate constant is identical to the exchange rate constant. This rapid coagulation model has been presented by Towey et al. (1990). They analyzed the absorbance change a t 280 nm in the initial period of up to 80-500 ms using this model and showed that the coagulation rate was controlled by the exchange rate. The intermicellar exchange rate was varied by employing several continuous phase solutions. In this model, the coagulation rate is expected to be independent of the material of the particles. The results in this study were analyzed in terms of second-order kinetics. The particle coagulation rate constant, k,, was calculated by dividing the rate of decrease in the concentration of particles by the square of their concentration and is shown in Figure 4. At the smallest limit of particle diameter, the value of k, converges to a maximum, which may correspond to the intermicellar exchange rate. The converged value was estimated at about 5.6 x lo7 M-l s-l, for the Wo = 6 reverse micelles, which is between two reported values for the exchange rate constant for the AOTIisooctane reverse micelles (Fletcher et al.,1987; Lang et al.,1988). The effect of water content on the coagulation rate is shown in Figure 5, with the coagulation rate constant increasing with increasing water content. The maximum rate constant, which corresponds to the exchange rate constant, also is increased. This is consistent with the exchange rate constants, measured by time-resolved
~
l
~
Ind. Eng. Chem. Res., Vol. 33,No. 12, 1994 3265 intermicellar fluorescence quenching (Verbeeck and De Schryver, 1987; Lang et al., 1988). The coagulation rate constant, however, decreased with increasing the particle diameter greater than 2.4 nm. Moreover, the value of k, of CdS was greater than that of ZnS, for the same diameter. CdS particles coagulate faster than ZnS and accordingly the number of CdS particles was less than that of ZnS, for the same reaction time. The rapid coagulation model of Towey et al. (1990) can be applicable only for the initial part of the coagulation process, that is, for particles smaller than about 2.4 nm. The average diameter of the particles was calculated from the model and assuming an exchange rate constant of 5.6 x lo7 M-l s-l, for the W O= 6 reverse micellar system. The calculation showed that the particle diameter increased up to 2.2 nm in a time of 0.02 s after initiation, for the case of W O= 6, M. This is smaller than [Cd(N0&1= [NazSI= 1 x the observed diameter of 2.6 nm shown in Figure 2. This difference may be caused by the problem in estimating the exchange rate constant and by the effect of dead time in the stopped-flow measurement. The exchange rate constant producing the best correlation with the observed diameter of 2.6 nm a t 0.02 s is given by 9.2 x lo7M-l s-l, which is consistent with the value reported by Lang et al. (1988) but which is greater than that of Fletcher et al. (1987). Model for Reduced Rate of Coagulation Process following Initial Rapid Coagulation. When the particles achieve diameters greater than about 2.4 nm, the coagulation rate then decreases with particle size. Since the rate for the intermicellar exchange is now faster than that for particle coagulation, the particles distribute among the micelles according to an equilibrium distribution, as a result of intermicellar exchange. In this case, coagulation occurs in micelles containing two or more particles. The coagulation rate is considered to be proportional to the number of such pregnant micelles (Nmc). Thus,
where k, is the first-order rate constant for the reduced rate of coagulation process, taking into account the probability of coagulation, and where Npis the number of particles. To determine Nmc,the distribution of the particles among the reverse micelles needed t o be estimated. Water-soluble molecules are considered t o distribute according to a Poisson distribution (Atik and Thomas, 1981). The probability of having i molecules in a micelle is given by
where A is the average number of molecules in a micelle. The distribution of particles, pi, can be calculated using N J N m for A. The value of N m c is calculated by the following equation: I
1
\
The first-order rate constant for the reduced rate of coagulation process, kmc, was calculated by dividing the rate of decrease in the particle number (-dNJdt) by the number of micelles containing two or more particles (Nmc).
0.1M AOT/isooctane [CdS]([ZnS]) = ~ x I O - ~
2.5
3
3.5
d, (nm) Figure 6. Effect of water content on first-order coagulation rate constant. Open symbols, CdS; Closed symbols, ZnS.
