45882-AC7
Novel Brownian Dynamics Simulation Methods for Polymer Solutions
Two projects are being carried out, one of which is the development of a method for including rare entanglements into Brownian dynamics simulations, and the second is the investigation into the high-frequency behavior of dilute polymer solutions. Three Ph.D. students have been supported partially by the grant. Sean Holleran, who worked on the first projected graduated with a Ph.D., and has become a Lecturer in Chemical Engineering at the University of Pennsylvania. Semant Jain, who worked on the second, is now a scientist at Praxair Corporation. A third Ph.D. student, Indranil Saha Dalal, is continuing to work on the second project. All three were greatly benefitted by the financial support; the first two landing their positions after giving research talks based on the work done under the PRF grant. In addition, two self-funded undergraduate students, Nick Orichella and Jeremy Shum, worked on the second project, and gained experience in research. Because of space constraints, the results of only the second project will be summarized here. The slow dynamics of polymers in dilute solution are well described in the linear viscoelastic regime by the Rouse-Zimm theory which coarse-grains a polymer into a sequence of frictional beads connected by Hookean (or linear) springs. What is left unresolved by this theory is the way in which the coarse-grained bead-spring model breaks down at shorter time and distance scales than those for which linear ‘springs' can capture the configurations of the chain. One expects that at short times, viscoelastic response should be controlled by motions of small groups of bonds and should not be describable by a coarse-grained bead-spring model. Nevertheless, very surprisingly, experiments by Schrag, Lodge, and coworkers (see Peterson et al. J. Polym. Sci. B, 39, 2860, 2001) have shown that the Rouse-Zimm bead-spring chain model can actually describe reasonably well the entire frequency range of dilute polystyrene or polyisoprene chains—even at frequencies high enough that single springs are expected to be strongly excited. This is true as long as the number of springs is chosen so that each spring represents a sub-molecule of molecular weight 4500 for the case of polystyrene and 2400 for polyisoprene. As an explanation, it has been suggested that torsional barriers to bond rotation might confer a large ‘dynamic stiffness' to polymers that slows down modes requiring fast bond motion causing their relaxation to overlap with that of slower collective modes that can be represented by a Hookean spring in a bead-spring model. To test such ideas and to better understand the mechanism of energy dissipation at high frequencies in dilute solutions, we conducted a Brownian dynamics study of a linear polymer chain in which the beads represent individual backbone atoms. We used stiff Fraenkel spring forces to maintain the distance between atoms near 1.53 Angstrom, bending forces to enforce tetrahedral bonding with a bending angle of 1090 47', and torsional forces to create realistic barriers to torsional transitions. Brownian forces were introduced through white noise. The simulations showed that both the bending and torsional potentials slowed down the contributions of local relaxation modes to such an extent as to bring the relaxation of short chains close to single exponential behavior. Thus, the local modes in dilute polymer solution relax at rates similar to that of a coarse-grain mode that can be represented by single Rouse-Zimm spring, encompassing the motion of dozens of backbone bonds. Our results in qualitative agreement with measurements of birefringence relaxation and the notion of a “dynamical Kuhn length”. These results are significant in showing the limits of a coarse-grained bead-spring model for polymers, and in defining how bending and torsional potentials affect the viscoelastic spectrum. Such results carry implications for local polymer dynamics more generally, and have connections to problems of solvent molecular transport through polymers, and to lubrication flows and tribology.
