Polarization Resistance

The polarization resistance is a slope, not a resistance, and keeping that distinction alive is most of understanding it. Apply a small potential shift to a corroding electrode, measure the current that flows, and divide: what you get is the local gradient of a curve that is exponential everywhere except right at the origin. A conductor's resistance is a property that holds over any voltage you like. This one is a tangent, and it is only the tangent at one point.

That is why the polarization has to be small. Ten to twenty millivolts either side of the corrosion potential is the conventional window, and it is chosen because it is where the potential–current relation is still linear to within the accuracy anyone needs. Polarize further and you begin measuring a chord across a curve rather than its tangent, which underestimates the slope and overestimates the corrosion rate — and further still, you start genuinely changing the surface you came to measure, stripping films or plating out species that were not there before.

Three practical errors all push in the same direction and all make the corrosion look slower than it is. The first is scan speed. The electrode interface behaves as a capacitor of a few tens of microfarads per square centimetre, and charging it draws current that has nothing to do with corrosion. Sweep quickly and that capacitive current inflates the measured $\Delta I$; on a coated or heavily filmed surface the time constant can run to minutes, and a scan that looked patient at 0.1 mV/s was still far too fast.

The second is solution resistance. Whatever resistance lies between the working electrode and the tip of the reference electrode adds directly to the measurement, and the instrument cannot tell the two apart. In seawater it is negligible; in soft water, condensate, fresh concrete or dry soil it can be the majority of the reading. Current interruption, a Luggin capillary placed close to the surface, or electrochemical impedance spectroscopy — which separates the two by frequency — are the standard answers.

The third is the area. Dividing by the wrong area scales the answer directly, and the right area is genuinely uncertain on a rough, scaled or partly coated surface. All three of these matter more as the reading gets larger, which is unfortunate, because a large $R_p$ is exactly the result you would most like to trust. The discipline that makes linear polarization valuable is not accuracy on any single reading — it is consistency across many of them. A probe read weekly for two years, on the same instrument in the same place, tells you when something changed, and that is usually the question that matters.