J. Phys. Chem. C 2007, 111, 16243-16248
16243
Stability and Growth of Titanium-oxo-alkoxy TixOy(OiPr)z Clusters R. Azouani,† A. Soloviev,‡ M. Benmami,† K. Chhor,† J.-F. Bocquet,† and A. Kanaev*,† Laboratoire d’Inge´ nierie des Mate´ riaux et des Hautes Pressions, C. N. R. S., Institut Galile´ e, UniVersite´ Paris-Nord, 93430 Villetaneuse, France, and Center of Microtechnology and Diagnostics, St. Petersburg State Electrotechnical UniVersity, 197376 St. Petersburg, Russia ReceiVed: May 22, 2007; In Final Form: July 9, 2007
Nucleation and growth of TiO2 clusters and nanoparticles have been studied in the sol-gel process at the hydrolysis ratio, H, between 1.0 and 2.6. A quasi-monodispersed size distribution of the condensed species has been obtained in each experimental series due to an efficient turbulent micromixing of two reactive fluids containing titanium tetraisopropoxide and water in 2-propanol. This approach enables identification of four different domains of the cluster/nanoparticle stability and growth kinetics: H < 1.45 (I), 1.45 e H e 1.75 (II), 1.75 < H e 2.0 (III), and H > 2.0 (IV). Small stable clusters of radius R ) 0.95 ( 0.1 nm appearing in domain I may be assigned to the Keggin-type structure observed earlier for Ti17-oxo-alkoxy clusters by Steunou et al. (J. Chem. Soc., Dalton Trans. 1999, 21, 3653). The next-stable cluster with R ) 1.60 ( 0.05 nm appears in domain II as a result of the assembling of five smaller clusters. Domain III is characterized by cluster instability: they agglomerate in short chains, whose limit size depends on H. After the chain size reaches 2.6 nm (H > 2.0), nuclei are formed and subject to steady irreversible growth until the powder precipitates at the induction time (domain IV).
1. Introduction The basic sol-gel chemistry of many metal alkoxides has been studied extensively and is now well-characterized.1-2 It is known that reactive clusters and nanoparticles serve to be building blocks of the issued condensed matter.3 They define in many respects useful properties of the final materials, including bulk solids and coatings. Knowledge of their structure and reactivity is a way of optimizing the material composition. This is an important issue that may open many interesting applications in nanotechnology. In solutions with the titanium tetra-iso-propoxide (Ti(OiPr)4 or TTIP) precursor and at low hydrolysis ratio H ) CH2O/CTTIP < 1 there exist several stable clusters: Ti3O(OiPr)10, Ti11O13(OiPr)18, Ti12O16(OiPr)16, and Ti17O24(OiPr)20 (see ref 3). These oxoalkoxy units are noncrystalline, possessing an inorganic titanium oxide core and surface propoxy and hydroxy groups. Taking into account possible hydrolysis of the clusters, their general chemical composition is TinOm(OiPr)4n-2m-l(OH)l, where m/n ) k is called the condensation ratio. By using 17O NMR analysis, Blanchard et al.4 have observed that the smallest stable Ti3oxo-cluster dominates at H ≈ 0.05, whereas the Ti11 one appears at H g 0.2. At higher hydrolysis ratios, H g 0.7, larger oxopolymer clusters and nanoparticles appear. The condensation ratio of these structures increases from k3 ) 0.33 for Ti3O(OiPr)10 to k11 ) 1.18 for Ti11O13(OiPr)18, and to k g 1.45 for larger nuclei,5 indicating that an increase in H results in the formation of more-condensed species through further hydrolysis accompanied by reorganization of the low condensed clusters.3 Difficulties of experimental studies of these systems are related to a high chemical reactivity of the metal alkoxide precursors. As a result of this, reaction products are highly * Correspondent author. E-mail:
[email protected]. † C. N. R. S.. ‡ St. Petersburg State Electrotechnical University.
