# Modeling scattered intensities for multiple particle TIRM using Mie theory

## Abstract

Single particle TIRM experiments measure particle-surface separation distance by tracking scattered intensities. The scattered light is generated by an evanescent wave interacting with a levitating microsphere. The exponential decay of the evanescent wave, normal to the surface, results in scattered intensities that vary with separation distance. Measurement of the separation distance allows us to calculate the total potential energy profile acting on the particles. These experiments have been shown to exhibit nanometer spatial resolution and the ability to detect potentials on the order of kT with no external treatment of the particle. We find that the separation distance is a function of the decay of the evanescent wave and the size of the sphere. Different sizes of spheres, located the same distance from the surface, exhibit varying scattered intensity distributions. Single particles have been studied extensively but multiple particle experiments are needed for studies of more complex systems and surfaces. Increasing the number of colloidal particles in a TIRM experiment greatly increases the complexity of the system. Calculation of separation distances and potentials over a large group of microspheres requires that the spheres display a uniform stuck-particle intensity distribution. But, for large numbers of particles, this is not the case. In some instances, stuck-particle intensities can vary more than an order of magnitude. This research involves creating a mathematical model to study scattered intensity distributions for a large size range of polystyrene microspheres. The model is based on basic Mie theory. We compare the theoretically simulated results to the experimentally obtained results and find that scattered intensity variations in multiple particle TIRM experiments are attributed to particle polydispersity (particle size variation). This is a very important result because we know that if we can maintain a relatively uniform particle size distribution, then we will see a relatively uniform stuck-particle intensity distribution. The model can then be used to select a size range of microspheres that will exhibit a more uniform distribution so as to increase the sensitivity and feasibility of multiple particle TIRM.