Effect of Brownian probe collision and rotation on diffusion coefficient measurements: Mean-squared-displacement vs. displacement-variance methods

Abstract

Accurate measurement of diffusion coefficients is crucial for characterizing transport processes in systems ranging from biological cells to colloidal suspensions. In this study, we investigate the impact of probe-to-probe collisions and rotations on the accuracy of diffusion coefficient measurement methods in Brownian systems. Using LAMMPS simulations, 100 spherical probes randomly arranged in a simulation box were immersed in an implicit water solvent across a temperature range of 10–50°C with 5°C increments. Two complementary approaches—one based on the mean-squared-displacement (MSD) and the other on the variance of displacement distributions—were employed to capture both translational and rotational motions. The simulations were performed under four conditions: without interactions (R₀₀), with only collisions (R₁₀), with only rotations (R₀₁), and with both interactions (R₁₁). Our results show that enabling probe-to-probe collisions significantly worsened the accuracy of the MSD method at increasing temperatures, whereas probe rotations caused translational MSD measurements to read faster diffusion. On the other hand, the variance-based approach was less sensitive to these interactions and provided more consistent estimates. These findings underscore the need to account for both collisions and rotational dynamics when measuring diffusion coefficients in complex systems.