MgO Substitution on the

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J. Phys. Chem. C 2009, 113, 15723–15730

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Computational Insight into the Effect of CaO/MgO Substitution on the Structural Properties of Phospho-Silicate Bioactive Glasses Alfonso Pedone, Gianluca Malavasi, and M. Cristina Menziani* Dipartimento di Chimica, UniVersita` di Modena e Reggio Emilia, Via G. Campi 183, 41100 Modena, Italia ReceiVed: May 4, 2009; ReVised Manuscript ReceiVed: July 2, 2009

The effect of the replacement of CaO for MgO on the structural properties of the 45S5 Bioglass with composition 46.2SiO2 · 24.3Na2O · (26.9 - x)CaO · 2.6P2O5 · xMgO where x ) 0, 5, 10, 15, 20, and 26.9 mol has been studied by means of molecular dynamics simulations. The results confirmed the complexity of the local environment of Mg ions which are coordinated by 5 nonbridging oxygens of different TO4 tetrahedra (T ) Si/P) leading to large rings in the structures. A rough correlation between the average dimension of the rings found in the structure and the computed Young’s modulus is obtained. The Young’s modulus decrease at low Mg-content reaching a minimum for the 46.2SiO2 · 24.3Na2O · 16.9CaO · 2.6P2O5 · 10MgO glass. At this composition, Mg is homogeneously distributed in the silica rich region together with Ca and Na ions but is almost totally absent from the Ca-Na-phosphate rich regions. The results suggest that the ideal glass composition for lowering the Young’s modulus preserving a specific bioactivity can be found below 10% of MgO content. Introduction Once implanted in the body, bioactive glasses react chemically with body fluids1,2 forming a layer of biologically active bonelike carbonate-containing hydroxyapatite on their surface, which triggers tissue reparation processes. The ability of the 45S5 Bioglass3 (45%SiO2, 24.5%CaO, 24.5% Na2O, and 6%P2O5 wt %) to induce new bone regeneration very shortly after being implanted explains its frequent use in clinical applications. However, the relatively poor mechanical properties of this material limit its uses to low-load bearing applications, such as otolaryngological, maxillofacial, dental, and periodontal implants.4-7 Therefore, over the past few years, much research has been focused on the addition of doping atoms into the original 45S5 Bioglass to improve its elastic and other specific properties.8-11 Among the dopants tested, magnesium, one of the most abundant cations in bone,12,13 is of particular clinical interest since it has been shown to stimulate directly osteoblast proliferation.14 Notwithstanding, the bioactivities of some Bioverit glass-ceramics, containing a significant amount of MgO, have been clinically confirmed for years,15 and contradictory explanations of the structural role of MgO on surface bioactivity of CaO-MgO-SiO2-P2O5 sol-gel bioglasses have been provided; some in vitro results indicate that, in specific concentration ranges, MgO does not affect apatite formation,16-18 but others suggest that it inhibits mineralization.19 It is also now largely recognized that substitutions of CaO by MgO in the composition of silica glasses modify their chemical durability20 and increase their mechanical properties:21 the replacement of CaO for MgO in soda lime glasses leads to a significant increase of the fracture toughness and fracture surface energy with simultaneous decrease of the Young’s modulus.21 It is also known that the partial substitution of CaO by MgO and Na2O by K2O is required to match the thermal expansion of bioactive glass coatings to that of Ti-based alloys.22 * Corresponding author. E-mail: [email protected]. Phone: +39 059 2055091. Fax: +39 059 373543.

Nevertheless, the structural role of Mg itself is still poorly understood due to the lack of unambiguous information on its local environment. In fact, depending on the glass composition and the experimental techniques employed, Mg was found to be present in four-,23,24 five-,25-28 and six-fold29,30 coordination. Further investigation of key structural factors and their effect on elastic properties can be greatly improved with the atomistic resolution of modern computational techniques, such as classical MD simulations, provided that a reliable force-field is available.31-37 A shell-model (SM) interatomic potential for phospho-silicate glasses including Na and Ca network modifiers, which provided a superior structural medium range properties description than the simple ionic rigid model,38 has recently been developed by Tilocca et al.37 Among the computational studies found in the literature, few works have been devoted to the simulation of the effect of Mg on the structure, elastic, and transport properties of glasses, except for windows soda-lime glasses.39,40 In these previous works, carried out within the rigid body approximation, almost 90% of Mg was found to be 4-fold coordinated with the remaining amount being 5-fold coordinated; moreover, the substitution of CaO by MgO resulted in a reduction of the Young’s modulus and enhancement of Na diffusivity.39 However, different conclusions were drawn from the results obtained in other computational works.41-43 In this paper, MD simulations using the SM potential have been carried out in order to provide structure-property relationships on CaO substitution by MgO in the parent 45S5 Bioglass. To this purpose the SM potential has been “inhouse” extended to include the Mg-O interaction. The compositions of the series of glasses studied is in the range 46.2SiO2 · 24.3Na2O · (26.9 - x)CaO · 2.6P2O5 · xMgO, where x ) 0, 5, 10, 15, 20, and 26.9 mol. Computational Methods Force-Field. Classical molecular dynamics simulations were carried out by means of the DL_POLY code44 using the SM

10.1021/jp904131t CCC: $40.75  2009 American Chemical Society Published on Web 08/07/2009

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TABLE 1: Shell Model Interatomic Potential: Analytic Functions and Parameters Buckingham Ae-r/F - C/r6

Os-Os Si-Os P-Os Na-Os Ca-Os Mg-Os

A (eV)

F (Å)

C (eV Å6)

