Modeling Active Particle Motion from Fluorescence Correlation Spectroscopy Data

Active colloids have attracted enormous attention in the past two decades. The field has evolved rapidly, resulting in diverse motor designs used to navigate in different environments. However, the question of the extent to which 2D and 3D analysis methods can be directly compared remains challenging to address. Here, we relate the motion of particles when assessed by fluorescence correlation spectroscopy (FCS) in a 3D volume to the standard optical microscopy-based tracking method in 2D. We select three types of motors that exemplify different common mechanisms of propulsion, i.e., self-diffusiophoresis, bubble propulsion, and magnetic guidance. We define minimal FCS detectability criteria for colloids and apply conditions to quantify locomotion of single and mixed motor populations. Specifically, we can distinguish between a mixed population of active and passive colloids in the same solution. Extending the existing FCS model, we can assess directed particle motion, which provides estimated velocities close to those reported by optical tracking methods. The results suggest that, while FCS and optical tracking show consistent trends in motor dynamics, they can differ in the absolute values of the effective diffusion coefficient. Nonetheless, FCS enables reliable assessment of the transport properties of motors when appropriate data treatment and evaluation procedures are applied. Taken together, FCS and optical tracking are complementary methods to determine the diffusivity values of the entire particle population and individual motors, respectively.