Transient Changes in Topology and Energy on Extension of Polybutadiene Networks

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Abstract
The theory of elasticity of polymer networks has been developed along two lines. The phenomenological approach leads to the Mooney-Rivlin relation between stress and extension ratio for uniaxial extension. The statistical theory of elasticity, based on a model for polymer molecules, predicts a similar relation with one of the constants zero. Actual elastic properties of rubbers do not agree fully with either theory. Experimental results are reported obtained with quantitatively cured polybutadiene and polyisoprene vulcanizates. These data are near-equilibrium results through the use of a cyclic stress sequence which largely eliminates the influence of long-time creep. The dependence of the initial modulus and the parameters of the Mooney-Rivlin relation on the chemical nature and the degree of branching of the polymer, the type of cross-links, and temperature has been investigated. A possible relation between the energy component of the elastic force and one of the parameters is discussed. These results as well as those in the literature refer to irreversible processes. It is proposed that this irreversibility results from friction accompanying slippage of chain entanglements. This mechanism is compatible with the observed dependences. It is concluded that the variation of elastic properties with elongation is due to changes in network topography. Some observations are made on the topological changes of vulcanizate networks at very high elongations. Similarities are pointed out between reinforcement by stress crystallization and by addition of carbon black. The effect of blacks is attributed mainly to preferential adsorption on the carbon particles of short network chains which become overstressed at high deformation. On adsorption the kinetic energy of these particular chains will be dissipated in the form of heat of adsorption. Examples are given of the applicability of F. Bueche's relation between extension of the sample and that of the elastomer matrix in a filled vulcanizate. This equation differs from that based on Einstein's relation for the viscosity of suspensions, which has been shown to be applicable in other filled rubbers. The difference between the two relations may be associated with the absence or presence of chemical bonding of elastomer to filler. Network topography has an influence on the ultimate properties of vulcanizates. Polybutadiene samples in which the cross-links are single bonds break at lower elongation than those with equal concentrations of cross-links consisting of 18-atom chains.