**2.2.3 Effect of P2O5 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 Q1 and Q2 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 Q1 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 PO4 (for fully isolated groups) and PO4(SiO4)1,2 (for the other cases) shows a good agreement

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

Figure 11 illustrates a specific example of how to detect the various phosphate groups in terms of Qn (isolated or connected phosphates) by IR spectroscopy. We reported at the bottom of the graph the P2.5 IR spectrum of the phosphates computed applying the aforementioned procedure (fragment mode). The three bar charts refer each one to the Qn species present inside the structure and show only the frequencies involving that specific class of phosphate groups (isolated or connected to the network). It is interesting to note the shift of the highest and lowest bands comparing Q1 and Q2 cases: the highest frequency – indicated with the label *h* – corresponds to the stretching of the P=O bond and is shifted to higher values in case of Q2, with respect to Q1 and Q0. On the contrary, in the region of low frequencies, modes involving the Q2 species are shifted to lower values compared to the Q1

Figure 12 illustrates the graphical representation of the normal modes displacement for the

ones. The OPO bending region (600-700 cm-1) remains almost unaffected.

five stretching and bending modes of the Q2 species present in the P2.5 glass.

Fig. 12. Schematic representation of the normal mode displacement assigned to the Q2 species for the P2.5 model (PO4 structural unit connected to 2 SiO4 groups). Colour coding:

The simulated IR spectra for the phosphate groups of the three phosphorous-containing models have been then compared one to each other and to the phosphorous-free structure

The first evident difference between phosphorous-free P0 and the other models is the absence of bands in the spectral region at high frequencies (1200-1400 cm-1). As we have discussed above, that is the typical region of the P=O stretching mode of phosphate groups. This mode is shifted to lower frequencies and the band is broadened when passing from P2.5 to P9.5. Another clear indication of the presence of phosphate groups is the band at about 600-700 cm-1, which corresponds to the O-P-O bending region. The 1100-800 cm-1 spectral range, on the contrary, is not easily assigned to phosphate groups inside the bioglass since also Si-O stretching are located in that zone. However, the effect of increasing the P2O5 content inside the unit cell is reflected in a general broadening of the P-O stretching

Si light blue, oxygen red, phosphorous yellow; frequencies expressed in cm-1.

P0, as displayed in Figure 13.

and O-P-O bending modes.

291

with the black spectrum, so that this methodology has been adopted to compute the spectra for the larger structures with variable P content. In other words, the differences in peaks between the red and the blue spectra of Figure 10 are due to the presence (blue line) or absence (red line) of the extra SiO4 group.

Fig. 10. Simulated IR spectra of the similar 45S5 Bioglass® model in the following sequence from bottom to top: full frequency calculation (black line), full frequency calculation including only PO4-involved modes (red line) and fragment calculation considering in the fragment PO4 and SiO4 which is directly bonded to PO4. No IR intensities are reported and the chosen band width is of 20 cm-1.

Fig. 11. IR peaks assignment for phosphate groups of the P2.5 model based on the different Qn species. Label *h* and *l* refer to the peculiar bands at high and low frequencies, respectively, that allow us to distinguish the Q0 species from the Q1 and Q2. In case of Q2, see Fig. 12 for the schematic representation of the associated normal modes.

with the black spectrum, so that this methodology has been adopted to compute the spectra for the larger structures with variable P content. In other words, the differences in peaks between the red and the blue spectra of Figure 10 are due to the presence (blue line) or

Fig. 10. Simulated IR spectra of the similar 45S5 Bioglass® model in the following sequence from bottom to top: full frequency calculation (black line), full frequency calculation including only PO4-involved modes (red line) and fragment calculation considering in the fragment PO4 and SiO4 which is directly bonded to PO4. No IR intensities are reported and

Fig. 11. IR peaks assignment for phosphate groups of the P2.5 model based on the different

respectively, that allow us to distinguish the Q0 species from the Q1 and Q2. In case of Q2, see

Qn species. Label *h* and *l* refer to the peculiar bands at high and low frequencies,

Fig. 12 for the schematic representation of the associated normal modes.

absence (red line) of the extra SiO4 group.

the chosen band width is of 20 cm-1.

Figure 11 illustrates a specific example of how to detect the various phosphate groups in terms of Qn (isolated or connected phosphates) by IR spectroscopy. We reported at the bottom of the graph the P2.5 IR spectrum of the phosphates computed applying the aforementioned procedure (fragment mode). The three bar charts refer each one to the Qn species present inside the structure and show only the frequencies involving that specific class of phosphate groups (isolated or connected to the network). It is interesting to note the shift of the highest and lowest bands comparing Q1 and Q2 cases: the highest frequency – indicated with the label *h* – corresponds to the stretching of the P=O bond and is shifted to higher values in case of Q2, with respect to Q1 and Q0. On the contrary, in the region of low frequencies, modes involving the Q2 species are shifted to lower values compared to the Q1 ones. The OPO bending region (600-700 cm-1) remains almost unaffected.

