Measurement of the Brownian motion diffusion coefficient: Displacement-distribution versus mean-squared-displacement trajectory technique
We investigate the possible difference in the diffusion coefficient D value when measured from the variance of the normal displacement-distribution (Dvar), and from the slope of the linear mean-squared-displacement (MSD) against sampling time interval, (DMSD). We considered the pure Brownian motion (BM) of solid 2μm spheres in water, with a viscosity of 0.89mPa-s at 25°C, observed over 60s every 0.1s. For each generated trajectory, Dvar and DMSD were calculated and compared against the theoretical D of 0.245 μm2/s. For the DMSD measurements, the effect of the number of fitting points, f, used for plotting the MSD graph and the number of displacement steps, s, for computing each MSD per 𝜏 were studied. We have observed that DMSD accuracy increases with f (DMSD is within 5% accuracy at f > 30). We have also found that Dvar is more accurate (to within one percent) and precise than DMSD, regardless of the f and s parameters. Our results indicate that using the variance of the displacement distribution may lead to more accurate and precise D measurements of BM trajectories.