sensitive to the local microcomposition of the reactive fluid. Its initial nonhomogeneity results in generally broad particle size distribution. Because of that, substantially polydispersed samples are often subjected to analysis. This is a case of TiO2 nanoparticles and clusters prepared from the TTIP precursor. In particular, the condensation ratio of the above-mentioned Ti11O13(OiPr)18 cluster allows one to maintain a monodispersed colloid of these clusters at hydrolysis ratios as high as H ) k11, which disagrees with experimental observations of ref 4. A study of this issue can be carried out at perfect micromixing of the reaction components. The micromixing time has to be shorter compared to a characteristic time of the primary hydrolysis-condensation reaction in sol-gel solutions, which is in the range of tens of milliseconds in the case of the TTIP precursor.6 Such a rapid physical process can be achieved in turbulent flow in the static T-mixer.7 Recently, a sol-gel reactor has been built up on this approach allowing (i) good reproducibility of the process kinetics (∼5%) and (ii) a monodispersed initial nuclei population of size 2R ≈ 6.0 nm at relatively high hydrolysis ratios, H > 2.0, in the TTIP-based sol-gel process.8 In the present communication, we report on kinetic study of the nucleation-growth process in basic TTIP/H2O/isopropanol solutions at the hydrolysis ratios 1.0 e H e 2.6. A perfect and rapid micromixing of highly reactive sol-gel solutions is achieved in the static turbulent T-mixer. The size of the growing clusters and nanoparticles has been measured in situ by the dynamical light-scattering method. 2. Experiment The sol-gel reactor used in the present study is described in refs 8-11. Its main part is the T-mixer of Hartridge and Roughton type. Two thermostated stock solutions of TTIP/2propanol and water/2-propanol are injected into the mixer trough two input tubes. This injection is exocentric: two fluids form
10.1021/jp073949h CCC: $37.00 © 2007 American Chemical Society Published on Web 10/06/2007
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a vortex before entering the main tube. Two reagent flow velocities are maintained equal and varied from 2 to 12 m/s by applying an external gas pressure (N2). The diameters (d) of the two input (1.0 mm) and the main (2.0 mm) tubes are chosen to conserve the Reynolds number, Re ) 4QF/πηd, where Q, F, and η are the fluid flow rate, density, and dynamic viscosity. In the experimental conditions, the Reynolds number can be changed within Re e 104. At long mixing times, the basic colloids are strongly polydispersed. However, when the flow rate increases, the mean particle size and polydispersity decrease. We have observed this kinetics crossover at the Reynolds number12 Re ≈ 4400, which corresponds to the micromixing time of tm ) 8 ms. Both the minimal mean particle size and the narrowest size distribution are attained at the Kolmogorov length12 of LK e 3 µm. In these operating conditions, the reagent mixing time in the T-mixer is expected to be shorter than the characteristic time of primary hydrolysis-condensation reactions resulting in nucleation. Assuming the Damko¨hler number12 Da ≈ 1, the characteristic time of the hydrolysis-condensation reactions leading to nucleation τ ≈ 10-2 s has been obtained at CTi ) 0.146 M and H ) 2.0.13 In the present experiments, the sol particles were generated in 2-propanol solutions with TTIP at concentration CTi ) 0.146 M and hydrolysis ratio H varying between 1.0 and 2.6. The reactor temperature was maintained 20.0 °C using a thermocryostat (Haake, DC10K15). TTIP of 98% purity, 2-propanol (Interchim), and distillated water were used. A monomode optical fiber probe was developed to monitor in situ the particle size (2R) and the scattered-light intensity (I) of the He-Ne laser by the photon-correlated spectroscopy method, using a 16-bit, 255-channel PC board plugged digital correlator (PhotoCor Instruments) developed by Yudin et al.14 The observation volume defined by a mutual positioning of two monomode optical fibers is small enough (10-4-10-5 cm3) to prohibit multiple scattering events. The measurements (I,R) are carried out in automatic sampling mode with the data accumulation over 60 s during the period of the solution stability (induction period) or over 24 h if no solid precipitation (turbidity) was observed. This relatively short accumulation time and small observation volume considerably decrease experimental series rejection because of a non-desirable strong light-scattering on rare dust particles (because of the I∝R6 dependence, large micrometer-size dust particles prohibit the observation of nanometer-size TiO2 clusters). In the case of the smallest clusters, which provide the weakest scattering of light, averaging over many short-lasting measurement series (with the exclusion of rare noisy series) was employed to increase the signal-tonoise ratio. The solution stability was controlled to avoid a decrease in the temporal resolution of the growth kinetics, and the averaging was only applied on a time scale of a mean cluster size stability. 3. Results and Discussion In the dynamic light-scattering method, the diffusion coefficient (D) of particles in a solution is directly accessed by an exponential fit of the autocorrelation curves (ACF). Then, the mean hydrodynamic radius of particles (Rh) is calculated via the Einstein-Stokes formula as a radius of an equivalent spherical particle with the same diffusion coefficient
Rh )
kT 6πη D
(1)
where k, η, and T are, respectively, the Boltzmann constant, dynamic viscosity, and temperature. A deviation from the pure
Figure 1. Characteristic ACFs of TiO2 clusters appeared at low hydrolysis ratios of H e 1.75 ([TTIP] ) 0.146 M, T ) 20 °C).
