J. Phys. Chem. C 2008, 112, 1463-1467
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Ripening Effects in ZnS Nanoparticle Growth Michael Tiemann,*,† Frank Marlow,‡ Juha Hartikainen,§ O 2 zlem Weiss,§ and Mika Linde´ n*,§ Institut fu¨r Anorganische und Analytische Chemie, Justus-Liebig-UniVersita¨t, Heinrich-Buff-Ring 58, D-35392 Giessen, Germany, Max-Planck-Institut fu¨r Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mu¨lheim an der Ruhr, Germany, and Institutionen fo¨r Fysikalisk Kemi, Åbo Akademi, Porthansgatan 3-5, FIN-20500 Åbo, Finland ReceiVed: September 26, 2007; In Final Form: October 27, 2007
The growth of ZnS nanoparticles during precipitation from aqueous solution is studied by in situ stoppedflow UV absorption spectroscopy at temperatures between 283 and 323 K. Particle growth is marked by substantial ripening during the first 60 ms. Kinetic data suggest that a ripening mechanism by coalescence (oriented attachment) is predominant over Ostwald ripening, although the latter seems to coexist to a significant degree at early temporal stages, predominantly at low temperatures.
r - r0 ) at1/n
Introduction The kinetics and mechanisms of crystal growth during the early stages of precipitation reactions are currently attracting increasing interest.1,2 On the one hand, computational power today provides efficient means to simulate the earliest instances of particle formation from solution.3-7 On the other hand, modern instrumental techniques now facilitate experimental investigation of crystal growth with high time resolution, e.g., by small-angle X-ray scattering,8,9 X-ray absorption spectroscopy,8 or UV spectroscopy.10,11 In particular, the stopped-flow technique12 has shown to be a versatile means to study fast reactions with time resolutions in the microsecond regime.13-16 II/VI semiconductors, such as ZnS, are suitable systems to study early stages of crystal growth, because their optical signatures are strongly size dependent in the region of a few nanometers or below. Hence, spectroscopic methods provide the opportunity to study nanoparticle sizes in situ. We have recently demonstrated that UV absorption spectroscopy can be combined with the stopped-flow method to monitor both the average particle radius as well as the relative concentration of ZnS particles in the sub-nanometer range. Our experiments afford the investigation of the first 127 ms of precipitation from purely aqueous solution, i.e., without capping ligands or other additives, with a time resolution of ca. 1 ms. We found that particle growth is marked by significant ripening.15,16 “Ripening” is the growth of particles in combination with a decrease in particle concentration, i.e., the number of particles per volume of colloidal suspension goes down while their average size increases. The term “ripening” as such is a purely phenomenological expression, as it does not specify the mechanism behind the observation. More than one explanation is possible: (I) Ostwald Ripening. Small crystals redissolve while larger crystals grow by consumption of the solute species. This mechanism is basically described by the Lifshitz-SlyozovWagner model17,18 * To whom correspondence should be addressed. E-mail:
[email protected] (M.T.);
[email protected] (M.L.). † Justus-Liebig-Universita ¨ t. ‡ Max-Planck-Institut fu ¨ r Kohlenforschung. § Institutionen fo ¨ r Fysikalisk Kemi.
(1)
where a is a material constant and r0 is the mean particle radius at t ) 0; n is expected to have a value between 2 and 4, depending on whether ripening is controlled by surface diffusion at the solid/liquid interface (n ) 2), volume diffusion in the liquid medium (n ) 3), or dissolution kinetics (n ) 4). (II) Coalescence. Two particles collide due to Brownian motion and form a larger crystal. This requires suitable crystallographic orientation of the two coalescing particles. The term “oriented attachment” is frequently used for this general mechanism; the underlying idea is depicted in eq 2. The two particles (A) are not necessarily correctly oriented already at the instant of collision; instead they may first form a complexlike agglomerate (AA) and then align by reorientation, i.e., by rotational movement relative to each other, before they coalesce to form the larger particle (B)
A + A / AA f B
(2)
A short review on contemporary work concerning growth by “oriented attachment” has recently been published by Penn.19 Strong experimental evidence for this mechanism has been obtained from electron microscopic investigations of particle morphology and crystallographic irregularities;20,21 additional information was gained by computer simulation.22 The reorientation of the two particles within the intermediate agglomerate may or may not require activation. Accordingly, two distinct models for coalescence (or oriented attachment) are possible: (IIa) Attachment by Barrierless Coalescence. Ribeiro et al. have recently developed a kinetic model for particle growth by oriented attachment in which they do not assume an activation energy.23 In the following we will refer to this model as “barrierless coalescence”. The authors show that the rate constant k for the entire process may then by approximation be considered independent of the particle size; their model leads to a rather simple prediction for k
k)
RT η
10.1021/jp077729f CCC: $40.75 © 2008 American Chemical Society Published on Web 01/15/2008
(3)
