Correlating structural distributions in silica glass with two-dimensional J -resolved spectroscopy

Abstract

A two-dimensional (2D) $J$-resolved magic-angle spinning nuclear magnetic resonance (NMR) spectrum of silica glass at $^{29}\mathrm{Si}$ natural abundance levels, 4.7%, was measured using the shifted-echo phase-incremented echo train acquisition (SE-PIETA) pulse sequence. At $^{29}\mathrm{Si}$ natural abundance levels the ${J}_{\text{Si-O-Si}}$ coupling splittings appear as overlapping doublet patterns arising from isolated $^{29}\mathrm{Si}\ensuremath{-}\mathrm{O}\ensuremath{-}^{29}\mathrm{Si}$ linkages. The experimental 2D $J$-resolved spectrum is analyzed to obtain a bivariate probability distribution correlating the central Si-O-Si angle of a ${\mathrm{Q}}^{4}\ensuremath{-}{\mathrm{Q}}^{4}$ linkage to its mean Si-O-Si angle (seven angles) using relationships between $^{29}\mathrm{Si}$ isotropic chemical shifts and geminal ${J}_{\text{Si-O-Si}}$ coupling of a ${\mathrm{Q}}^{4}\ensuremath{-}{\mathrm{Q}}^{4}$ to its local structure. To obtain a self-consistent bivariate probability distribution it was necessary to introduce an additional dependence of the $^{29}\mathrm{Si}$ chemical shift of a ${\mathrm{Q}}^{4}$ on mean Si-O distance as well as mean Si-O-Si angle. The implication of this necessary modification is a positive correlation between Si-O-Si angle and Si-O distance in the silica glass, consistent with recent $^{17}\mathrm{O}$ NMR measurements on ambient and densified silica glasses but running opposite to the trend generally found in crystalline silica polymorphs. From the analysis of the $^{29}\mathrm{Si}$ 2D $J$-resolved spectrum we determine a Si-O-Si bond angle distribution in silica glass as having a mean at $147.{8}^{\ensuremath{\circ}}$, a mode at ${147}^{\ensuremath{\circ}}$, and a standard deviation of $10.{7}^{\ensuremath{\circ}}$. Our statistical model for analyzing the experimental $^{29}\mathrm{Si}$ 2D $J$-resolved spectrum also indicates that the individual Si-O-Si bond angle distributions are relatively uncorrelated.