**2.2.1 Multi-scale strategy for the modelling of 45S5 Bioglass®**

The *ab initio* modelling of an amorphous material as the 45S5 Bioglass® has straightway caused a number of challenges. As the internal coordinates are not available from classical structural analysis, we have developed a multi-scale strategy to obtain a feasible amorphous bioglass model similar in composition to the 45S5. This approach has been largely illustrated in previous papers (Corno & Pedone, 2009; Corno et al., 2008; A. Pedone et al., 2008) so that here we only summarize the most important steps.

Firstly, we adopted classical molecular dynamics simulations to model a glassy bulk structure which could be close to the 45S5 composition keeping the size of the unit cell small enough for *ab initio* calculations, *i.e.* 78 atoms. In order to reproduce the correct ratio between SiO2, P2O5, Na2O and CaO components, the experimental density of 2.72 g/cm3 has been maintained fixed in a cubic box of 10.10 Å per side. After randomly generating atomic

*In Silico* Study of Hydroxyapatite and Bioglass®: How Computational Science Sheds Light on Biomaterials

and mobile (Tilocca & Cormack, 2007).

a.

al., 2008b). Indeed, it is well known that structural and compositional features of bioactive glasses are strongly connected to their bioactivity (Clayden et al., 2005; Lin et al., 2005). In particular, it has been demonstrated (Tilocca, 2010) that in compositions less bioactive than the 45S5 the majority of phosphate groups are linked to one or two silicon atoms. Conversely, in bioactive glasses as the 45S5, almost all the phosphate groups are isolated

c. d.

In our research work, we have aimed to correlate the change in phosphorous content with the change in structural and vibrational properties, these latter as a tool to detect the local

Fig. 8. Best views of the optimized structures of the four studied glass models: a. no phosphorous (P0); b. 2.5% phosphorous (P2.5); c. 5.5% phosphorous (P5.5) and d. 9.5% phosphorous (P9.5). Colour coding: silicon light blue, oxygen red, sodium pink, calcium dark blue and phosphorous yellow. Cell parameters drawn in red for *a*, in green for *b* and in

blue for *c*, while cell borders are in black (their values listed in Table 5).

287

b.

positions, a melt-and-quench procedure was simulated: heating at 6000 K and then equilibrating for 100 ps. Next, continuously cooling from 6000 to 300 K in 1140 ps with a nominal cooling rate of 5 K/ps was performed. The temperature was decreased by 0.01 K every time step using Nose-Hoover thermostat with the time constant parameter for the frictional coefficient set to 0.1 ps (Hoover, 1985). Simulations were carried out in the constant volume NVT ensemble and 100 ps of equilibration at constant volume and 50 ps of data production were run at 300 K. On the derived structures, static energy minimizations were carried out at constant pressure and volume and the most representative model was chosen for *ab initio* calculations.

The final candidate structure was minimized both in terms of internal coordinates and lattice parameters, performing full relaxation runs. In Figure 7a the quantum-mechanical optimized structure of the selected Bioglass model is displayed. In the unit cell, which has become triclinic due to the lattice parameter deformation, two phosphate groups are present: one isolated (orthophosphate) and the other linked to one silicon atom. The structural analysis was followed by the simulation of the IR spectrum. Figure 7b reports the comparison between experimental (Lusvardi et al., 2008b) and computed spectra, which shows a very good agreement between the two spectra. The punctual assignment of each peak in the simulated case has been published in a previous paper (Corno et al., 2008), where the 45S5 model has been compared with an amorphous silica structure, to investigate the role of network modifier cations and phosphate groups in structural and vibrational properties of a pure SiO2 framework. Hence, the reliability of the chosen multi-scale strategy has been proved.

Fig. 7. 45S5 Bioglass model: a. best view of the optimized structure (Na12Ca7P2Si13O44 composition), colour coding: silicon light blue, oxygen red, sodium pink, calcium dark blue and phosphorous yellow; cell parameters drawn in red for *a*, in green for *b* and in blue for *c*, while cell borders are in black; b. experimental (red line) and B3LYP (black line) IR spectra. (Corno et al., 2008; Lusvardi et al., 2008b)

#### **2.2.2 Simulation of bioactive glasses with different P2O5 content**

More recently, the influence of P2O5 content on the structure of bioactive glass compositions has been object of investigation (O'Donnell et al., 2009; O'Donnell et al., 2008a; O'Donnell et

positions, a melt-and-quench procedure was simulated: heating at 6000 K and then equilibrating for 100 ps. Next, continuously cooling from 6000 to 300 K in 1140 ps with a nominal cooling rate of 5 K/ps was performed. The temperature was decreased by 0.01 K every time step using Nose-Hoover thermostat with the time constant parameter for the frictional coefficient set to 0.1 ps (Hoover, 1985). Simulations were carried out in the constant volume NVT ensemble and 100 ps of equilibration at constant volume and 50 ps of data production were run at 300 K. On the derived structures, static energy minimizations were carried out at constant pressure and volume and the most representative model was

The final candidate structure was minimized both in terms of internal coordinates and lattice parameters, performing full relaxation runs. In Figure 7a the quantum-mechanical optimized structure of the selected Bioglass model is displayed. In the unit cell, which has become triclinic due to the lattice parameter deformation, two phosphate groups are present: one isolated (orthophosphate) and the other linked to one silicon atom. The structural analysis was followed by the simulation of the IR spectrum. Figure 7b reports the comparison between experimental (Lusvardi et al., 2008b) and computed spectra, which shows a very good agreement between the two spectra. The punctual assignment of each peak in the simulated case has been published in a previous paper (Corno et al., 2008), where the 45S5 model has been compared with an amorphous silica structure, to investigate the role of network modifier cations and phosphate groups in structural and vibrational properties of a pure SiO2 framework. Hence, the reliability of the chosen multi-scale strategy

Fig. 7. 45S5 Bioglass model: a. best view of the optimized structure (Na12Ca7P2Si13O44 composition), colour coding: silicon light blue, oxygen red, sodium pink, calcium dark blue and phosphorous yellow; cell parameters drawn in red for *a*, in green for *b* and in blue for *c*, while cell borders are in black; b. experimental (red line) and B3LYP (black line) IR spectra.

