Viscoelasticity of homogeneous polymer melts near a critical point

Abstract

The anomalous contribution to the shear stress caused by critical fluctuations in homogeneous polymer melts is investigated. Mean field expressions for the critical contributions to the stress tensor, dynamic shear modulus, and nonlinear steady shear viscosity are derived. These expressions are applied to the case of a homogeneous diblock copolymer near its microphase separation transition. The low frequency scaling behavior of the storage modulus is found to be G′(ω)∼ω2a−5/2, while the loss modulus is predicted to scale like G″(ω)∼ωa−3/2. The dimensionless parameter a is defined by a=2(χN)s−2χN, where χN is the product of the Flory interaction parameter and the number of Kuhn segments per chain, and (χN)s is the value of χN on the spinodal computed by Leibler. The linear steady shear viscosity is also found to be singular as a→0. A comparison is made between the present theoretical predictions and the recent experiments of Bates on 1,4/1,2 polybutadiene block copolymers.