A new proposal for polymer dynamics in steady shearing flows

Beginning with a recently proposed expression for the drag force on a singl e macromolecule pulled with constant velocity through a fluid of long-entan gled molecules (V. R. Mhetar and L. A. Archer, Macromolecules 1998, 31, 663 9), we investigate the effect of entanglement loss on polymer dynamics in s teady shearing flows. At steady-state, a balance between the elastic restor ing force and viscous drag acting on entangled polymer segments reveals a c ritical molecular strain gamma(m,c) beyond which the drag force exerted on polymer molecules by their neighbors is insufficient to support arbitrarily small orientation angles. Specifically, we find that in fast steady shear flows tau(d)(-1) < (gamma) over dot < tau(Rouse)(-1), polymer orientation i n the shear plane approaches a limiting angle chi(c) approximate to atau(1/ (1 + gamma(m,c))) beyond which flow becomes incapable of producing further molecular alignment. Shear flow experiments using a series of concentrated polystyrene/diethyl phthalate solutions with fixed entanglement spacing, bu t variable polymer molecular weight 0.94 X 10(6) less than or equal to <(M- omega)over bar> less than or equal to 5.48 X 10(6), reveal a limiting stead y-state orientation angle between 6 degrees and 9 degrees over a range of s hear rates; confirming the theoretical result. Orientation angle undershoot s observed during start-up of fast steady shearing flows are also explained in terms of a transient imbalance of elastic restoring force and viscous d rag on oriented polymer molecules. Our findings suggest that the Doi-Edward s affine orientation tensor (Q) is not universal, but rather depends on def ormation type and deformation history through a balance of elastic force an d viscous drag on polymer molecules. (C) 2000 John Wiley & Sons, Inc.