Kinetic theory and rheology of bead—rod models for macromolecular solutions. II. Linear unsteady flow properties

The behavior of macromolecules in solutions undergoing slow unsteady flow is considered. A general procedure for obtaining the relaxation modulus of linear viscoelasticity of any bead—rod model without internal potentials is presented. The general form of the relaxation modulus is such as to predict dynamic moduli monotonically increasing with frequency; the storage modulus tends to a limiting value and the polymer contribution to the loss modulus increases beyond all bounds at large frequencies.

The method is applied to the general rigid collection of beads with two principal moments of inertia equal. For this group of models only one relaxation time is found. A short table with values of the parameters of the storage and loss moduli is included for several models: the rigid dumbbell, rigid plane polygons, the rigid tridumbbell, and other structures.

The method is also applied to the model of three beads connected by two rigid freely jointed rods. For this model two dominant relaxation times are found. It is shown that the introduction of a flexible joint in a rigid macromolecule decreases the loss modulus over the entire frequency range; the storage modulus on the other hand is decreased at low frequencies but increased at high frequencies.