Hindered diffusion of colloidal particles very near to a wall: Revisited

Total internal reflection microscopy is a technique for monitoring changes in the distance between a single microscopic sphere and a flat plate by measuring the intensity of light scattered by the sphere when illuminated by an evanescent wave. A histogram of scattering intensities can be used to construct the potential energy profile as a function of distance relative to the most probable distance. Thus potential energies can be measured to within a fraction of kT while changes in distance can be measured to within 1 nm. An autocorrelation of the scattering intensities can be used to deduce an average diffusion coefficient of the sphere, which is found to be only a few percent of the Stokes–Einstein value, owing to the close proximity of the plate. The analysis of the intensity-autocorrelation function presented here can be used to deduce an absolute value for the most probable separation distance, without a priori knowledge of the functional form of the PE profile and in the presence of a constant background scattering intensity. This “hydrodynamic” separation distance is found to be within a few percent of the “optical” separation distance found independently by comparing the intensity at the most probable distance with the intensity of the same particle in contact with the plate. Since the particle does not need to be brought into contact with the plate, the hydrodynamic method is well suited for determining the absolute separation distance with deformable particles like liquid droplets, vesicles or biological cells. Moreover, the hydrodynamic separation can be immediately calculated without any additional experiments. However, accurate determination of the hydrodynamic separation requires an accurate value for the particle size, which must be determined independently.