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Monodispersed Silica-Titanyl Sulfate Microspheres Jeannie Han and Eugenia Kumacheva* Department of Chemistry, University of Toronto, 80 St. George Street, Ontario, M5S 3H6, Canada Received May 21, 2001. In Final Form: September 18, 2001 We report on the synthesis of monodispersed individual silica-titanyl sulfate (SiO2-TS) spheres with the dimensions varying from 350 to 900 nm. An important factor leading to complete and uniform coating of SiO2 spheres with a ca. 40 nm thick layer of TS is the ratio, φ, between the amount of TS added to the silica dispersion and the total available surface area of SiO2 spheres. For the size range of SiO2 particles varying between ca. 300 and 800 nm, the optimum value of φ varied from 0.05 to 0.09 g/cm2, above which extensive aggregation of composite particles occurred. The encapsulation of SiO2 microspheres was driven by heterocoagulation between the positively charged TS clusters and the negatively charged SiO2 particles.
Introduction Recently, nanostructured materials with periodically modulated structure and composition have attracted significant attention.1-5 Among these materials, nanocomposites containing titania (TiO2) have great potential due to the optical, photocatalytic, and semiconductor properties of TiO2. Inverse opal structures for threedimensional photonic band gap materials have been reported, in which the periodic microporous framework was made from TiO2.1,2 Alternatively, nanocomposites with a periodic direct structure can be obtained, in which colloid TiO2 particles are embedded in a low-refractive-index material such as a polymer. For example, nanocomposites of titania/p-type semiconducting polymers show promise as photochromic, photoluminescent, and nonlinear optics materials.6 In these systems, monodispersity of the colloidal TiO2 particles is a strict requirement for producing materials with a periodicity on the submicrometer scale. However, up to date synthesis of monodispersed titania particles with dimensions ranging from 0.2 to 1 µm remains a challenge for materials scientists. For instance, Matijevic et al.7 prepared colloidal TiO2 particles in the size range from 0.5 to 3 µm by aging titanium(IV) tetrachloride at elevated temperatures and low pH in the presence of sulfate ions. The shape of the particles obtained following this procedure was not very well controlled, and the polydispersity indices were not explicitly reported. In addition, the length of the aging process could reach time periods of over 1 month. In a different approach, titanium(IV) tetraethoxide was used as a precursor to colloidal TiO2 particles.8-10 By use of this method, small TiO2 (1) Holland, B. T.; Blanford, C. F.; Stein, A. Science 1998, 281, 538. (2) Wijnhoven, J. E. J.; Vos, W. L. Science 1998, 281, 802. (3) (a) Kalinina, O.; Kumacheva, E. Macromolecules 1999, 32, 4122. (b) Vickreva, O.; Kalinina, O.; Kumacheva, E. Adv. Mater. 2000, 12, 110. (4) Xu, L.; Zhou, W.; Kozlov, M. E.; Khayrullin, I. I.; Udod, I.; Zakhidov, A. A.; Baughman, R. H.; Wiley, J. B. J. Am. Chem. Soc. 2001, 123, 763. (5) Park, S. H.; Xia, Y. N. Chem. Mater. 1998, 281, 538. (6) Gratzel, M. Semiconductor Nanoclusters - Physical, Chemical and Catalytic Aspects, Nanocrystalline Electronic Junctions; Studies in Surface Science and Catalysis, Vol. 103; Elsevier: Amsterdam, 1997; p 353. (7) Matijevic, E.; Budnik, M.; Meites, L. J. Colloid Interface Sci. 1977, 61, 302. (8) Ghenne, E.; Dumont, F.; Buess-Herman, C. Colloids Surf., A 1998, 131, 63. (9) Nagpal, V. J.; Davis, R. M.; Riffle, J. S. Colloids Surf., A 1994, 87, 25. (10) Nagpal, V. J.; Davis, R. M. J. Mater. Res. 1995, 10, 3068.
