Biomedical Engineering Reference
In-Depth Information
In general, an electrostatic interaction, a hydrophobic
interaction and a “cementing” effect of water molecules are
among the main factors holding ions of a cluster altogether [231].
Again, a “cementing” effect of water molecules is applied for ACPs
precipitated from aqueous solutions only. Theoretical investigations
on the stability of different calcium orthophosphate clusters with an
increasing number of ions have confirmed that Posner's clusters are
the most stable arrangement [232]. The potential energy surfaces
associated with [Ca
(PO
)
]
clusters were analyzed in details using
3
4
2
n
ab initio
ranging from 1 to 4 [233]. The energy
criteria were found to favor the Posner's cluster, which is the core
of the actual structural model of ACP (more precisely, of amorphous
TCP). Moreover, the calculations showed that an aggregation of the
clusters corresponded to a large energy stabilization whatever the
cluster considered [233], which is in agreement with the Posner's
hypothesis in which clusters are proposed to be closely packed in
the ACP structure. Furthermore, the vibration spectra of ACP have
been modeled as well [234]. In spite of the aforementioned, it is
not quite clear from what experimental, spectroscopic, and/or
structural data the cluster model (Fig. 1.7) has been derived, except
the TCP composition. Further, it is not entirely clear whether there
are volumetric regions within the large 300-1000 Å particles that
are free from the 9.5 Å clusters. In other words, are there some
volumetric regions within the large 300-1000 Å particles where the
atoms are completely random with no SRO? Moreover, the results of
EXAFS analysis indicated that the range of orderly Ca-Ca and Ca-P
interactions in ACP were much shorter than would be predicted from
the Betts and Posner model [116, 226]. Another weakness in the
model is that water only serves to fill the interstices between the HA
subsets and is not an essential part of the ACP structure, contrary to
the assumptions by Sedlak and Beebe [213]. Both of these weaknesses
could possibly be remedied if a smaller spatial domain is carved from
a portion of the OCP unit cell that contains a part of the hydration
layer. However, this suggestion has not been examined in details. It
is also possible, however, that the defining structural unit for ACP
is a truly unique entity with no satisfactory crystallographic model.
In fact, there is no
calculations for
n
need for such a model, as the defining
unit for ACP would not be constrained structurally by the symmetry
requirements for crystalline arrangements. Furthermore, it will also
depend on the Ca/P ratio. Therefore, ACP could have a structural
a priori
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