Brownian dynamics simulation of linear polymers under elongational flow: Bead–rod model with hydrodynamic interactions

Abstract

Brownian dynamics (BD) simulations of a linear freely jointed bead–rod polymer chain with excluded volume (EV) interaction have been performed under elongational flow with and without the use of fluctuating hydrodynamic interactions (HI). The dependence of the chain size, shape and intrinsic elongational viscosity on the elongational rate ε̇ are reported. A sharp coil–stretch transition is observed when ε̇ exceeds a critical value, ε̇c. The inclusion of the HI leads to a shift in the coil–stretch transition to higher flow values. Chain deformation due to elongational flow is observed to first consist of the alignment of the chain with the direction of flow without significant chain extension followed by additional alignment of the bond vectors with the flow direction and chain extension as flow rate is increased further. The distribution function for the chain’s radius of gyration becomes significantly broader within the transition region which implies an increase in fluctuations in the chain size in this region. The structure factors parallel and perpendicular to the flow direction illustrate different elongational rate dependencies. At high rates, the structure factor in the direction of the flow exhibits an oscillating dependence which corresponds to the theoretically predicted shape for a rigid-rod model. The mean squared orientation of each bond within the chain with respect to the flow direction as function of bond number is nearly parabolic in shape with the highest degree of orientation found within the chain’s interior. The dependence of the critical elongational rate, ε̇c, on the chain length, N, is observed to be ε̇c∼N−1.96 when hydrodynamic interactions are not employed and ε̇c∼N−1.55 when they are invoked. These scaling exponents agree well with those obtained in previous BD simulations of bead-FENE (i.e., finitely extensible nonlinear elastic) spring chains as well as with the theoretical predictions of ε̇c∼N−2 and ε̇c∼N−1.5 without and with hydrodynamic interactions based on the Rouse and Zimm models, respectively.