Numerical study of plateau modulus in glass transition

• 1、Technical Department, Houghton China, Shanghai 201112

Abstract：According to the study, when the free volume fraction of the polymer is less than $\frac{1}{2\mathrm{e}^3}$, the movement of some main chain carbon atoms will be frozen.Combining the ratio formula of frozen atoms with the hole model and the elastic theory of amorphous polymer, the modulus formula of amorphous polymer in the glass transition zone is obtained. The modulus formula will be validated by the experimental data of tensile stress relaxation. For polystyrene/polyvinyl chloride, forthe decimal logarithmic of plateau modulus, the relative error between the calculated value and the value obtained from literature is less than 6\%. Then based on the modulus formula, for polymers without long alkyl side chains, the variation curve of $\Delta aT_g$, which is the product of expansion coefficient change value $\Delta a$ and glass transition temperature $T_g$, with $T_g$ from 200 K to 600 K are calculated. The Pearson correlation coefficient between calculated curve and drawn curve by empirical formula is 0.98, and the standard error is 0.003.

Keywords： Polymer physics,Glass transition, modulus,free volume fraction, frozen fraction with hole fraction