The mechanism of proton conduction in phosphoric acid
Linas Vilčiauskas, Mark E. Tuckerman, Gabriel Bester, Stephen J. Paddison, Klaus-Dieter Kreuer
There are several reasons why neat liquid phosphoric acid (H3PO4) is such an interesting system
- the highest intrinsic proton conductivity of any known substance and is σ ≈ 0.15 S cm−1 above Tmelt = 42 °C. This is like the conductivity of a bad metal but orders of magnitude larger than that of neat water.
- hydrogen bonded phosphates are ubiquitous in bimolecular systems and often involved in proton transport
- hydrogen bonded phosphates are electrolytes in high-temperature polymer electrolyte membrane fuel cells
- hydrogen bonded phosphates feature in many ferroelectric materials
- short intermolecular hydrogen bonds (the oxygen atom separation, R_OO ≈ 2.60 Å, compared to R_OO ≈ 2.85 Å in liquid water)
- it has a high dielectric constant (61), comparable to that of liquid water, but in the gas-phase the dipole moment of a phosphoric acid molecule is only 0.45 Debye compared to 1.85 Debye for a water molecule.
- Hydrogen bonded chains are central to the proton conductivity. there is an ten per cent chance of a quasi-coherent hop along four H-bonds.
- proton transport occurs via a structural diffusion mechanism similar to the Grotthuss mechanism involved in water
- however, due to the presence of the short H-bonds a co-operative compression of the bond lengths in the molecular chain, such as occurs in liquid water, is not required.
One thing I found a bit strange was that the presence of short H-bonds was hinted to be an argument for neglecting quantum nuclear effects. I would have thought the opposite.
It has been shown before, including by Tuckerman, that for R_OO ≈ 2.60 Å that quantum nuclear effects can be significant, because then the proton transfer potential is not barrier less but has an energy barrier comparable in magnitude to the vibrational zero-point of the O-H stretch, as discussed here.
Hopefully, someone will do a full path integral simulation with quantum nuclei soon.
Experimentally, a first estimate of quantum nuclear effects can be found by deuterium substitution. Surprisingly, in a quick search I could not find any measurements of deuterium conductivity/mobility/diffusivity in the deuterated acid. If they have not been done, hopefully, someone will do the measurements soon.