The results are shown in Figure 6. In contrast to the second-order rate constant for the rapid coagulation model (k,) (Figure 51, the first-order coagulation rate constant (kmc)for ZnS particles up t o 3 nm is independent of the water content, namely, the size of micelles. This indicates that the kinetics of reduced rate of coagulation can be expressed by eq 5. However, k,, decreased with increasing particle diameter. Assuming the surface potential of the particles t o be independent of the particle diameter, the potential barrier between two particles will increase with increasing particle diameter (McCartney and Levine, 1969) and the coagulation rate will decrease. In the case of CdS particles, however, kmc depends on the water content as shown in Figure 6. The average diameter of CdS is larger than that of ZnS (Figure 2) and approaches that of the micelles (Table 1). This indicates an effect of the size of the micelles on the coagulation rate. When the diameter of the particles approaches that of the micelles, two effects on the particle coagulation may appear. Firstly, a difficulty arises in the containment of two particles in any given micelle. This causes the decrease in the number of micelles containing two or more particles. Secondly, when the diameter of particle reaches that of the water core in the micelle, the particle is surrounded by AOT molecules. Surfactant molecules a t the surface of particle may then act as a protective agent. Both effects interfere with the coagulation of the particles. Since the diameter of CdS particles approaches that of the micelles, the first-order coagulation rate constant for CdS decreases with decreasing micellar size, namely, decreasing water content. These are possible interpretations to the present results for the different behavior of CdS and ZnS particles. The proposed first-order particle coagulation model successfully explains the coagulation kinetics for the size range from 2.4 nm to the size of micelles.
Conclusion The mechanism of formation of cadmium sulfide and zinc sulfide ultrafine particles in AOThsooctane reverse micelles by the reaction between Cd(N03)~ or Zn(NO3)z and Na2S was studied. The particle formation process was followed by W-visible absorption spectra. The following results were obtained: 1. The nucleation and the particle growth occurred very rapidly and complete within 0.02 s. A red shift in the spectrum was observed, expressing an increase in the particle diameter. This was caused by particle coagulation.
3266 Ind. Eng. Chem. Res., Vol. 33,No.12,1994
2. An increase in reactant concentration or water content was found to increase the particle diameter. The diameter for ZnS particles was smaller than that for CdS. 3. The coagulation rate was estimated by the rate of decrease in the number of particles. In the early stage for times of up to 0.02 s, particle coagulation was controlled only by the intermicellar exchange rate. When the particles achieved diameters greater than about 2.4 nm, the coagulation rate decreased with particle size and was controlled by the distribution of the particles among the micelles. When the particles grew to be as large as the micelles, the coagulation became restricted also by the micellar size. Acknowledgment "he authors gratefully acknowledge financial support from a Grant-in-Aid for Scientific Research of the Ministry of Education, Science and Culture, Japan (No. 04453124, 19921, and from a Grant-in-Aid of Izumi Science and Technology Foundation. Nomenclature C, = molar concentration of reverse micelles, M (mol&) d = density of particles, g/cm3 d, = average outer diameter of reverse micelles, nm d, = average diameter of particles, nm e = charge of electron, C E, = band gap of semiconductor particles, eV Eg,buk= band gap of bulk semiconductor, eV 12, = second-order coagulation rate constant for rapid