A simple scaling derivation of the shear thinning power-law exponent in entangled polymer melts

By suggesting that the polymer dynamics in entangled polymer melts possesses the property of dynamical self-similarity, we argue that the power-law exponent of the Carreau-Yasuda law, which empirically describes the shear thinning effect of the polymer melt viscosity, is inversely proportional to the exponent of the molecular mass dependence of the terminal relaxation time. This finding is obtained in cases where the shear rate dependence of the segmental relaxation time is negligible. If such dependence is essential, the Carreau-Yasuda law is slightly modified at high shear rates: instead of a power-law dependence with a small shear rate independent exponent, a weaker logarithmic dependence is found both for shear rate and molecular mass dependence, which resembles the approach to zero of an effective shear rate and molecular mass dependent power-law exponents at sufficiently high shear rates.