A new approach for analyzing particle motion near an interface using total internal reflection microscopy

A new method was developed for analyzing the normal motion of a single colloidal particle near an interface. The optical technique of total internal reflection microscopy (TIRM) was used to determine the distribution of vertical displacements of a particle from a specific starting position as a function of time. At very small displacement times, the displacements are normally distributed with a variance that is proportional to the diffusion coefficient times the displacement time. The change in the diffusion coefficient with separation distance between the particle and plate was found to match that predicted by Brenner (Chem. Eng. Sci. 16 (1961) 242). As the sampling time becomes very large, the variance reaches a constant value determined strictly by the shape of the local potential energy profile holding the particle. A major advantage of this approach, relative to other measurement methods, is that the particle's spatially variant diffusion coefficient can be determined without any knowledge of the forces acting on the particle.