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I'm an electrical engineer who has been taught transistors and silison and solid state theory and all that. But when I apply the theory to batteries and cathodic protection, my understanding seems to break down. Can someone explain how batteries and cathodic protection work, from the point of view of band diagrams?

I understand that when two metals touch, their outer electrons will not be of the same energy, so the electrons will move from one metal to the other, leaving both metals charged. I also understand that this charge will dissipate at the other surfaces of both metals, such that near the surface, the metals appear far less charged.

Band diagram of the interface of 2 different metals

Then, if this combination is dunked in an ionic solution (such as lead and lead oxide in sulphuric acid, or zinc and steel in salt water) then ions of opposing charge will each gather at one of the metals, pulled in by the charge (I guess?), then react at the surface, causing .... the charge to build the other way? This part has me confused.

In a battery the metals are not touching, so the charge builds up and a voltage appears across the terminal, and this charge pushes away the ions, slowing the reaction and slowing the build up of charge. If a circuit is connected, then the metals are "touching" via this circuit and charge flows from one metal to the other, allowing the reaction with the disolved ions to proceed.

But then in cathodic protection, the metals are bolted to one another, and both will react with the ions, causing a build up of charge, which can dissipate to the other metal via the interface. I understand that then a big metal boat, with a big cathodic protection, would have a voltage (and current flow) across its hull, as the reaction with the steel of the hull will be spread across the surface of hull where it meets the water. But then why would this potential difference continue above the water, and if and anchor were tossed over to land, and the chain didn't touch the water, why would there be current through to ground? Why does it not all flow back through the bolt connecting the zinc and to the boat?

Cathodic protection of boat tied to land

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  • $\begingroup$ This is a standard exercise in electrochemistry- specifically corrosion science. A textbook on corrosion will answer all your questions. $\endgroup$ – niels nielsen Feb 14 at 18:08
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In a battery and electrochemical cells we typically explain the phenomenon using reduction potentials (these can be gotten from a standard reduction potential table). The Gibbs free energy dictates whether a reaction will happen and for electrochemical cells is given by the Nernst equation $$\Delta G=-nFE=-RT\ln K_\mathrm{eq}+RT\ln Q$$ so we need negative Gibbs free energy for a reaction to occur which means positive $E$ (cell potential). Also we can relate the Gibbs free energy to the chemical potential through thermodynamics $$\Delta G=\mu\,\mathrm dN$$ The reaction is between the two metals where one is oxidized (loses electrons) in this case the zinc anode and one is reduced (gains electrons) in this case the iron cathode. Oxidation happens at the anode and reduction happens at the cathode, thus cathodic protection as metal oxides are reduced back to their pure metals. When the metals are not touching as is typically the case in batteries(galvanic cells) the electrons travel through an outer circuit creating electrical energy and half cell redox reactions occur at each terminal(anode and cathode). The reactions cannot occur if the circuit is not closed as the cathodes sides reaction needs electrons and the anodes sides reaction expels electrons. The electrolyte serves to prevent charge buildup as during the oxidation reaction at the anode the positive metal ions are produced and need negative electrolyte ions to balance while at the cathode the positive metal ions are reduced leaving their negative counter parts that need to be balanced by positive electrolyte ions. If charge buildup occurs the reaction will stop and no current will flow (this is almost immediate). Cathodic protection can occur with the metals touching or not touching. When the metals are touching the full redox reaction occurs and no external circuit is necessary.

PS the reactions ideally do not involve the electrolyte. It serves simply to prevent charge buildup(like a salt bridge) and complete the current loop through ion migration.The reactions here for example are:
Zn(s) ⇌ Zn2+ + 2 e− anode(oxidation)
and
Fe3+ + 3 e− ⇌ Fe(s) cathode(reduction)

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  • $\begingroup$ So electrons transfer into the cathode via the connection to the anode (circuit or metal-metal interface), and out of it via ions and the half-reaction. Then why is current flow observed between a ship and ground observed when cathodic protection is in place? What causes this second loop and why would those electrons not take the first loop? $\endgroup$ – Smyther Feb 14 at 18:24
  • $\begingroup$ I believe there is a small charge buildup that can cause a minuscule current. But the resistance of ground would be huge so the current would be really small at these small voltages. The "battery" is already internally short circuited, the large resistance ground is connected in parallel. There is a better path to conduct, it is negligible $\endgroup$ – ChemEng Feb 15 at 3:16

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