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.

Tabulated numerical data, nut hitherto available, are presented for the number fraction distribution of residence times of particles in fluid which passes through a series of 1, 2, 3, … up to 75 mixing zones in series. For the special case in which the weight of particles varies linearly with time, the weight fraction distributions of residence time are also tabulated. The theory is recapitulated and extended to include the effect of recycle.

The present study and that published previously show that crosslinks based on quaternary ammonium halide salts introduced into emulsion SBR-type polymers confer green strength on blends with other compatible rubbers. The crosslink density employed did not exceed 1 link per 3000 combined monomer groups, equivalent to two links per weight-average polymer chain. Judging by the positive slopes of stress-strain curves, green strength obtained in this manner will persist up to at least 50°C. The crosslinks can be broken by mechanical shear and will re-form under resting conditions during times ranging from days at room temperature to minutes at 150°C. Prolonged mechanical shear in laboratory mixing equipment causes progressive loss of modulus and reduction in the slope of the stress-strain curves of compounds containing these labile crosslinks. Similar effects are observed in corresponding control compounds containing no labile crosslinks, but the initial advantage of the crosslinked compounds is progressively reduced and may be lost if shearing is sufficiently prolonged. Available evidence suggests that the principal cause of loss of modulus through shear is selective breakdown of the high molecular weight fraction of the base polymer. The breakdown of the longer chains, which are those most likely initially to carry three or more crosslinks, eliminates most of the network structure responsible for enhanced modulus. Whether chemical effects contribute to loss of modulus remains to be determined, but the evidence suggests that any such effects will be of lesser importance. Because the shear encountered in small laboratory mixing devices differs from that in full-scale factory equipment and stress-strain curves may not reliably predict green-stock behavior, the significance of the present findings can only be determined by factory trials. It is evident, however, that for the most efficient utilization of high green-strength SBR, exposure of the crosslinked SBR component to mechanical shear during mixing should be held to a minimum. On the other hand, to achieve smooth sheets or profiles at the forming stage, the final compound should be subjected briefly to a high degree of shear at as low a temperature as practicable, to break the labile crosslinks in the stock. Green strength will be recovered during subsequent rest periods. The present study suggests that these conditions should be readily achieved in a calendering operation, such as normally used for preparing carcass plies. However, to a greater extent than in most polymer developments, the final proving ground for applications for this new modification of SBR must be full-scale factory trials.

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I n t r o d u c t i o nThe work of Hadman, Thompson and Hinshelwood (1932 a, b)