22764.30 1283.91 1120.09133 56465.3453 2152.3566 3885.967

0.1490 0.32052 0.334772 0.193931 0.309227 0.253337

27.88 10.661580 0.0 0.0 0.09944 0.0

Three-Body Potential 1/2kb(θ - θ0)2 exp(-[r12/F + r13/F])

O-Si-O O-P-O

kb (eV rad-2)

θ0 (deg)

F (Å)

100.0 50.0

109.47 109.47

1.0 1.0

Core-Shell Potential 1/2ksr2

Oc-Os

ks (eV Å-2)

Y (e)

74.92

-2.8482

interatomic potential model recently parametrized by Tilocca et al.37,45 In the present work the force-field parametrization was extended to incorporate the Mg cation. The shell model approach46 is used in the potential to include polarization effects, by taking into account the large polarizability of oxygen ions. The total charge Z of oxygen ions is split between a core (of charge Z + Y) and a massless shell (of charge -Y) which are coupled by a harmonic spring. Besides the damped harmonic interaction with the corresponding core, the oxygen shells interact with each other and with Si, Na, Ca, Mg, and P cations through a short-range Buckingham term, whereas Coulombic forces act between all species, which bear full formal charges. Three-body screened harmonic potentials are used to control the intratetrahedral O-Si-O and O-P-O angles during the dynamics. The derivation of the SM parameters was described in refs 37 and 45. The parameters describing Na-O and Ca-O interactions were fitted to the structures of crystalline silicate phases as identified in typical bioglass and glass-ceramics,47,48 whereas the P-O pair interaction parameters were fitted to the structures of R-Na3PO4, β-NaCaPO4, and β-Ca3(PO4)2.49-51 In addition to these pre-existing parameters, in the present work the Mg-O pair interatomic parameters were obtained by means of the relaxed method52 using as reference structures the atomic positions and cell parameters of the MgO and Mg2SiO4 unit cells, keeping the other interaction parameters fixed. The complete potential model used is reported in Table 1. A test of the agreement between the experimental structural features (cell parameters and bond distances) of Mg-containg crystal silicates and those obtained after energy minimization with the fitted parameters is reported in Table 2. Mg-O distances are reproduced with a typical error less than 0.02 Å. A small time step is required to control the high frequency motion of the core-shell spring during MD simulations. The choice of a 0.2 fs time step leaded to fluctuations of less than 0.005% and no overall drift in the total energy. Cubic periodic boundary conditions were applied, with a cutoff of 8 Å for shortrange interations. Ewald summation method was used for the long-range coulomb interactions. Glass Generation. The structures of phospho-silicate glasses of composition 46.2SiO2 · 24.3Na2O · (26.9 - x)CaO · 2.6P2O5 · xMgO where x ) 0, 5, 10, 15, 20, and 26.9 mol % were modeled by means of a standard molecular dynamics melt and quench approach.

The initial configurations were generated by placing randomly 2835 atoms in a cubic box, three simulations were carried out with different starting configurations. Atomic compositions and size length of the simulation boxes are reported in Table 3, together with the glass densities at room temperature calculated according to the Priven’s empirical method53 implemented in the SciGlass software.54 The random initial configuration was heated and held at 3200 K for 100 ps in the NVT ensemble ensuring a suitable melting of the sample. The liquid was then cooled to 300 K at a nominal cooling rate of 10 K/ps. The resulting glass structure was subjected to a final NVT trajectory of 200 ps; the last 150 ps were included in the structural analysis. It is worth noticing that the short time scale of computer simulations requires a cooling rate several orders of magnitude higher than typical experimental rates. This is known to result in a glass transition temperature significantly higher than the actual one. Tilocca et al.,37 by using this procedure, estimated a Tg of 1030 K for 45S5 Bioglass, about 220 K higher than the experimental value.8 However, previous simulations showed that, despite the different Tg, a cooling rate around 10 K/ps yields converged and accurate structural properties,55 and it is currently used on most MD studies of melt-derived glasses and bioglasses. Elastic Properties. The elastic properties (Young’s modulus E, shear modulus G, bulk modulus B, and Poisson’s ratio ν) of the MD simulated glasses were obtained via the static method implemented in the GULP package.56 The stiffness matrix elements for a crystalline system are defined as the second derivative of the energy U with respect to the strain tensor components.57 Once the stiffness matrix is obtained, several related mechanical properties of anisotropic materials can be derived from their matrix elements or from the matrix elements of the compliance matrix. The procedure to calculate elastic properties by using static methods has been fully described in previous papers.58,59 To handle the amorphous character of the glass a cubic cell with no symmetry (space group P1) has been used, which is the MD simulation cell obtained by using the SM potentials. Since the SM force-field was not derived to this purpose, both the cell parameters and the atomic coordinates have been optimized and the elastic properties calculations performed by using a rigid ionic potential previously parametrized by us.34 This was shown to reproduce well the structure, transport, and mechanical properties of oxides, silicates, and silica based glasses.39,40,58-60 This procedure only enables short-range relaxations with the new force-field, whereas the medium range structure, such as the connectivity of the glass-forming sites, is “frozen” to the initial configuration obtained by the SM MD simulation. However, it is worth noting that the short-range order obtained is very similar to the one obtained with SM potential as demonstrated by comparing the pair distribution functions and the bond angle distributions of the constituent atoms of the 45S5M10 glass reported in Figure S1 and S2 of the Supporting Information.61 Results and Discussion Short Range Order around Network Former Ions. The cation-oxygen bond distances and coordination numbers for the glasses studied are reported in Table 4. The general features around silicon and phosphorus are unchanged in the six compositions studied. The shorter intertetrahedral P-O distance (1.55 Å) with respect to the typical Si-O distance (1.60 Å) of

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TABLE 2: Experimental Structural Data for the MgO, Mg2SiO4, CaMgSiO4, and Mg2Si2O6 Crystals and Calculated Structural Features Obtained by Means of the Newly Derived Parameters Fitted on the Structure of Mg2SiO4 MgO a [Å] b [Å] c [Å] V [Å3 ] Si-O [Å] Mg-O [Å] Ca-O [Å]

Mg2SiO4

CaMgSiO4

Mg2Si2O6

exp.

calc.

exp.

calc.

exp.

calc.

exp.

calc.

