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Nanomaterials Fabrication 35

structural changes in order to preserve the coordination of the cation.
Usually, elements with a 2 charge precipitate as hydroxides, and those
with a 3 charge as oxyhydroxides (the final stage of evolution is the
oxide). Those of higher charge form oxides of various level of hydration [14].
This sequence is a clear illustration of the increasing polarization of the
hydroxo ligands by the cation, which is associated with the covalent nature
of the metal-oxygen bond.
In summary, condensation of cations in solution is initiated when
acidity allows the presence of the hydroxo ligand in the coordination
sphere of the cation. This occurs through addition of a base to aquo
complexes of elements of formal charge equal to or smaller than 4, or
through addition of an acid to oxo complexes of elements of charge equal
to or greater than 4 (Figure 3.1). Two reactions, olation and oxolation,
respectively, ensure the development of condensation. The condensation
of cationic and anionic hydroxylated complexes is always limited. It
leads to polycations and polyanions, respectively. Formation of a solid
requires the presence of zero-charge complexes. It is also possible
(although less common) to involve redox phenomena in order to decrease
the formal charge on the metal and force the appearance, under given
acidic conditions, of the hydroxo ligand in the coordination sphere of the
cation.
Hydroxide, oxyhydroxide, or hydrated oxide solid phases obtained via
precipitation are made of particles whose average size may range from
a few nanometers to a few microns. Particle morphology may vary
depending on synthesis conditions. Moreover, aging in aqueous solution
may bring about significant dimensional, morphological, and structural
changes. In order to understand how small particles form and what
role the experimental parameters play on their characteristics and on
evolution, it is useful to review the kinetic aspects of condensation
reactions.
The precipitation of a solid involves four kinetic steps [15–17]:

0
1. Formation of the zero-charge precursor [M(OH) z (H 2 O) n z ] , which is
able to condense and form a solid phase. Hydroxylation of the cation
is a very fast acid/base reaction, but the rate of formation of the zero-
charge precursor in solution can largely vary depending on whether
the reaction starting from cationic complexes for example, takes place
through addition of a base, thermohydrolysis, or slow thermal decom-
position of a base such as urea.
2. Creation of nuclei, through condensation (olation or oxolation) of
zero-charge precursors. The condensation rate is a function of pre-
cursor concentration, and as long as it is small at the onset of cation
hydroxylation, the rate is almost zero (zone I, Figure 3.2a). Beyond
, the condensation rate increases abruptly
a critical concentration C min