Local area distribution of quasi-2D colloidal dispersions and its relation to particle diffusion: a Voronoi tessellation approach†

The dynamical properties of the local area available per particle and its relationship with the self-diffusion coefficient of colloids in quasi-2D colloidal dispersions are studied using video microscopy, supported by Brownian dynamics simulations. The local area is determined via the well-known Voronoi tessellation technique. Our findings reveal that local areas per particle are highly dispersed, exhibiting slow dynamics over time. Additionally, the evolution of the ensemble-averaged area distribution as a function of concentration shows a long tail at large and small areas for low and high concentrations, respectively, leading to a maximum in information entropy when the distribution becomes symmetric. We introduce and analyze several expressions for local area-weighted diffusion coefficients. Notably, we find that the contribution of the averaged diffusion coefficient can be expressed in terms of local areas, establishing a new framework to determine the weighted influence of each local area on particle dynamics.