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

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.

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

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.

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.