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How to understand the shear modulus of polymers
Hi everybody,
I have a question about the shear modulus of polymers. As we know, the general engineering polymers （rubbers） are highly extensible and elastic. The shear modulus，G， for the polymers subjected to the small-strain conditions, can be defined by G=NkT, where N is the number of network chains, k is Boltzmann's constant and T is temperature in Kelvins.
It can be seen from the formula,the modulus increases with temperature. That is to say, the polymer gets stiffer rather than softer when increasing environment temperature. However in reality, the polymer would become softer as temperature increases, and the modulus is expected to decrease.
so,my question is how to understand the dependence of shear modulus on temperature? Maybe the formula, G=NkT, is limited to a special range of application. (entropic
elasticity)
Can anyone give me more details about this?
Thanks in advance!
Lianhua
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Comments
For the polymers in
For the polymers in reality, I think the contribution of internal energy to the shear modulus should be considered when we increase temperatures.
The expression G=NkT is only applicable for the entropic elasticity, whereas the enthalpy variation is eliminated.
Hi, Lianhua, I don't
Hi, Lianhua,
I don't think there is anything wrong with this formula. Because at higher temp, entropy change per incresed length is greater, thus the modulus is larger. I am not an experimentalist, but I believe the stiffening of rubber is observed by Gough 150 years ago.
Regards.
Xiao
Re：
Yep， I can not agree with you any more! The formula G=Nkt is suitable for calculating the shear modulus of entropic elasticity, not the enthalpic elasticity.
Thanks to Xiao and Feihu.
Thanks to Xiao and Feihu.
In the classical polymer theory, the elasticity of the rubber network is
mainly induced by entropic elasticity of the chains.
Only in entropic elasticity, the shear modulus increases with temperature.
RE
Hi Lianhua,
DMA test can be used to characterize some properties, such as storage modulus and loss modulus, as a function of temperature. In many polymeric materials, storage modulus is observed to decrease as the temperature increases even higher than the glass transition. However, it's not true for all polymers. I believe this is due to the contribution of intermolecular resistance, which should play a minor role when the temperature is much higher than the glass transition.
But I did observe some rubber increases the storage modulus as the temperature increases in my own DMA tests. Just for your reference.
Lifeng