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

A two-dimensional (2D) J-resolved magic-angle spinning nuclear magnetic resonance (NMR) spectrum of silica glass at Si29 natural abundance levels, 4.7%, was measured using the shifted-echo phase-incremented echo train acquisition (SE-PIETA) pulse sequence. At Si29 natural abundance levels the JSi-O-Si coupling splittings appear as overlapping doublet patterns arising from isolated Si29−O−Si29 linkages. The experimental 2D J-resolved spectrum is analyzed to obtain a bivariate probability distribution correlating the central Si-O-Si angle of a Q4−Q4 linkage to its mean Si-O-Si angle (seven angles) using relationships between Si29 isotropic chemical shifts and geminal JSi-O-Si coupling of a Q4−Q4 to its local structure. To obtain a self-consistent bivariate probability distribution it was necessary to introduce an additional dependence of the Si29 chemical shift of a Q4 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 O17 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 Si29 2D J-resolved spectrum we determine a Si-O-Si bond angle distribution in silica glass as having a mean at 147.8∘, a mode at 147∘, and a standard deviation of 10.7∘. Our statistical model for analyzing the experimental Si29 2D J-resolved spectrum also indicates that the individual Si-O-Si bond angle distributions are relatively uncorrelated.