Proton Conductivity in Phosphoric Acid: The Role of Quantum Effects

Phosphoric acid has one of the highest intrinsic proton conductivities of any known liquids, and the mechanism of this exceptional conductivity remains a puzzle. Our detailed experimental studies discovered a strong isotope effect in the conductivity of phosphoric acids caused by (i) a strong isotope shift of the glass transition temperature and (ii) a significant reduction of the energy barrier by zero-point quantum fluctuations. These results suggest that the high conductivity in phosphoric acids is caused by a very efficient proton transfer mechanism, which is strongly assisted by quantum effects.

Figure 1

Dielectric spectra of $R=3$ H-PA (solid symbols) and D-PA (lines) at select temperatures. (a) Real part of the dielectric permittivity ${ϵ}^{\prime }(\nu )$; (b) real part of the conductivity ${\sigma }^{\prime }(\nu )$; and (c) imaginary part of the electric modulus $M^{\prime \prime }(\nu )$.

Figure 2

Temperature dependence of (a) conductivity and (b) of the conductivity relaxation time in H-PAs (open symbols) and in D-PAs (closed symbols) for several selected water content $R$ values. Arrows in (b) indicate $T_g$ values for H-PAs from DSC measurements. (c) The ratio of conductivities in protonated ${\sigma }_{\mathrm{H}}$ and deuterated ${\sigma }_{\mathrm{D}}$ samples with different $R$. The horizontal dashed line in (c) presents the value 1.4 expected for classical proton transfer mechanism. (d) Temperature dependence of viscosity in H-PA (open triangles) and D-PA (closed triangles) with $R=5$.

Figure 3

Dependence of the isotope effect on molar content of water $R$: (a) Isotope shift of the glass transition temperature $\mathrm{\Delta }{T}_g=T_g(\mathrm{D})-T_g(\mathrm{H})$ measured by DSC (closed symbols) and BDS (open symbols). The error bars for the shift in $T_g$ are larger for samples with low $R$ due to significantly higher sensitivity of $T_g$ in theses samples to the water content. (b) The ratio of the conductivities and conductivity relaxation times at $T_g$. The dashed line shows the ratio ${\sigma }_{\mathrm{H}}/{\sigma }_{\mathrm{D}}\sim 1.4$. (c) The activation energy for the conductivity relaxation time in the Arrhenius regime $T<T_g$ for D-PAs (closed symbols) and H-PAs (open symbols). Accuracy of estimated $E_a$ for $R=4$ and 5 is low due to more limited temperature range investigated below $T_g$.

Figure 4

Conductivity vs viscosity in protonated (open symbols) and deuterated (closed symbols) PA with $R=5$. Inset shows the ratio of conductivities at the same viscosity that increases with decrease in temperature (increase in viscosity), and the star shows the ratio of conductivities at $T_g$ that should correspond to $\eta \sim {10}^{12}\mathrm{Pa}\mathrm{s}$.