Biomedical Engineering Reference
In-Depth Information
of calcium cations. According to the chemical model, an interaction
between calcium cations and anions of acid adsorbed from a solution
is believed to happen in such places [91-93]. This interaction results
in breaking of surface �O-Ca bonds (“�” stands for the surface) and
detachment of some calcium from the kink sites followed by their
diffusion away from crystal steps and further into the bulk solution
(the diffusion-controlled model [126, 140]). Detachment of calcium
might occur as calcium-acid complexes (the ion exchange model).
Recent computer simulations revealed that a local excess charge of
+3 and +4 must be created to cause exothermic Ca
2+
displacement
from Ca(1) and Ca(2) cites, respectively [122]. If so, under otherwise
equal conditions, detachment of Ca
2+
ions from Ca(1) cites of the
apatite surface should happen faster and/or easily than that from
Ca(2) cites.
Detachment of calcium ions results in formation of dissolution
nuclei. These nuclei are defined as collections of vacant sites for
Ca
2+
4
3−
−
ions on the crystal surface of apatite [51, p.
30]. According to the polynuclear model, removal even of one ion
might result in further dissolution because critical nuclei (x*) were
calculated to consist of 1-26 ions for dissolution of HA and 0.3-34
ions for dissolution of FA. (According to the authors, x* < 1 means
that there is no nucleation barrier to be overcome [56, p. 309]. Since
one unit cell of apatite contains 18 ions (Table 1.3), x* > 18 means
that more than one unit cell should be dissolved for a nucleus to
form). The numeric values for x* were found to depend on solution
pH and solution undersaturation [55, 56]. Furthermore, due to
charge repulsion, adsorbed protons (as HPO
, PO
, and X
groups)
might catalyze detachment of calcium ions from the kink sites (the
hydrogen catalytic model).
After being detached, calcium cations (possibly, as calcium-acid
complexes (the ion exchange model)) diffuse along the surface
away from the dissolution steps before entering the solution [126].
For dissolution of OCP (see Table 1.1) in slightly acidic (pH = 5.66)
solutions numeric values for the mean surface diffusion distance of
the lattice ions detached from steps were calculated. These values
were found to depend on the edge free energy and be within (17
±
and/or H
PO
4
2
4
±
≈
3.7 Å is the size of a growth unit (or
mean ionic diameter) [140]. Numeric values of mean ionic diameter
for apatites were also calculated. They appeared to be less than
that for OCP: 3.09 Å for HA and 3.07 Å for FA [57]. Taking into
4)α − (41
10)α, where α
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