exponential shape of ACF allows judging of the particle polydispersity. Conducting present experiments at low Damko¨hler numbers Da e 1 allows homogenization of the reactive mixture before the sol-gel process begins and assures almost δ-like nucleus and cluster size distributions. In the following, we present experimental analysis of the size of the reactive clusters and nanoparticles appearing in the sol-gel solution. We distinguish four kinetic domains: H < 1.45 (I), 1.45 e H e 1.75 (II), 1.75 < H e 2.0 (III), and H > 2.0 (IV). Domains I and II: H e 1.75. No changes of the ACFs were measured at low hydrolysis ratios, H e 1.75, during the period of times longer than 24 h. This fact accounts for highly stable colloids. To increase the signal-to-noise ratio, which is generally low in these conditions, the averaging over the full observation period has been applied. Several examples of as-obtained ACF’s are shown in Figure 1. Their deviation from the exponential decay law is not significant, which characterizes the quasimonodispersity of the particle population. The particle size is smaller than that reported earlier by Soloviev for the TiO2 nuclei:15-16 R1 ) 0.95 ( 0.1 nm for domain I: H e 1.35 and R2 ) 1.60 ( 0.05 nm for domain II: 1.5 e H e 1.75. Moreover, the size exhibits a change at the hydrolysis ratio of h*1 )1.45 ( 0.05. The radii ratio R2/R1 ) 1.7 is not a whole number. We will call these species oxo-clusters as suggested in ref 3 because by forming larger units their structure is reorganized. They are composed of the titanium oxide core surrounded by the surface alkoxy and hydroxy groups as discussed in early experimental and theoretical studies.17-21 In the following, we label them C(1) and C(2) clusters. To gain deeper insight into the formation process, we consider the scattered-light intensity (I) variation in the sol-gel solutions. This is shown in Figure 2. One can see that I(H) forms two plateaus separated by H ≈ h*1 ) 1.45. The intensity changes
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Figure 2. Changes of scattering-light intensity for two cluster populations: P1 at 1.10 e H e 1.70 and P2 at 1.50 e H e 1.70 ([TTIP] ) 0.146 M, T ) 20 °C).
by a factor of ∼4.5 at this point (we remark that the background scattering signal accounted for ∼400 Hz should be subtracted). This is not surprising because larger species may appear by aggregation of smaller ones. Let us discuss this process. The scattered-light intensity by particles in the Rayleigh domain can be expressed as
I ) cNR2Df
Figure 3. Size evolution of TiO2 clusters in the domain of intermediate hydrolysis ratios 1.8 e H e 2.0 ([TTIP] ) 0.146 M, T ) 20 °C). Solid lines show a theoretical model of the H2O-limited growth.