coagulation model of particles, M-l s-l k,, = first-order coagulation rate constant for proposed coagulation model, s-l mo = free electron mass, kg me = effective mass of electron, kg mh = effective mass of hole, kg N , = number of reverse micelles, L-l N,, = number of reverse micelles containing two or more particles, L-' N p = number of formed particles, L-l pi = probability to have i molecules in a reverse micelle W O= [H2OY[AOT] = water to surfactant molar ratio (water content) E = dielectric constant of semiconductor, C2 J-' m-l EO = dielectric constant of vacuum, C2 J-l m-l II = average number of molecules in a reverse micelle Y = frequency of light, Hz u = molar absorption coefficient, cm-l M-l urn = standard deviation of size distribution of reverse micelles [ 3 = molar concentration of species in the brackets, M (mol/
Aveyard, R.; Binks, B. P.; Clark, S.; Mead, J. Interfacial Tension Minima in Oil-Water-Surfactant Systems. J.Chem. SOC.,Faraday Trans. 1 1986,82(11,125-142. Brus, L. E. Electron-electron and electron-hole interactions in small semiconductor crystallites: The size dependence of the lowest excited electronic state. J. Chem. Phys. 1984,80 (91, 4403-4409. DUM, C. M.; Robinson, B. H. Photon-correlation spectroscopy applied to the size characterization of water-in-oil microemulsion systems stabilized by Aerosol-OT effect of change in counterion. Spectrochim. Acta 1990,46A (6),1017-1025. Fletcher, P. D. I.; Howe, A. M.; Robinson, B. H. The Kinetics of Solubilisate Exchange between Water Droplets of a Water-inoil Microemulsion. J. Chem. SOC.,Faraday Trans. 1 1987,83 (4),985-1006. Hirai, T.; Sato, H.; Komasawa, I. Mechanism of Formation of Titanium Dioxide Ultrafine Particles in Reverse Micelles by Hydrolysis of Titanium Tetrabutoxide. Ind. Eng. Chem. Res. 1993,32(12),3014-3019. Kuboi, R.; Mori, Y.; Komasawa, I. Reverse Micelle Size Distribution and Mechanism of Protein Solubilization into Reverse Micelles (in Japanese). Kagaku Kogaku Ronbunshu 1990,16(4),763771. Lang, J.;Jada, A.; Malliaris, A. Structure and Dynamics of Waterin-Oil Droplets Stabilized by Sodium Bis(2-ethylhexyl) Sulfosuccinate. J.Phys. Chem. 1988,92(7),1946-1953. McCartney, L. N.; Levine, S. An Improvement Derjaguin's Expression at Small Potentials for the Double Layer Interaction Energy of T w o Spherical Colloidal Particles. J. Colloid Interface Sci. 1969,30(3),345-354. Muiioz, E.; mmez-Herrera, C.; Graciani, M. M.; MoyB, M. L.; Stinchez, F. Kinetics of the Oxidation of Iodide by Persulphate in AOT-Oil-Water Microemulsions. J. Chem. SOC.,Faraday Trans. 1991,87(l),129-132. Oldfield, C. Exchange Concept in Water-in-oil Microemulsions: Consequences for 'Slow' Chemical Reactions. J. Chem. SOC., Faraday Trans. 1991,87(16),2607-2612. Petit, C.; Lixon, P.; Pileni M.-P. In Situ Synthesis of Silver Nanocluster in AOT Reverse Micelles. J. Phys. Chem. 1993,97 (491,12974-12983. Smoluchowski, M. Three Lectures on Diffusion, Brownian Movement and Coagulation of Colloidal Particles (in German). Phys. 2. 1916,17 (231,585-599. Towey, T. F.; Khan-Lodhi, A.; Robinson, B. H. Kinetics and Mechanism of Formation of Quantum-sized Cadmium Sulphide Particles in Water-Aerosol-OT-Oil Microemulsions. J. Chem. Soc., Faraday Trans. 1990,86(221, 3757-3762. Verbeeck, A.; De Schryver, F. C.; Fluorescence Quenching in Inverse Micellar Systems: Possibilities and Limitations. Langmuir 1987,3(4),494-500. Wang, Y.; Suna, A.; Mahler, W.; Kasowski, R. PbS in Polymers. From Molecules to Bulk Solids. J. Chem. Phys. 1987,87 (12), 7315-7322.
L)
Received for review March 15, 1994 Accepted August 26, 1994 *
Literature Cited Atik, S. S.; Thomas, J. K. Transport of Photoproduced Ions in Water in Oil Microemulsions: Movement of Ions from One Water Pool to Another. J.Am. Chem. SOC.1981,103(12),35433550.
@
Abstract published in Advance ACS Abstracts, November
1, 1994.
