HINDERED DIFFUSION OF A SINGLE SPHERE VERY NEAR A WALL IN A NONUNIFORM FORCE-FIELD

Total internal reflection microscopy is used to monitor Brownian fluct uations in the elevation of a single 10 mum sphere, levitated 0.05 to 0.35 mum above a glass plate by double-layer repulsion in a dilute aqu eous salt solution. An analysis reveals that the initial slope of the autocorrelation function of the scattering intensity yields the diffus ion coefficient evaluated at the weighted-average elevation in which t he product of the Boltzmann factor and the square of the scattering in tensity for that elevation are used as the weighting factor. When the sphere is very close to the wall, its mobility is expected to be signi ficantly reduced owing to hydrodynamic interactions with the wall. Dif fusion coefficients as small as 1.5% of the Stokes-Einstein value in t he bulk were measured. Using Brenner's relation between mobility and e levation [Chem. Eng. Sci. 16, 242 (1961)], the average elevation was i nferred from the ratio of the average diffusion coefficient to its bul k value. The result is compared to the elevation obtained from the bri ghtness of the sphere. Good agreement is obtained between the elevatio ns inferred from the two independent measurements.