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where R is the universal gas constant, T is the temperature, and η is the liquid-medium viscosity. The temperature dependence of k is essentially given by the viscosity. With the expression of k according to eq 3 the temporal evolution of the average particle size r follows23
r3 - r03 )
k[A]0t
‚r03
(4)
‚r0
(5)
k[A]0t + 1
which can be rearranged to give
r)
(
)
2k[A]0t + 1 k[A]0t + 1
1/3
where r0 and [A]0 are the mean radius and concentration of the particles at the onset of attachment by barrier-less coalescence (t ) 0). (IIb) Attachment by Barrier-Controlled Reorientation. Huang et al. proposed a model in which the rate constant is a function of the activation energy of the reorientation process,20 which we will refer to as “barrier-controlled reorientation”. The authors find a particle growth function
r)
x3 2k′t + 1 ‚r0 k′t + 1
(6)
where k′ is the rate constant. Equations 5 and 6 resemble each other to a high degree. As long as the changes in r remain small, the different exponent (1/3 vs 1) does not play a significant role. The long-time behavior of both functions is the same if the numerical parameters have the ratio 1.238 k[A]0 ) k′. The authors assume that the temperature dependence of k′ is Boltzmann-type. The activation energy EA of the attachment process can then be calculated by the Arrhenius equation
ln k′ ) -
EA + ln x RT
(7)
where x is the pre-exponential factor. It should be kept in mind that the kinetic models mentioned above can only be approximations of a rather complex growth mechanism. In particular, any coalescence mechanism may often be accompanied by other coexisting mechanisms, such as Ostwald ripening. On the other hand, in the early stages of crystal growth the existence of substantial amounts of solute species must not be ruled out in the first place, especially when the solubility of the precipitated species is high. The Ostwald ripening mechanism does not account for such unreacted solute precursor species as it is based on the assumption of an equilibrium between the growing particles and solute ions originating from redissolution of small particles. Finally, the situation during the earliest (subsecond) stages may be distorted due to inhomogeneities immediately after mixing the precursor solutions. Therefore, kinetic studies may fail to deliver unambiguous proof for one particular mechanism but still succeed in elucidating the role of each ripening model to some degree. Here we attempt to investigate if ripening of ZnS nanoparticles at the very early stages of growth occurs by an Ostwald ripening or by a coalescence mechanism. Experimental Section Zinc sulfate monohydrate (99%, Fluka) and sodium sulfide nonahydrate (99%, Sigma) were used as received; water was purified (Millipore Academic A10). UV absorption spectroscopy
Figure 1. (a) A series of spectra recorded during the first 127.4 ms of precipitation of ZnS at 293 K (10 out of 100 spectra shown). The shift of the absorption toward lower energy corresponds to the particle growth. (b) Exemplified deconvolution of a spectrum by least-square fitting of three Gaussian (A-C) and one exponential function;15 the first Gaussian peak (A) corresponds to the first excitonic transition and serves for the calculation of the average particle radius and relative concentration.
was performed on an Applied Photophysics SX.18MV-R Stopped-Flow spectrometer equipped with a PDA.1 photodiode array detector and a UV.1 deuterium light source. Aqueous solutions of ZnSO4 and Na2S (0.5 mmol L-1, 10 µL each) were simultaneously injected into the observation cell (10 mm optical path length) from pressure-driven syringes; both the syringes and the observation cell were at a constant temperature of 293 K. The stopped flow signal triggered the data acquisition with a dead time of approximately 2 ms; the first data used for analysis was at t ) 3.2 ms. Spectra (100) were recorded within 127.4 ms, resulting in an integration time of 1.28 ms (time resolution). All data were referenced against water. It was verified that the measurements were not influenced by deposition of ZnS on the observation cell windows; spectra of pure water showed identical zero absorption before and after the experiment. For data analysis the spectra were subjected to a least-square fit deconvolution procedure, using three fully coupled Gaussian profile functions for the first three absorption bands as well as an exponential function. The energy of the first excitonic band is correlated with the particle radius r on the basis of the effective mass approximation,24 assuming a finite potential model.25 The integral intensity of the band is a relative measure for the particle concentration, assuming that the absorption cross section scales with r3. Details on the data treatment are described in former work.15 Results and Discussion A series of UV absorption spectra recorded during the first 127.4 ms of the precipitation of ZnS from aqueous solution at 293 K is shown in Figure 1a. During this time interval the absorption shifts toward lower energy as a consequence of the growth of ZnS nanoparticles. This kind of size dependence of the UV absorption energy is a well-studied effect of so-called quantum confinement.24-27 A deconvolution analysis of the spectra comprising least-square fits of Gaussian profiles (Figure
Ripening Effects in ZnS Nanoparticle Growth
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Figure 2. Temporal evolution of (a) the average particle radius r (and the energy E0,0 of the first excitonic transition from which r is derived) and (b) the particle concentration c as well as the overall mass of all particles m (T ) 293 K).
