Numerical Calculations of the Viscoelastic Properties of Dilute Solutions of Comb-Shaped Branched Polymers

Abstract

The viscoelastic properties of dilute solutions of comb-shaped branched polymers have been calculated from the bead-spring model, following the Zimm and Zimm-Kilb theories, with exact numerical evaluation of eigenvalues by the method of Lodge and Wu. Eigenvalues, relaxation times, and frequency dependence of the reduced intrinsic shear moduli [G′]R and [G″]R have been obtained for various combinations of number of branch points (f) 1 to 10, beads per branch (Nb) 1 to 37, backbone beads between branches (Na) 1 to 22, and the reduced hydrodynamic interaction parameter (h*) 0 to 0.25. Since the total number of beads (f+1) Na+fNa+fNb−1 is restricted to an unrealistically small value of 111 by computer limitations, attention is focused on the low-frequency behavior where this restriction will have the least influence. Here, the behavior is characterized by the reduced steady-state shear compliance. This quantity is quite sensitive to f when the mass backbone fraction λ is small (approaching starshaped geometry); and for larger λ, it can detect the presence of a small number of branches.