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Nanomaterials Fabrication  45

        boehmite nanoparticles. In strongly acidic media used for thermolysis,
        the solubility of the solid is high because the surface is totally protonated
        and the ionic atmosphere near the surface of particles during formation
        is very likely high and constant, so that the surface energy is always low.
        Depending on their structure, some faces can be energetically favored,
        but dissolution-crystallization processes very likely play a role in the
        growth of particles. Other parameters such as thermolysis temperature,
        concentration, and presence of specific ligands have to be taken into
        account in the describing nanoparticle formation.

        Hydrolysis of metallo-organic compounds. Metallo-organic compounds,
        and especially metal alkoxides [40, 41], are largely involved in so-called
        sol-gel chemistry of oxide nanomaterials [42]. Metal alkoxides are also pre-
        cursors of hybrid organic-inorganic materials, because such compounds
        can be used to introduce an organic part inside the mineral component
        [43–45].
          Sol-gel chemistry mainly involves hydrolysis and condensation reac-
        tions of alkoxides M(OR) in solution in an alcohol ROH, schematically
                               z
        represented as:
               M(OR)   z H O → M(OH)   z ROH → MO      z/2    z/2 H O
                                                                 2
                                       z
                           2
                     z
        These two reactions, hydroxylation and condensation, proceed by nucle-
        ophilic substitution of alkoxy or hydroxy ligands by hydroxylated species
        according to:
                   M(OR)   x HOX L [M(OR)    z x (OX) ]   x ROH
                          z
                                                    x
        If X   H, the reaction is a hydroxylation. For X   M, it is a condensa-
        tion (oxolation) and if X represents an organic or inorganic ligand, the
        reaction is a complexation. There is a deep difference with the processes
        in aqueous medium where condensation and complexation are nucle-
        ophilic substitutions while hydroxylation is an acid-base reaction. In
        organic medium, both hydrolysis and condensation follow an associative
             mechanism in forming intermediate species in transition states in
        SN 2
        which the coordination number of the metal atom is increased. That
        explains why the reactivity of metal alkoxides toward hydrolysis and con-
        densation is governed by three main parameters: the electrophilic char-
        acter of the metal (its polarizing power), the steric effect of the alkoxy
        ligands, and the molecular structure of the metal alkoxide.
          Generally, the reactivity of alkoxides toward substitutions increases
        when the electronegativity of the metal is low and its size is high. That
        lowers the covalence of the M-O bond and enhances the reaction rates.
        Silicon alkoxides are weakly reactive in the presence of water s  5 1.74d
                                                                Si
        while titanium alkoxides  s   5 1.32d  are very sensitive to moisture.
                                   Ti
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