# Bridging the gap between molecular dynamics and hydrodynamics in nanoscale Brownian motions

## TL;DR

This study uses molecular dynamics simulations to connect nanoscale Brownian motion with hydrodynamic behavior, revealing how solvation and molecular interactions influence particle dynamics and hydrodynamic properties.

## Contribution

It bridges molecular dynamics and hydrodynamics in nanoscale Brownian motion, highlighting the effects of solvation structure and molecular interactions on hydrodynamic behavior.

## Key findings

- Hydrodynamic radius varies with solvation free energy and potential type.
- VACF matches Navier-Stokes analytical expressions at long times.
- Long-time tail of VACF follows a t^{-3/2} decay.

## Abstract

Through molecular dynamics simulations, we examined hydrodynamic behavior of the Brownian motion of fullerene particles based on molecular interactions. The solvation free energy and the velocity autocorrelation function (VACF) were calculated by using the Lennard-Jones (LJ) and Weeks-Chandler-Andersen (WCA) potentials for the solute-solvent and solvent-solvent interactions and by changing the size of the fullerene particles. We also measured the diffusion constant of the fullerene particles and the shear viscosity of the host fluid, and then the hydrodynamic radius $a_\mathrm{HD}$ was quantified from the Stokes-Einstein relation. The $a_\mathrm{HD}$ value exceeds that of the gyration radius of the fullerene when the solvation free energy exhibits largely negative values using the LJ potential. In contrast, $a_\mathrm{HD}$ becomes comparable to the size of bare fullerene, when the solvation free energy is positive using the WCA potential. Furthermore, the VACF of the fullerene particles is directly comparable with the analytical expressions utilizing the Navier-Stokes equations both in incompressible and compressible forms. Hydrodynamic long-time tail $t^{-3/2}$ is demonstrated for timescales longer than the kinematic time of the momentum diffusion over the particles' size. However, the VACF in shorter timescales deviates from the hydrodynamic description, particularly for smaller fullerene particles and for the LJ potential. This occurs even though the compressible effect is considered when characterizing the decay of VACF around the sound propagation time scale over the particles' size. These results indicate that the nanoscale Brownian motion is influenced by the solvation structure around the solute particles originating from the molecular interaction.