More recently, the influence of P2O5 content on the structure of bioactive glass compositions has been object of investigation (O'Donnell et al., 2009; O'Donnell et al., 2008a; O'Donnell et

a. b.

**2.2.2 Simulation of bioactive glasses with different P2O5 content** 

(Corno et al., 2008; Lusvardi et al., 2008b)

chosen for *ab initio* calculations.

has been proved.

al., 2008b). Indeed, it is well known that structural and compositional features of bioactive glasses are strongly connected to their bioactivity (Clayden et al., 2005; Lin et al., 2005). In particular, it has been demonstrated (Tilocca, 2010) that in compositions less bioactive than the 45S5 the majority of phosphate groups are linked to one or two silicon atoms. Conversely, in bioactive glasses as the 45S5, almost all the phosphate groups are isolated and mobile (Tilocca & Cormack, 2007).

Fig. 8. Best views of the optimized structures of the four studied glass models: a. no phosphorous (P0); b. 2.5% phosphorous (P2.5); c. 5.5% phosphorous (P5.5) and d. 9.5% phosphorous (P9.5). Colour coding: silicon light blue, oxygen red, sodium pink, calcium dark blue and phosphorous yellow. Cell parameters drawn in red for *a*, in green for *b* and in blue for *c*, while cell borders are in black (their values listed in Table 5).

In our research work, we have aimed to correlate the change in phosphorous content with the change in structural and vibrational properties, these latter as a tool to detect the local

*In Silico* Study of Hydroxyapatite and Bioglass®: How Computational Science Sheds Light on Biomaterials

models P2.5 (blue), P5.5 (green) and P9.5 (red).

P2.5, P5.5 and P9.5 models are reported in Å.

without its connected oxygen atoms.

linked to the Q1 species.

**2.2.3 Effect of P2O5 content on the simulated IR spectra** 

a. b.

Model <P-NBO> Q0 <P-NBO> Q1 <P-NBO> Q2 <P-BO> Q1 <P-BO> Q2 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

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 Q1 and Q2 species, the question was to decide whether to include or not the linked silicon atom with or

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

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 PO4 (for fully isolated groups) and PO4(SiO4)1,2 (for the other cases) shows a good agreement

Fig. 9. a. Radial distribution function of the total P-O bonds, distinguishing between nonbridging oxygen (NBO, orange dotted line) and bridging oxygen (BO, blue line); b. percentage distribution of the phosphate groups in terms of Qn species for the three large

289

coordination of the PO4 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.


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 Å3.

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 %P2O5 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 Qn species (a Qn species is a network-forming ion, like Si or P, bonded to *n* bridging oxygens), the 60% of the total number of PO4 groups is represented by Q0 (orthophosphates), while the remaining 40% is equally divided among Q1 and Q2 (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 Qn 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 Q1 and for the total 19 phosphate groups of the P9.5 model, 37% are isolated, 58% are Q1 and the 5% Q2, in other words 7 Q0, 11 Q1 and a Q2. 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 Qn species, as reported in Table 3.

As a general comment, P-NBO distances follow the trend: Q0 > Q1 >Q2 while for P-BO values in case of Q1 and Q2 species there is no definite trend, probably due to the limited number of sites in the considered structures.

coordination of the PO4 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

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 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

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

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 Qn species (a Qn species is a network-forming ion, like Si or P, bonded to *n* bridging oxygens), the 60% of the total number of PO4 groups is represented by Q0 (orthophosphates), while the remaining 40% is equally divided among Q1 and Q2 (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

Considering the Qn 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 Q1 and for the total 19 phosphate groups of the P9.5 model, 37% are isolated, 58% are Q1 and the 5% Q2, in other words 7 Q0, 11 Q1 and a Q2. The graph in Figure 9a.

The P-O bond distances, both for bridging and non-bridging oxygens, vary according to the

As a general comment, P-NBO distances follow the trend: Q0 > Q1 >Q2 while for P-BO values in case of Q1 and Q2 species there is no definite trend, probably due to the limited

unit cell parameter values of the optimized structures illustrated in Fig. 6. Lattice

 

 

Volume

"P0" structure refers to a phosphorous-free soda-lime glass.

Model SiO2 CaO Na2O P2O5 *a b c*

parameters expressed in Å, angles in degrees and volumes in Å3.

exists between the increase in %P2O5 and volume.

less, as visible from the part b. of the same Figure 9.

different Qn species, as reported in Table 3.

number of sites in the considered structures.

schematizes the different distribution for the larger models.

materials.

Fig. 9. a. Radial distribution function of the total P-O bonds, distinguishing between nonbridging oxygen (NBO, orange dotted line) and bridging oxygen (BO, blue line); b. percentage distribution of the phosphate groups in terms of Qn species for the three large models P2.5 (blue), P5.5 (green) and P9.5 (red).


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.
