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

Area of Science:

• Computational physics
• Polymer science
• Statistical mechanics

Background:

• Accurate simulation of polymer solutions requires modeling long-range hydrodynamic interactions (HI) and short-range excluded volume (EV) forces.
• Conventional Brownian dynamics simulations (BDS) often use Ewald summation for HI, which is computationally expensive.
• Krylov subspace methods offer improvements but still have significant computational costs (O(N^2)).

Purpose of the Study:

• To develop and implement a more computationally efficient matrix-free approach for calculating hydrodynamic interactions in polymer simulations.
• To validate the fidelity of the new algorithm by evaluating polymer properties in dilute and semidilute solutions.
• To compare simulation results with established theoretical models like blob theory.

Main Methods:

• Implementation of a matrix-free algorithm for computing hydrodynamic interactions.
• Utilized Brownian dynamics simulations (BDS) with the new method.
• Calculated center-of-mass diffusivity and radius of gyration for polymer molecules.

Main Results:

• The matrix-free approach achieves a computational cost scaling of O(NlogN), significantly faster than previous methods.
• The algorithm accurately reproduces asymptotic center-of-mass diffusivity at low concentrations.
• Radius of gyration scaling aligns with theoretical predictions for dilute and semidilute polymer solutions.

Conclusions:

• The developed matrix-free method provides a computationally efficient and accurate way to simulate hydrodynamic interactions in polymer solutions.
• This advancement facilitates the study of concentration-dependent properties of macromolecules.
• The results show good agreement with blob theory, validating the simulation approach.