Characterization of the Dynamics in the Protonic Conductor CsH ₂PO ₄ by ¹⁷O Solid-State NMR Spectroscopy and First-Principles Calculations: Correlating Phosphate and Protonic Motion

Abstract

¹⁷O NMR spectroscopy combined with first-principles calculations was employed to understand the local structure and dynamics of the phosphate ions and protons in the paraelectric phase of the proton conductor CsH ₂PO ₄. For the room-temperature structure, the results confirm that one proton (H1) is localized in an asymmetric H-bond (between O1 donor and O2 acceptor oxygen atoms), whereas the H2 proton undergoes rapid exchange between two sites in a hydrogen bond with a symmetric double potential well at a rate ≥10 ⁷ Hz. Variable-temperature ¹⁷O NMR spectra recorded from 22 to 214 °C were interpreted by considering different models for the rotation of the phosphate anions. At least two distinct rate constants for rotations about four pseudo C ₃ axes of the phosphate ion were required in order to achieve good agreement with the experimental data. An activation energy of 0.21 ± 0.06 eV was observed for rotation about the P–O1 axis, with a higher activation energy of 0.50 ± 0.07 eV being obtained for rotation about the P–O2, P–O3 ^d, and P–O3 ^a axes, with the superscripts denoting, respectively, dynamic donor and acceptor oxygen atoms of the H-bond. The higher activation energy of the second process is most likely associated with the cost of breaking an O1–H1 bond. The activation energy of this process is slightly lower than that obtained from the ¹H exchange process (0.70 ± 0.07 eV) (Kim, G.; Blanc, F.; Hu, Y.-Y.; Grey, C. P. J. Phys. Chem. C2013, 117, 6504−6515) associated with the translational motion of the protons. The relationship between proton jumps and phosphate rotation was analyzed in detail by considering uncorrelated motion, motion of individual PO ₄ ions and the four connected/H-bonded protons, and concerted motions of adjacent phosphate units, mediated by proton hops. We conclude that, while phosphate rotations aid proton motion, not all phosphate rotations result in proton jumps.