Brownian dynamics simulations of linear polymers under shear flow

Abstract

Brownian dynamics simulations of a polymer chain described by three different models under the influence of a shear flow have been performed. Model A is a freely jointed Kramers chain consisting of beads connected by rigid rods. Model B is a freely jointed chain consisting of finitely extensible nonlinear elastic (FENE) springs. Excluded volume and hydrodynamic interactions are not taken into account in either of these two models. Model C is a chain with rigid bonds, valence, and torsional angle potentials, excluded volume and hydrodynamic interactions. Asymptotic dependencies [η]∼γ̇−1/3 and [η]∼γ̇−2/3 for the intrinsic viscosity [η] at large shear rates γ̇ for models A and B, correspondingly, have been obtained. Asymptotic dependencies for the first normal stress coefficient Ψ1∼γ̇−4/3 do not depend on the particular choice of model. At intermediate shear rates [η]∼γ̇−1/2 is followed for all models. Scaling dependencies of rheological properties on molecular weight have been studied. Results of the simulations show that chains are not fully stretched even at extremely high shear rates but form rather compact anisotropic objects. Correlation functions of the chain end-to-end vector relax quicker with increasing shear rate and reveal evidence of the end-to-end vector flipping between orientations parallel and antiparallel to the flow direction.

Semidilute Polymer Solutions at Equilibrium and under Shear Flow

“…Various experiments confirm the predicted dependencies for the relaxation time and viscosity [29][30][31][32][33]. However, a systematic simulation study is still lacking, even though single-chain hydrodynamic simulations are well established [26,27,[34][35][36][37][38][39][40][41][42][43]. The difficulty is that in the semidilute regime a large polymer overlap is necessary, whereas at the same time the segmental density has to be rather low to retain hydrodynamic interactions, which requires the simulation of long polymers [44].…”

An alternative to the bead-rod model: Bead-spring chains with successive fine graining

“…Different algorithms have been developed in the last decade to address these issues [1,[10][11][12][13][14][15][16][17][18]. Inclusion of HI and EV introduce further complexity and ambiguity in the bead-rod model formulation and implementation [14,[19][20][21][22]. To date, the results of Petera and Muthukumar [23] and Liu et al [24] are considered to be the most accurate rheological property predictions in the literature with the bead-rod model in the presence of EV and HI.…”

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

“…Here, the same time-step and equilibration length were used as for the lowest finite shear simulation of a given molecule, with R g data being sampled from up to 2ϫ10 6 steps of subsequent production. Further simulation details can be found in the work of Lyulin et al 47 Error bars in all plots are smaller than the size of the data symbols used and lines on graphs are guides to the eye, unless otherwise indicated.…”