H 1 NMR study of proton dynamics in the inorganic solid acid Rb 3 H ( SO 4 ) 2

Proton dynamics in ${\mathrm{Rb}}_{3}\mathrm{H}({\mathrm{SO}}_{4}{)}_{2}$ has been studied by means of $^{1}\mathrm{H}$ NMR. The $^{1}\mathrm{H}$ magic-angle-spinning (MAS) NMR spectra were traced at room temperature (RT) at Larmor frequency of $400.13\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$. $^{1}\mathrm{H}$ static NMR spectra were measured at frequencies of $200.13\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$ and $400.13\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$ in the ranges of 165\char21{}513 and $300\char21{}513\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, respectively. $^{1}\mathrm{H}$ spin-lattice relaxation times, ${T}_{1}$, were measured at 200.13 and $19.65\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$ in the ranges of 260\char21{}513 and $260\char21{}470\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, respectively. The $^{1}\mathrm{H}$ MAS NMR spectrum at $294\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ has an isotropic chemical shift of $16.3\phantom{\rule{0.3em}{0ex}}\mathrm{ppm}$ from tetramethylsilane, demonstrating very strong hydrogen bonds. In RT phase, a wobbling motion of the $\mathrm{O}\text{\ensuremath{-}}\mathrm{H}$ axis in one direction at the fast motional limit takes place above $400\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, being supported by the $^{1}\mathrm{H}$ static NMR spectral line shapes and by the $^{1}\mathrm{H}$ ${T}_{1}$ values. In the high temperature (HT) phase, the sharp $^{1}\mathrm{H}$ static NMR spectra indicate translational proton diffusion. From the analysis of $^{1}\mathrm{H}$ ${T}_{1}$, protons diffuse with the inverse of the frequency factor $({\ensuremath{\tau}}_{0})$ of $9.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}\phantom{\rule{0.3em}{0ex}}\mathrm{s}$ and the activation energy $({E}_{a})$ of $25\phantom{\rule{0.3em}{0ex}}\mathrm{kJ}\phantom{\rule{0.2em}{0ex}}{\mathrm{mol}}^{\ensuremath{-}1}$. These parameters can well explain the macroscopic electric conductivity in HT phase.