nanoparticles with the dimensions varying from ca. 30 to 50 nm could be obtained; however, their substantial polydispersity counteracted the requirements for the preparation of periodic nanostructured materials. Barringer et al.11 reported on the preparation of 300-600 nm titania particles via the sol-gel process of titanium alkoxides; however, the authors did not provide the polydispersity index for this range of particle size. An alternative approach to the preparation of monodisperse TiO2 particles with tunable dimensions was pioneered by Matijevic et al.12 and was later modified by several groups.13,14 In this approach, monodispersed silica spheres of the required size were used as templates onto which a titania coating with a varying thickness was grown. By aging an acidic solution of titanyl sulfate (TS) in the presence of the silica microbeads, the authors12 obtained an amorphous coating with the molecular structure TiO1.9(SO4)0.1‚0.6 H2O, which upon calcination at 1000 °C produced TiO2 rutile crystalline structure. It was also demonstrated that in order to screen the properties of the core silica particles, it was desirable to obtain thick layers of TiO2 which make up approximately 13 wt % of the total particle diameter. A further increase in the titania concentration in the composite particles (up to 50 wt %) was reached via a two-step coating procedure: this process involved separating the particles by filtration after the first coating stage, redispersing them in pure water, and then repeating the coating procedure. Hanprasopwattana et al.13 and Guo et al.14 used hydrolysis of titanium alkoxide precursors to produce composite titania-silica (TiO2-SiO2) spheres. In contrast to the “raspberry”-structured TS-SiO2 particles,12 these authors obtained smooth TiO2 shells on the surface of silica. It was shown that thick titania coatings could be obtained by increasing the amount of alkoxide precursor and by using a multistep SiO2 particle encapsulation procedure. In the latter method, titanium n-butoxide was hydrolyzed in the presence of silica particles up to five times to increase the thickness of the TiO2 layer. Ultimately, the weight concentration of titania in the composite particles increased from 5.0 wt % for a single-layer (11) Barringer, E. A.; Kent Bowen, H. Langmuir 1985, 1, 414. (12) Matijevic, E.; Hsu, W. P.; Yu, R. J. Colloid Interface Sci. 1993, 156, 56. (13) Hanprasopwattana, A.; Srinivasan, S.; Sault, A. G.; Datye, A. K. Langmuir 1996, 12, 3173. (14) Guo, X.; Dong, P. Langmuir 1999, 15, 5535.
10.1021/la010745y CCC: $20.00 © 2001 American Chemical Society Published on Web 12/04/2001
Monodispersed Silica-Titanyl Sulfate Microspheres
coating procedure to 64 wt % for the five-step coating procedure. However, in the later stages of this process, particle aggregation was indicated by the existence of broad peaks in the size distribution curves. Holgado et al.15 focused on studies of the parameters controlling the uniformity and the thickness of the titania shells. The authors found that the repulsive steric forces generated by the polymer stabilizer, hydroxypropyl cellulose, determined the growth of the TiO2 coating. For example, for stabilizer concentrations above 5.0 g/L, silica encapsulation by titania did not occur, whereas for stabilizer concentrations below 0.1 g/L, an irregular coating was formed. Furthermore, when the water concentration in the system was increased, the TiO2 coating on the silica particles became thinner and free titania particles formed in the system. Despite the advancements made in template-driven synthesis of titania microspheres, no direct relationship was found between the size and the concentration of the silica particles and the amount of titania precursor in the system required for synthesis of monodispersed particles. It is not clear yet under which conditions silica particles are incompletely covered and when composite microbeads aggregate. Moreover, for further use of the core-shell particles in hybrid nanostructured materials with periodic morphology, it is important to examine the stability of the silica-titania interactions in the composite particles. In this paper, we used the approach developed by Matijevic et al.12 to prepare TS-SiO2 particles, in which TS after heat processing could be converted into TiO2 rutile form. Our first objective was to find the conditions under which monodispersed TS-SiO2 spheres in a wide size range, for example, from ca. 350 to 900 nm, could be prepared. In this study, the experimental variables were the concentration of TS and SiO2 in the system and the size of silica particles. Second, we examined the nature of TS-SiO2 interactions in the core-shell particles and the stability of the coating. In particular, we were interested in the “peeling-off” effect which was defined as the deterioration of the composite particles and the appearance of unattached TS clusters and bare SiO2 beads. Experimental Section Materials. Tetraethyl orthosilicate and ethanol (spectral grade) were purchased from Aldrich. Methanol and 2-propanol were obtained from ACP Chemicals Inc. Saturated ammonia (15 M), concentrated sulfuric acid (18 M), and