Biomedical Engineering Reference
In-Depth Information
As the main interest in the type A defect is the stability of the OH
-
-CO
3
2-
substitution as a
function of CO
3
2-
content, we modeled three cases using a 2x2 supercell:
(4-x)Ca
10
(PO
4
)
6
(OH)
2
+ xCa
10
(PO
4
)
6
(CO
3
) → Ca
40
(PO
4
)
24
(CO
3
)
x
(OH)
8-2x
(3)
The most stable case occurs (see Fig. 6A) when three out of four pairs of OH ions (x=3) were
substituted with carbonate ions (ΔE
r
= -24 kJ/mol). It is notable that the percentage of
carbonate related to this minimum energy structure (4.4%) is close to that found in dentine
tissue (5.6%) and in tooth enamel (3.5%) (Dorozhkin, 2009).
Among the five typologies of B type defect, we investigated only the substitution of Ca with
Na or H. As all the phosphate ions are equivalent by symmetry, the substitution with
carbonate is easy. On the contrary, in the cationic substitution to restore the neutrality, there
is a choice among ten Ca ions. These are not equivalent, as the symmetry is broken by the
carbonate substitution. We selected only four Ca ions, those nearest to the carbonate,
because from the experiment it is known that the two defective substituents are close to each
other. Indeed, in the four selected cases, the most stable structures are those in which the
distance between the substituents is minimum. The different stabilities were obtained by
calculating the energy variation (ΔE
r
) for the following reactions:
Ca
10
(PO
4
)
6
(OH)
2
+ NaHCO
3
→ Ca
9
Na(PO
4
)
5
(CO
3
)(OH)
2
+ CaHPO
4
(4)
Ca
10
(PO
4
)
6
(OH)
2
+ H
2
CO
3
→ Ca
9
H(PO
4
)
5
(CO
3
)(OH)
2
+ CaHPO
4
(5)
The ΔE
r
is 108 kJ/mol for reaction (4) and -94 kJ/mol for reaction (5), indicating that the
inclusion of H is much more preferable than Na. The reason relies upon the formation of
bulk water between the H and the OH ion of the column. This water molecule stabilizes the
structure and its removal requires 136 kJ/mol, because of the occurrence of rather strong H-
bonds. The two structures are reported in Fig. 6 (B/Na and B/H).
We also calculated some bulk structures in which both typologies (A and B) of substitutions
were present at the same time, in order to better mimic the bone features. Among all the
simulated structures, the most favorable situation is the one reported in Fig. 6 (A+B/H): a
carbonate ion substitutes a pair of OH ions while another carbonate replaces a phosphate
with formation of a water molecule. The hydrogen bonds formed by the water molecule are
stronger than those of the B defect model, highlighting that the two defects interact and
influence each other. The energy of formation of the mixed A+B/H structure is -752 kJ/mol
for the reaction 6.
11.5 Ca
3
(PO
4
)
2
+ 1.5 CaCO
3
+ 3 Ca(OH)
2
+ 0.5 H
2
CO
3
→ Ca
39
H(PO
4
)
23
(CO
3
)
2
(OH)
6
(6)
2.2 Bioglass: the effect of varying phosphorous content
As already described in the Introduction of this Chapter, bioactive glasses are extensively
studied as prostheses for bone and tooth replacement and regeneration. In particular, the
45S5 composition has continuously been investigated, not only in its compact form, whose
applications are limited to low load-bearing, but also as particulates and powders for bone
filler use. Hence, the computational investigations of the variation in composition for the
different glass components still represent a very interesting and stimulating task.
In the computational area, the most natural method to simulate glassy materials is usually
classical molecular dynamics via the melt-and-quench procedure. Recently, much