4.217 4.217 4.217 74.99

4.188 4.188 4.188 73.46

4.753 10.19 5.978 289.53 1.6355 2.1117

4.731 10.20 5.994 289.24 1.6350 2.1143

4.822 11.108 6.382 341.84 1.626 2.131 2.370

4.768 11.411 6.421 349.32 1.635 2.140 2.406

18.235 8.818 5.179 832.76 1.634 2.120

17.7629 8.643 5.223 801.94 1.634 2.100

2.1085

2.0941

TABLE 3: Input Data (Compositions, Priven-Derived Densities,53 Number of Atoms, and Cell Sizes) for the Modelled Glasses composition

density (g/cm3)

atom number

cell size (Å)

45S5 45S5M5 45S5M10 45S5M15 45S5M20 45S5M26.7

2.719 2.689 2.659 2.632 2.610 2.583

2800 2835 2835 2835 2835 2835

33.4169 33.4142 33.4600 33.4263 33.3705 33.2771

silicate glasses is due to both a significantly shorter P-NBO and P-BO bond lengths compared to Si-NBO and Si-BO ones. The O-T-O bond angle distributions (BAD) (not shown here) are centered at a value corresponding to the tetrahedral angle; the O-P-O BAD distribution is narrower than the O-Si-O one, suggesting a more rigid phosphorus local environment. Short Range Order around Modifier Ions. The distribution curves of modifier-oxygen pairs (Mg-O, Ca-O, and Na-O) for the 45S5M10 glass are shown in Figure 1, together with their bridging (BO) or nonbridging (NBO) oxygen components. The Na-O, Ca-O, and Mg-O peak positions are at 2.34, 2.32, and 1.98 Å, in agreement with the range of values obtained by X-ray and neutron diffraction measurements for phosphate and soda-lime silicate glasses.23,24,29,62-70 Mg is almost exclusively coordinated by NBOs and Ca has a higher preference for coordination by NBOs compared to sodium. The data listed in Table 4 show that both Na and Ca are enclosed in a pseudooctaedral coordination shell of about six oxygens, and Mg is surrounded by 5 oxygens arranged in a bipyramid fashion (see Figure 2a). The coordination environment is also unveiled by the distribution of O-M-O (M ) Na, Ca, and Mg) angles reported in Figure 3. Both Na and Ca distributions show a peak close to 90°, which generally results from Na or Ca atoms connecting two NBOs belonging to different tetrahedra. This result suggests an important structural role of modifier cations in controlling the folding of the silicate network by connecting and arranging together different chain-like and isolated fragments. The second peak at 60° (more pronounced for Na) results from modifiers coordinated to two NBOs (or one NBO and one BO) belonging to the same tetrahedron. The broad distributions of Figure 3 also denote a high flexibility in the geometries of the coordination shell of these cations. In the O-Mg-O BAD a small shoulder at around 75° is observed instead of the peak at 60°. This results from distortions caused by the formation of 2-member rings of Mg ions (see Figure 2b) as already reported by previous MD simulations.39 In these 2-member rings Mg is 6-fold coordinated by NBOs belonging to different TO4 (T ) Si/P) tetrahedra. A detailed analysis of the coordination numbers of Mg ions, reported in Figure 4, shows that MgO5 polyhedra decrease as a function of the MgO content favoring the formation of MgO4 tetrahedra. Moreover, a minimum in the MgO6 polyhedra occurs for the 45S5M10 and 45S5M15 glasses.

The replacement of CaO for MgO does not affect much the short-range order around modifiers as reported in Table 4 except for small changes in the O-M-O BADs (Figure 3). In fact, the peak centered at 90° decreases its intensity and shifts to larger angles for Na and Ca as a function of Mg content, whereas the intensity of peak at 60° increases in the O-Na-O BAD showing that Na ions tends to be preferentially coordinated by oxygens belonging to the same TO4 tetrahedron unlike Mg ions that prefer to coordinate different TO4 tetrahedra. Qn Species Distributions. The distributions of Qn species (n is the number of bridging oxygens bounded to the network former cations Si or P) of the glasses studied are reported in Table 5 together with the connectivity of the silicate and phosphate networks, denoted NC(Si) and NC(P) and computed as weighted averages of the corresponding Qn(Si) and Qn(P) distributions.32 Table 5 shows that silicon is predominantly Q2 in all of the glasses studied; Q1 and Q3 species are also present in a relevant amount, about 17-20 and 23-29%, respectively. The existence of more than two different Qn species of silicon for glasses with compositions similar to that of the 45S5 glass is the subject of active debate; although a binary model (with only Q2 and Q3 species) is sometimes assumed,71-73 a threecomponent model with Q1, Q2, and Q3 species has been proposed to fit Raman spectra,74 and recent 1D MAS NMR data.32,48 Moreover, the presence of more than two Qn(Si) species had been inferred from several classical molecular dynamics simulations making use of both the rigid ionic model32-34 and the shell-model35-37 and by Carr-Parrinello molecular dynamics simulations.75,76 The general features of the Qn(Si) distributions do not change upon CaO/MgO substitution, and the network connectivity remains approximately equal to 2.09. Phosphorus is predominantly present as orthosphosphate but a small fraction of pyrophosphate (Q1 or Si-O-P) species is also detected. In fact, the existence of small percentages of Si-O-P linkage was confirmed by CP MAS NMR experiment on phosphosilicate, microporous silicoaluminophosphates, and bioactive phosphosilicates glasses.77 Table 5 shows that there is not a clear trend in the Qn(P) distribution when CaO is replaced for MgO. In fact, two minima in the Q0 species occur for the 45S5M5 (67%) and 45S5M20 (71%) glasses which correspond to two maxima in the Q1 distributions, whereas the 45S5M15 glass shows the greater amount of orthophosphate units (90%). The overall partitioning of the T-BO-T bridges in the glasses is quantitatively examined in Figure 5, which shows that the Si connectivity is dominated by “self” Si-O-Si linkages; the situation is reversed for P, which prefers to crosslink with silicon. Ring-Size Distributions and Elastic Properties. Although the Si Qn distributions of the modeled glasses are very similar as well as the number of NBO, the topology of the rings in the

