Scaled Brownian motion as transient behavior of individual particle diffusion due to multiple probe-to-probe collisions

Abstract

We investigate the possible transient effect of elastic probe-to-probe collisions on the diffusion of individual probes and ensembles through the changes in the diffusion coefficient D and the anomalous exponent α . Coefficient D quantifies the diffusion speed of the system while exponent α measures the deviation from normal diffusion or pure Brownian motion (BM) where: α = 1 indicates pure BM, and α ≠ 1 indicates anomalous diffusion (AD) or scaled BM. We modeled originally pure BM ensembles subjected to collisions using a combination of time-driven BM and event-driven collisions algorithms. Using the time-averaged mean-squared displacement analysis technique of the scaled BM theory, we measured D_iso and α_iso from the collision-less pure BM trajectories, and D_col and α_col from the collision-laden trajectories. Results show that the ensemble- and individual probe-levels of diffusion slow down (D_col < D_iso) due to collisions. At the ensemble-level, there is persistence of pure BM (α_col ≈ α_iso = 1) despite collisions. Results at the individual-level reveal that the ensemble pure BM behavior is due to the dominant pure BM-behaving probes in the population. Yet, a significant fraction of the particle population exhibited AD (α_col ≠ α_iso) at short sampling periods of T < 4590 time intervals. As T increases, the ensembles eventually reach a steady-state condition where all probes diffuse normally. We conclude that probe-to-probe collisions cause the transient AD of individual particles at short T. Thus, anomalous diffusion emerges even without complex attractive and repulsive probe-probe and probe-medium interactions.