hydrochloric acid (12 M), all ACS grade, were purchased from BDH. Titanyl sulfate (TiOSO4‚xH2O) was purchased from GFS Caledon. All materials unless otherwise indicated were used without further purification. Water was obtained from a Millipore Plus Ultrapure Water System. Particle Synthesis. Preparation of Silica Spheres. The silica particles were obtained within the range of 0.2-0.8 µm via the Sto¨ber process.16 In a typical experiment, alcohol (14 M), NH4OH(aq) (0.7-1.2 M), and the double-distilled water (6.5-7.5 M) were stirred at 42 °C in a three-neck, double-walled flask for 15 min. The system was purged with nitrogen, and a slight positive pressure was kept inside the vessel throughout the reaction. Then, tetraethyl orthosilicate (TEOS, 0.3 M) was injected into the reaction flask. The total reaction time was 1 h; the turbidity of the solution increased within the first 1-5 min of the reaction. Large-scale reactions with a total volume of 1 L or more were done in a similar manner, except that heating to 40-45 °C was administered by a heating mantle, the reaction vessel was a 2 L Erlenmeyer flask, and the total reaction time was 3 h. At the end of the reaction, the concentration of silica particles was (15) Holgado, M.; Cintas, A.; Ibisate, M.; Serna, C. J.; Lopez, C.; Meseguer, F. J. Colloid Interface Sci. 2000, 229, 6. (16) Sto¨ber, W.; Fink, A.; Bohn, E. J. Colloid Interface Sci. 1968, 26, 62.
Langmuir, Vol. 17, No. 25, 2001 7913 approximately 2 wt %. The dispersions were purified in three steps. First, ethanol and ammonia were removed by distillation at 80 °C. Then, to remove TEOS and residual alcohol and ammonia, the mixture was centrifuged using a Sorvall Superspeed RC-2 automatic refrigerated centrifuge at 8000 rpm for 10 min. The supernatant was carefully decanted, and the remaining solid was redispersed in the Milli-Q water and stirred overnight. Finally, the dispersions were dialyzed against Milli-Q water using Spectra/Por1 regenerated, natural cellulose membranes (MWCO: 6000-8000 g/mol). The medium was refreshed every hour for 5 h. Once clean, the purified SiO2 dispersions were stored in Nalgene polypropylene bottles. Coating of Silica Particles with Titanyl Sulfate. A dispersion of silica microbeads (1 wt %, 400 mL) was heated to 90 °C in a double-walled thermostated flask under rapid stirring. An aliquot of TS stock solution (0.2 M TiOSO4 in 1.0 M H2SO4) was added dropwise into the reaction vessel at the rate of 2-4 mL per minute using a fluid-metering pump (model FMI QG 50). After the addition of TS was complete, the dispersion was aged for an additional 30 min at 90 °C under gentle stirring. The dispersion was cooled to room temperature and then was diluted to approximately 1 L using Milli-Q water. The pH of the resultant dispersion varied from 1.5 ( 0.5. Successive dilution/decantation was used to reduce the ionic strength of the mixture. The final pH of the dispersion was 4.0 ( 0.5. To encapsulate 250 nm silica spheres with TS, 1.4 mL of saturated ammonia was added to the dispersion before the regular coating process took place. Titanyl sulfate particles for electrokinetic measurements were prepared in a similar fashion as the TS-SiO2 composite particles except that the template silica particles were not introduced into the system. Methods of Characterization of Composite Particles. The surface morphology and the dimensions of the SiO2 and the TS-SiO2 core-shell colloid particles were characterized by scanning electron microscopy (SEM). The instrument used was the Hitachi S-570 scanning electron microscope at a working distance of 1 mm. Image analysis (Image Tool Software, Health Science Center, University of Texas, San Antonio, TX) was used to determine the average particle size and monodispersity and the fraction of silica particles fully coated with TS. At least 200 particles were counted to obtain each parameter. In addition, particle size was determined by photon correlation spectroscopy (PCS) experiments using the Zetasizer 3000HSa (Malvern Instruments). The same instrument was used for measurements of electrokinetic potentials of SiO2, TS, and SiO2-TS particles. In these experiments, the dispersions were diluted in 1 × 10-3 M KBr. To adjust the value of pH from 6 to 2, either 1 M or 1 × 10-3 M solution of HCl was added to the dispersion in the appropriate amount. Elemental analysis was performed using energy-dispersive X-ray spectroscopy (EDS). The equipment used for EDS was the Hitachi S-570 scanning electron microscope, the XR 400, Link Analytical EDS Processor, and the software Ultra Rapid Spectrum Analyzer (URSA) (Mektech). Carbon SEM specimen stubs (Marivac Inc.) were polished with 360 A Silicon Carbide Waterproof Paper and 0.3 µm 3M Abrasives Lapping Film and then sonicated in Milli-Q water for 1 min. Dilute droplets of the dispersion were air-dried on the polished carbon specimen pegs. Monolayer regions of close-packed TS-SiO2 microbeads were analyzed yielding the weight ratio Ti/Si in the composite particles. Further characterization of the surface of colloid particles was accomplished using Fourier transform infrared spectroscopy, FTIR (Perkin-Elmer, Spectrum BX FT-IR System).