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TABLE 4: Bond Lengths (Å) and Coordination Numbers (In Parentheses) of the Modelled Glasses Obtained by Averaging upon Three Different Simulationsa dSi-O dSi-NBO dSi-BO dP-O dP-NBO dP-BO dMg-O dMg-NBO dMg-BO dCa-O dCa-NBO dCa-BO dNa-O dNa-NBO dNa-BO dO-O dSi-Si

45S5

45S5M5

45S5M10

45S5M15

45S5M20

45S5M27

1.58 (4.0) 1.58 (1.9) 1.66 (2.1) 1.55 (4.0) 1.55 (3.8) 1.62 (0.2)

1.58 (4.0) 1.58 (1.9) 1.66 (2.1) 1.55 (4.0) 1.55 (3.6) 1.62 (0.4) 1.98 (5.0) 1.98 (4.9) 2.08 (0.1) 2.32 (6.0) 2.32 (5.4) 2.56 (0.6) 2.37 (5.9) 2.35 (4.4) 2.43 (1.5) 2.66 3.07

1.60 (4.0) 1.58 (1.9) 1.65 (2.1) 1.55 (4.0) 1.55 (3.8) 1.62 (0.2) 1.98 (5.0) 1.98 (4.8) 2.13 (0.2) 2.32 (5.9) 2.32 (5.3) 2.53 (0.6) 2.34 (5.8) 2.34 (4.3) 2.45 (1.5) 2.66 3.06

1.60 (4.0) 1.58 (1.9) 1.65 (2.1) 1.55 (4.0) 1.55 (3.9) 1.62 (0.1) 1.98 (4.8) 1.98 (4.6) 2.17 (0.2) 2.30 (5.7) 2.30 (5.2) 2.59 (0.5) 2.35 (5.8) 2.35 (4.3) 2.46 (1.5) 2.66 3.09

1.60 (4.0) 1.58 (1.9) 1.65 (2.1) 1.55 (4.0) 1.55 (3.7) 1.62 (0.3) 1.98 (5.0) 1.98 (4.8) 2.16 (0.2) 2.32 (5.9) 2.32 (5.3) 2.53 (0.6) 2.37 (5.7) 2.37 (4.2) 2.46 (1.5) 2.66 3.09

1.60 (4.0) 1.58 (1.9) 1.66 (2.1) 1.55 (4.0) 1.55 (3.8) 1.62 (0.2) 1.98 (4.9) 1.98 (4.7) 2.25 (0.2)

2.30 (5.9) 2.30 (5.3) 2.59 (0.6) 2.35 (5.9) 2.32 (4.4) 2.42 (1.5) 2.66 3.06

2.37 (5.6) 2.35 (4.2) 2.43 (1.4) 2.66 3.10

a Standard deviations of 0.01 Å and 0.1 atoms were determined for distances and coordination numbers, respectively. The cation-oxygen bond lengths have been estimated by the peak position of their pair distributions and the CNs have been calculated based on cutoffs obtained from the first minimum. They are 1.9 Å for Si-O and P-O, 2.6 Å for Mg-O, and 3.1 Å for Na-O and Ca-O.

Figure 1. Modifier-oxygen PDFs and NBO/BO relative contributions.

glasses changes drastically (see Figure 6). The replacement of CaO for MgO favors the formation of larger rings in the silica matrix. In fact, the 45S5 Bioglass shows major peaks at 4, 7, and 12 membered rings; the addition of Mg produces a decrease in the amount of small rings and an increase in the amount of rings constituted by more than 12 members. The different ring size distribution caused by the substitution of Ca ions by Mg ions is probably due to the higher field strength of the latter that is able to influence the connectivity between the SiO4 tetrahedra. In fact, at low concentration, Mg tends to be coordinated by 5 oxygens belonging to different TO4 tetrahedra. This might be explained by the shorter Mg-O distances with respect to the Ca-O ones which would generate higher tension between the sharing edges of MgO5-SiO4 polyhedra than between the CaO6-SiO4 ones. The average ring size dimensions 〈n〉 for the modeled glasses, weighted by the fraction of rings for a given n value, are plotted in Figure 6b. This analysis shows that the glass with the larger 〈n〉 value is the 45S5M10 one. A qualitative inverse trend between the average dimension of the rings found in the structure and the computed Young’s modulus (E) is highlighted in Table 6. However, further simulations with different glass compositions should be carried out to support this finding by increasing the statistical accuracy allowing a quantitative correlation.

Figure 2. (a) Bipyramid coordination arrangement around Mg. (b) Two membered rings of MgO5 and MgO6 polyhedra. Coulor codes: red, oxygen; light blue, silicon; light green, sodium; light magenta, calcium; and light cyan, magnesium.

