Abstract
This paper gives the results of a recalculation of the data in Paper I of this series, with an expression for strain energy which is a special case of the Mooney-Rivlin theory, instead of the ideal theory based on Gaussian networks. It was shown in Paper I that the apparent concentration of elastically effective network strands terminated by entanglements, νN, can be estimated by crosslinking linear polymers in states of strain. The maximum value of νN found by this method was about one-half the value obtained from viscoelastic measurements in the rubbery plateau zone, νc=2.5×10−4 mol cm−3. The low value of νN was primarily attributed to the crosslinking temperature being too far (12°) above the glass-transition temperature, Tg. Crosslinking temperatures closer to Tg give values of νN close to νc, as will be shown in Paper III of this series. In addition, it was found that these networks behave slightly differently from the predictions of the ideal Gaussian composite network theory: ideal Gaussian composite networks are isotropic relative to the state of ease whereas these networks exhibit anisotropy of equilibrium swelling, relative to the state of ease, in n-heptane; and νN, instead of being a constant, was found to decrease with increasing extension ratio during crosslinking, λ0. The latter result is illustrated in Figure 1 for irradiation times from 3 to 5 h; here, νN is plotted against the extension ratio, λs, in the state of ease in which the retractive force of the entanglement network and the compressive force of the crosslink network are equal and opposite in direction. The experimental points can be fitted rather well by a curve (not the one shown) with the functional form of a constant divided by λs, like the C2 term in the Mooney-Rivlin equation.
Bivariate Lagrange interpolation at the Padua points: the ideal theory approach