Figure 12 illustrates the graphical representation of the normal modes displacement for the five stretching and bending modes of the Q2 species present in the P2.5 glass.

Fig. 12. Schematic representation of the normal mode displacement assigned to the Q2 species for the P2.5 model (PO4 structural unit connected to 2 SiO4 groups). Colour coding: Si light blue, oxygen red, phosphorous yellow; frequencies expressed in cm-1.

The simulated IR spectra for the phosphate groups of the three phosphorous-containing models have been then compared one to each other and to the phosphorous-free structure P0, as displayed in Figure 13.

The first evident difference between phosphorous-free P0 and the other models is the absence of bands in the spectral region at high frequencies (1200-1400 cm-1). As we have discussed above, that is the typical region of the P=O stretching mode of phosphate groups. This mode is shifted to lower frequencies and the band is broadened when passing from P2.5 to P9.5. Another clear indication of the presence of phosphate groups is the band at about 600-700 cm-1, which corresponds to the O-P-O bending region. The 1100-800 cm-1 spectral range, on the contrary, is not easily assigned to phosphate groups inside the bioglass since also Si-O stretching are located in that zone. However, the effect of increasing the P2O5 content inside the unit cell is reflected in a general broadening of the P-O stretching and O-P-O bending modes.

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

Fig. 14. Surface model of the P2.5 bioglass with adsorbed water molecules at both top and bottom faces. Colour coding: silicon light blue, oxygen red, sodium pink, calcium dark blue,

In the present Chapter it has been explained how crucial the computational techniques are when applied together with experimentalist measurements in the understanding of biological complex systems and mechanisms dealing with biomaterials for a large number of reasons. Indeed, computational methods are extremely powerfully applied to predict structure formation and crystal growth as well as to describe at a molecular level the real interactions responsible of the attachment of the inorganic biomaterial to the organic tissue. In the investigation of phenomena related to a complex system such as the human body, many approximations are required, so a reductionist approach is employed also in the

In this Chapter, the approach has been explained for two typical biomaterials: hydroxyapatite and Bioglass® 45S5. In particular, for the first material, the aim was to describe the study of its (010) non-stoichiometric surfaces in interaction with water and carbon monoxide. For the latter, the adopted strategy has been analyzed and then a specific example has been reported, dealing with the spectroscopic characterization of computed vibrational features with the increasing amount of phosphorous in a sufficiently large unit

The general knowledge gained in recent years through the use of computational techniques such as those described in this chapter is great, but not enough to fully understand the peculiar characteristics of the materials that make up the musculo-skeletal system and to provide appropriate care for important illnesses such as osteoporosis or degenerative and

phosphorous yellow, hydrogen bonds black dotted line.

cell starting from the well-know 45S5 Bioglass® composition.

metabolic diseases, benign and malignant tumors and trauma.

**3. Conclusion** 

computational analysis.

293

Fig. 13. Simulated IR spectra of the four models of glasses at increasing %P2O5 content.

#### **2.2.4 Future perspectives: Surface modelling**

The natural subsequent step in bioactive glass simulation deals with the modeling of surfaces. Indeed, each process of the Hench mechanism that leads to the implant integration typically occurs at the interface between the inorganic material and the biological fluid. Thus, the knowledge of surface properties, such as electrostatic potential and adsorptive behavior towards simple molecules as water, becomes essential in the investigation of bioglasses (Tilocca & Cormack, 2009).

Modeling surfaces is generally not a trivial task, particularly when the bulk material is amorphous. For an amorphous material the identification of a particular face by crystallographic indexes is rather arbitrary as the atomic density is statistically distributed in space in a rather uniform way. A second difficulty is the need of breaking both ionic and covalent bonds during the slab definition which may render the system non-neutral.

In Figure 14, the model of one of the many possible bioglass surfaces extracted from the P2.5 bulk of Figure 8b is presented. The surface was cut out from the bulk as a real 2D slab (infinite in the two dimensions), dangling bonds were saturated with hydrogen atoms and a full optimization run was performed. The resulting surface is very interesting per se, but much more considering its behaviour when hydrated, since water molecules are ubiquitously present in the biological fluids where the material is immersed. In particular, a key issue is to see whether H2O will chemisorb by dissociating on the exposed Na+ and Ca2+ cations, a step essential in the Hench mechanism.

In our laboratory a systematic study of the several possible surfaces of the structure with the 45S5 composition is on-going. The application of different methodologies, such as *ab initio* molecular dynamics, already used in the literature (Tilocca, 2010), will be considered to fully characterize the adsorption processes of water and even collagen occurring at the interface between bioactive material and the biological tissue.

Fig. 14. Surface model of the P2.5 bioglass with adsorbed water molecules at both top and bottom faces. Colour coding: silicon light blue, oxygen red, sodium pink, calcium dark blue, phosphorous yellow, hydrogen bonds black dotted line.
