Fine- and Coarse-Grained Modeling of Yielding and Strain Hardening in Glassy Polymers

We present both molecular dynamics (MD) simulations and coarse-grained Brownian dynamics modeling of glassy polymers under uniaxial extensional flow. The MD simulations show that individual Kremer-Grest chains collapse into folded states at Hencky strains of order 2, which then undergo unraveling upon further straining, analogous to that in extensional flows of dilute polymer chains. This motivates a coarse-grained picture that divides the stress into a segmental mode governing monomer friction, and a “polymer” mode contributed by the configuration of polymer chains. The Brownian dynamics model uses a schematic model of yielding of the segmental mode, analogous to that of small-molecule glasses (Fielding, et al. Phys. Rev. Lett., 108.048301, 2012), while the polymer mode is represented by finitely extensible bead-spring chains whose bead drag coefficient is proportional to the viscosity of the segmental mode. This produces behavior consistent with experimental work of the Ediger group (Lee et al., Science, 323, 231-324, 2009), and produces folded states similar to those observed in the MD simulations. The modeling provides strong evidence that strain hardening arises from the high tensions in the folded polymer strands, consistent with earlier suggestions of Fielding et al.