An Integral Constitutive Equation Based on Molecular Network Theory

A new constitutive equation for concentrated polymer solutions and melts is presented that is based on the entanglement theory of Lodge. The strain rate dependence of the memory function is determined using a physical hypothesis of interacting spheres where the spheres represent spheres of influence of the network junctions. The resulting equation has one constant that can be estimated theoretically in addition to the natural relaxation spectrum. At high strain rates, a second empirical constant is introduced to account for the orientation of the spheres of influence. Predictions of the equation and the equations of Bogue, Bird-Carreau, and Tanner were compared to steady and transient shear stress and normal stress data obtained on a Weissenberg rheogoniometer. The new equation fits nonlinear transient data more satisfactorily than other equations of similar complexity.