The third-normal stress difference in entangled melts: Quantitative stress-optical measurements in oscillatory shear

Abstract

Stress-optical measurements are used to quantitatively determine the third-normal stress difference (N ₃ = N ₁ + N ₂) 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 N ₃ in oscillatory shear: the real and imaginary parts of its complex amplitude ψ ^*₃ = ψ ^′₃ - iψ ^″₃ , and its displacement ψ ^d₃ . The results confirm that these functions are related to the dynamic modulus by ω²ψ ^*₃ (ω)=(1-β)[G ^*(ω))−$\frac{1}{2}$ G ^*(2ω)] and ω²ψ ^d₃ (ω)=(1- β)G′(ω) as predicted by many constitutive equations, where β = −N ₂/N ₁. The value of (1-β) is found to be 0.69±0.07 for poly(ethylene-propylene) and 0.76±0.07 for polyisoprene. This corresponds to −N ₂/N ₁ = 0.31 and 0.24±0.07, close to the prediction of the reptation model when the independent alignment approximation is used, i.e., −N ₂/N ₁ = 2/7 − 0.28.