# Demystifying the Stern Geary Equation

From all the applications of electrochemistry, corrosion is one of the most studied due to its wide range of applications in industry. Thanks to this interest, there are multiple electrochemical models out there to characterize corrosion rates. In this post, we talk about the Stern Geary equation. We explain what it is, who developed it, how to use it and some considerations to take into account before using it.

## What is the Stern-Geary Equation?

The Stern Geary equation is a mathematical model used routinely in corrosion science. With this model, it is possible to predict the corrosion rate of a metal or alloy in specific environmental conditions. It is widely used in a number of industries were corrosion control and prevention is of ultimate importance such as oil and gas, aerospace and construction.

### The scientists behind the Stern-Geary Equation

This equation was developed by scientists from Union Carbide Milton Stern and A. L. Geary in the 1957 in a paper of the Journal of The Electrochemical Society entitled “Electrochemical Polarization: I. A Theoretical Analysis of the Shape of Polarization Curves”.

In this paper, the authors looked for an alternative model for corrosion where interfering reactions prevent the accurate determination of Tafel slopes.

### The Stern-Geary equation

The Stern-Geary equation describes the relationship between the polarisation resistance and the corrosion current of a system. It can be expressed as:

where:

icorr is the corrosion current in mA,

Rpol is the polarisation resistance in Ω,

βanodic is the anodic Tafel slope in mV/decade,

βcathodic is the cathodic Tafel slope in mV/decade

## How to use the Stern-Geary Equation for corrosion measurements

The Stern-Geary equation is mostly used to estimate corrosion rates and is an alternative model to the Tafel and Butler-Volmer equations for estimating the corrosion current.

In order to be able to use the Stern-Geary equation the potential range of the experiment needs to be restricted to a very narrow window around the corrosion potential of the electrochemical cell, normally +/- 10 mV. In this range, the potential vs current plot is mostly linear and its slope is known as polarization resistance. It is also recommended that the scan rates of the experiment are kept very slow, around 0.1 mV/s, to ensure a steady-state measurement where diffusion effects are kept to a minimum.

## 6 things to take into account when using the Stern-Geary Equation

### 1. It has limited applicability

This equation is only applicable to corrosion reactions that follow a Tafel-like behavior and consist in the transfer of a single electrons. While other types of reactions may be modeled with the Stern-Geary equation, the prediction may not be accurate and require adjusting.

### 2. It’s results are environment dependent

The resulting corrosion current calculated is only valid for the material tested in the specific environment it was tested. Corrosion is affected by multiple factors, inclulding temperature, pH, and inhibitors. Therefore, if the material or environment (i.e. electrolyte) is modified, the experiment should be run again.

### 3. Assumes resistance is solely due to corrosion

The Stern-Geary equation assumes that the polarisation resistance is a result of only the corrosion of the metal being studied. Therefore, other factors like electrolyte resistance, double layer capacitance, diffusion effects, etc, are not considered as contributing factors.

### 4. Constants require validation for each specific case

The Tafel constants obtained from the Stern-Geary equation are linked to the conditions of the test. That is, material being corroded and its environment. Thus, these constants can’t be extrapolated to other cases, and if done, they should be experimentally tested to ensure they are valid for the new electrochemical system.

### 5. Assumes surface is uniform

The Stern-Geary equation assumes that the corrosion is happening equally throughout the surface of the electrode and does not take into account the effects of any localized corrosion.

### 6. Results must be interpreted as predictions rather than facts.

The results obtained from the Stern-Geary equation should be interpreted cautiously. While in the lab the results may be accurate and very reproducible, it must be noted that the experimental conditions are also tightly controlled. In the real world there may be environmental variations that can accelerate or limit the corrosion. Therefore, the corrosion rates estimated by the Stern-Geary equation should be used as a guideline to obtain the best corrosion resistance possible, and acknowledge that the actual corrosion in the target application may deviate from the prediction.

We hope you learned a lot about the Stern-Geary equation and its use for predicting corrosion from polarisation resistance measurements. If you would like to know more about corrosion and its electrochemistry models, check out our blog. We have a lot of content about electrochemistry and corrosion.

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