Abstract

The two-dimensional Magic Angle Flipping Nuclear Magnetic Resonance (2D MAF NMR) experiment on $^{29}$Si nuclei is used to determine the distribution of $Q^{(n)}$ sites in two $^{29}$Si-enriched magnesium silicate glasses with compositions 2 MgO $\cdot$ SiO$_{2}$ and MgO $\cdot$ SiO$_{2}$. A significant degree of polymerization is observed in the 2 MgO $\cdot$ SiO$_{2}$ glass, supporting previous studies using Raman and $^{29}$Si NMR spectroscopy. Relative abundance of $0.629 \pm 0.001$ for $Q^{(0)}$ and $0.371 \pm 0.001$ for $Q^{(1)}$ were obtained from spectral fits of the 2D MAF spectrum of the 2 MgO $\cdot$ SiO$_{2}$ glass. Mole fractions for the free oxygen anion and each $Q^{(n)}$-species were calculated and used in a thermodynamic model of $Q^{(n)}$ disproportionation to calculate an equilibrium constant of $k_0 = 0.04 \pm 0.02$ in 2 MgO $\cdot$ SiO$_{2}$. In the MgO $\cdot$ SiO$_{2}$ glass relative abundance of $0.014 \pm 0.001$ for $Q^{(0)}$, $0.191 \pm 0.003$ for $Q^{(1)}$, $0.530 \pm 0.004$ for $Q^{(2)}$, $0.252 \pm 0.003$ for $Q^{(3)}$, and $0.014 \pm 0.001$ for $Q^{(4)}$ were measured. The mole fractions for the free oxygen anion and each $Q^{(n)}$-species in MgO $\cdot$ SiO$_{2}$ were used to calculate corresponding disproportionation equilibrium constants of $k_1 = 0.19 \pm 0.02$, $k_2 = 0.174 \pm 0.009$, and $k_3 = 0.11 \pm 0.01$. A comparison of $k_3$ values from previous MAF studies of various alkali and alkaline earth silicate glasses indicate an exponential increase in $k_3$ with the increasing modifying cation potential. Using the van't Hoff relation, we show that differences in both thermal history and modifier cation potential contribute to this spread in $k_3$ values. Nuclear shielding tensor anisotropy, $\zeta$, and asymmetry, $\eta$, values of $\zeta = 0.0$ ppm and $\eta = 0.0$ for $Q^{(0)}$ and $\zeta = 33.0 \pm 0.1 $ ppm, $\eta = 0.4 \pm 0.1$ for $Q^{(1)}$ in 2 MgO $\cdot$ SiO$_{2}$ glass were determined from its 2D MAF spectrum. These values were used in obtaining the remaining values of $\zeta = -36.0 \pm 0.5$ ppm and $\eta = 0.99 \pm 0.01$ for $Q^{(2)}$, and $\zeta = -27.5 \pm 0.5$ ppm and $\eta = 0.45 \pm 0.11$ for $Q^{(3)}$, $\zeta$ = 0.0 ppm and $\eta = 0.0$ for $Q^{(4)}$ in the MgO $\cdot$ SiO$_{2}$ glass from its 2D MAF spectrum. The magnitude of $\zeta$ values observed are lower than those reported in previous MAF studies of alkali and alkaline earth silicate glasses containing different modifier cations, consistent with previously reported trends in $\zeta$ versus modifying cation potential.