Linear Polarization Resistance

date2026-07-24tags:chem:

Linear Polarization Resistance or LPR is a real time electrochemical technique. It directly measures the corrosion rate of a material in a conductive liquid. Cell current readings are taken over a small voltage range. The range is typically plus or minus 10 to 20 mV centered on the open circuit potential. The range is small for reasons covered below. The data produce a current versus voltage graph that is roughly linear.

The slope of that curve yields an estimate of the polarization resistance Rp. This value represents the material resistance to electrochemical polarization caused by corrosion. Higher polarization resistance means lower corrosion rate. Rp calculates I_corr. I_corr leads to a corrosion rate. That is the Stern Geary relation. This page derives it. Corrosion and EIS both point back to this page instead of repeating it. EIS reaches the same Rp from the frequency domain. It finds the low frequency limit of a fitted Randles cell.

Explanation for forgetful Vishakh

Metal corrodes through an electrochemical process when it sits in a conductive and corrosive fluid. The process acts like a tiny battery. It happens at the metal surface through two linked actions:

Anodic sites: Metal atoms leave the surface and enter the fluid. They release electrons. This is the metal wearing away.
Cathodic sites: These electrons flow to nearby locations on the metal surface. Corrosive elements in the fluid use these electrons to react. This is the fluid attacking the metal by taking electrons.

This electron flow between anodic and cathodic sites is the corrosion current I_corr. The corrosion points constantly move. The current spreads across the metal surface. Direct measurement of the corrosion current is therefore hard.

LPR avoids this by applying a small external voltage change to the metal. It measures the resulting current change. The key idea is simple: resistance to corrosion equals resistance to current change. A metal highly resistant to corrosion also resists external voltage changes from causing current changes. A metal that corrodes easily allows external voltage changes to change the current more readily.

Deriving Stern Geary

Time to make that resistance idea precise. A freely corroding electrode sits at its corrosion potential E_corr. At that potential the anodic metal dissolution partial current and the cathodic partial current are equal and opposite. This is Wagner Traud mixed potential theory. It is the same picture behind E_corr and E_OC on the Corrosion page.

Away from E_corr by a small polarization Delta E = E - E_corr, each partial reaction still follows its own Tafel law:

I_a(Delta E) = I_corr * 10^(Delta E / beta_a) I_c(Delta E) = -I_corr * 10^(-Delta E / beta_c)

The variables beta_a and beta_c are the anodic and cathodic Tafel slopes. The net measured current is the sum of the two:

I(Delta E) = I_corr [ 10^(Delta E/beta_a) - 10^(-Delta E/beta_c) ]

This also equals I_corr [ e^(2.303 Delta E/beta_a) - e^(-2.303 Delta E/beta_c) ] using the identity 10^x = e^(2.303 x).

Differentiate with respect to E and evaluate at Delta E = 0:

dI/dE at Delta E=0 = 2.303 * I_corr * (1/beta_a + 1/beta_c)

The polarization resistance is the inverse of that slope. It is literally Rp = Delta E / Delta I in the small signal linear limit. So Rp = (dE/dI) at Delta E=0:

Rp = 1 / (2.303 * I_corr) * (beta_a * beta_c) / (beta_a + beta_c)

Rearranged to solve for the corrosion current, this is the Stern Geary equation:

I_corr = B / Rp B = (beta_a * beta_c) / (2.303 * (beta_a + beta_c))

The value B bundles the two Tafel slopes into a single constant with units of volts. If you do not know beta_a and beta_c independently, the corrosion engineering literature uses a generic assumed B. Two common values are 0.026 V for an actively corroding system and 0.052 V for a passive one. Both come from the same formula under different simplifying assumptions. Beta_a = beta_c = 0.12 V/decade gives B = 0.026 V for active corrosion. A passive film removes anodic Tafel behavior. The film, not activation kinetics, controls anodic current. Beta_a approaches infinity. Taking that limit collapses B to just beta_c / 2.303. That gives 0.052 V for a cathodic slope of 0.12 V/decade. Either substitution replaces a measurement with an assumption. It turns an exact calculation into an order of magnitude estimate. Verify beta_a and beta_c independently whenever precision matters. A borrowed generic B can be off by a factor of two or more if the real Tafel slopes do not match what was assumed.

Why plus or minus 10 to 20 mV

The derivation relies on one assumption: I(Delta E) is linear near Delta E = 0. This licenses treating Rp as a single slope. Tafel kinetics are exponential in Delta E. Linearity is only an approximation over a limited range. Expand e^(2.303 Delta E/beta) as a Taylor series. The linear term is 1 + 2.303 Delta E/beta. The next quadratic term is (2.303 Delta E/beta)^2 / 2. The linear approximation holds while that quadratic term is small compared to the linear term. This requires Delta E much less than beta / 4.6. For Tafel slopes in the tens of mV per decade range typical of corroding metals, this bound lands around 10 to 20 mV. This matches LPR practice and ASTM G 59. Push Delta E wider and the curve bends away from a straight line. This biases the fitted Rp. Keep it narrower and the current change shrinks toward the instrument noise floor. This is a real problem for corrosion resistant samples with naturally low corrosion currents. Plus or minus 10 to 20 mV is the practical compromise between those two failure modes. It is not an arbitrary round number.

From Rp to a corrosion rate

I_corr on its own is a current. It is not yet a corrosion rate. Converting charge flow into metal lost requires Faraday's law. ASTM Standard G 102 formalizes this. The standard title is Standard Practice for Calculation of Corrosion Rates and Related Information from Electrochemical Measurements.

CR = K1 * (I_corr * EW) / rho

CR is the corrosion rate in units like mm per year. EW is the metal equivalent weight in g per equivalent. rho is its density in g per cm cubed. I_corr is the corrosion current density in microamps per cm squared. K1 = 3.27 times 10 to the minus 3. This is a units conversion constant that carries Faraday's constant inside it. For a pure metal, EW is the atomic weight divided by the oxidation state valence. For an alloy, EW comes from the mole fraction of each element in solution. Elements do not always dissolve in the same fraction as in the bulk alloy. Some dissolve preferentially. The full chain is: Rp measured gives I_corr = B/Rp from Stern Geary. That gives CR from ASTM G 102 and Faraday's law. Three separate steps exist. Each has its own assumption: linearity, known or generic B, and correct EW. Check each before trusting blindly.

Practical notes

The corrosion current density of coated samples should change slowly over time. The thickness of the coating reduces as it wears or degrades.

ASTM Standard G 59 contains useful information about polarization resistance measurements. It describes how to run the sweep. G 102 is the companion standard for the math that turns Rp into I_corr and a corrosion rate.

Track all three together over time in a monitoring campaign:

Open circuit potential
Polarization resistance
Corrosion current