Examination of near-wall hindered Brownian diffusion of nanoparticles: Experimental comparison to theories by Brenner (1961) and Goldman et al. (1967)

Multilayered distributions of hindered mean square displacement (MSD) for nanoparticles are measured in the near-wall region within 500 nm from the solid surface using total internal reflection fluorescence microscopy, an evanescent wave microscopic imaging technique. Examined particles are yellow-green (505/515) polystyrene fluorescent nanospheres of 100, 250, and 500 nm radii with a specific gravity of 1.055. To ensure the measurement accuracy, special care is taken to minimize photobleaching of fluorescent particles by adding neutral density filters to optimally reduce the excitation power. The experimental results for parallel MSDs to the solid surface validate the theory of hindered diffusion [A. J. Goldman, R. G. Cox, and H. Brenner, 'Slow viscous motion of a sphere parallel to a plane - I: Motion through a quiescent fluid', Chem. Eng. Sci. 22, 637 (1967)] of spheres based on viscous slow-down in the near-wall region. It is also reported that the effect of adding sodium chloride up to 10 mM to the solution has little effect on the parallel diffusive motion of the tested nanoparticles. Experimental evidence shows that normal MSDs, for submicroscopic charged nanoparticles, are substantially different from Einstein's 2DΔt due to the deterministic motion arising from electrostatic forces