Table 6 also lists the computed G, B, and ν data values of the modeled glasses. It is worth noting that the calculated elastic properties of the 45S5 Bioglass model are underestimated with respect to those measured by means of Brillouin scattering experiments78 (E ) 77.9 GPa, G ) 30.7 GPa, B ) 55.6 GPa, and υ ) 0.267). Since previous simulations showed a very good agreement of the elastic calculated properties of binary alkalinesilicate59 and soda-lime glasses39 with the experimental ones,

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Figure 3. O-M-O bond distribution angles (BADs, M ) Na, Ca, and Mg) of the modeled glasses.

Figure 6. (a) Ring size distribution of the modeled glasses and (b) weight-average ring size as a function of MgO content. Both Ca and Mg are considered as modifier cations. The algorithm developed by Yuan and Cormack has been used for this analysis.82

TABLE 6: Elastic Properties and Fractional Free Volume (FFV) of the Modelled Glassesa Figure 4. Mg coordination numbers as a function of MgO content in the glasses studied.

TABLE 5: Qn Distributions and Corresponding Network Connectivity Averaged upon Three Simulationsa Si 0

45S5 45S5M5 45S5M10 45S5M15 45S5M20 45S5M27 a

1

Q

Q

0.9 0.2 0.9 0.7 1.1 0.6

17.3 19.1 16.9 19.5 19.9 20.6

Q

2

54.0 56.0 56.0 49.8 50.1 50.0

P Q

3

27.4 22.8 24.7 28.8 27.5 26.9

Q

4

0.4 1.9 1.5 1.1 1.3 2.0

Q

0

78.4 67.3 80.8 90.4 71.2 78.8

Q1 Q2 NC (Si) NC (P) 19.6 28.8 19.2 9.6 28.8 21.2

2.0 3.8 0.0 0.0 0.0 0.0

2.09 2.07 2.09 2.10 2.08 2.09

0.24 0.36 0.19 0.10 0.29 0.21

A standard deviation of 2% is computed for Qn speciations.

Figure 5. Number of T-BO-T bridges (T ) Si and P) normalized to the total number of oxygens.

this result might be imputable to the parametrization of the P-O force-field which was derived by using structural properties only, since experimental elastic properties are not available in the literature.34 However, despite the poor estimate of the absolute value, the trend of the values in the series could be informative since the phosphorus content and the P-O bond density are constant in all the compositions studied. However,

45S5 45S5M5 45S5M10 45S5M15 45S5M20 45S5M27

E (GPa)

G (GPa)

B (GPa)

ν

FFV

55.8 52.1 50.9 53.1 54.3 52.0

20.7 19.6 20.6 20.6 21.2 20.5

46.3 45.5 45.2 44.0 41.8 40.3

0.300 0.309 0.313 0.300 0.293 0.285

0.453 0.449 0.456 0.458 0.459 0.460

a The statistical spreads for the calculated data are (1.0 GPa, (0.9 GPa, (0.6 GPa, and (0.007 for Young’s modulus E, bulk modulus B, shear modulus G, and Poisson’s ratio υ.

the standard deviations of E, G, B, and V, (1.0 GPa, (0.9 GPa, (0.6 GPa, and (0.007, respectively, indicate that, in general, the variation of elastic properties with MgO content is poorly defined. A clear behavior is instead observed for the Young’s modulus of the 45S5M10 glass with respect to the 45S5 glass: a decrease of 5 GPa is detected. It has recently been reported that the replacement of CaO by MgO in soda-lime silica glasses39 yields a softening of the glass; this effect has been explained by two concurrent factors: (a) the bond density of the glass, weighted by the strength of the different bonds in the network and (b) the fractional free volume (FFV) and packing of the structures. Therefore, by taking into account these factors, one would expect a monotonic decrease of the elastic properties with Mg content due to a significant decrease of bond density and a slightly increases of the fraction of free volume (see Table 6). However, the results of the present work reveal that the situation is more complex in phospho-silicate bioactive glasses, because of the formation of silica-rich and phosphorus rich regions and the different distribution of modifier ions between them (see the following paragraph). Network Forming-Modifier Interactions and Possible Implications on Glass Solubility. In order to investigate the effect of Mg inclusion and how modifier ions are partitioned T ) between silicate and phosphate tetrahedra the ratio RM1/M2

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T Figure 7. RM1/M2 ratio as a function of MgO content in the modeled glasses. T ) Si and P, M1 and M2 ) Na, Ca, and Mg cations. The Si-M and P-M coordination numbers have been calculated by integrating the corresponding Si, P-M radial distribution function up to the first minimum at Rc ) 4.5 and 4.2 Å. Data points have an error bar of 0.03 and are smaller than the symbol sizes.

