Matrix-free Brownian dynamics simulation technique for semidilute polymeric solutions.

Evaluating the concentration dependence of static and dynamic properties of macromolecules in semidilute polymer solutions requires accurate calculation of long-range hydrodynamic interactions (HI) and short range excluded volume (EV) forces. In conventional Brownian dynamics simulations (BDS), computation of HI necessitates construction of a dense diffusion tensor commonly performed via Ewald summation. Krylov subspace techniques allow efficient decomposition of this tensor [computational cost scales as O(N^{2}), where N is the total number of beads in bead-spring representation of macromolecules in a simulation box] and computation of Brownian displacements in the box. In this paper, a matrix-free approach for calculation of HI is implemented which leads to O(NlogN) scaling of computational expense. The fidelity of the algorithm is demonstrated by evaluating the asymptotic value of center-of-mass diffusivity of polymer molecules at very low concentrations and their radius of gyration scaling as a function of number of beads for dilute and semidilute solutions (with concentrations up to 5 times the overlap concentration). In turn, a favorable comparison between our results and the blob theory is shown.