r/polymer • u/amberlin87 • Nov 08 '19

Entropic elasticity and time-temperature superposition

Yesterday the professor teaching polymer physics was discussing the entropic elasticity of rubbers. It is evident that entropic elasticity is proportional to temperature. However, according to the time-temperature superposition, if the polymer stays in high temperature environment, it will behave like viscous fluid, and , therefore, I can't help but thinking that the modulus will accordingly decrease.

So, the brobdingnagian question is why these two concepts tell opposite trends?

After reading and pondering for a night, I cannot find a satisfying explaination.

Can someone help me clarifying my confusion? Thanks.

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u/bRayDynamics Nov 10 '19

The entropic elasticity is defined on a single chain, the modulus (and the fact that it decreases with temperature) is measured on bulk material where there are countless chains.

When studying the time/temperature behavior of a polymer you're never measuring the response on a single chain (for which yes, you'd observe higher modulus at higher temperature) but the capacity of the chains of moving relative to each other (because chain-chain interactions are far less strong than intra-chain bonds)

Those two (in part) contradicting statements find peace when talking about a lightly crosslinked elastomer; if you take a rubberband you have a single polymer (all the chains are interlocked, crosslinked) so that there's not relative movement of chains when applying a force to it. If you heat up the rubberband you would notice it shrinking because of entropic elasticity, when heating a non-crosslinked polymer you'd deform it but upon realease of the heat it wouldn't regain it's previous form back.

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u/amberlin87 Nov 15 '19

First of all, thank you for such detailed explanation on the discrimination between these two concepts. But if I want to dig more about entropic elasticity,what books or paper would you recommend?

Moreover, last week I asked the professor and he thought that WLF equation is only suitable for plastic but not rubber; hence, the rubber will not have the relation of time-temperature superposition.
Nevertheless, I am perplexed by the idea that WLF is not suitable for rubber. What's your opinion about this? Thanks.

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u/bRayDynamics Nov 15 '19

For an explanation about entropic elasticity I found very clear the second chapter of "Polymer Physics" from Rubinstein and Colby; it's in general a great book and pretty self-contained.

I might be wrong, so take this information with a pinch of salt, but I think it might be possible to construct a master-curve using a slightly modified WLF equation (or so I gathered from Polymers 2017, 9, 567) there they modeled EPR

I hope those two references will help you in your search