Biomedical Engineering Reference
In-Depth Information
coordination of the PO
4
group. To this extent, four models of phosphate soda-lime glasses
were studied by applying the same melt-and-quench procedure used for the 45S5 Bioglass®.
The unit cell size has also been increased from the former 78 atoms to new models
containing an average of 250 atoms. The larger size has allowed us to derive models which
could be more representative of the amorphous long-range disorder typical of glassy
materials.
The main structural features of the four modelled structures, whose correspondent images
are displayed in Figure 8., are listed in Table 2, together with their molar composition. The
“P0” structure refers to a phosphorous-free soda-lime glass.
Model SiO
2
CaO Na
2
OP
2
O
5
a b c
Volume
P0 45 24 22 - 14.97 14.23 14.77 91.3 90.7 89.2 3144
P2.5 41 23 20.5 2.5 14.47 14.72 14.69 90.0 91.5 90.9 3128
P5.5 35 23 20.5 5.5 14.68 14.47 15.08 91.4 90.0 87.9 3199
P9.5 27 21 19.5 9.5 14.71 14.78 14.50 92.2 90.2 90.1 3150
Table 2. Molar per cent composition of the four studied models of glasses together with the
unit cell parameter values of the optimized structures illustrated in Fig. 6. Lattice
parameters expressed in Å, angles in degrees and volumes in Å
3
.
A direct comparison of volume values for the four models is not reasonable, since there are a
number of tiny differences in molar composition in order to maintain the desired ratios
between components as well as the total electroneutrality. Indeed, no linear relationship
exists between the increase in %P
2
O
5
and volume.
A comparison between the structural and vibrational features of the two models mostly
similar in composition to the 45S5 Bioglass® has been carried out,
i.e.
the unit cell with 78
against that with 248 atoms (P2.5 of Figure 8b). In the smaller structure, as already described
and illustrated in Figure 7, two phosphate groups are present: one isolated and the other
connected to the silicon framework. In the larger model, five phosphate groups are located
inside the unit cell, three of which are isolated, while the others linked to the siliceous
network. In terms of Q
n
species (a Q
n
species is a network-forming ion, like Si or P, bonded
to
n
bridging oxygens), the 60% of the total number of PO
4
groups is represented by Q
0
(orthophosphates), while the remaining 40% is equally divided among Q
1
and Q
2
(see Figure
9b, blue curve). If we analyse the total radial distribution function g(r) for the P2.5 model
plotted in Figure 9a., it clearly appears by the two peaks that the bond length of the P-NBO
bond (NBO stands for non-bridging oxygen) is slightly shorter than that for the P-BO bonds
(1.552 compared to 1.616 Å, respectively). Moreover, the P-BO bonds are numerically much
less, as visible from the part b. of the same Figure 9.
Considering the Q
n
distribution for the other two phosphorous-containing models, namely
P5.5 and P9.5, it results: for P5.5 the 73% of the total 11 phosphate groups are isolated while
the rest are Q
1
and for the total 19 phosphate groups of the P9.5 model, 37% are isolated,
58% are Q
1
and the 5% Q
2
, in other words 7 Q
0
, 11 Q
1
and a Q
2
. The graph in Figure 9a.
schematizes the different distribution for the larger models.
The P-O bond distances, both for bridging and non-bridging oxygens, vary according to the
different Q
n
species, as reported in Table 3.
As a general comment, P-NBO distances follow the trend: Q
0
> Q
1
>Q
2
while for P-BO
values in case of Q
1
and Q
2
species there is no definite trend, probably due to the limited
number of sites in the considered structures.
