Separability criteria for entangled polymer liquids

Requirements for factorable nonlinear shear relaxation moduli were investig ated using a series of entangled polystyrene/diethylphthalate solutions. Po lymer solutions were formulated to maintain fixed entanglement spacing over a broad range of polymer molecular weights, 7 < N/N-e < 90, 1.3X10(5) < ph i M-w < 1.6X10(6). For all polymers studied, a separability time lambda(k) was identified beyond which step shear relaxation moduli could be factorize d into separate strain and time-dependent functions. In every case, lambda( k) exceeded the most optimistic estimates for the longest Rouse relaxation time tau(Rouse) , in some cases by as much as 2 orders of magnitude. lambda (k) was also found to scale nearly as strongly with polymer molecular weigh t as the terminal relaxation time and limiting shear viscosity. These resul ts provide convincing evidence against a Rouse origin for the separability criterion in entangled polymer liquids, and could help explain previous exp erimental observations of "delayed" factorability and/or nonfactorable rela xation moduli in well entangled polymer liquids. The experimental findings are discussed in the context of a modified tube model that takes into accou nt tube deformation in flow. (C) 1999 The Society of Rheology. [S0148-6055( 99)01006-8].