Biomedical Engineering Reference
In-Depth Information
A polynuclear model [50-59] was created from the study on apatite
dissolution and growth kinetics under the constant composition
conditions. Polydispersed samples of apatite were put into a stirred
undersaturated (for dissolution experiments) or supersaturated (for
those on crystal growth) solutions and the solution pH and amount
of chemicals added (an acid for the dissolution experiments and a
base for those on crystal growth) were permanently recorded as
functions of time. The results obtained were plotted versus either
undersaturation or supersaturation values: straight lines were
obtained in the specific logarithmic coordinates typical for this model
[60]. According to this model, dissolution nuclei, i.e. collections of
vacant sites for Ca
2+
4
3−
−
ions, are formed on the crystal
surface of apatite and spread over the surface with a definite lateral
rate [51, p. 30].
In polynuclear model, the nucleation rate is assumed as a function
of the mean ion activity. A lateral growth rate of the nuclei is assumed
proportional to the difference between the total concentration of
calcium ions in the saturated solution and in a solution, while the
rate constant is related to the frequency for calcium ions to make
a diffusion jump into a kink and, simultaneously, partly dehydrate
[57, 58]. Investigations on apatite dissolution and crystal growth
using atomic force microscopy revealed that the rate-determining
step was not the diffusion but two-dimensional surface nucleation
[61, 62]. These observations provided a valuable support for the
polynuclear model.
The experimental data on dissolution and growth rates versus
undersaturation (S < 1) and supersaturation (S > 1) values,
respectively, were obtained. Numeric values of surface tension (40
mJ/m
, PO
and OH
2
2
for apatite growth [57,
58]), ionic frequencies to enter or leave a kink (1.6 × 10
for apatite dissolution and 100 mJ/m
5
/s [56]), the
mean distance between kinks in a surface nucleus (approximately
3.07 Å [55]) and the critical nuclei for both HA [50-54, 57, 58], and
FA [55, 56] were calculated. Furthermore, within 5.0 < pH < 7.2 the
dissolution kinetics was found to follow the polynuclear model, while
that of growth appeared to follow the polynuclear model within 5.5
< pH < 6.5 and the combined mono-polynuclear model at pH = 5.0
[55, 56].
A new idea about hydroxide ions formation at the hydroxide
sites of HA from water molecules trapped under the crystal surface
appeared in the most recent papers of this series [57, 58]. Probably,
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