Hindered diffusion of a single sphere very near a wall in a nonuniform force field

Abstract

Total internal reflection microscopy is used to monitor Brownian fluctuations in the elevation of a single 10 μm sphere, levitated 0.05 to 0.35 μm above a glass plate by double-layer repulsion in a dilute aqueous salt solution. An analysis reveals that the initial slope of the autocorrelation function of the scattering intensity yields the diffusion coefficient evaluated at the weighted-average elevation in which the product of the Boltzmann factor and the square of the scattering intensity for that elevation are used as the weighting factor. When the sphere is very close to the wall, its mobility is expected to be significantly reduced owing to hydrodynamic interactions with the wall. Diffusion coefficients as small as 1.5% of the Stokes–Einstein value in the bulk were measured. Using Brenner’s relation between mobility and elevation [Chem. Eng. Sci. 16, 242 (1961)], the average elevation was inferred from the ratio of the average diffusion coefficient to its bulk value. The result is compared to the elevation obtained from the brightness of the sphere. Good agreement is obtained between the elevations inferred from the two independent measurements.