(2)
where c is a constant, and N and Df are, respectively, the concentration and fractal dimension of particles. Here we assume that the hydrodynamic radius R is close to the geometrical one, which is usually used in the definition of fractal dimension. This equation can be completed by the Ti-mass conservation:5
NRDf ) const
(3)
The cluster size and intensity ratios
R2/R1 ) 1.7 I2/I1 ) 4.5
(4)
are obtained from Figures 1 and 2. Equations 2-4 can be solved relative to Df and the population ratio of clusters C(1) and C(2):
Df ) ln(I2/I1)/ln(R2/R1) ≈ 3
(5)
N1/N2 ) I2/I1 ≈ 5
(6)
As it is followed from eqs 5 and 6, the larger C(2) cluster is a compact almost spherical-shaped object formed of five smaller C(1) clusters. Domain III: 1.75 < H e 2.0. With further increase of the hydrolysis ratio, the colloid kinetics change. As Figure 3 shows, the clusters grow in size, attaining saturation on a time scale of tens of minutes. We call it the limited-growth period. The size at saturation depends on H: more water is added as larger units are produced. After attaining the plateau, the clusters remain stable on a long time scale (>24 h). A deeper inspection into the growth process allows us to assign it to the 1D aggregation. This is shown in Figure 4 where the logarithmic plot of I versus R is presented. As shown earlier by Soloview,22 a linear fit of these data reflects the geometry of the growing species and can be a measure of their fractal
Figure 4. Log(I) versus log(R) plot for the determination of the fractal dimension of the agglomerated clusters.
dimension, Df. Figure 4 indicates that the clusters aggregate in domain III in short linear chains characterized by Df ≈ 1. A simple theoretical model can describe the observed kinetics. We assume that the clusters react via the surface hydroxyl groups if their concentration exceeds the critical one attained at h*2 ) 1.75. At H > h*2, the clusters aggregate. The kinetic equation is then
dC ) -KC(H - h*2) dt
(8)
where K ) kCTi is the reaction rate (k is the reaction constant) and C is the relative cluster concentration normalized on the initial Ti-atom concentration in the solution CTi. Because of this definition, C represents the inverse of the cluster aggregation number (naggr):
C ) 1/naggr
(9)
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We can relate the cluster concentration and the consumed water as
C0 - C ) a(H0 - H)
(10)
where C0 and H0 stand for the cluster concentration and hydrolysis ratio H at t ) 0 and a represents a part of the consumed water molecules per aggregation event. Substituting h ) H0 - h*2, one can solve eqs 8-10:
C ) C0
C0 - ah C0 - ah e-(C0-ah)Kt
(11)
Keeping in mind the linear cluster chain growth (Figure 4), one can set in relation the cluster concentration and size:
()
R ) R0
C0 C
1/Df
≈ R0(C0/C)
(12)
Finally, we obtain
R ) R0
C0 /ah - e-(C0/ah-1)Kaht C0/ah - 1
(13)
The cluster growth defined by eq 13 is limited, Rtf∞ ) R0(1 - ah/C0)-1. The fit of the experimental data results in the expression for the reaction rate constant k and a:
kCTi a ) 0.10 ( 0.02 s
-1
a/C0 ) 1.5 ( 0.2
(14) (15)
From eqs 15 and 9 and assuming naggr(t ) 0) ) 85 (if we assume Ti17 is C(2) clusters) we obtain a ) 1.8 × 10-2. Using this a value, the reaction rate from eq 14 is kCTi ) 5.7 s-1. The small value of a indicates a low water consumption that is related to a low hydrolysis probability. The majority of water molecules apparently remains free and maintains the equilibrium with surface hydroxyls, OH(s): Keq
...Ti - OR(s) + H2O 798 ...Ti - OH(s) + ROH (16) Free water concentration increases with H in domain III. The limited growth may also be explained by a reversible condensation of clusters. Further experiments are needed to verify this issue. Domain IV: H > 2.0. The initial nuclei size at H > 2.0 does not change. However, their growth kinetics changes. From the limited one in domain III, it transforms into the accelerated one at H > h*3 ) 2.0. A series of the measured characteristic kinetic curves of the growing nanoparticles is shown in Figure 5. This is characteristic of the induction period of the sol-gel chemistry.2 The particular case of the TiO2 sol kinetics using TTIP precursor has been studied intensively by our team.10,22,23 The induction kinetics critically depend on the reagent concentration as -5 tind ∝ C-6 Ti (H - h*)
(17)
where h* ) 1.45.16,22 The smallest nanoparticles of 2R ) 5.2 nm undergo irreversible growth allowing them identifying with nuclei. The nuclei are stable units and do not decay into smaller clusters at dilution in alcohol.23 Equation 17 describes the threshold behavior of the induction kinetics: according to it, the particles aggregation requires the hydrolysis ratio H > 1.45.
