The contribution of internal energy to the elastic force of natural rubber

Abstract

AbstractData are reported for the temperature coefficient of the retractive force for a natural rubber sample which had been crosslinked by irradiation. These measurements differ from those previously reported in allowing a longer interval for the attainment of equilibrium, in covering a wider range of elongations, and in a somewhat greater precision of the tension measurement. The Mooney equation constants for the tension at 45°C. are 2C1 = 2.617 kg./cm.2 and 2C2 = 0.876 kg./cm.2. The latter, although smaller than the values reported by other workers for similar samples, is far from vanishing. A comparison is given of (∂f/∂T)V,L as evaluated from the measured (∂f/∂T)V,L according to various proposals. Approximately 20% of the total force arises from the internal energy contribution, fe, when the relative elongation, α, is near unity. The fe/f ratios calculated from our measurements stand in good agreement with those obtained from Ciferri's data, despite the fact that the latter correspond to a much larger C2 value. Furthermore, both sets of data indicate that fe/f decreases with increasing α. The entropy component of the force, when fitted to the Mooney equation, yields C1s ≅ C1 but C2s < C2. This suggests that the C1 term is primarily due to entropy effects, whereas the internal energy makes a larger contribution to C2. The nonvanishing C2 and the variation of the fe/f ratio with α, represent deviations from the gaussian model treatment of Flory, Hoeve, and Ciferri. Criferri and Flory have expressed the opinion that finite C2 values arise solely from the failure to attain mechanical equilibrium. However, the cubic lattice model treatment of Krigbaum and Kaneko indicated that although the two discrepancies cited above may be accentuated by nonequilibrium effects, they can only be expected to vanish under equilibrium conditions in the limit of infinite chain length between crosslinks.