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34   Principles and Methods

          For oxohydroxo complexes, there is no water molecule in the coordina-
        tion sphere of the complexes and therefore no leaving group. Condensation
        has to proceed in this case via a two-step associative mechanism leading
        to the formation of oxo bridges (oxolation):



                δ−        δ−            H  O   δ−
         O  δ+  OH  O  δ+  OH    O     O      OH     O      O     O
            M          M            M     M              M     M    + H 2 O
                O                                           O
         O                 O     O      O    O       O            O
                    O                O                       O


          The hydroxylation rate, h, of the complexes represents their func-
        tionality toward condensation, and it controls the type and the structure
        of condensed species. It is obvious that h is a function of the pH of the
        medium. Its also depends on the characteristics of the cation such as
        size, formal charge, and electronegativity.
          Condensation of hydroxylated and electrically charged complexes
        (h 	 z) always ends at a more or less advanced stage, leaving discrete
        species in solution, either polycations or polyanions, depending on
        whether the monomeric complex is a cation or an anion. Indeed, elec-
        trical charges cannot indefinitely accumulate on a metal-oxo-polymer,
        and condensation stops as soon as conditions allowing nucleophilic
        substitution are no longer present. As condensation causes water
        elimination, there is a change in composition of the reaction product that
        produces a variation of its average electronegativity, causing charge
        redistribution within its structure and, therefore, a change in the
        reactivity of the functional groups [10]. Hence, OH ligands in the grow-
        ing species may lose their nucleophilic character, and cations may lose
        their electrophilic character. Usually, during condensation, the nucle-
        ophilic character of hydroxo ligands cancels in polycations, and the elec-
        trophilic character of the cation cancels in polyanions. Condensation of
        electrically neutral ions (h   z) continues always indefinitely until there
        is precipitation of a solid (hydroxide, oxyhydroxide, or more or less
        hydrated oxide) or of a basic salt in the presence of complexing ligands.
        Elimination of water from noncharged complexes never leads to a
        sufficient change in the average electronegativity to cancel the reactivity
        of functional groups.
          In theory, an hydroxide M(OH) is formed via endless condensation of
                                      z
        aquo-hydroxo complexes. However, the hydroxide may not be stable.
        Its spontaneous dehydration, more or less rapid and extensive, gener-
        ates an oxyhydroxide MO (OH) z 2x  or a hydrated oxide MO z/2    (H O) .
                                x
                                                                        x
                                                                     2
        The reaction takes place via oxolation in the solid phase with elimina-
        tion of water from hydroxo ligands. The reaction is associated with
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