Figure 5. Size evolution of TiO2 particles at high hydrolysis ratios H > 2.0 ([TTIP] ) 0.146 M, T ) 20 °C).
This has been interpreted previously as TiO2 particles nucleation at H ) h*. The nuclei composition then corresponds to the condensation ratio k ) h*: TixO1.45x(OR)1.1x. The nuclei then slowly aggregate into chains of low dimension branching, in which Df depends on temperature.11 At the induction time, the colloid loses stability and TiO2 precipitates as a macroscopic powder, which is observed in Figure 5 by a rapid increase in the particle size. The present results allow us to complete this concept. First, the critical hydrolysis ratio h*1 agrees well with h* defined previously by Soloviev. However, it corresponds to a creation of large C(2) clusters (3.2 nm) that are, however, smaller in size than nuclei. Second, the relevant concentration of water in the solution at H ) 2 (CH2O ) 2CTi) is theoretically sufficient for the formation of TiO2 solids following hydrolysis and alcoxolation reactions:
Ti(OR)4 + 2H2O f TiO2 + 4ROH The fact that oxo particles constitute the colloid has been assigned to an increase in the reaction activation barrier with the number of hydrolyzed alkoxy groups of the Ti atom. It seems, however, intriguing that the nuclei appear only when the critical hydrolysis ratio H ) h*3 ) 2.0 is attained. Their creation apparently requires some critical cluster-chain length at which the energetically more-stable nucleus is formed by internal structural reorganization. The kinetics crossover observed at H ) 2.0 can then be explained by a change in the nature of the growing units. Our final remark concerns an important question: the forms observed at low H, are they a unique feature of the TiO2 solgel growth kinetics? The reply on it requires more time-resolved experiments. However, an indication of the limited growth (inherent to the domain 1.75 < H e 2.0) can be seen in Figure 5, which precedes the accelerated particle growth on the
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induction period. This observation supports a hypothesis that clusters on growth evolve through similar basic forms. Nature of Titanium-oxo-alkoxy Clusters. Let us now discuss the nature of the observed clusters. To derive an empirical formula for the geometrical size of a family of titanium-oxo-alkoxy clusters, we considered that the cluster consists of a core containing titanium and bridging oxygen atoms and terminal alkoxy groups. We also assumed that the core radius, Rc, increases with the increasing number of titanium atoms, NTi, following an approximative scaling law Rc ≈ (NTi)1/3. Terminal groups should give a constant contribution to the cluster size. Then, the geometrical (rotational) cluster radius, Rr, can be written as follows:
Rr ) AN 1/3 Ti + B
(18)
To find the constants A and B, we analyzed the Ti11-Ti12 clusters described by Day et al.17-18 The cluster core was obtained by removing all of the hydrocarbon groups and oxygen of alkoxy groups connected to titanium atoms. All distances between pairs of atoms in a cluster core were calculated, and the maximum distance was taken as a core size (2Rc). The value of 2Rc of about 8.0 Å has been obtained. Moreover, the size of a nonbridging isopropoxy group has been estimated. The characteristic lengths of the Ti-O, O-C, and C-H bonds are about 1.8, 1.5, and 1.0 Å, respectively, and the Ti-O-C angle is about 142°. Then, the size of the group is about 4.0 Å. Using these approximations, eq 18 was solved using values of A ) 1.75 Å and B ) 4.0 Å. In the dynamic light-scattering method, the diffusion coefficient, D, of colloidal particles is directly accessed. Then, the cluster’s hydrodynamic radius, Rh, is defined via the EinsteinStokes eq 1 as the radius of a spherical particle with the same diffusion coefficient. The hydrodynamic radius, Rh, correlates with the geometrical one Rr . However, the layer of solvating molecules adjacent to the surface of a cluster has to be taken into account when relating Rh and Rr . This layer moves together with the cluster, which can significantly decrease its