# Is there any electronic component to water conductivity?

Answers to Decrease in temperature of a aqueous salt solution decreases conductivity indicate that the electrical conductivity of salt solutions arises from the mobility of ionic species and therefore the temperature dependence of conductivity is related to viscosity.

Question: Is there any measured or predicted electronic component to water conductivity as well, where the charge carriers are electrons rather than ions?

This could take place via charge exchange (migration of bound electrons) or even perhaps via solvated electrons, or some other mechanism.

In this case I'm interested in both pure water, and salt solutions.

• Well, while sodium dissolved in ammonia may get you solvated electrons, same metal leads to explosion in water, so it's still no. – Mithoron Feb 4 at 1:06
• There might be other ways for the solvated electrons to occur. But regardless of their origins, all solvated electrons will react with water, and that quite vigorously. – Ivan Neretin Feb 4 at 8:39
• @IvanNeretin freeing up extra electrons to water (say by ionizing radiation) may result in some vigorous recombination of course, but that's not the same thing as claiming there is zero ionization and zero free electrons in equilibrium. If there is a source that says so, it would be great to mention it or even include it in an answer. I'm trying to move towards an answer and away from continuing to justify why it's okay to ask the question. Thanks! – uhoh Feb 4 at 8:52
• The question Is there any electronic component to water conductivity? is clear and narrowly defined. It's a yes or no question! Votes to close as "too broad" without any helpful comments or suggestions seem spurious. These may be helpful 1, 2 though they are at extreme temperature and/or pressure; unfortunately they're paywalled and the libraries here are closed for lunar new year: – uhoh Feb 8 at 6:02
• @TryHard I would be happy with any electronic component to water electrical conductivity. I've mentioned "electrical" once in the question and the linked question is about electrical conductivity as well. I can add a few more instances of "electrical" if that's what you're getting at? – uhoh Feb 8 at 13:39

I agree with the commenters that electrical conduction is very unlikely, but it's worth going through some possible mechanisms:

1. actual solvated electrons: As others have noted, free electrons would be expected to react rapidly with protons, even in a basic solution, so this changes quickly to a scenario of sequential electron transfer between protons, so let's do that next.

2. Sequential electron transfer between $$\ce{H.}$$ and $$\ce{H+}$$: Let's assume the solution is strongly acidic, so protons are abundant, and a proton gets reduced at the cathode to a hydrogen atom radical. Based on the bond dissociation energies, abstraction of $$\ce{H.}$$ from water to form $$\ce{H2}$$ and $$\ce{HO.}$$ is slightly unfavorable, the hydrogen radical would be preferred over the hydroxyl radical. (The H-H bond formed has a BDE of ~ $$\pu{105 kcal/mol}$$, while the $$\ce{H-OH}$$ bond broken has a BDE of ~$$\pu{120 kcal/mol}$$.) The problem is the rate of quenching by reaction of two hydrogen atom radicals to form $$\ce{H2}$$ (which is water electrolysis produces hydrogen gas). I couldn't find a rate constant for that, but there is a published rate constant for recombination of hydroxyl radicals in water that is around $$\pu{10^10 M-1 s-1}$$. As you might expect, that's essentially diffusion limited, so the rate constant of hydrogen atom recombination is going to be at least as high. If we optimistically assume that transfer of the electron from $$\ce{H.}$$ to $$\ce{H+}$$ has a comparable rate constant, you would still have to have a very low concentration of radical and very short path to travel in order for an electron to make it from a cathode to an anode, but it doesn't seem theoretically impossible.

3. The third possibility would be sequential transfer of electrons from $$\ce{HO-}$$ to $$\ce{HO.}$$. In a strongly basic solution, this also seems like a theoretical possibility given a very short path and a very low concentration of radical, assuming there are no other molecules in solution that can quench the radical.

I'm not suggesting that either of these theoretical possibilities actually ever occurs, just that these are the mechanisms that seem most likely to me.

• Thanks for your answer, and for taking the question seriously! – uhoh Feb 15 at 15:48

Actually electronic conduction can occur in water. You'll probably find it in your daily rounds, if you know where to look.

Water, like all condensed matter, has a band structure. This is discussed with some references below, as the presence of band structures in liquids is not as intuitive as that in crystalline solids. Its valence band is filled with the electrons from the bonding molecular orbitals of the water molecules, while the conduction band that lies higher in energy, derived from antibonding orbitals, is empty. As with insulators generally, transport of an electron into the conduction band requires a much larger amount of energy input than is available to an average molecule from thermal energy, so we expect hardly any electrons make to this transition and be electrically conducted.

But in the presence of an electric field, which is necessary to make electrical conduction meaningful anyway, the energy levels of the bands are not uniform; they depend on the position in the electric field as well as the molecular orbital structure. An energy level corresponding to the valence band at one place may correspond to the conduction band some distance away. And that means an electron can become a conduction electron by quantum tunneling through that distance. This picture (source[1])

shows what is happening to the band structure given such a strong electrical field, in this case at an electrode surface. Which gives a hint as to what's coming...

There's a catch. The chapter in our quantum mechanics textbook that describes tunneling also tells us that tunneling is most probable if the particle/wave has to move only a short distance. With the electric fields we ordinarily experience macroscopically, the distance required to get the valence and conduction bands to line up energetically is too long; the tunneling probability is too small to notice. But if there were a field of at least hundreds of millions of volts per meter, then the required distance becomes short enough to make significant tunneling a realistic scenario. We have broken the insulator down.

