Tuesday, January 13, 2015

Kinetics, Thermodynamics and Polymer Phase Transitions

Polymers appear to break many rules of thermodynamics on a regular basis, when in actuality nothing of the sort occurs. I bring this up after reading an article in the Guardian yesterday about glass transitions in polymers that has too many errors to just let slide. I don't think that these errors are acceptable. While explaining the glass transition of polymers can run you afoul of numerous difficulties, The Wall Street Journal did an admirable job a few years back, so I don't think my standards are too high.

Consider this excerpt, which really is logically incoherent:
"Every polymer locks up ...at its own particular temperature, known as the glass transition temperature, usually denoted Tg. This is the temperature at which the chains can no longer move fast enough to respond to any external forces to allow deformation to occur. If you hit the polymer fast with a hammer this means that a higher glass transition temperature is recorded than if you slowly pull on it."
If that last sentence came to you as out of nowhere, or maybe better, as a sudden blow to the head with a hammer, you're not alone. It's quite a non sequitur The discussion starts on Tg as a temperature, but then a hammer enters the picture and that changes everything about that temperature? And how is that change in temperature "recorded" when the hammer comes down? This is horribly unclear but I understand where the author wants to go.

A polymer can act glassy in two entirely different manners. First, it will behave as a glass when it is cooled below its glass transition temperature. But it can also act glassy (and the emphasis here in on "act") even if it is above its Tg when too great a stress is applied too quickly. In this latter case, the polymer strands do not have the time to relax and flow past each other and so they have to stay in place and take the stress without moving - just like a glass. I'm guessing that that is where the "hammer" comes from - a short, sharp blow from a hammer can shatter some polymers like glass. But to suggest that this glasslike behavior "changes" the Tg is entirely incorrect. And it contradicts the first sentence - "Every polymer locks up...at its own particular temperature...."

Then consider this:
"The glass transition temperature is quite different: its value depends on how you measure it. This makes it something of a thermodynamic oddity; it isn’t a true phase transition at all. "
Oh boy, them's fighting words [*]. The glass transition temperature is a true phase transition, but it is a 2nd-order phase transition, not a first order phase transition such as the boiling of water that the author compares it to.

Measuring any phase transition (1st- or 2nd-order) in a polymer takes patience, at least if you want to measure a true equilibrium value. Ideally you need to cool down the sample very slowly so that the polymer chains can relax any internal stresses and reach a true equilibrium configuration. But the cooler you go, the longer it takes since the viscosity of the polymers increase rapidly. And so compromises between cooling speed and data accuracy need to be made. By looking at data from multiple tests, it is possible to extrapolate an equilibrium value which is why we can have tables of glass transition temperatures. Extrapolations like this a very common in science. Think about absolute zero. We've never been able to cool a sample to 0 K, but we still know that the temperature exists and we can extrapolate numerous thermodynamic data to it as well. And so it is with the glass transition temperature.

I stated that patience is need for measuring any phase transition in polymer. For even a 1st-order phase transition such as melting, the values you record will depend on the heating rate. Because polymers are such poor thermal conductors, measuring the melting transition at higher rates would increase the "thermal lag" between the transition and the applied temperature. Measurements are typically made at 10 oC per minute, a completely arbitrary value (since the rate has dimensions, it is arbitrary) that is a compromise between accuracy and measurement rate. If that rate is changed, the temperature of the transition would be reported differently. To requote the article, "...its value depends on how you measure it". No, the values don't vary in this case either. It is an experimental error, nothing more, and results from our impatience in waiting for equilibrium data.

You may have noticed the two main points here both rely on the balance between kinetics and thermodynamics.
  • Because of the sometimes slow kinetics polymer have in relaxing internal stresses, they can be glasslike in appearance. This can appear at conditions well removed from the equilibrium glass transition temperature, but it does not mean that the glass transition temperature has changed.
  • Because of the slow rate at which polymers conduct heat, measuring any phase transition for a polymer is a compromise between getting the data at a reasonable rate and the accuracy of the data.

[*] Three times in my professional life I have witness arguments get so heated that I thought it would break out into a barehanded brawl. Two of those arguments were over the glass transition and statements just like this.

Previous Years


Bend said...

Will you get the same value for Tg if you measure it via DSC or DMA, so long as you keep the rate of temp change the same? I seem to remember slightly, but consistently different values.

John said...

The reported Tg's will vary because the sample size and heat transfer kinetics are different.

DSC is usually a small sample (up to about 10 milligrams) heated in a pan (sealed or not) from below. The pan has it's own heat transfer characteristics.

For DMA, samples are usually much larger (about 25 mm in diameter and a few millimeters thick). Controlled strains instruments heat the sample (and the plates) in an oven while controlled stress instruments heat the sample directly off a Peltier pile.

Anonymous said...

I agreed to most of your comments. But I think the glass transition is not a real 2nd order phase transition as suggested in the Introduction Chapter of the book 'The physics of glassy polymers (Haward RN)'.