Langevin dynamics and Stokes-Einstein's diffusion relation

LAMMPS
1

I have been using LAMMPS for 3 years now, mainly to simulate polymer cross-linking and biomolecular phase transition. Recently I was curious to know how diffusion of a polymer chain (or a multi-chain cluster) scales with its size. From the short term displacement analysis (MSD vs time plot) done for a single bead/atom (or single chain, or multi-chain cluster), diffusion coefficient (D) is inversely proportional to mass (m) of the object, and proportional to the t_damp parameter that is part of the “fix langevin” command.

Going to the langevin documentation, I found that, viscous drag force is proportional to m/t_damp in the LAMMPS implementation.

Now the question: Since D ~ 1/m, D ~ 1/r^3, where r is the radius of a spherical particle. Stokes-Einstein relation states that D ~ 1/r.

Also, I understand that one can define mass of an atom, but not radius which comes from interaction potentials like LJ. So for an isolated particle, size/radius can not be defined in the input file.

Just wondering whether anyone has any comment on this. Thanks for your time.

2

Lennard Jones and most other models in LAMMPS define point particles. If you need finite size spherical particles where the radius can be specified for each particle, you can use the sphere atom style instead, see atom_style command — LAMMPS documentation.