Scaling relations in nonlinear viscoelastic behavior of aqueous PEO solutions under large amplitude oscillatory shear flow

We have found empirical scaling relations in nonlinear viscoelasticity of poly(ethylene oxide) (PEO) solutions under large amplitude oscillatory shear flow. The scaling relations superpose dimensionless nonlinear viscoelastic functions, such as the normalized amplitudes of elastic and viscous stresses and normalized Fourier intensities, measured at different strain amplitudes and frequencies on a single curve irrespective of the molecular weight and the concentration of the polymer solutions. The scaling relations reveal that the nonlinear viscoelastic functions are functions of dimensionless variable ζ ≡ γ_o cos δ (ω), where δ is the phase lag of linear viscoelasticity. The validity of our superposition was checked for PEO aqueous solutions under the conditions that concentration: 3<_c/ce <7; molecular weight: 400kg/mol<M<1000 kg/mol; τ_m ω<10. We suggest some material parameters, which are expected to indicate chain architecture as well as to measure the strength of nonlinearity because the parameters are independent of the test conditions and compositions of the polymer solutions.