# Residual stress in polymer coatings

A paper talks about the residual stress when coating polymers.
It says that residual stress is the sum of the "heat stress" (due to the difference in thermal expansion coefficients) and the "shrinkage stress" (due to the solvent evaporation and changes in volume). It then states that heat stress usually increases with temperature while shrinkage stress decreases with temperature. Therefore the shape of the graph of residual stress vs temperature would be a parabola with the minimum changing depending on the polymer/system system.
It then goes to find the starting point of the shrinkage stress and states that it is dependant on the glass transition temperature.
From what I understand, that would happen when the glass transition temperature is between room temperature and the drying temperature.
However, if the glass transition temperature is below both room temperature and drying temperature, what would happen? How this would affect the shrinkage stress? Or did I get the whole connection between glass transition temperature and shrinkage stress wrong? Thank you

EDIT:

I read the paper linked in your comment, and see that my initial guess was incorrect (see below) - for this system, it is as you say - for temperatures above the bulk pure polymer glass transition temperature, you would not expect to see shrinkage stress due to evaporation.

END EDIT

I don't have access to that paper - so this is just an educated guess, but usually physicists use the glass transition temperature to characterize polymer behavior as a function of temperature because things roughly (very roughly) scale with $T_g$. In other words, if I know how the behavior of one linear homopolymer depends on temperature, and I know a certain response curve scales with $T_g$, then I can scale the temperature curve of another linear homopolymer using the $T_g$ and sometimes get accurate results.

They could be linking it to shrinkage stress because $T_g$ also characterizes the dynamic behavior of polymers (how they "move" in response to thermal fluctuations and external stress). This is essentially the principle of time-temperature superpostion - or the idea that as temperature increases, polymers move the same way, only faster. So heating up is like fast-forwarding time, and cooling down is like slowing time down.

The glass transition temperature is a discontinuity in this behavior - at a certain low temperature, the polymers freeze in place (on large length scales). This phenomenon is not well understood, but we have found empirically that the temperature at which it occurs can be used to scale response curves in certain situations, and since it is fairly easy to measure, it gets used a lot in these types of models.

So in summary, and again this is an educated guess, I would imagine that the glass transition temperature would be used in this model regardless of the temperature you were actually operating at - it is probably a fundamental parameter of the curve that is used to put the "reality" (the type of polymer) into the model.

• Im not sure as it says that the shrinkage stress arises when the temperature equals the glass transition temperature so that stress shouldnt arise if those temperatures dont cross right? This is the paper mediafire.com/?kflzazi435xf3x4 – Daniel Antón García Aug 22 '14 at 12:31
• @Daniel - I read the paper and have updated my answer - it looks like you are correct, and for systems above the glass transition temperature, you would not expect to see a shrinkage stress due to evaporation. – thomij Aug 23 '14 at 23:23