Tuesday, August 12, 2014

Proton transport in phosphoric acid

There is a very interesting paper
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.
The main result of this paper is to use ab initio molecular dynamics simulations to show
  • 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.
The simulation treats the nuclei in a purely classical fashion.
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.


  1. Thanks for bringing this up! This is an extremely exciting thing to see one's work featured in the blog one's following!!!

    I think it is my duty as one of the authors of this paper to comment on some of the inetersting remarks/questions you raised here:

    1. As far as I have recently encountered, it is a common misconcept among to the solid-state physicists to compare/contrast the metallic electronic conductivity versus the ionic one. In fact, except for some Marcus-like electron transport, they have very different origins, mechanisms and limits. In the world of ionics 0.15 S/cm is a pretty impressive value, which is not the case in the world of electronics. The highest reported ionic conducttivities typically are <1 S/cm. Protons (H+ ions) are the smallest ions and usually show higher conductivities than other "fast ions" (Li+, Na+, Mg2+, F-, O2-, I-) in liquids or solids (e.g. ~0.5 S/cm in diluted aqueous HCl). Of course, free H+ do not exist in condensed matter, and are usually transported via some form of "structural diffusion".

    2. The origin of dielectric response in these systems is something which is not very well understood especially at the molecular level. We are still working both experimentally and theoretically in order to shine some light on this. The ab initio analysis suprisingly shows how much the dipolardistribution is different (it is very broad with many competing contributions) in the condensed phase from the gas phase (hint: much more than in water) and how strongly it affects the dielectric response. We hope to submit a manuscript on this soon.

    3. The 10% chance of proton transfer is not for the quasi-coherent process, which is almost neglible in H-bonds that are not nearest neighbours, but for a case when we allow the H-bonds to relax a little bit but not break (~50fs waiting time).

    4. It is recently becoming clear that most of the H-bonded systems show a lot of similarities, yet they are very succeptible to all kinds of "perturbations" which at the same time make them different. The older work of Chandler&Parrinello and recently of Hassanali&Parrinello indicate that the same kind of chains have to form in water as well, in order for the charge defects to form, however this is an extremely rare process. In H3PO4 on the other hand, this happens very easily and the transient charges form all the time. Howver, this is not enough to form a pair of charged defects which could separate and transport current. Here the H3PO4 "frustrated" H-bonds come into play and provide sort of a "shortcut" for the charge separation and the system's ability to carry current. In fact we are preparing a report on another study where we show that once the degree of "frustration" is reduced, the correlated hops still hapen, but most of the long-range proton transport is gone.

    5. Our main motivation in this sudy was to explain the long-range proton conductivity which usually happens at higher temperatures and is diffusion controlledwhich in fact show neglible isotope effects. Nevertheless, quantum effects in these systems could be particularly interesting not only due to this classical copperativity we saw but also due to this double population of protons (normal vs "frustrated") and H-bonds they are forming. These populations must overlap and exchange a lot, which could be a particularly inetersting playfield for quantum nuclear effects.

    One of the older studies on the quantum effects on diffusion was performed by one of the authors. See for example Fig. 26 in http://dx.doi.org/10.1021/cm950192a. It is clear that the nuclear quantum effects on the proton transfer are quite small, with much of it coming from the overall slowing down of the solvent and slight differences in the ZPE. The effect is even more visible in the mixtures of H3PO4 and D3PO4.

  2. Dear Linas,

    Thanks for your detailed comment and clarifications.

    With regard to 1.
    Comparing to solid state physics is useful for elucidating the incoherent nature of the transport.
    My post links to an earlier post that showed the misunderstanding of some physicists who claimed proton transport in ice was "metallic".

    The solid state comparison is not for the purpose of "putting down" phosphoric acid.
    I realise it does have a very high proton conductivity compared to other materials and that is interesting and important for applications.

    Thanks for the reference about isotope effects.