diffusion coefficient and, hence, increase its hydrodynamic radius. Clusters with Rh ) 9.5 Å were observed in hydrolysis/ condensation of titanium ispopropoxide with H ) 1.1-1.35. If we neglect the solvating layer and put Rh ) Rr , then the corresponding number of titanium atoms in a cluster, found by using eq 7, would be about 31. Alternatively, if we assume that the observed cluster contains 11 or 17 titanium atoms, then we should suppose the presence of a solvating layer with an effective thickness of about 1.5 or 1.0 Å. This seems to be quite reasonable. Three known titania clusters, Ti11O13(OiPr)18, Ti12O16(OiPr)16, and Ti17O24(OiPr)20, can be candidates for identification with the observed units. Earlier, Day et al.18 have reported a synthesis of Ti11 clusters at room temperature in the range of H between 0.3 and 0.8 as the major product (95%) and suggested that it is the principal building unit of large Ti-oxo-alkoxy polymers. However, they are synthesized in conditions different from ours. We use the simplest bicomponent TTIP/H2O solution in isopropanol at room temperature. A problem related to the strong reactivity of the system is overcome in our case by ultrafast physical mixing. At the same time, the Ti12 clusters (two isomers R1 and R2 are known) were observed in sol-gel synthesis at a relatively high temperature of 100 °C.18 The stabilization of Ti11 and Ti17 clusters was achieved in the presence of diacetone alcohol20 and acetic acid,21 making direct extrapolation to our neutral conditions of the basic composition misleading.
For more argumentation, the Ti11, Ti12, and Ti17 cluster condensation ratios k11 ) 1.18, k12 ) 1.33, and k17 ) 1.41 can be taken into account. Because of good micromixing, the same kinds of clusters dominate our solutions. Moreover, at hydrolysis ratios H e 1.35 the cluster size remains stable. This fact allows us to disregard the Ti11 cluster and makes assignment of our scattering units to Ti12 or Ti17 clusters preferable. However, because of the above-discussed synthesis conditions, only Ti17O24(OiPr)20 can be selected. This cluster has first been reported by Steunou et al.21 possessing the so-called Keggin structure, which basically consists of a central TiO4 tetrahedron encapsulated in a metal-oxygen cage of 12 TiO6 octahedra. They suggest that other compact arrangements may originate from this unit by capping their faces with extra polyhedra. We adopt this concept and tentatively assign our observed cluster of 1.9-nm size to a Keggin-type structure. An interesting point concerns the small range of H where the C(1)/C(2) cluster stability changes. Free water molecules in the solution are known to be a source of the solid condensation. The observed H-type instability suggests that water molecules are not in a free state but take part of the outer cluster shell as surface hydroxyl groups. The density of these groups increases with H and results in a complete reorganization of clusters when critical concentration is attained. Assuming that the smaller C(1) cluster is Ti17O24(OiPr)20 and that its reorganization into the larger C(2) cluster proceeds between H ) 1.4 and 1.5, one can derive chemical formula of the first instable cluster as H increases: Ti17O24(OH)(OiPr)19. This means that one surface hydroxyl group per cluster is required for their assembly. This is different from the case of oxo-TiO2 nanoparticle aggregation during the induction period, where according to Rivallin et al. (refs 8-11 and 13) condensation of twohydroxyl is required. This difference can be explained by the higher cluster reactivity compared to the nanoparticles. With the increase of H g 1.45 (domain II), the C(2) cluster size 2R ) 3.2 nm does not change. We believe that extra water triggers exchanges with alkoxy groups at the cluster surface until the hydroxyl concentration attains some critical value at H ) 1.75. At this point, further growth becomes possible. Assuming that the Ti85 cluster (5xTi17) bulk composition corresponds to the condensation ratio k ) h*1 ) 1.45 (at which it appears), it is easy to show that the critical cluster at