CNT-M1/CNT-M2, normalized with respect to the ratio of the number of ions M1 and M2 in the cell (NM1/NM2), has been calculated.37 In the above formula T is a network former cation (Si and P in this work) while M1 and M2 are modifier ions (Na, Ca, and Mg ions). A unit ratio will then denote a statistical (random) distribution of M1 and M2 ions surrounding T, strictly following their different concentration, whereas a ratio greater than 1 denotes preference of T for coordination of M1 ions, and a ratio lower than 1 denotes preference for coordination of M2 ions. In agreement with experimental MAS NMR and Raman data on similar Na2O-MgO-CaO-P2O5-SiO2 glasses,79 previous molecular dynamics simulation studies of soda-lime phosphosilicate glasses have shown that Na and Ca modifier ions prefer to coordinate phosphate groups over the silicate ones leading to a general repolymerizing effect on the silicate rich domains.35 Overall, the results obtained in this study suggest a moderate preference of SiO4 tetrahedra for Na and Ca with respect to Si Si and RCa/Mg ; Figure 7). Moreover, Na and Ca ions Mg (RNa/Mg Si ) are almost homogeneously distributed around Silicon (RNa/Ca with a slightly propensity for Ca ions in all the glasses studied. Interesting, a peculiar behavior of the distribution of modifier around the tetrahedral sites is observed for the 45S5M10 glass. Si and the maximum The almost constant values of the ratio RM1/M2 P P observed for the RNa/Mg and RCa/Mg values reflect a marked aggregation of Na and Ca in the phosphate rich regions, with a P ) and slightly preference for Ca ions rather than Na ones (RNa/Ca a silicate matrix in which sodium, calcium, and magnesium ions are homogeneously distributed. It has been demonstrated that the increasing of the Na/Ca ratio in bioactive glasses leads to very soluble glasses, which are completely reabsorbed soon after the implant.80 This is interpreted as a consequence of the high solubility of sodium silicates in which sodium is coordinated to low-n Qn sites. When cations with higher strength fields are introduced they displace sodium from these sites promoting the formation of less soluble microphases. To study this microsegregation the coordination of Na, Ca, and Mg around the different Qn units has been determined by decomposing the M-T rdfs into the contribution Qn has been defined as of M-Qn pairs and the ratio RM1/M2 described above. Qn ratios for the Si and P Qn centers Figure 8 shows the RM1/M2 of the 45S5M10 glass. A clear preference of Ca and Mg for low-n Q silicate sites is observed. As a consequence the Na ions are displaced toward high-n sites. This is reflected in the high percentage of NBO in the Ca and Mg coordination shells. Magnesium prefers to coordinate Si Q0 species, whereas Ca ions

n

Q Figure 8. RM1/M2 ratios for Si (left) and P (right) Qn centers of the 45S5M10 glass. R > 1 denotes preference of Qn for M1 coordination, whereas R < 1 indicates M2 preference.

prefer to coordinate Qn species with n > 1. This would lead to an enhancement of chemical durability when magnesium substitutes for calcium, since low-n Si Qn sites are strongly associated to high strength field modifier cations. However, an increasing of the Na leaching could be expected because of the weaker interaction of sodium ions with bridging oxygens of high-n Si Qn sites that promotes Na diffusivity as reported for soda-lime glasses.39,81 Conclusions The results of the molecular dynamics simulations study on the effect of the replacement of CaO for MgO on the structural and elastic properties of the 45S5 Bioglass highlight the complexity of the local environment of Mg, which is mainly 5-fold coordinated with a non-negligible amount of 4- and a small amount of 6-fold coordinated Mg, depending on the MgO content. This is probably the cause of the stabilizing effect of MgO in soda-lime glasses: since the majority of the Mg-silicate crystal phases presents a 6-fold coordinated Mg ion, the kinetic of crystallization is hampered by the need for coordination changing. By substituting CaO by MgO, the overall network connectivity (NC) remains similar to that of the 45S5 Bioglass with an open structure dominated by Si Q2 species resulting from the unchanged number of NBOs. However, the higher field strength of Mg with respect to Ca provides for the former a sufficient driving force to rearrange the SiO4 tetrahedra in such a way that only NBOs belonging to different tetrahedra coordinate Mg ions. In this way the number of shared edges between MgO5 and SiO4 polyhedra is minimized with respect to the CaO6-SiO4 ones and the topology of the rings size moves to larger rings, a key features for lowering melt viscosities of Mg-containing silicate glasses.21 The 45S5M10 composition shows the most interesting behavior for potentially important Bioglass properties such as solubility and stiffness; it has the smaller Young’s modulus of

