# Applying Statistical Mechanics to Formulate Corrosion (Rusting)

I wanted to try and take my current knowledge of statistical mechanics (first quarter undergraduate course completed, beginning researcher in far from equilibrium statistical mechanics, basic knowledge of mean field approximation techniques) and apply it to create a rough estimate of corrosion. I want to try and keep this model simple enough that it might be usable in a demonstration to a scientifically/mathematically literate background (not assuming statistical mechanics experience) to showcase some of the interesting ways of applying stat mech to a phenomena.

The tricky part about a problem like this is trying to find the right approximations, so I wanted to try proposing several ideas I had on solving the problem, similar problems I've encountered that can serve as a good inspiration, and difficulties one might encounter. I'll list a few general questions I had about my problem and then follow with my thought process after at the very bottom. Essentially the primary questions I am going to ask are hopefully well encapsulated and (probably) have distinct methodologies to arrive at the conclusion.

Questions:

1. What types of values can we determine from statistical methods that can then be used to determine the kinetics of the reaction?

2. What types of basic model would be a good starting point to work on these calculations?(idea example: would we expect "state condensation" around certain energy levels (something like a bose-einstein model))

More context for what I'm trying to do follows:

Goals

1. Predict (with some accuracy) corrosion

2. Use variables of interest to be able to then create an approximation of reaction kinetics.

3. Constants are simple physical constants and basic information available in tables (heats of formations/free energy)

Assumptions

1. Pure Solid in a well mixed corroding fluid

2. Simple shapes (spherical or square)

3. We can represent energy levels from our possible chemical species

4. Surface rust; weathering operates in a simple, predictable manner, (if this is too complex I'd be willing to make the assumption that it is a weathering resistant material: http://en.wikipedia.org/wiki/Weathering_steel)

5. The energy level of each possible type of rust is known.

6. The environment is time-invariant

Difficulties (posed here as research questions as oppose to direct questions meant for SE community, can still be useful look at when trying to answer question 2):

How does geometry effect the calculation of our variables of interest? (example surface rust effecting lower layers? Let's ditch certain types of rusting that are hard to predict like pitting and exfoliating (unless we need to keep them).

Is it justifiable to just use energy levels corresponding to the energy of each chemical species we'd encounter or are there other energy levels to consider?

Would we need to perturb these energy levels as the system evolves?

Idea: Would statistical mechanical models of batteries work well for modelling this system? How would the math of those models need to be adjusted to account for differences in the two models? Or are they completely irreconcilable with each other?

• Here I've tried reducing it to the primary questions while putting the other questions more as context rather than questions I am asking the SE community. Do you think I've stated the difference between those two clearly enough Kyle? – Skyler Dec 14 '14 at 19:16
• That seems better. I know corrosion can be modeled via electrochemistry, not sure how statistical mechanics would be able to describe it (though someone else might, which why it's posted here ;) ). – Kyle Kanos Dec 14 '14 at 19:25
• As far as I can tell the kinetics of reactions can never be deduced from statistical methods. You can use statistical methods to calculate thermodynamic properties from the known kinetics, which is the other way around. Maybe I misunderstand what you are trying to do? You are talking about phenomena in structured solid/liquid/gas interfaces (layers in rust), which basically is the exact opposite of what thermodynamics does (treat homogeneous systems). For that you will probably have to use quantum chemistry methods to deal with the electron transfer from exposed ions into the liquid phase. – CuriousOne Dec 15 '14 at 1:13
• Let's say you were able to formulate the potential as a function of the rust that has formed on your material. This is where the statistical mechanics would end, and then you were to have a few measurements the rust plating with a time spacing between them. The ratio of voltages would then give you information about the relative rates wouldn't it? So what I was thinking of is a method to interpolate between data points. Basically I want to see if statistical mechanics methodology can be used to create a theoretical basis for given set of kinetics. – Skyler Dec 15 '14 at 2:21