Measurement of apparent Brownian motion diffusion coefficient under finite spatial and temporal detector resolution

Abstract

We investigate the effect of binning size, N, and sampling interval, τ, on the accuracy of the measured diffusion coefficient via extensive Brownian motion analysis of solid probe particles (radius = 0.5μm) in a liquid of viscosity 0.95mPa-s at 300.65K. The theoretical diffusion coefficient is 0.46μm²/s as calculated using Stokes-Einstein relation while the apparent (observed) diffusion coefficient value which is based on the binned Brownian motion trajectories is determined using mean-squared-displacement analysis. We have observed a nonlinear increase in the apparent coefficient value with N and a decrease with longer τ values (lower frame sampling rates) with N ≥ 2 sizes leading to ≥ 1% deviations and N ≥ 3 sizes leading to ≥ 5% deviations at τ ≤ 0.5s. A maximum of 5% deviation was observed at around τ ≥ 4.0s, regardless of N. Our results indicate that detectors with greater spatial resolution are more desirable over detectors with faster sampling rates when measuring an accurate diffusion coefficient using Brownian motion analysis.