h*2 ) 1.75 possesses approximately half of the surface alkoxy groups replaced by hydroxy groups. Apparently, further reaction between Ti85 clusters requires a critical concentration of the surface hydroxyls. Overview of the Growth Kinetics. A particularity of these measurements consists of the high initial homogeneity of the local fluid mixture composition. The bulk reactions thus proceed in a similar way, resulting in low polydispersity of the produced clusters and nanoparticles.13 This allows better selection of different building units of the sol-gel chemistry. The overview of the reaction kinetics and participating units observed in the present study is shown in Figure 6. It strongly supports the hierarchical growth model of the sol-gel process.24 However, the hierarchy not only concerns nanometric-tomicronic particles that appear after nucleation but also subnucleus condensed forms as clusters. In particular, two different stable clusters of the size 2R ) 1.9 and 3.2 nm are distinguished. These are highly stable species in our experimental conditions. However, one can see that their chemical reactivity progressively decreases as the size increases. Although the smaller clusters, C(1), condense by oxolation reaction as soon as one hydroxyl group is present at the surface of each one (H ) h*1), the
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Azouani et al. domain I may be assigned to the Keggin-type structure earlier observed for Ti17-oxo-alkoxy clusters by Steunou et al.21 The next-stable C(2) cluster of spherical shape with R ) 1.60 ( 0.05 nm appears in domain II. It is produced by condensation of five C(1) clusters. Domain III is characterized by cluster instability: they rapidly agglomerate in short chains, whose limit size depends on H. After the chain size reaches 2.6 nm (H ) 2.0), nuclei are formed and subject to a steady irreversible growth until TiO2 powder precipitates at the induction time (domain IV). We believe that the observed cluster hierarchy is a unique feature of the basic TiO2 sol-gel growth kinetics. Acknowledgment. This work is supported by the COST D41 Action of the European Commission. References and Notes
Figure 6. Particle size dependence of the hydrolysis ratio 1.0 e H e 2.6 ([TTIP] ) 0.146 M, T ) 20 C).
larger clusters, C(2), condense only after some critical water concentration in the colloid is attained (H ) h*2). Moreover, the reaction rate involving C(2) is much slower than that of C(1). We conclude that C(2) growth results in structural reorganization after some critical aggregation number is attained, which makes the nucleation process irreversible. Alternatively, a fusion of five C(1) takes place as soon as each cluster possesses one hydrolyzed alkoxy group at the surface. Our assignment of C(1) to the Keggin-type structure21 is based on in situ cluster-size measurements at the critical hydrolysis ratio H ) h*1. The Ti17O24(OiPr)20 cluster may be a candidate. The fact that its hydrodynamic radius Rh ) 0.85 nm is smaller compared to the measured one (R ) 0.95) nm may be explained by a shell of solvent molecules involved by the cluster into Brownian movement. The size of the solvating layer (δ ) 1.0 Å) is smaller than that of the 2-propanol molecule (L ) 4.0 Å). High reactivity due to low-coordinated bonds inherent to titanium-oxo-alkoxy clusters may account for this effect. 4. Conclusions Nucleation and growth of TiO2 clusters and nanoparticles has been studied in the sol-gel process at the hydrolysis ratio, H, between 1.0 and 2.6. A quasi-monodispersed size distribution of highly reactive clusters or nanoparticles has been obtained in each experimental series due to an efficient turbulent micromixing of two reactive fluids containing titanium tetraisopropoxide and water in 2-propanol. This approach enables identification of four different domains of the cluster/nanoparticle stability and growth kinetics: H < 1.45 (I), 1.45 e H e 1.75 (II), 1.75 < H e 2.0 (III), and H > 2.0 (IV). The smallest stable C(1) clusters of radius R ) 0.95 ( 0.1 nm appearing in
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