Effect of probe-to-probe collisions in three-dimensional space on the measured diffusion coefficient

Abstract

We investigate the effects of elastic probe-to-probe collisions at diluted to dense probe crowding conditions on the diffusion coefficient D of numerically-modelled 3D Brownian motion (BM) ensembles. Homogeneous ensembles of pure isolated BM (iso) and collision-laden BM (coll) probes with a specified volume fraction ϕ (measure of crowding) are generated using an algorithm consisting of a time-driven BM subroutine and an event-driven elastic collisions subroutine. We found that despite probe-to-probe collisions, the displacement distribution of the collision-laden probes reveal approximately Gaussian distributions (implying pure BM despite collisions). Diffusion coefficients D_coll of collision-laden probes and D_iso of the isolated probes were measured using the variance of the displacement distributions. Increasing ϕ leads to a nonlinear increase in the recorded collisions in an ensemble and a higher collision probability per time step. Probe-to-probe collisions significantly affect the diffusion behavior of the system. Results show that collision-laden probes exhibit slower diffusion than isolated probes (D_coll < D_iso) where increasing crowding ϕ leads to larger deviations between D_coll and D_iso and introduce anomalous diffusion. Our work provides valuable insights into the behavior of BM probes under crowded environments.