JOURNAL OF MATERIALS SCIENCE LETTERS 20, 2 0 0 1, 905 – 906 Nanoparticle growth during the induction period of the sol-gel process A. SOLOVIEV ∗ , D. IVANOV ‡ , R. TUFEU, A. V. KANAEV § Laboratoire d’Ing ´ enierie des Mat ´ eriaux et des Hautes Pressions, C. N. R. S., Institut Galil ´ ee, Univerit ´ e Paris-Nord, 93430 Villetaneuse, France E-mail: kanaev@limhp.univ-paris13.fr The sol-gel synthesis of oxide materials provides a new approach to the preparation of ceramics, glasses, fine monodisperse powders, films, fibers and other materi- als with desired properties [1]. Understanding of the mechanisms that govern the formation of metal oxide particles is important to both basic research and applied engineering. It is especially important to understand the phenomena taking place in the early stages of the sol- gel process because they may determine properties of synthesized materials. It is generally assumed that in the first stage of the sol-gel process, hydrolyzed monomers are created and accumulated [2, 3]. The induction time (t ind ) corre- sponds to the moment when the concentration of these monomers reaches the level of critical supersaturation. As a result of nucleation, primary particles are formed. They then grow by monomer addition and aggrega- tion. This model was used to describe the hydrolysis- condensation of silicon alkoxides [1, 4] as well as tran- sition metal alkoxides [5–7]. In dynamic light scattering (DLS) experiments [4, 6, 7], first particles were found only after the induction period. It seems to confirm the model. Some observations, however, indicate that the model of monomer accumulation during the induction period is not always valid. It is known that transition metal alkoxides are susceptible to oligomerization via addi- tion reactions [8]. For Ti-based systems, for example, X-ray absorption near edge structures (XANES) experi- ments performed immediately after solution mixing showed spectra characteristic of Ti atoms in the six- fold coordination. It indicated the presence of olation products. Furthermore, in the case of titanium alkox- ides, measurements of water consumption by the cobalt chloride method [7], Karl Fisher method [9] and Raman spectroscopy [10], indicated that the initial hydrolysis is fast compared to the induction period. Therefore, most of the induction period can be attributed to the delay between the completion of the initial hydroly- sis and the subsequent precipitation reaction [7]. It is assumed that supersaturation of hydrolyzed monomers is achieved during the initial hydrolysis. It is not clear then why nucleation does not occur immediately after the initial hydrolysis. To elucidate the system behavior during the induc- tion period of the sol-gel process, we have conducted ∗ Present Address: Institute of Chemistry of Silicates Ac. Sci., St. Petersburg, Russia. ‡ Present Address: University of Low Temperature Technologies, St. Petersburg, Russia. § Author to whom all correspondence should be addressed. high sensitivity DLS measurements of particle growth during hydrolysis-condensation of titanium isopropox- ide. We found that nanoparticles were present during the entire induction period. The results of a typical mea- surement of the mean particle radius as a function of time are shown in Fig. 1. Particles with R = 2 nm are present at the beginning of the reaction. They grow slowly until approximately R = 4 nm. Afterwards, the velocity of growth increases drastically. This moment corresponds to the first visual observation of turbidity, which is used usually to define the induction time [5]. We have performed the analysis of induction time (t ind ) as a function of isopropoxide (c t ) and water (c h ) molar concentrations. The following approximate for- mula has been derived t ind ∝ c -α t · (c h - c t h 0 ) -β (1) with parameters h 0 = 1.45,α = 1.5,β = 4.7. It is sig- nificant that the universal representation of all kinetic data became possible only after the introduction of the parameter h 0 : the initial water consumption ratio. The value c hl = c h - c t h 0 is the amount of water remain- ing after the initial hydrolysis. The high reaction order with respect to c h1 may be explained by the possible par- ticipation of several water molecules in the transition Figure 1 Particle mean radius as a function of time in the process of the titanium isopropoxide hydrolysis-condensation (c t = 0.28 M, c h = 0.52 M). 0261–8028 C  2001 Kluwer Academic Publishers 905