Properties of Phospho-Silicate Bioactive Glasses the composition studied here. This can be related to several structural features such as the larger average ring sizes and peculiar distribution of Mg ions in the glass; in fact, at this composition, Mg is homogeneously distributed in the silica rich region together with Ca and Na ions but is expelled from the Ca-phosphate rich regions. Putting together the main findings of this work with the knowledge that the presence of Magnesium slows down the rate of formation of the apatite layer for MgO content above 7 mol % the ideal glass composition for lowering the Young’s modulus preserving a specific bioactivity can be found below 10% of MgO content. Acknowledgment. The authors thank the Italian Ministry of University and Research for funding (Project COFIN2006, Prot. 2006033728 “New computational strategies for modelling nanostructured glasses and their spectroscopic properties”). A.P. would like to thank the “Fondazione Cassa di Risparmio di Modena” for financial support. Supporting Information Available: Comparison of the Si-O, P-O, Na-O, Ca-O, and Mg-O PDFs (Fgiure S1) and O-M-O BADs (Figure S2). This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Hench, L. L. J. Am. Ceram. Soc. 1998, 81, 1705. (2) Kokubo, T.; Kushitani, H.; Sakka, S. J. Biomed. Mater. Res. Symp. 1990, 24, 721. (3) Hench, L. L.; Splinter, R. J.; Alen, W. C.; Greenlee, T. K. J. Biomed. Mater. Res. 1971, 2, 117. (4) Yamamuro, T. Reconstruction of the iliac crest with bioactive glassceramic prostheses. In Handbook of bioactiVe ceramics; CRC Press: Boca Raton, FL, 1990; Vol. 1. (5) Hench, L. L.; Stanley, H. R.; Clark, A. E.; Hall, M.; Wilson, J. Dental applications of bioglass implant. In Bioceramics; Butterworth Heinmann: Oxford, U.K., 1991; Vol. 4. (6) Wilson, J.; Low, S. B. J. Appl. Biomater. 1992, 3, 123. (7) Wilson, J.; Douek, E.; Rust, K. Bioglass Middle Ear Devices: Ten Year Clinical Results. In Bioceramics; Pergamon: Oxford, U.K., 1995. (8) Hench, L. L.; Andersson, O. H. Bioactive glasses. In An introduction to Bioceramics; World Scientific: Singapore, 1993. (9) Lusvardi, G.; Malavasi, G.; Cortada, M.; Menabue, L.; Menziani, M. C.; Pedone, A.; Segre, U. J. Phys. Chem. B 2008, 112, 12730. (10) Lusvardi, G.; Malavasi, G.; Menabue, L.; Menziani, M. C. J. Phys. Chem. B 2002, 106, 9753. (11) Lusvardi, G.; Malavasi, G.; Menabue, L.; Menziani, M. C.; Pedone, A.; Segre, U.; Aina, V.; Perardi, A.; Morterra, C.; Boccafoschi, F.; Gatti, S.; Bosetti, M.; Cannas, M. J. Biomater. Appl. 2008, 22, 505. (12) Rude, R. K.; Gruber, H. E. J. Nutr. Biochem. 2004, 15, 710. (13) Okuma, T. Nutrition 2001, 17, 679. (14) Liu, C. C.; Yeh, J. K.; Aloia, J. F. J. Bone Miner. Res. 1988, 3, S104. (15) Vogel, W.; Holand, W. J. Non-Cryst. Solids 1990, 123, 349. (16) Moya, J. S.; Tomsia, A. P.; Pazo, A.; Santos, C.; Guitian, F. J. Mater. Sci. Mater. Med. 1994, 5, 529. (17) Pereira, M. M.; Clarck, A. E.; Hench, L. L. J. Am. Ceram. Soc. 1995, 78, 2463. (18) Leonova, E.; Izquierdo-Barba, I.; Arcos, D.; Lopez-Noriega, A.; Hedin, N.; Vallet-Regi, M.; Eden, M. J. Phys. Chem. C 2008, 112, 5552. (19) Ebisawa, Y.; Miyaji, F.; Kokubo, T.; Okura, K.; Nakamura, T. Biomaterials 1997, 18, 1277. (20) Barrere, F.; Van Blitterswijk, C. A.; De Groot, K.; Layrolle, P. Biomaterials 2002, 23, 1921. (21) Wilantewicz, T. The effects of Lithium, Boron, and Magnesium oxides on the mechanical properties of silicate glasses, Alfred University, 1998. (22) Lopez-Esteban, S.; Saiz, E.; Fujino, S.; Oku, T.; Suganuma, K.; Tomsia, A. P. J. Eur. Ceram. Soc. 2003, 23, 2921. (23) Waseda, Y.; Toguri, J. M. Metal Trans. B 1977, 8B, 563. (24) Tabira, Y. Mater. Sci. Eng. 1996, B41, 63. (25) Wilding, M. C.; Benmore, C. J.; Tangeman, J. A.; Sampath, S. Chem. Geol. 2004, 213, 281. (26) Ildefonse, P.; Calas, G.; Flank, A. M.; Lagarde, P. Nucl. Instrum. Methods Phys. Res. Sect. B 1995, 97, 172.