Figure 3. Temporal evolution of the average particle radius r at various temperatures (0: 283 K; O: 293 K; 4: 303 K; 3: 313 K; ]: 323 K) and results of least-square fits of eq 6 (attachment by barrier-controlled reorientation, solid line) and eq 1 (Ostwald ripening, dashed line).
1b) delivers a series of absorption bands that correspond to excitonic transitions, as recently shown.15 The band with the lowest energy can serve for the calculation of the average particle radius r by eq 8 where E0,0 is the band’s energy and Eg is the bulk band gap energy (3.6 eV for ZnS). The area a0,0 under the first excitonic band gives the relative particle concentration c by eq 9 and is thus proportional to the overall mass of all precipitated particles according to eq 10. Further details are given in ref 15
r/nm )
x
1.236 - 0.290 (E0,0 - Eg)/eV c∝
a0,0 r3
(8)
(9) (10)
Figure 4. Detail of Figure 3 showing the first 16 ms of the temporal evolution of the average particle radius r at various temperatures on logarithmic time scale.
Figure 2 shows that particle growth, i.e., the increase of the average radius r, is clearly accompanied by a decrease in particle concentration c during the first ca. 60 ms after the onset of precipitation, while the overall mass of all particles is approximately constant (within the experimental error). This finding corresponds to a reaction mechanism that is governed by coalescence (“oriented attachment”) and/or Ostwald ripening, as described above. The temporal evolution of the average ZnS particle radii for various temperatures between 283 and 323 K is shown in Figure 3; in all cases the particle concentration (not shown) decreased in a similar way as shown for 293 K in Figure 2. To study the impact of the temperature on the kinetics of the precipitation reaction it must be taken into account that the excitonic energy itself is slightly temperature dependent. Experimental data have revealed that bulk ZnS films show an approximately linear shift toward lower energy by ca. 5 × 10-4 eV K-1 when the temperature is raised within this range.28 It is reasonable to assume a similar effect for ZnS nanoparticles studied here. Therefore the values of E0,0 were corrected for this temperature effect before calculating the average particle radii; hence, all
differences are attributable solely to kinetic effects. Figure 3 shows that higher temperatures lead to the formation of larger particles. To investigate the mechanism by which ripening occurs, we have carried out least-square fits of eq 1 (Ostwald ripening), eq 5 (attachment by barrier-less coalescence), and eq 6 (attachment by barrier-controlled reorientation) to the data from 3.2 to 60 ms. The fits are shown in Figure 3; for clarity Figure 4 shows the same data for the first 16 ms on a logarithmic time scale. The resulting parameters as listed in Table 1. Equation 1 was fitted with the restriction that 2 e n e 4. The fit results for eqs 5 and 6 turned out to be identical, which is not surprising in the light of the above-mentioned similarity between the two formulas. By use of eq 3, we can calculate the universal rate constant k for the attachment mechanism by barrierless coalescence. With the results of the least-square fits of eq 5, which deliver the term k[A]0, we can therefore calculate [A]0 (Table 1). This is the initial particle concentration, i.e., the concentration of particles with an average size r0 at the moment when ripening starts (t ) 0) and not to be mistaken for the concentration of
m ∝ r c ∝ a0,0 3
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TABLE 1: Results of the Least-Square Fits of the Kinetic Models to the Experimental Data T (K)
ηa (10-3 Pa s)
kb (109 L mol-1 s-1)
k [A]0c (s-1)
[A]0 (10-6 mol L-1)
r0c,d (nm)
kd (s-1)
ne
ae (nm s-0.25)
r0e (nm)
283 293 303 313 323
1.31 1.00 0.80 0.65 0.55
1.80 2.43 3.16 3.99 4.91
318 319 323 524 823
0.125 0.114 0.088 0.120 0.142
0.621 0.640 0.654 0.667 0.681
399 401 405 654 1026
4 4 4 4 4
0.205 0.205 0.207 0.144 0.108
0.681 0.705 0.721 0.769 0.805
a Viscosity of water.30 b Calculated by eq 3. c Fit result of eq 5 (attachment by barrierless coalescence). d Fit result eq 6 (attachment by barriercontrolled reorientation). e Fit result eq 1 (Ostwald ripening, restriction: 2 e n e 4).