Results and Discussion Synthesis of “Template” Silica Particles. In this particular stage, our focus was on the preparation of monodispersed SiO2 spheres with different dimensions, since the size and the monodispersity of the template particles determined the quality of the composite TSSiO2 microbeads. The diameter of the SiO2 particle was controlled by three factors: the type of the alcohol used, the concentration of water, and the concentration of ammonia in the system. The recipes used for the prepa-
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Table 1. Synthetic Routes to Colloidal Silica of Various Diametersa sample code S-2 S-3 S-4 S-8
solvent 1:1 methanol/ ethanol ethanol 2-propanol 3:1 ethanol/ 2-propanol
av SiO2 av SiO2 [H2O] [NH3] diameter diameter b (mol/L) (mol/L) SEM (nm) PCSc (nm) 7.3
1.14
253 ( 6
250 (0.009)
7.7 7.3 7.0
0.74 1.1 1.48
315 ( 3 475 ( 1 680 ( 2
334 (0.1) 585 (0.01) 820 (0.1)
a The conditions for all the above reactions: 300 mL total volume; nitrogen atmosphere at 42 °C; reaction time 1 h; [TEOS] ) 0.3 M. b The error is given by the standard deviation. c The polydispersity index given by photon correlation spectroscopy appears in the brackets.
ration of monodispersed silica in the size range varying from 250 to 820 nm are given in Table 1. Despite the fact that the diameters of the silica particles measured by analyzing the SEM images and by using PCS showed a difference varying from 20 up to 240 nm, both methods of particle characterization showed a similar trend. Generally, the size of SiO2 spheres increased with the molecular weight of the alcohol, which can be explained by the variation in solubility of TEOS. The solubility parameters of ammonia, methanol, ethanol, 2-propanol, and TEOS are 33.4, 29.7, 26.0, 23.5, and 7.2 MPa1/2, respectively.17,18 Due to the greater affinity of TEOS to 2-propanol, the TEOS oligomers were more stable in this alcohol and reached a larger size before transforming into silica nuclei. Moreover, since the rate-limiting step, namely, the rate of hydrolysis of TEOS, is the highest in methanol and the slowest in 2-propanol,19 a greater number of short oligomers could be formed in methanol generating a larger number of nuclei and hence smaller silica particles. In all of the dispersions, the polydispersity of the silica spheres characterized by the standard deviation given by image analysis did not exceed 2.5%. The SEM images of the silica particles are shown in Figure 1. The surface of the SiO2 spheres is smooth (in comparison with the TS-coated surface). This feature was used as a diagnostic to identify the presence of TS on the silica surface. Coating of Template Silica Spheres with Titanyl Sulfate. To produce a uniform TS coating on the surface of silica particles, several factors were examined such as the rate of addition of TS to the silica dispersion, the rate of stirring, the concentration and the size of the silica spheres in the system, and the amount of TS added to the silica dispersion. It was found that slow stirring ( 0.09 g/cm2, TS preferentially grew as a secondary phase in the bulk forming necks between the composite particles. The weight ratio of the core-forming silica and the shellforming TS in the composite particles was characterized by EDS elemental analysis. The ratios of weight fractions of titanium and silicon were measured (as is shown in the inset to Figure 4) and then recalculated to obtain the ratio TS/SiO2 in the microspheres (Figure 4). When the amount of TS per unit surface area of silica increased, its fraction in the composite particles grew due to the more complete coverage of SiO2 and the increase in the size of TS clusters. On the basis of the EDS measurements, for the complete coverage of the silica cores with TS at φ ≈ 0.085 g/cm2, the weight ratio TS/SiO2 reached ca. 35%, which corresponded to the weight fraction of TS in the particles of about 26%. For φ > 0.085 g/cm2, no further growth of the fraction of TS in the composite particles was observed, which correlated well with the results shown in Figure 2 (column 3) and in Figure 3. In Figure 4, the experimental results
