Kinetic theory and rheology of bead-rod models for macromolecular solutions. I. Equilibrium and steady flow properties

Abstract

The behavior of macromolecules in solutions at rest and undergoing steady flow is considered. The Kramers' freely jointed bead‐rod model (the ``pearl‐necklace'' model) is used. It is shown that the distribution function for a random walk process is a good approximation to the true equilibrium distribution function for the pearl necklace as obtained by the methods of classical statistical mechanics. The rheological behavior in slow steady flow is solved exactly for the case of two links, and in an approximation for an arbitrary number of links. It is shown how the zero shear rate viscosity of the once‐broken rod model may be obtained by a minor modification of the case with two links. The behavior in large deformation rate elongational flow is investigated, including a comparison of rigid and flexible molecules, and an estimate of the elongation rates necessary to produce uncoiling of flexible macromolecules. It is finally shown that a bead‐rod model with a large number of links is approximated by a ``corresponding'' bead‐spring model.