THE 3RD-NORMAL STRESS DIFFERENCE IN ENTANGLED MELTS - QUANTITATIVE STRESS-OPTICAL MEASUREMENTS IN OSCILLATORY SHEAR

Stress-optical measurements are used to quantitatively determine the third-normal stress difference (N3 = N1 + N2) in three entangled polymer melts during small amplitude (< 15%) oscillatory shear over a wide dynamic range. The results are presented in terms of the three material functions that describe N3 in oscillatory shear: the real and imaginary parts of its complex amplitude psi3* = psi3' - ipsi3'', and its displacement psi3d. The results confirm that these functions are related to the dynamic modulus by -omega2psi3*(omega) = (1 - beta) [G*(omega) - 1/2G* (2omega)] and omega2psi3d(omega = (1 - beta) G'(omega) as predicted by many constitutive equations, where beta = -N2/N1. The value of (1 - beta) is found to be 0.69+/-0.07 for poly(ethylene-propylene) and 0.76+/-0.07 for polyisoprene. This corresponds to -N2/N1 = 0.31 and 0.24+/-0.07, close to the prediction of the reptation model when the independent alignment approximation is used, i.e., -N2/N1 = 2/7 congruent-to 0.28.