Using simultaneous rheometric and particle-tracking velocimetric measurements, we show that the long-time rheological states of well-entangled polymer solutions are not unique in simple shear. Shear banding emerges upon a sudden startup shear as well as during conventional large amplitude oscillatory shear at rates higher than the overall chain relaxation rate. However, shear homogeneity prevails when the final conditions of continuous shear and oscillatory shear are approached gradually from rates lower than the terminal relaxation rate. This suggests that the observed shear banding as nonlinear response to sudden large deformation is only metastable and not unique.

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