Experimental verification of near-wall hindered diffusion for the Brownian motion of nanoparticles using evanescent wave microscopy

Abstract

A total internal reflection fluorescence microscopy technique coupled with three-dimensional tracking of nanoparticles is used to experimentally verify the theory on near-wall hindered Brownian motion [Goldman et al., Chem. Eng. Sci. 22, 637 (1967); Brenner, Chem. Eng. Sci. 16, 242 (1967)] very close to the solid surface (within $\sim 1\mu \mathrm{m}$). The measured mean square displacements (MSDs) in the lateral $x\text{−}y$ directions show good agreement with the theory for all tested nanoparticles of radii 50, 100, 250, and 500 nm. However, the measured MSDs in the $z$ direction deviate substantially from the theory particularly for the case of smaller particles of 50 and 100 nm radius. Since the theory considers only the hydrodynamic interaction of moving particles with a stationary solid wall, additionally possible interaction forces like gravitational forces, van der Waals forces, and electro-osmotic forces have been examined to delineate the physical reasons for the discrepancy.