compared well with the theoretical curve, which was calculated from the weight ratio of TS and SiO2 added to the bulk system. The difference of 5.0-10% between the experimental and the calculated data for 0 < 0.85 g/cm2 originated presumably from the presence of the residual TS in the bulk system after coating was complete.12 In series 3, φ was increased by adding TS in a sulfuric acid solution. Therefore as φ increased, the ionic strength of the system also increased, which in turn could have led to particle destabilization. However, similar results on particle encapsulation as a function of φ were observed when φ was modified by varying the size and the concentration of SiO2 particles at a fixed acid concentration of 0.1 M. Silica-Titanyl Sulfate Interactions. Understanding of the origin of TS-SiO2 interactions and the examination of the TS coating stability under different conditions are important in selection of appropriate strategies for further modification of the composite particles. The TS-SiO2 particles were subjected to ultrasonication and centrifucation and exposed to different organic solvents for time periods ranging from several hours to several days. It was found that the TS-SiO2 particles withstood ultrasonication for at least 30 min and ultracentrifugation for 10 min under 3600g indicating that the TS layer was strongly attached to the silica surface. On the other hand, exposure of the bilayer particles to polar solvents such as methanol, ethanol, 2-propanol, and N,N-dimethylformamide (the dielectric constants of these solvents varied from 20 to 3817,21) peeled off the TS coating producing essentially bare silica microspheres. However, this effect was suppressed in nonpolar tetrahydrofuran whose dielectric constant was 7.52. The peeling-off effect in polar solvents supported the electrostatic nature of the coating process, since the strength of interaction between the charged surfaces is inversely proportional to the dielectric constant of the medium.22 The electrokinetic properties of SiO2, TS, and TS-SiO2 particles were studied by examining the variation in their ζ-potentials under different pH conditions. As shown in Figure 5, each dispersion featured a strong dependence of ζ-potential on the value of pH. However, in the entire range of pH examined, the TS-containing particles showed a more positive value of ζ-potential than the SiO2 beads. For example, at pH ≈ 4 the values of ζ-potential for SiO2 and TS particles were -40 and -5 mV, respectively. When the pH decreased to 1.8, the value of ζ-potential for SiO2 (21) Dielectric constants: water, 80.1; methanol, 33.0; ethanol, 25.3; isopropyl alcohol, 20.18; N,N-dimethylformamide, 38.25; tetrahydrofuran, 7.52. (22) Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: New York, 1992; p 52.
Monodispersed Silica-Titanyl Sulfate Microspheres
changed to +1.4 mV indicating that the isoelectric point was just above this pH value. In contrast, the isoelectric point for pure TS particles was close to pH ) 4.5. For the lower values of pH, the ζ-potential of pure TS was strongly positive reaching +46.2 mV at pH 2.0, while silica spheres carried an almost zero ζ-potential at this pH. In the encapsulation process, upon addition of TS to the silica dispersion the pH ultimately reached a low value ranging between 1 and 2. In this interval, the TS particles have a high positive charge, while the SiO2 microbeads have a slightly negative charge; thus, it is plausible to explain the coating process by electrostatically driven heterocoagulation of TS clusters with SiO2 spheres. Following this mechanism, instability of the double layer particles, that is, a peeling-off effect, would be anticipated for the higher values of pH, when TS particles acquire a negative ζ-potential. Indeed, the instability of the TS coating on the surface of silica particles was observed for pH ) 5 after 3-day dialysis of the dispersion against Milli-Q water. However, for the marginal value of pH 4, the TS clusters uniformly coated the SiO2 particles. Another feature supporting the electrostatic origin of the attachment of the TS clusters to the SiO2 surface is the dependence of the uniformity of the TS coating on the rate of addition of TS to the silica dispersion. When the rate of TS addition was too slow, the acidity of the system did not grow sufficiently fast to allow for the electrostatic attachment of the TS clusters to the template silica particles. In contrast, at low pH TS particles had a large positive surface charge, and