monomers before precipitation ([Zn2+] ) [S2-] ) 0.5 mmol L-1). The obtained values of [A]0 are not realistic, as they are lower than the initial monomer concentration by approximately 4 orders of magnitude. Since the initial average particle radius r0 (between 0.6 and 0.7 nm) shows that the particles consist of less than 100 atoms at this stage,29 the very low values of [A]0 would mean that most of the precursor ions are still in solution at the onset of ripening, which is not in agreement with the nearly constant overall mass of the particles. Hence, attachment by barrierless coalescence seems highly unlikely as a mechanism here (because it produces meaningless fit parameters). All further consideration will focus on the two remaining ripening mechanisms, namely, Ostwald ripening (eq 1) and attachment by barrier-controlled reorientation (eq 6). In general the fit quality for the attachment mechanism is better than that for the Ostwald ripening mechanism; this is the case especially for short reaction times and at higher temperatures. The fit quality of the attachment model is poorest for the lowest temperature (283 K). Here, in turn, the Ostwald ripening model shows its best resemblance to the data within this temperature series. These results suggest that both mechanisms play a role during the particle growth in the time frame studied here and that attachment becomes more and more predominant the higher the temperature is. This is consistent with the fact that Brownian motion-driven collision of particles (as necessary for attachment) occurs more frequently at higher temperatures. The direct effect of temperature on the intensity of Brownian motion is low, but the viscosity η (see eq 3) shows a pronounced temperature dependence, as listed in Table 1. The data suggest that the mechanism and kinetics are significantly more complex at very early stages of particle growth than to be attributable to one single type of ripening. Non-negligible amounts of solute monomeric species may be expected at very early stages of precipitation in the first place, apart from the possible coexistence of Ostwald ripening and coalescence (barrier-controlled reorientation). More than just one mechanism will take place at the earliest stages of particle growth. The rate constant k′ (Table 1) corresponds to the assumption that particle growth occurs by barrier-controlled attachment (eq 6). According to eq 7, k′ can be used to calculate the activation energy EA for this attachment process; ln k′ is supposed to be a linear Arrhenius function of the reciprocal temperature. Figure 5 shows the Arrhenius plot of the experimental data, which deviates quite substantially from the expected linear correlation. As discussed above, however, the fit quality of eq 6 is very low for the lowest temperature of 283 K (Figure 4), which is why this data point should be disregarded in the Arrhenius plot; the remaining four values are then much closer to linearity. A linear least-square fit to these four data points is also shown in Figure 5; the slope corresponds to -EA/R, delivering an activation energy of EA ) 25.7 kJ mol-1. This value is lower than the one reported by Huang et al.20 (137 kJ mol-1), who have studied ZnS particle growth under considerably different conditions. Apart from a different time scale (several hours)
Figure 5. Arrhenius plot (eq 7) of ln k′ (from eq 6) vs the reciprocal temperature. The slope of the linear fit delivers the activation energy for attachment by barrier-controlled reorientation. The data point for the lowest temperature is not taken into account (see text).
and hydrothermal temperature conditions (140-225 °C), their study was performed with the utilization of mercaptoethanol as a stabilizing ligand. It should be expected that this increases the activation energy in oriented attachment growth, since additional energy is required for the displacement of the ligands. Hence, our value for EA appears reasonably consistent with the one reported before. Conclusion The growth of ZnS nanoparticles during the first ca. 60 ms of precipitation from aqueous solution is marked by a substantial decrease in particle concentration, indicating pronounced ripening. Kinetic modeling of the average particle size suggests that the mechanism of ripening corresponds to coalescence with barrier-controlled attachment rather than Ostwald ripening, although the latter seems to coexist, especially at low temperature and during the very first few milliseconds. The activation energy for the attachment process is found to be within reasonable proximity to existing literature data. Acknowledgment. Part of this work was funded by the European Union project Atomic Level Studies of Solids Nucleation and Reactions (NUCLEUS, HPRN-CT-1999-00025) and by the Finnish Academy of Sciences. M.T. thanks Prof. Michael Fro¨ba for continuous support. References and Notes (1) Schu¨th, F. Curr. Opin. Solid State Mater. Sci. 2001, 5, 389-395. (2) Schu¨th, F.; Bussian, P.; Ågren, P.; Schunk, S.; Linde´n, M. Solid State Sci. 2001, 3, 801-808. (3) Rein ten Wolde, P.; Frenkel, D. Phys. Chem. Chem. Phys. 1999, 1, 2191-2196. (4) Auer, S.; Frenkel, D. Nature 2001, 409, 1020-1023. (5) Ojo, S. A.; Whitmore, L.; Slater, B.; Catlow, C. R. A. Solid State Sci. 2001, 3, 821-826. (6) Talapin, D. V.; Rogach, A. L.; Haase, M.; Weller, H. J. Phys. Chem. B 2001, 105, 12278-12285. (7) Hamad, S.; Cristol, S.; Catlow, C. R. A. J. Am. Chem. Soc. 2005, 127, 2580-2590. (8) Meneau, F.; Sankar, G.; Morgante, N.; Winter, R.; Catlow, C. R. A.; Greaves, G. N.; Thomas, J. M. Faraday Discuss. 2002, 122, 203-210.
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