J. Phys. Chem. C, Vol. 113, No. 35, 2009 15729 (27) Li, D.; Peng, M.; Murata, T. Can. Mineral. 1999, 37, 199. (28) Bugaev, L. A.; Sokolenko, A. P.; Dmitrienko, H. V. Phys. ReV. B 2001, 65, 024105. (29) Yin, C. D.; Okuno, M.; Morikawa, H.; Marumo, F. J. Non-Cryst. Solids 1983, 55, 131. (30) Shimoda, K.; Nemoto, T.; Saito, K. J. Phys Chem. B 2008, 112 (22), 6747. (31) Mead, R. N.; Mountjoy, G. J. Phys. Chem. B 2006, 110, 14273. (32) Linati, L.; Lusvardi, G.; Malavasi, G.; Menabue, L.; Menziani, M. C.; Mustarelli, P.; Pedone, A.; Segre, U. J. Non-Cryst. Solids 2008, 354, 84. (33) Malavasi, G.; Menziani, M. C.; Pedone, A.; Civalleri, B.; Corno, M.; Ugliengo, P. Theor. Chem. Acc. 2007, 117, 933. (34) Pedone, A.; Malavasi, G.; Menziani, M. C.; Cormack, A. N.; Segre, U. J. Phys. Chem. B 2006, 110, 11780. (35) Tilocca, A.; Cormack, A. N. J. Phys. Chem. B 2007, 111, 14256. (36) Tilocca, A.; Cormack, A. N.; de Leeuw, N. H. Faraday Discuss. 2007, 136, 45. (37) Tilocca, A.; Cormack, A. N.; De Leeuw, N. H. Chem. Mater. 2007, 19, 95. (38) Tilocca, A. J. Chem. Phys. 2008, 129, 084504. (39) Pedone, A.; Malavasi, G.; Menziani, M. C.; Segre, U.; Cormack, A. N. J. Phys. Chem. C 2008, 112, 11034. (40) Pedone, A.; Malavasi, G.; Cormack, A. N.; Segre, U.; Menziani, M. C. Theor. Chem. Acc. 2008, 120, 557. (41) Kubiki, J. D.; Lasaga, A. C. Phys. Chem. Minerals 1991, 17, 661. (42) Tsuneyuli, S.; Tsukada, M.; Aoki, H.; Matsui, Y. Phys. ReV. Lett. 1988, 61, 869. (43) Shimoda, K.; Okuno, M. J. Phys.: Condens. Matter 2006, 18, 6531. (44) Smith, W.; Forester, T. R. J. Mol. Graph. 1996, 14, 136. (45) Tilocca, A.; De Leeuw, N. H.; Cormack, A. N. Phys. ReV. B 2006, 73, 104209. (46) Dick, B. G.; Overhauser, A. W. Phys. ReV. 1958, 112, 90. (47) Peitl, O.; Zanotto, E. D.; Hench, L. L. J. Non-Cryst. Solids 2001, 292, 115. (48) Linati, L.; Lusvardi, G.; Malavasi, G.; Menabue, L.; Menziani, M. C.; Mustarelli, L. P.; Segre, U. J. Phys. Chem. B 2005, 109, 4989. (49) Harrison, R. J.; Putnis, A.; Kockelmann, W. Phys. Chem. Chem. Phys. 2002, 4, 3252. (50) Yashima, M.; Sakai, A.; Kamiyama, T.; Hoshikawa, A. J. Solid State Chem. 2003, 175, 272. (51) Ben Amara, M.; Vlasse, M.; Le Flem, G.; Hagenmuller, P. Acta Crystallogr. Sect. C 1983, 39, 1483. (52) Gale, J. D. Phil. Mag. B 1996, 73, 3. (53) Priven, A. I. Glass Technol. 2004, 45, 244. (54) SciGlass. In UniVersal System of Glass Properties, 3.5 ed.; SciVision: Burlington, 1997. (55) Vollmayr, K.; Kob, W.; Binder, K. Phys. ReV. B 1996, 54, 15808. (56) Gale, J. D.; Rohl, A. L. Mol. Simul. 2003, 29, 291. (57) Ney, J. F. Physical Properties of Crystals; Oxford Scientific Publications: Oxford, 1985. (58) Pedone, A.; Malavasi, G.; Menziani, M. C.; Cormack, A. N.; Segre, U. J. Phys. Chem. B 2006, 110, 11780. (59) Pedone, A.; Malavasi, G.; Cormack, A. N.; Segre, U.; Menziani, M. C. Chem. Mater. 2007, 19 (13), 3144. (60) Pedone, A.; Malavasi, G.; Menziani, M. C.; Segre, U.; Cormack, A. N. Chem. Mater. 2008, 20, 4356. (61) Pedone, A. Computer Simulations of Chemical Physical Properties of Amorphous Inorganic Materials. Ph.D Thesis, University of Modena and Reggio Emilia, 2008. (62) Taniguchi, T.; Okuno, M.; Matsumoto, T. J. Non-Cryst. Solids 1997, 211, 56. (63) Okuno, M.; Marumo, F. Mineral J. 1993, 16, 407. (64) Yin, C. D.; Okuno, M.; Morikawa, H.; Marumo, F.; Yamanaka, T. J. Non-Cryst. Solids 1986, 80, 167. (65) Eckersley, M. C.; Gaskell, P. H.; Barnes, A. C.; Chieux, P. Nature 1988, 335, 525. (66) Combes, J.-M.; Brown Jr., G. E.; Waychunas, G. A. X-ray adsorption study of the local Ca environment in silicate glasses. In XAFS VI, Sixth Int’l Conf on X-ray Absorption Fine Structure; Hasnain, E. H. S. S. , Ed.; Oxford: Chichester, U.K., 1991. (67) Taniguchi, T.; Okuno, M.; Matsumoto, T. Mineral J. 1995, 17, 231. (68) Henderson, C. M. B.; Charnock, J. M.; van dei Laan, G.; Schreyer, W. Appendix Daresbury Ann. Rep. 1991/92, 1992, 77. (69) Brow, R. K. J. Non-Cryst. Solids 2000, 1, 263–264. (70) Dubiel, M.; Brunsch, S.; Kolb, U.; Gultwerk, D.; Bertagnolli, H. J. Non-Cryst. Solids 1997, 220, 30. (71) Elgayar, I.; Aliev, A. E.; Bocaccini, A. R.; Hill, R. G. J. NonCryst. Solids 2005, 351, 173. (72) Lockyer, M. W. G.; Holland, D.; Dupree, R. J. Non-Cryst. Solids 1995, 188, 207.

15730

J. Phys. Chem. C, Vol. 113, No. 35, 2009

(73) Abgelopoulou, A.; Montouillout, V.; Massiot, D.; Kordas, G. J. Non-Cryst. Solids 2008, 354, 333. (74) Lin, C. C.; Huang, L. C.; Shen, P. J. Non-Cryst. Solids 2005, 351, 3195. (75) Tilocca, A.; de Leeuw, N. H. J. Mater. Chem. 2006, 16, 1950. (76) Tilocca, A. Phys. ReV. B 2007, 76, 224202. (77) Lejeune, C.; Coelho, C.; Bonhmme-Coury, L.; Azai’s, T.; Maquet, J.; Bonhomme, C. Solid State Nucl. Magn. Reson. 2005, 27, 242. (78) Lin, C.-C.; Huang, L.-C.; Shen, P. J. Non-Cryst. Solids 2005, 351, 3195.

Pedone et al. (79) Aguiar, H.; Solla, E. L.; Serra, J.; Gonza´lez, P.; Leo´n, B.; Malz, F.; Jager, C. J. Non-Cryst. Solids 2008, 354, 5004. (80) Hench, L. L.; Wilson, J. An Introduction to Bioceramics; World Scientific: Singapore, 1993. (81) O’Connell, M. J. The Effects of MgO Replacement of CaO on the Ion Exchange Behaviour, Alfred University, 1998. (82) Yuan, X.; Cormack, A. N. Comput. Mater. Sci. 2002, 24, 343.

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