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What is the meaning of overpotential in the context of photocatalytic water-splitting? That is light drives charge separation inside TiO2 and the generated electrons and holes react with water to produce hydrogen and oxygen.

I have seen many papers talk about the high overpotential associated with the oxygen evolution half of the reaction. I understand overpotentials as the potential you apply to (an electrochemical) cell in order to drive the reaction without energy barriers. However, in a photocatalytic system, there are no bias voltages. So, what is the physical significance of overpotential here?

Thanks!

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Photon absorption by titania results in an excitation of an electron from the valence band to the conduction band. The difference in energy of an electron in the valence band and the conduction band is the band gap, which for titanium dioxide is about 3.3 eV.

What matters for electrochemistry, though, is the absolute voltage of (i) the excited electron, and (ii) the absolute voltage of the "hole" left in the valence band, not the just the difference between them (gap). That is far more difficult.

The effective electrochemical voltages of the excited electron (or hole) can differ from what the desired electrochemical reaction is. So there could still be an overpotential. For titania, one paper I found estimates of the absolute energies of the valence band "hole" and the conduction band electron of -7.8 eV and -4.5 eV, respectively (at pH 0). The thermodynamic potential for water oxidation is -5.8 eV, 2 eV higher than the hole energy. That energy is lost if the hole is used to power water oxidation. You could thus view excited titania having an overpotential of 2 eV for the water oxidation reaction. In contrast, the theoretical potential for proton reduction is -4.5 eV, close to the conduction band electron energy.

Thus the energetics of bulk titania provide lots of overpotential for the water oxidation reaction but the tradeoff is that a high band gap means only high-energy photons can power the electrochemistry. Lowering the band gap would make more and longer wavelengths of radiation available to power water photolysis, but the band gap can only be lowered in certain ways. For titania, it would not be very desirable to lower the energy of the conduction band, because that would mean excited electrons would not be able to reduce protons to hydrogen . Thus, the only way to lower the band gap is by raising the energy of the valence band, which would both lower the overpotential and and make more types of radiation accessible for powering water photolysis.

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    $\begingroup$ Hi Curt, I sort of see what you are saying. But I'm still a bit confused. I'm linking a paper here if you don't mind (pubs.acs.org/doi/abs/10.1021/ja105340b). According to this paper, there is an overpotential of around 0.7 eV for oxygen evolution - which I understand to be the highest free energy barrier in the free energy profile for oxygen evolution. However, they also use a U value (which I believe is well known in electrochemistry circles) of 1.93 eV. $\endgroup$ – user34801 Aug 12 '15 at 16:09
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    $\begingroup$ This they say is the electropotential of a hole at the VBM (that I would interpret as the band gap of the material). What I don't understand though is the relation between this U value and the overpotential. Most of the electrochemistry papers I've read don't explain the connection between them, so I'm wondering if it is well-known in the electrochemistry field. $\endgroup$ – user34801 Aug 12 '15 at 16:14
  • $\begingroup$ Specifically if you read the abstract of the paper I linked, it says that the overpotential is 0.7 V (which is the highest free energy barrier in the free energy profile for the OER), which is 1.93 V wrt the SHE (and this enters the equation for calculating the free energy change as the eU term, which I interpret as the bandgap). Thanks for your help! $\endgroup$ – user34801 Aug 12 '15 at 16:16
  • $\begingroup$ I'm afraid I'm getting out of my depth pretty quickly...sorry I can't help more and thanks for posting the paper, it was interesting to look at. $\endgroup$ – Curt F. Aug 12 '15 at 21:09
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    $\begingroup$ @NikolajK: Bard is a classic. Gileadi's physical electrochemistry is also supposed to be good. Disclaimer: I just started working on electrochemistry, so I haven't read Bard's book fully and only just borrowed Gileadi's book. $\endgroup$ – user34801 Aug 19 '15 at 17:19

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