First-harmonic intrinsic nonlinearity of model polymer solutions in medium amplitude oscillatory shear (MAOS)

Abstract

First-harmonic MAOS moduli were demonstrated experimentally using monodisperse linear polystyrene (PS) solutions at different concentrations. Two first-harmonic intrinsic nonlinearities are asymptotic deviations from two linear viscoelastic moduli and obtained in medium amplitude oscillatory shear (MAOS) regime. Master curves of first-harmonic MAOS moduli for PS solutions provided novel information which has never been reported before. The interrelationship between first-harmonic and third-harmonic MAOS moduli was evaluated at low and high De. At the low-De limit, all solutions followed the universal interrelation predicted by fourth-order fluid expansion. At the high-De limit, where no universal interrelation exists, the average first-harmonic to third-harmonic elastic MAOS moduli ratio was −22.26, and for viscous counterparts, the magnitude and sign of this ratio changed on increasing frequency. Unentangled and entangled solutions were distinguished using normalized viscous moduli at De > 1. Viscous MAOS moduli normalized by SAOS complex modulus displayed a plateau for unentangled solutions and a decreasing behavior for entangled solutions. First-harmonic MAOS moduli of entangled solutions agreed well with multimode molecular stress function (MSF) predictions under the all relaxation mode assumption, which contrasted with third-harmonic MAOS predictions using the terminal relaxation mode assumption. It is expected that the first-harmonic MAOS results in this paper will be good reference information for future MAOS studies and computer simulations.