# Surface modelization of an electrode

I am trying to model the interaction between an electrode and a saline solution through an RC circuit.

A reference electrode is placed in the saline solution to measure the voltage between the electrode used to inject or retrieve charges and the reference electrode.

I then perform a 3 phases cycle using current square waves.

Phase 1: Charge injection through the electrode

During this phase, $$e^{-1}$$ are injected in the saline solution. At $$t = 0$$, $$C$$ is not charged, thus the voltage measured between the electrode and the reference electrode is equal to the votlage drop on $$R1$$. This phase uses a current $$i$$.

Phase 2: Wait a bit

During this phase, charges are not injected or retrieved through the electrode. Thus, $$C$$ is discharging its charges in $$R2$$. This phase is very short, and $$C$$ will not be fully discharge at the end.

Phase 3: Retrieve charges through the electrode

During this phase, the current flows in the other direction: $$e^{-1}$$ are retrieve from the saline. At $$t = 0$$, since $$C$$ was not fully discharge, the voltage measured between the electrode and the reference electrode is equal to the votlage drop on $$R1$$ plus the votlage drop on $$R2$$. This phase is 3 times longer than the first one and uses a current $$-i/3$$. Thus, the same amount of charges is injected and retrieved.

The measured voltage looks like:

The general equation for the voltage measured given by the circuit above is:

$$V_{measured} = K*e^{-\frac{t}{R2*C}} + R1*i + R2*i$$

with $$i$$ the current through the system.

As you can see, the time constant only depends on $$C$$ and $$R2$$, however, when fitting an exponential on the data, I get 2 completely different time-constant for the first phase ($$e^{-1}$$ injection phase) and the third phase ($$e^{-1}$$ retrieve phase). For the third phase, the time-constant is about 5 times larger...

My current guess is that either $$C$$, or $$R2$$, or both are not linear and do not behave the same way depending on the current flow direction. Especially since I think phase 3 is influenced by phase 1. What could explain this behavior? What chemicals reaction happens when a current is injected and retrieved? How could I model this phenomenon?

Thanks for the help to understand this behavior :)

• This question seems to be perfect for Physics.SE. There is not much chemistry going on. – andselisk Sep 12 at 15:03
• @andselisk I will post it as well on that forum, ty. I thougt it was a good match with chemistry because I feel like the problem lies in the ions movement and the chemical reaction between the electrode and the saline. – Mathieu Sep 12 at 15:11
• I'd probably wait for a while, and if there won't be any answers on Chemistry.SE, it would make sense to move your question to Physics.SE. Cross-posting isn't always a desirable thing to do. – andselisk Sep 12 at 15:13
• Typically, reference electrodes are designed to conduct extremely low currents, e.g., a few pA at most. I suggest looking up three and four wire potentiostats (and how they work): there should be information available about solution impedances. Another posting option is at EE.SE, if posting here or at Physics.SE does not get results. – Ed V Sep 12 at 18:23
• @EdV Well it is not really an electrical problem as the Capacitance/Resistance equation part is clear. The only problem is that the values of this capacitance are not the same depending on the current flow direction... And we are using mA currents and checked the reference electrode already. – Mathieu Sep 12 at 20:26