Brownian dynamics simulations of single polymer chains with and without self-entanglements in theta and good solvents under imposed flow fields

Abstract

The effects of self-entanglements (spring-spring uncrossability) and solvent quality on the static and dynamic properties of a polymer chain in shear and extensional flows are investigated using Brownian dynamics simulations. We model the polymer chain by a sequence of beads connected by finitely extensible non-linear elastic springs, and spring-spring uncrossability is enforced by applying a spring-spring repulsive potential together with an adaptive time-stepping. Our findings suggest that chain uncrossability has an insignificant effect on the dynamics of a polymer chain. Furthermore, we considered four different combinations of intramolecular interactions: (i) no interactions, (ii) repulsive spring-spring and attractive bead-bead interactions, (iii) only repulsive bead-bead interactions, and (iv) only repulsive spring-spring interactions. The first two cases model “theta” solvents, where the radius-of-gyration of a polymer chain, Rg∼N0.5, where N is the number of beads. For appropriately chosen parameters of interaction potentials, the last two cases model good solvents, where Rg∼N0.59. In the presence of a simple shear flow, the stretching behavior is alike in all the cases except case (ii). In case (ii), the polymer chain forms “pearl-necklace-like” structures at zero Weissenberg number, Wi. With an increase in Wi, Rg first increases due to stretching of bonds between neighboring “pearls,” and then decreases when the decrease in the number of pearls becomes limiting. In the presence of an extensional flow, normal stretching behavior is observed even in case (ii); the number of pearls increases with increasing extension rate because larger pearls break into smaller “pearls.” The results show that even for fixed overall solvent quality for a chain at rest (e.g., a theta solvent), the ability of the chain to stretch in a shear flow is sensitive to the nature of intramolecular interactions. A chain with short-range attraction (between beads) and a long-range repulsion (between springs) tuned to balance each other and so create a theta condition at rest does not stretch much in a shear flow, while a chain for which the theta condition is achieved by applying no interactions at all does stretch in a shear flow.