What sort of monstrous device is needed to create such a field? How about the battery in your car or smoke detector? As illustrated here is a basic form, electrochemical reactions at solid electrodes depend on forcing electron transfer into the electrolyte; the surface automatically builds up enough of an electric field to enable electrons to tunnel and react. This conduction occurs over only a few atomic layers, so we don't see the electronic conduction in the watery phase directly. We can, however, see the resulting reaction and, of course its energy input or output as voltage.

The band structure of water has been widely studied. For example, this paper[2] uses calculations on water clusters to identify a gap of 6.9 electron volts in water, exceeding even the electronic band gap in diamond. Another reference from this answer gives an even higher band gap. Quoting from that answer:

do Couto et al have published an article[3] characterizing the density of states (band structure) of water using DFT theory combined with MC sampling. Extrapolating from clusters to bulk water, the HOMO-LUMO gap is 8.55 eV (Table 3).

### References:

1. Saraf, S.; Giraldo, M.; Paudel, H. P.; Sakthivel, T. S.; Shepard, C.; Gupta, A.; Leuenberger, M. N.; Seal, S. Photoelectrochemical analysis of band gap modulated TiO2 for photocatalytic water splitting. Int. J. Hydrogen Energy 2017, 42 (15), 9938–9944 DOI: 10.1016/j.ijhydene.2017.01.232.
2. Coe, J. V.; Earhart, A. D.; Cohen, M. H.; Hoffman, G. J.; Sarkas, H. W.; Bowen, K. H. Using cluster studies to approach the electronic structure of bulk water: Reassessing the vacuum level, conduction band edge, and band gap of water. The Journal of Chemical Physics 1997, 107 (16), 6023–6031 DOI: 10.1063/1.474271.
3. Cabral Do Couto, P.; Estácio, S. G.; Costa Cabral, B. J. The Kohn-Sham density of states and band gap of water: From small clusters to liquid water. The Journal of Chemical Physics 2005, 123 (5), 054510 DOI: 10.1063/1.1979487.
• Never say anything is impossible unless dictated so by a law of physics. – Oscar Lanzi Feb 9 at 13:49
• Some models have electrons tunneling from one site (transition metal ion) in an enzyme complex to another over distances of a couple of nanometers. I'm not sure that this behavior could be excluded for a solution of a transition metal complex in water. ncbi.nlm.nih.gov/pmc/articles/PMC4213181 – user5713492 Feb 9 at 15:56
• Could this current be continued over some period, or would it in practice degenerate into a spark? – James Gaidis Feb 10 at 14:29
• – uhoh Jul 13 at 22:35

Besides the useful answers above, search the keyword "aquated electron" or better still "solvated electron". People have been studying theses systems.

For example: Barnett, R. N.; Landman, U.; Nitzan, A. Dynamics and spectra of a solvated electron in water clusters. The Journal of Chemical Physics 1988, 89 (4), 2242–2256 DOI: 10.1063/1.455067.

Of course a free electron cannot exist in water before that will reduce water. It would an interesting thought experiment to irradiate water with gamma rays and simultaneously measure conductivity. You can search along those lines. On the other hand, Grotthus mechanism takes a "proton" movement in solution. For example people still do not fully understand as to why H+ ion has the highest conductivity in aqueous solution. The Grotthus mechanism was proposed a century ago and it resurfaced again.

• From here "Other ions with low surface charge density (such as Cl-, ClO-, HO2- and O2·-) will also favor the gas/liquid interfaces [928a] as probably do hydrated electrons 1841, 1874." I don't have the background to interpret these; can't even access them until the lunar new year is over and the libraries here open up. I understand that there is a continuum of theories about water, from widely accepted, to... not so much. – uhoh Feb 9 at 5:06
• Once a professor joking said that a physical chemist cannot differentiate between methane and a cow! Sometimes the pure simulations are far from reality. The two suggested papers are highly quantum mechanical in nature (pure simulations). I don't have the background either. I can send those papers if I have your email. Can you contact via Researchgate? – M. Farooq Feb 9 at 5:14
• Okay I understand what you mean, some might say all models are wrong; some are useful. I can just wait until Monday to have a look, thank you! – uhoh Feb 9 at 5:16

Any conduction by non-ionic electrons in water would require some concentration of these electrons. Mithoron pointed out the extreme reactivity of sodium as an example of how it couldn't work. Using a less-reactive metal, such as zinc, might put electrons into the water, but they would be quickly attracted to aquated H+ ions that exist at 10 e-7 moles/liter and turned into molecular hydrogen. The zinc would go in as Zn++.

So the prediction of electronic conduction in water has to be negative, because even pure water contains an electron-grabbing, electron-neutralizating component that wouldn't allow free electrons to travel across any significant distance between electrodes.

• This is a helpful answer, thank you! I mentioned two possibilities I could think of; I wonder if you can also rule out charge exchange (migration of bound electrons) with a similar argument? – uhoh Feb 8 at 20:15
• Charge-transfer complexes can exhibit high conductivity, apparently even in solution (en.wikipedia.org/wiki/Charge-transfer_complex). But this apparently thru the complex, not completely thru the solvent. I think passage of electrons past the H+ ions in water is not likely. – James Gaidis Feb 9 at 13:52