Analysis of Evanescent Waves Scattering by a Single Particle in Total Internal Reflection Microscopy

Abstract

Since its invention in the mid of eighties (1) Total Internal Reflection Microscopy (TIRM) has proven to be an effective technique to measure weak interactions between spherical colloidal particles and surfaces with a resolution of a few femtonewton. It is a single particle evanescent light scattering technique. In an experimental setup a laser beam is coupled into a prism and hits the glass-water interface with an angle slightly above the critical angle of total internal reflection. This generates an evanescent field near the interface that decays in the lower refractive index medium (water) with a characteristic penetration depth which depends on the angle of incidence. A colloidal particle that is dispersed in the medium will scatter light from the evanescent wave if it is in the vicinity of the surface. By registering a scattered intensity it is possible to deduce the particle- substrate distance. Compared to other methods for measure particle wall interactions like the surface force apparatus or the atomic force microscopy where a colloidal particle is attached to the tip, TIRM is the most sensitive technique because thermal fluctuations where limit the other methods in their resolution are exploited to determine the interaction potential. In this way forces in the order of a few femtonewton can be detected. TIRM has proven to be a valuable tool for the precise measurement of weak colloidal interactions as double layer forces, van der Waals forces, magnetic interactions and depletion forces. Review on TIRM can be found for example in (2,3). To compare experimental results with results of mathematical modeling an effective light scattering method is needed. For this purpose the Discrete Sources Method (DSM) has been chosen. The DSM is a well-known method for light scattering analysis, which has recently been applied for evanescent wave scattering (4). 1. Discrete Sources Method For the theoretical modeling the Discrete Sources Method (DSM) has been chosen. The DSM is a well-known method for the analysis of light scattering. It has recently been applied to the evanescent wave scattering (4). In frame of the DSM the mathematical statement can be presented as follows: