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Carbon electrodes are very popular, because unlike metal electrodes, carbon is quite inert during electrolysis (I'm sure that has some explanation based on electronegativity).

However they too are not eternally lasting. Especially the pencil graphite bars will slowly release black chunks into the solution.

My question is, what's happening them. The black chunks seem like carbon, so it's probably not reacting. What's damaging the structure?

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Pencil leads aren't pure graphite, they're generally graphite powder with various polymers to hold them together and make sure they have the correct hardness (after all, you wouldn't be able to use them to write if they didn't leave graphite on the paper or if they crumbled under slight pressure. This is why the much more rigid glassy carbon is a popular material for carbon electrodes. My guess is that there's no reaction with the electrode happening but gas being produced is causing mechanical damage to the electrode. If you work at less extreme potentials, you might be able to reduce this effect. Otherwise, pure graphite rods should be more durable. Of course, if you're using pencil leads, they're obviously cheap to replace so it might be easier to just use them until they fall apart, then switch to a new one.

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  • $\begingroup$ And you think pure, hard graphite wouldn't fall apart? I remember that even electrodes from batteries slowly decayed and left black stuff all over the solution. $\endgroup$ – Tomáš Zato - Reinstate Monica Oct 14 '14 at 18:26
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    $\begingroup$ I'm not sure. I've only ever used graphite electrodes at relatively low potentials and I've never had that problem. I can't attest to the quality of graphite that's used in batteries. Since they're disposable anyways, they really don't have to be that durable. If you're running at high potential, it's possible to actually oxidize the graphite, a known problem with strong oxyacid solutions, though the binder seems to be more strongly attacked than the actual graphite, so it depends on how the electrode is made.—doi:10.1149/1.2411746 $\endgroup$ – Michael DM Dryden Oct 15 '14 at 0:08
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This article here indicates that carbon/graphite electrodes are attacked both chemically (oxygen gets converted to $\ce {CO2}$, removing carbon from the electrode) and mechanically (gas bubbles form in pores in the surface and break it apart). Pencil leads fall apart quickly because of the clay content. A high-quality graphite electrode will last far longer but will also eventually decay. The rate of erosion goes up rapidly with increased voltage across the electrodes. In my personal experience doing water electrolysis I got almost no mechanical erosion at 10V but obvious mechanical erosion at 24V.

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