Na. Frej et Dc. Prieve, HINDERED DIFFUSION OF A SINGLE SPHERE VERY NEAR A WALL IN A NONUNIFORM FORCE-FIELD, The Journal of chemical physics, 98(9), 1993, pp. 7552-7564
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.