Theory and simulation of polymer liquids under extensional and shear flows

We examine several aspects of the dynamics of linear polymers under shear and extensional flows. We use nonequilibrium molecular dynamics (NEMD) to simulate systems under planar Couette flow (PCF) and planar extensional flow (PEF). In addition we look at several kinetic models of polymer melts, in particular the Curtiss-Bird model, for which we calculate the predictions of steady-state viscosity under PEF. To the best of our knowledge this is the first time that these results have been presented for this kinetic model. Our simulations under PEF are enabled by the use of Kraynik-Reinelt periodic boundary conditions (pbcs). We include here our observation that these pbcs are closely related to the Arnold cat map, a simple example of a dynamical map with chaotic properties. This observation enhances our understanding of this simulation technique. We compare directly under flow for the first time two commonly used coarse grained models of linear polymers. The first, a bead-spring model which uses the flexible finitely extensible nonlinear elastic potential (FENE) to bond adjacent beads. The second, a bead-rod model which uses a constraint force algorithm to fix the bond length. For this model we use the name freely jointed chain (FJC). The comparison is based on viscometric, structural and dynamical properties. We find that results for FENE and FJC systems are almost identical. Comparing results with predictions of the Curtiss-Bird model under PEF we find that values for the parameters of the Curtiss-Bird model required for a fit with the simulation data fall outside the range allowed by the Curtiss-Bird model and we conclude that assumptions of the Curtiss-Bird model deviate from dynamics observed in liquids under extensional We then focus on the self-diffusion of molecules under PEF and PCF, calculating elements of the diffusion tensor using appropriate mean-squared displacement formulae. Our interpretation of these results incorporate properties from the FENE and FJC comparison and results for the velocity autocorrelation function in these systems. We find anisotropy of diffusion more significant under PEF than under PCF. We conclude that this arises due to the significant enhancement of alignment under PEF. Our simulations represent the widest range of molecular systems under shear flow for which self-diffusion has been calculated. Results for PEF represent the first examination of self-diffusion for molecular systems under an extensional flow.