Fokker-Planck analysis of separation dependent potentials and diffusion coefficients in simulated microscopy experiments

Total internal reflection microscopy (TIRM) and video microscopy (VM) are methods for nonintrusively measuring weak colloidal interactions important to many existing and emerging applications. Existing analyses of TIRM measured single particle trajectories can be used to extract particle-surface potentials and average particle diffusion coefficients. Here we develop a Fokker-Planck (FP) formalism to simultaneously extract both particle-surface interaction potentials and position dependent diffusion coefficients. The FP analysis offers several advantages including capabilities to measure separation dependent hydrodynamic interactions and nonequilibrium states that are not possible with existing analyses. The FP analysis is implemented to analyze Brownian dynamic simulations of single particle TIRM and VM experiments in several configurations. Relative effects of spatial and temporal sampling on the correct interpretation of both conservative and dissipative forces are explored and show a broad range of applicability for accessible experimental systems. Our results demonstrate the ability to extract both static and dynamic information from microscopy measurements of isolated particles near surfaces, which provides a foundation for further investigation of particle ensembles and nonequilibrium systems.