2755
2827
2695 2783
Si-1892
Figure 3.34. The motion of four different Ca ions and one Si ion over 1 ns in 1000 K 45S5 simulation.
cause a greater number of channels connecting the surface to the bulk of the glass, allowing a greater diffusion of sodium out of the bulk, and water into the bulk. The increased presence of water in the bulk of the glass would also lead to an increase in the rate of hydrolysis of network bonds (Stage 2). Further, by intrinsically having fewer network bonds, the 45S5 composition would have a greater dissolution rate, as compared to the other two compositions.
The property of crosslink density, borrowed from polymer chemistry, is also instructive in showing the effect of glass composition on network connectivity. Good agreement between theoretical and simulated values of CLD was shown.
Investigation of ring size distributions showed few small-membered rings and an increased number of large rings (as compared to pure silica), consistent with previous models of high-modifier content glass. Fewer overall rings were observed for the 45S5 composition, as expected due to the decreased network connectivity.
However, based on calculation of the number of rings per node, there may not be a difference between the other two compositions. No simulation size effect was found when the simulation size was tripled. The visualization of large-membered rings was done to confirm ideas about the nature of large rings in modified glasses and how they are counted in a ring-statistics program.
Local structure was addressed with calculation of the Qn-species distributions for P and Si. The observed distributions were not consistent with an ordered binary model, but showed the presence of at least three species of P and Si for all compositions. The predominant species are Si2 and P0 in 45S5, and Si3 and P1 for 55S4.3 and 60S3.8. Overall, the presence of smaller n species correlated with a greater bioactivity. Some P-O-Si linkages were observed, though their presence in these glasses have not been confirmed. Agreement with experimental evidence was not good overall, as not all species were considered for each glass, due to peak overlap, low signals of the symmetric Q0 and Q4 species, and different methods of peak integration.
Qn-species connectivity was calculated to determine how the Q-units were distributed throughout the glass. Results show clustering of high-connectivity units
(particularly for larger simulations), suggesting silica-rich regions (and thus, alkali- rich regions as well), rather than a random distribution.
Bond angle distributions show similar features to previous models of high modifier content glass, e.g., a shift to lower angles and narrower peak width for the Si-O-Si bond angle, as compared to pure silica. These suggest a less-strained network due to the presence of NBO introduced by the network modifier content.
Similar O-Si-O and Si-O-Si distributions existed among the three glasses. The distributions were deconvoluted into contributions from NBO and BO bonding, which showed that NBO are associated with higher bond angles. The O-P-O distributions were had similar MPBA to the O-Si-O distributions, but smaller FWHM by about 3°, indicating a more regular PO4 tetrahedron. BAD for O-Na-O and O-Ca- O also agreed qualitatively with previous studies of modified glasses, showing a distinct peak around 60°, a broad peak around 90°, and a shoulder around 150°.
Coordination numbers were calculated for oxygen surrounding each cation.
Ideal values of 4.0 were found for Si and P. The CN of oxygen around Na and Ca is around six for all compositions, and slightly higher for Ca than Na in each case, in agreement with previous experimental and simulation studies. The concentration of NBO and BO in the simulations followed theoretical values (based on the assumption that each Na and P contributed one NBO and each Ca contributed two NBO to the bulk structure).
Correlation functions were used for further discussion of the short and medium range orders of glass structure. Shorter average bond lengths are found for P-O, as compared to Si-O. Bond lengths for Si-O were in the range 1.60-1.61 Å, slightly lower than the 1.62 Å found for pure silica, due to the large concentration of NBO in the bioactive glasses. Deconvolution of P-O and Si-O RDF shows shorter bond lengths for NBO, and an increasing contribution from BO with increasing silica content, as expected. RDF for Na-O and Ca-O were similar for all compositions, again, with an increasing contribution from BO with increasing silica content. A greater preference of Ca for NBO was noted, likely due to its greater ionic strength (i.e., charge). Distinct peaks in modifier-modifier correlations indicate a regular
influence on the glass structure, suggesting a modified random network, i.e., modifier clustering separate from silica-rich regions.
The P-cation and Si-cation pair distributions show a higher probability for P to be coordinated by both types of modifier for all compositions. Disagreement with NMR studies exists with regard to the presence of sodium disilicate-like Na-Si3
regions; simulation results suggest a preference of Na for Si2. However, some agreement with experiment is noted, as Ca also prefers Si2 to Si3.
An extensive study of bulk dynamics was undertaken for these glasses. Long- range diffusive behavior was only observed for sodium. Calcium showed only local movements (jumps between adjacent sites), while phosphorus showed only local vibrations. It is presumed that calcium migration may be restricted by its greater tendency for charge compensation of local NBO ions, but paths for phosphorus migration do not exist because it would move as relatively large PO4 groups.
However, it is suggested that following the ion-exchange and hydrolysis reactions, a more open network would be conducive to PO4 migration to the surface to participate in HCA formation.
A 5 ns simulation was performed for 45S5 at 1000 K to test the effect of simulation length on MSD plots. It was shown that increasing the simulation length can have a significant effect on the shape and slope MSD plots, confirming that simulations were not run for sufficient time to observe long-range diffusion for Ca, but that long-range diffusive motion is still only observed for Na in the time regime of the current study.
Self-diffusion coefficients were calculated from the MSD data, from which activation energies were calculated for Na and Ca diffusion. The calculated values show the same trend as dielectric spectroscopy results; an increasing network connectivity corresponds to a decrease in ion-hopping activation energy. This agrees with the assertion that ionic diffusion is not the rate-limiting step in the dissolution of these glasses.
The maximum displacement of each ion from its original position was shown to be a useful measure of diffusion differences among ions of a particular type. A considerable spread of values was shown for Na for each composition. Interestingly,
nearly every Na ion had moved from its original position (i.e., at least 3-4 Å) at some point during the simulation, again underlining the diffusive nature of Na in these glasses. Some evidence of Ca ions moving ~10 Å was also found, though most did not move any more than the average oxygen ion. Evidence for long-range diffusion of Na between a number of distinct sites was shown, as well as “sampling” of sites that were only momentarily occupied before the ion jumped back to a previous site.