therefore attraction of the TS clusters to the negatively charged silica spheres was favored. Moreover, slow stirring of the system increased the probability of the attachment of the TS clusters to the SiO2 spheres by increasing the contact time. The ζ-potential of the TS-SiO2 microspheres was very similar to that of the pure TS particles: in the range of pH from 1.8 to 4.5, the composite particles had a positive ζ-potential indicating a recharging of the silica spheres, whereas at higher pH, the ζ-potential of the TS-SiO2 spheres dropped into the negative region with the value of -21.6 mV at pH 5.5. Despite the fact that the shape of the ζ-potential curve for the TS-SiO2 particles was similar to that of pure TS, the value of ζ for the composite particles was somewhat lower than that of the pure TS particles indicating that the electrokinetic properties of the silica core particles were not completely screened. Due to the clusterlike structure of the composite particles, small, uncoated regions of bare silica surface with a negative charge partly counteracted the positive ζ-potential of the TS shell. The electrostatic origin of attachment of TS to silica spheres was also supported by the “raspberry” morphology of the coating in contrast to the smooth coating of SiO2 obtained from titanium alkoxides.13 A smooth coating would suggest heterogeneous nucleation of the hydrous titanium oxide on the silica particle surface, while a clusterlike coating would point to homogeneous nucleation of TS in the bulk accompanied by attachment to the SiO2 surface. In principle, the electrostatic origin of silica encapsulation with TS should not rule out the presence of chemical bonds between SiO2 and TS, though this effect would not be dramatic. Indeed, experiments carried out using FTIR indicated that weak chemical bonding existed between SiO2 and TS. The fragment of the spectra for SiO2 and
Langmuir, Vol. 17, No. 25, 2001 7917
Figure 6. FTIR spectra of SiO2 (dashed line) and composite TS-SiO2 (solid line) particles.
TS-SiO2 spheres is shown in Figure 6. For pure silica, the peak at 800 cm-1 was assigned to the symmetric stretching motion of the oxygen atoms along the bisector of the intertetrahedral Si-O-Si bridging angle θ, while the peak observed at 470 cm-1 was due to the motions of the oxygen atoms perpendicular to the Si-O-Si plane.23-25 The small peak observed at 944 cm-1 was assigned to the Si-O- stretching vibration in Si-OH groups remaining in SiO2 cores for the experimental temperature range. It has been shown that Si-OH contribution to this peak disappears when calcination above ca. 600 °C is administered to hybrid silica-titania films.23,25 The spectrum of TS-SiO2 had all peaks characteristic for SiO2 spheres; however, a small shift in the peak at 944 cm-1 was observed. The shifted peak at 957 cm-1 was assigned to be a combination of the stretching modes of the Si-Ospecies in Si-OH groups and in Si-O-Ti4+ sequences involving tetrahedrally coordinated Ti4+ ions.26 This feature indicated some extent of chemical attachment of TS either through partial heterogeneous nucleation of TS on the surface of silica or after attachment of the TS clusters nucleated in the bulk phase. Conclusion Monodispersed individual titanyl sulfate-silica spheres with diameters ranging from 350 to 900 nm were prepared, in which the fraction of TS reached 26 wt %. It was shown that the quality of TS coating was controlled by the ratio between the amount of TS in the dispersion and the total available silica surface area. The TS shells were mechanically stable but peeled off in polar solvents. We suggest that the encapsulation of the SiO2 particles with TS was dominated by homogeneous nucleation of titanyl sulfate clusters in the liquid bulk phase accompanied by electrostatically driven coagulation with the silica spheres. The clusterlike structure of the TS coating explained incomplete screening of the negative charge of silica particles and penetration of polar solvents through the TS shell. LA010745Y (23) Seco, A. M.; Goncalves, M. C.; Almeida, R. M. Mater. Sci. Eng. 2000, B76, 193. (24) Zenkovets, G. A.; Tsybulya, S. V.; Burgina, E. B.; Kryukova, G. N. Kinet. Catal. 1999, 40, 562. (25) Almeida, R. M. J. Sol.-Gel Sci. Technol. 1998, 13, 51. (26) Du, X. M.; Almeida, R. M. J. Mater. Res. 1996, 11, 353.
