The effect of dynamic tube dilation on chain stretch in nonlinear polymer melt rheology

Abstract

The pressures exerted by a polymer chain on the walls of an anisotropic confinement are anisotropic (Doi and Edwards [10]). At deformation rates larger than the inverse Rouse time of the polymer chain, chains are stretched and their confining tubes become increasingly anisotropic. In a tube model with variable tube diameter, this leads to an interchain tube pressure term in the lateral direction of the tube (Marrucci and Ianniruberto [15]), which limits chain stretch. Here we assume that chain stretch is balanced by two restoring tensions with weights of 1/3 in the longitudinal direction of the tube, due to a linear entropic spring force, and 2/3 in the lateral direction, due to a nonlinear interchain tube pressure, both of which are characterized by the Rouse stretch relaxation time τ R . This approach is in quantitative agreement with the time-dependent and steady-state elongational viscosity of two monodisperse polystyrene melts with molar masses of 390,000 and 200,000 kg/mol as investigated by Bach et al. [2] and Hassager [12]. In bidisperse polymer blends, the interchain pressure is reduced in accordance with dynamic dilation of the tube. Implementation of the dilation effect into the evolution equation of the stretch leads to a quantitative description of the elongational behavior of bidisperse polystyrene blends consisting of a long and a short chain component as investigated by Nielsen et al. [22]. Due to the effect of chain ends, dynamic tube dilation is also of importance for monodisperse polymer melts with low molar masses having few entanglements, as demonstrated for two polystyrene melts with molar masses of M w = 102,800 and 51,700 g/mol. If dynamic tube dilation is taken into account, quantitative agreement between highly nonlinear viscoelastic experiments and predictions can be obtained based exclusively on the linear-viscoelastic characterization of polymer melts.