Optimisation of a Brownian dynamics algorithm for semidilute polymer solutions

TL;DR

This paper develops an efficient Brownian dynamics algorithm for simulating semidilute polymer solutions, improving computational scaling and validating results against hybrid LB/MD methods, with potential for further optimization.

Contribution

The authors introduce a scalable Brownian dynamics algorithm with O(N^{1.8}) cost, adapting Ewald summation for systems with bead overlap, and validate it against LB/MD simulations.

Findings

The new BD algorithm scales as O(N^{1.8})

Modified Ewald sum enables heta-solutions simulation

LB/MD method outperforms BD in efficiency for semidilute solutions

Abstract

Simulating the static and dynamic properties of semidilute polymer solutions with Brownian dynamics (BD) requires the computation of a large system of polymer chains coupled to one another through excluded-volume and hydrodynamic interactions. In the presence of periodic boundary conditions, long-ranged hydrodynamic interactions are frequently summed with the Ewald summation technique. By performing detailed simulations that shed light on the influence of several tuning parameters involved both in the Ewald summation method, and in the efficient treatment of Brownian forces, we develop a BD algorithm in which the computational cost scales as O(N^{1.8}), where N is the number of monomers in the simulation box. We show that Beenakker's original implementation of the Ewald sum, which is only valid for systems without bead overlap, can be modified so that \theta-solutions can be simulated by switching off excluded-volume interactions. A comparison of the predictions of the radius of gyration, the end-to-end vector, and the self-diffusion coefficient by BD, at a range of concentrations, with the hybrid Lattice Boltzmann/Molecular Dynamics (LB/MD) method shows excellent agreement between the two methods. In contrast to the situation for dilute solutions, the LB/MD method is shown to be significantly more computationally efficient than the current implementation of BD for simulating semidilute solutions. We argue however that further optimisations should be possible.