Elasticity of molten polymers from stress relaxation data

When a steady viscous flow of a molten polymer is suddenly stopped, the stress τ can be recorded as a function of the time t . By means of inverse Laplace transforms, a system of linear Maxwell bodies relaxing in the same way can be defined. It is shown that the elastic energy W M stored within this system is equal to \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \gamma \limits^ \cdot_0 $ \end{document} A /2, where \documentclass{article}\pagestyle{empty}\begin{document} $ \mathop \gamma \limits^ \cdot _0 $\end{document} is the rate of shear of the steady flow and where\documentclass{article}\pagestyle{empty}\begin{document}$ A = \int_0^\infty {\tau dt} $\end{document} is the “stress relaxation area.” Thus, for a calculation of W M the inverse Laplace transforms are not needed. Then, the following parameters are defined: ( 1 ) the shear compliance J w , ( 2 ) the relaxation time λ w of a single Maxwell body storing the same energy W M under the same steady viscous flow (λ w is also equal to the double of the ratio of W M to the power dissipated in the steady flow), and ( 3 ) a “nonlinearity exponent of elasticity” given by the slope of the log‐log plots of the J w against the initial stresses. Stress relaxations in low‐ and high‐pressure polyethylenes and natural rubber have been measured by means of a coneplate consistometer. The above‐defined parameters are calculated and discussed as possible means of characterizing the polymer structure.