Deterioration of hydrogen-bonded superprotonic conductors belonging to CsHSO₄–CsH₂PO₄–H₂O salt system: a single-crystal neutron diffraction investigation

Abstract

Single-crystal neutron diffraction investigation on Cs₄(HSO₄)₃(H₂PO₄) and Cs₆H(HSO₄)₃(H₂PO₄)₄ superprotonic crystals, belonging to CsHSO₄–CsH₂PO₄–H₂O salt system, is under taken to elucidate the precise hydrogen atom positions in these crystals. The investigation revealed that these crystals are very sensitive to the ambient conditions and can undergo deterioration due to fluctuation in air moisture content. Cs₆H(HSO₄)₃(H₂PO₄)₄ crystals are more stable as compared to Cs₄(HSO₄)₃(H₂PO₄). Crystal structure of Cs₆H(HSO₄)₃(H₂PO₄)₄ is obtained both before and after deterioration, it is found that the asymmetric O–HO hydrogen bond between the PO₄ and SO₄ ions of this crystal becomes stronger after deterioration. This led to the shrinkage of the unit cell, and most likely prevented further deterioration. Diabatic state model for hydrogen bonds is used to obtain the energy contour for the O–H···O hydrogen bond of Cs₆H(HSO₄)₃(H₂PO₄)₄ crystal. The influence of this change in the hydrogen bonding on the proton conduction ability of the crystal is discussed.

Appendix: Diabatic state model for H-bonding

According to the diabatic model the O–H···O hydrogen bond can be represented by two interacting diabatic states |O–H···O> and |O···H–O>. The effective Hamiltonian describing the two interacting diabatic states has the form

$$ {\text{H}} = \left( {\begin{array}{*{20}c} {V\left( r \right)} & {\Delta \left( R \right)} \\ {\Delta \left( R \right)} & {V\left( {R - r} \right) + V0} \\ \end{array} } \right) $$

Here r and R are the O–H and O–O distances, respectively, and r0 is the equilibrium free O–H distance of 0.96 Å. V₀ is the vertical off set to take into account the asymmetry of the O–H···O hydrogen bond. V(r) is Morse potential for O–H bond with a depth (D) of 120 kcal mol⁻¹, exponential parameter a of 2.2 Å⁻¹, corresponding to O–H stretch harmonic frequency of 3600 cm⁻¹.

$$ {{V}}\left( {{r}} \right) = {{D}}[e^{{ - 2a\left( {r - r0} \right)}} - 2e^{{ - a\left( {r - r0} \right)}} ] $$

The coupling between the diabats |O–H···O> and |O···H–O> is given by Δ(R) defined as

$$ \Delta \left( R \right) = \Delta_{1} \exp \left[ {{-}b\left( {R{-}R_{1} } \right)} \right] $$

This model has essentially two free parameters b and Δ₁. The parameter values used here are, Δ₁ = 0.4D ≈2 eV and b = 2.2 Å⁻¹. R₁ is a reference distance that is taken as R₁ = 2r0 + 1/a ≈ 2.37 Å.