Computationally efficient algorithms for incorporation of hydrodynamic and excluded volume interactions in Brownian dynamics simulations: a comparative study of the Krylov subspace and Chebyshev based techniques.

Abstract

Excluded volume and hydrodynamic interactions play a central role in macromolecular dynamics under equilibrium and non-equilibrium settings. The high computational cost of incorporating the influence of hydrodynamic interaction in meso-scale simulation of polymer dynamics has motivated much research on development of high fidelity and cost efficient techniques. Among them, the Chebyshev polynomial based techniques and the Krylov subspace methods are most promising. To this end, in this study we have developed a series of semi-implicit predictor-corrector Brownian dynamics algorithms for bead-spring chain micromechanical model of polymers that utilizes either the Chebyshev or the Krylov framework. The efficiency and fidelity of these new algorithms in equilibrium (radius of gyration and diffusivity) and non-equilibrium conditions (transient planar extensional flow) are demonstrated with particular emphasis on the new enhancements of the Chebyshev polynomial and the Krylov subspace methods. In turn, the algorithm with the highest efficiency and fidelity, namely, the Krylov subspace method, is used to simulate dilute solutions of high molecular weight polystyrene in uniaxial extensional flow. Finally, it is demonstrated that the bead-spring Brownian dynamics simulation with appropriate inclusion of excluded volume and hydrodynamic interactions can quantitatively predict the observed extensional hardening of polystyrene dilute solutions over a broad molecular weight range.