Computer Simulations of Hyperbranched Polymers in Shear Flows

Abstract

Brownian dynamics simulations of hyperbranched polymers with different degrees of branching have been performed under the influence of simple shear flow. Hydrodynamic and excludedvolume interactions have been taken into account explicitly. Shear-thinning effects have been observed for all simulated degrees of branching. As the molecular weight of highly branched structures increases, the zero shear rate intrinsic viscosity reaches a maximum and begins to fall similar to the intrinsic viscosity behavior of perfectly branched dendrimers. In the absence of shear, static structure factors, S(k), for hyperbranched polymers with the smallest number of monomers studied resemble those of a three-arm star. As the number of monomers increases and as the degree of branching increases, the S(k) curves for the hyperbranched polymers begin to illustrate features associated with S(k) curves for hard spheres. Further insight into the shape and interior density of these structures is obtained through the ratio of the radius of gyration, Rg, to the hydrodynamic radius, Rh. The ratio Rg/Rh is observed to approach unity as the number of monomers and the degree of branching increase.

Computer simulations of hyperbranched polymers: The influence of the Wiener index on the intrinsic viscosity and radius of gyration

“…The main group of HPs were irregular molecules resulting from the same sequential addition process used by Lyulin et al 14 Within this group, the HPs had the same degree of polymerization ͑N͒ as dendrimers of generations 4, 5, and 6 ͑i.e., Nϭ94, 190, 382͒. Lyulin et al revealed that simulated intrinsic viscosity values for these dendrimers peak near generation 5 (Nϭ190).…”

“…Lyulin et al revealed that simulated intrinsic viscosity values for these dendrimers peak near generation 5 (Nϭ190). 14,39 At each N, HP molecules with DB ϭ0.4, 0.6, and 0.8 were specified. For each of these DBs, at each N, two to three molecules were created having distinct Wiener indices selected according to a systematic procedure ͑detailed below͒.…”

“…These parameters are in keeping with work of Lyulin et al on similar molecules. 14,39 Simulation runs of 3ϫ10 5 to 1ϫ10 6 timesteps were used for equilibration, depending on molecular size. Typically, production runs spanned 2ϫ10 7 steps for N ϭ94 molecules, 1ϫ10 7 to 2ϫ10 7 steps for Nϭ190 molecules, and 3ϫ10 6 to 6ϫ10 6 steps for Nϭ382 molecules.…”

“…W is a direct measure of molecular compactness. 20 Converse to DB, W is lower for more compact molecules at a given N with more sprawled out, linearlike structures having higher W values at a given N. Widmann and Davies 13 and Lyulin et al 14 creased. Lyulin et al also obtained a power law relationship where aϭ1.1 to 1.6 following the same trend of a with N. Since the ͓ ͔ values of Widmann and Davies are calculated directly from simulated R g 's through the assumption that ͓ ͔ϳR g 3 , it can be seen that their RMMC simulations indicate R g ϳW c , where cϭ0.7 to 0.9.…”

“…Aerts used the kinetic bead-rod model of Lescanec and Muthukumar,11,12 Widmann and Davies performed RIS metropolis Monte Carlo ͑RMMC͒ simulations of phantom chains in the absence of solvent, 13 teractions and excluded volume. 14 In each case, the authors simulated several families of HPs and, in addition, a family of linear molecules of increasing molecular weight and a family of dendrimers of increasing generation. Each HP family was composed of molecules with a constant DB ͑Ͻ1͒, but with the same increasing N values as the dendrimers.…”