Written on: September 1, 2024 by W. Stephen Tait

Hello everyone. Corrosion is a probabilistic process, not a simple deterministic process with only one causative factor. There are approximately nine major factors that could cause corrosion, which means there are 362,880 possible combinations of these factors that could cause spray package corrosion. This is why corrosion is probabilistic.

There are three basic corrosion questions that should be addressed with each new or derivative formula in order to provide operational information about package-formula compatibility and avoid very costly corrosion failure:

1. Will a formula or a derivative formula corrode the chosen spray package?

2. What type of corrosion will occur?

3. How fast will corrosion penetrate the package materials?

In other words, what is the package service lifetime with your formulas?

In this month’s column, we’re going to use math to illustrate why corrosion is so complex and often (seemingly) unpredictable. I’ll use aerosol container corrosion as the example since aerosols are among the most widely used packages for consumer packaged goods (CPG).

**Figure 1** and **Figure 2** illustrate the multiple types of corrosion that often occur inside aerosol containers and on aerosol valves. In addition, the types of corrosion noted in **Figure 1** can be general corrosion and/or pitting corrosion. This means there are 14 possible types of corrosion in steel aerosol containers, 10 possible types of corrosion in aluminum aerosol containers and six types of corrosion on aerosol valves.

The percentages to the right of the steel aerosol container in **Figure 1** show how often corrosion was observed in ~7,500 steel aerosol containers used for a variety of CPG products. Similar percentages are expected for aluminum aerosol containers and aerosol valves. Simultaneous occurrence of several different types of corrosion inside a spray package is common, hence the percentages in Figure 1 add up to over 100%.

**Can corrosion be modeled mathematically?**

The Gibbs free energy equation in Equation 1 indicates that corrosion can be modeled mathematically:

**Equation 1**

∆G = nFK (corrosion potential)

Where:

• ∆G represents theoretical Gibbs free energy

• n is the number of electrons in the corrosion reaction

• F is a conversion factor known as the Faraday constant

Metal corrosion occurs when ∆G is a negative number.

There are published lists with corrosion potentials for specific metals and environments, but no lists for aerosol containers with a CPG. In addition, corrosion potentials are also probabilistic and the function of at least five factors for aerosol containers:

1. Formula water or contaminant water pH

2. The type of package (e.g., aerosol, laminated foil bag, etc.)

3. The formula-package surface tension

4. Electrochemically Active (ECA) ions and molecules in a formula

5. The internal package metal’s surface treatment, such as coated and uncoated

Hence, we need an empirical equation for the corrosion potential in **Equation 1**. **Equation 2** provides such an equation, written in the Gibbs free energy format.

These five factors are enclosed inside the Equation 2 brackets and the various symbols mean:

• ψ is the probability for each factor group. ψ ranges from 0–1 and has no effect on corrosion when it = 0 (and removed from the calculation). The greatest effect is when ψ is 1

• Γ indicates that a group has multiple sub-factors (from 1 to a number symbolized by a letter) that multiply together.

Notice there is also a probability associated with this type of group that allows for the magnitude of the affect by each group to be nothing 0–1.

• ϒj is the chemical activity coefficient for each ECA in a formula, such as water

• F is the Faraday constant, a conversion factor for electro-chemical corrosion

• K is the proportionality constant for the overall equation

• Concentrations are indicted by square brackets, such as [ECA]

• Exponents for each factor are the super-script lower-case letters

Most of the factors in **Equation 2** are unknown.

** Figure 1** shows that there are multiple corrosion types that can occur inside spray packages. Consequently, Equation 2 only determines that corrosion is possible and does not answer the other two basic questions:

- What type(s) of corrosion will occur?
- How fast will corrosion penetrate the package material?

The last two questions could be addressed with a single equation. However, this equation is much more complex than **Equation 2**.

Currently there are nine known factors that influence the magnitude of spray package *corrosion rates* and the *corrosion type(s)* that occur:

1.Water pH

2.Type of package metal

3. Surface tension

4. Chemical activity for each ECA ion and molecule in a formula

5. Package metal surface treatment

6. The cathode to anode area ratio

7. Emulsion stability

8. Package age (time)

9. Corrosion inhibitors (both added and ingredients that unexpectedly act as inhibitors)

These nine factors are all part of **Equation 3**, which will be discussed in the next issue.

Thanks for your interest and I’ll see you in September. Contact me at 608-831-2076; rustdr@pairodocspro.com or from our two websites: pairodocspro.com and aristartec.com. *SPRAY*