In the zone of transition from the glass-like to rubber-like state the change of polymer elasticity mechanism takes place from entropy to energy nature. On the basis of phenomenological photoelasticity theory in non-equilibrium state the separation method for the energy and entropy components of stress is suggested. It is pointed out that the correction for kinetic factor T/To (T and To are experimental and reduction temperatures, correspondingly) has to be introduced not for the entire stress but for its entropy component only while using the timetemperature reduction principle. The results of combined measurements on stress and birefringence relaxation in butadiene-acrylonitnile vulcanizate are presented within the temperature limits from -26.4 to 25°C and time limits from 0.4 to lo00 sec. From the data obtained the reduced master curves of entropy modulus component and entropy relaxation spectrum have been calculated. The latter has the form in accordance with the predictions of the molecular theory of polymer viscoelasticity.
Mechanical losses in rubber compounds per strain cycle are shown to be considerably greater under pulse loading, which simulates tire usage, than under sinusoidal loading. A method is suggested for using data obtained by ordinary laboratory techniques to calculate losses that would occur in an arbitrary anharmonic mode. Some data are given to show how such mechanical losses depend on formulations and processing factors of the rubber. Methods are then discussed for obtaining proper laboratory data on dynamic properties for use in optimizing formulations of tire rubbers.
According to the statistical theory of polymer chains in Gaussian approximation, their transversal dimensions, characterized by the root‐mean‐square distances between the chain segments and the straight line connecting the ends of the chain (r2 1/2 = r), do not depend on the end‐to‐end distance (h). Therefore, the classical rubber‐like elasticity theory takes into account only the entropy change (δSh) related to the variation of h. Upon instantaneous deformation, all linear dimensions of the chains are changed, and the establishment of equilibrium involves, in particular, the recovery of initial r. In the real network, the chains, having drawn together after deformation, hinder the completion of the process since they cannot pass through each other. Thus, in an equilibrium deformed network, r does not reach its actual equilibrium value, thus causing the additional entropy change (δSr). δSr and δSh depend on elongation ratios λi in different ways, for h and r change at deformation in a dissimilar manner.
The theory based on these premises describes well the regularities of various types of deformation. In particular, for the nominal stress f at uniaxial tension one gets the formula which is close to the Mooney‐Rivlin equation for 0.2 < λ−1 < 0.9. Here C1 is expressed through molecular parameters in the usual way, and K is a constant determined by arrangement of steric obstructions. The same ideas allow us to propose a qualitative explanation for a wide range of regularities found for the equilibrium properties of rubbers.
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