Separability criteria for entangled polymer liquids

Abstract

Requirements for factorable nonlinear shear relaxation moduli were investigated using a series of entangled polystyrene/diethylphthalate solutions. Polymer solutions were formulated to maintain fixed entanglement spacing over a broad range of polymer molecular weights, 7 <N/Ne <90, 1.3×105 <φMw <1.6×106. For all polymers studied, a separability time λk was identified beyond which step shear relaxation moduli could be factorized into separate strain and time-dependent functions. In every case, λk exceeded the most optimistic estimates for the longest Rouse relaxation time τRouse, in some cases by as much as 2 orders of magnitude. λk was also found to scale nearly as strongly with polymer molecular weight as the terminal relaxation time and limiting shear viscosity. These results provide convincing evidence against a Rouse origin for the separability criterion in entangled polymer liquids, and could help explain previous experimental observations of “delayed” factorability and/or nonfactorable relaxation moduli in well entangled polymer liquids. The experimental findings are discussed in the context of a modified tube model that takes into account tube deformation in flow.