Investigations of heterogeneous diffusion based on the probability density of scaled squared displacements observed from single molecules in ultra-thin liquid films

Diffusion processes in ultra-thin liquid films observed by video microscopy reveal a complex behavior. In contrast to homogeneous diffusion, dynamic and static heterogeneities are induced by layer transitions and compartments with differing diffusion coefficients, respectively. The objective of this research is the detection and distinction of such heterogeneities as well as an analysis of the underlying processes. Hence, a new method is proposed establishing a probability density of scaled squared displacements. This probability density allows for a simple and well-defined calculation of time-dependent diffusion coefficients and its fluctuations. Furthermore, by simulating a heterogeneous diffusion process these results are verified and compared to mean square displacement calculations. By means of the simulated probability density data, their dependency on the parameters is illustrated and further implications are pointed out. keywords: diffusion, dynamic and static heterogeneity, scaled squared displacements