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48   Principles and Methods

        are formed. Therefore, the morphology of the particles is heavily depend-
        ent upon the conditions of acidity in which condensation takes place. The
        catalysis of silica condensation may also be affected by nucleophilic acti-
        vation using additives such as 4-dimethylaminopyridine (DMAP, see
        Table 3.1). Particles and polymers may remain dispersed in the medium,
        forming sols, or they can agglomerate and gel more or less rapidly,
        depending on the surface charge density of particles and consequently
        on the pH of the medium. On either side of pH   2, gelation is faster
        because acid or base catalysis accelerate the condensation rate of Si-OH
        groups between particles. At pH 	 2, the surface charge is too small to
        provide efficient repulsion between particles. At pH   2, base catalysis of
        oxolation has the same effect, which is maximum for pH   6. For pH   6,
        the surface charge is high enough for the sol to remain stable.
          The reactivity of metal alkoxides is also deeply influenced by their
        molecular structure and complexity that depends on the steric hin-
        drance of the alkoxo ligands, OR, especially for the transition element
        alkoxides. Due to the fact that the oxidation state, z, is generally smaller
        than the coordination number of the metal, it inhibits coordination of
                                           species. For instance, this occurs
        the metal in the monomeric M(OR) z
                                           i
        in the case of titanium alkoxide Ti(O Pr) , which is a monomer in iso-
                                              4
        propanol. The coordination of titanium is only four and the reaction with
        water leads to instantaneous precipitation of heterogeneous and amor-
        phous titania particles. With ethoxy ligands, titanium forms oligomeric
        species [Ti(OEt) ] (n   3 in benzene, n   2 in EtOH) in which the tita-
                       4 n
        nium coordination is higher, n   5 in the trimer, n   6 in the dimer
        because of the formation of a solvate [Ti(OEt) ]   (EtOH) . Monodispersed
                                                4 2
                                                          2
        spherical particles have been synthesized by controlled hydrolysis of a
        diluted solution of Ti(OEt) in EtOH [47]. The monodispersity clearly
                                 4
        results from slower hydrolysis and condensation reactions with less
        reactive precursors allowing decoupling of the nucleation and growth
        steps. It is however possible to control the reactivity of low coordinated
        titanium in the presence of specific ligands. For instance, hydrolysis at
        60 C of titanium butoxide Ti(OBu) 4 in the presence of acetylacetone
        forms monodispersed 1–5 nm TiO 2 anatase nanoparticles [48]. A very ele-
        gant design of the shape of anatase nanospheres and nanorods is
                                                        i
        obtained by controlling the rate of hydrolysis of Ti(O Pr) at 80 C in the
                                                           4
        presence of oleic acid.
          In a general way, the rate of reactions and the nature of condensed
        species obtained depend also on the hydrolysis ratio defined as h   H O/M.
                                                                    2
        ■ Molecular clusters are formed with very low hydrolysis ratios (h 	 1).
          The condensation reactions are relatively limited. Hydrolysis of
          [Ti(OEt) ]   2(EtOH) forms soluble species such as Ti O (OEt) 20
                  4 2
                                                                  4
                                                               7
          (h   0,6), Ti O (OEt) 24  (h   0,8) or Ti O (OEt) 32  (h   1). A variety
                         8
                      10
                                                 16
                                              16
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