Rotation and Deformation of Polymer Molecules in Solutions Subjected to a Shear Flow

Abstract

The complex rotational and deformational behavior of polymer molecules in dilute solutions subjected to a shear flow as studied in non-equilibrium molecular dynamics computer simulations can be understood qualitatively within a simple dumbbell model. It allows a numerical test of a conjectured relation between the average angular velocity of a flexible polymer molecule and a ratio of components of the gyration tensor. The model involves a pseudo-friction coefficient which is chosen such that the peculiar kinetic energy is kept constant: Gaussian thermostat. The orbits show rotation, wagging and tumbling, depending on the shear rate, combined with radial stretching and compression. The angular velocity divided by minus the shear rate is equal to 1/2 at small shear rates, corresponding to a solid body like behavior. At high values of the shear rate the angular velocity decreases strongly with increasing shear rates. In both these regimes, the conjectured relation holds true. For intermediate shear rates, however, this relation between the true angular velocity and the corresponding expression inferred from the gyration tensor is violated. The behavior of the dumbbell is highly irregular for these shear rates, a sensitive dependence on the initial conditions and on the shear rate are noticed. The largest Lyapunov exponent is positive, indicating chaotic behavior for certain values of the shear rates. For certain shear rates, no unique assymtotic state exists. At some inermediate and at high shear rates, stable periodic orbits with long periods are observed. The irregular behavior of the angular velocity at intermediate shear rates persists when the Gaussian thermostat is replaced by a Nose-Hoover thermostat and even when an additional thermostat is applied which controls the configurational temperature.