Transient Changes in Topology and Energy on Extension of Polybutadiene Networks

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 nearequilibrium 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.

Modulus of natural rubber cross-linked by dicumyl peroxide. II. Comparison with theory

“…Considerable attention has been given by previous investigators [14][15][16][17][18][19][20][21][22][23][24][25][26] to a ratio they have denoted as I e/!, where I e is the energy component of the force and I (in contradistinction to the I used in this paper) is the total value of the force required to maintain a certain elongation at constant volume. Shen and co-workers [14,15,27] Our work yielding the value of C*/C is of course limited to very small deformations.…”

“…varies with deformation. Several observers [21,23,24,26,27] had reported that I e/! at a fixed amount of cross-linking increased rapidly as the deformation approached zero, rising from values near 0.2 to 0.6 or more.…”

Elasticity, Rubber‐like

“…The idea of entanglements acting as physical junctions was originally developed in the literature to explain deviations from the predictions for affine networks (185,213). The possibility of a contribution at equilibrium caused by trapped entanglements has been tested with model networks, ie, those prepared in such a way that the number and functionality of the cross-links are known.…”

Solid‐state 13C‐NMR and equilibrium‐swelling studies of filled, TBBS‐accelerated sulfur vulcanization of natural rubber

“…A linear relationship was observed which represents the correlation between the filler-reinforcement effect and the amount of physical crosslinking. It has been shown that the entanglement of the rubber chains plays a considerable role in the elastic properties [42][43][44] and also in the reinforcement effect of filler in rubbery matrices. 45 This concept has been further elaborated in terms of the effect of the entanglement of chains on the mechanical properties of the rubbery materials.…”