Biomedical Engineering Reference
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b.
Fig. 9. a. Radial distribution function of the total P-O bonds, distinguishing between non-
bridging oxygen (NBO, orange dotted line) and bridging oxygen (BO, blue line); b.
percentage distribution of the phosphate groups in terms of Q n species for the three large
models P2.5 (blue), P5.5 (green) and P9.5 (red).
a.
Model <P-NBO> Q 0 <P-NBO> Q 1 <P-NBO> Q 2 <P-BO> Q 1 <P-BO> Q 2
P2.5 1.556 1.539 1.508 1.597 1.602
P5.5 1.559 1.523 - 1.660 -
P9.5 1.557 1.531 1.515 1.631 1.588
Table 3. Average P-O bond lengths for both bridging and non-bridging oxygen of the three
P2.5, P5.5 and P9.5 models are reported in Å.
2.2.3 Effect of P 2 O 5 content on the simulated IR spectra
A complete vibrational analysis was outside our computational facilities, due to the size of
the simulated bioglass models (250 atoms inside the unit cell, no symmetry). An alternative
approach, here adopted, is the so-called “fragment” calculation of frequency. It consists on
the selection of the interesting atoms - in this case phosphate groups - to be considered for
the calculation of vibrational normal modes. Obviously this approach is an approximation
and needs to be first tested. Our test case was the 45S5 structure of Figure 7a, for which the
full IR spectrum was available. In particular for the phosphate groups containing Q 1 and Q 2
species, the question was to decide whether to include or not the linked silicon atom with or
without its connected oxygen atoms.
Figure 10 reports three simulated IR spectra of the 45S5 model: the full spectrum (black
line), the full spectrum including only modes involving phosphate groups (red line) and the
partial spectrum where the fragment contains only phosphate groups and silicon atoms
linked to the Q 1 species.
In order to dissect the contribution to the full IR spectrum (black spectrum, Fig. 10) of modes
involving the displacements of P atoms we rely on the Potential Energy Distribution (PED).
All modes involving the P atom in the PED of the full spectrum are included whereas the
remaining ones are removed from the spectrum (red spectrum, Fig. 10). The comparison
with the spectrum (blue spectrum, Fig. 10) computed by including as a fragment the PO 4
(for fully isolated groups) and PO 4 (SiO 4 ) 1,2 (for the other cases) shows a good agreement
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