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.

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Diffusion Weighted Magnetic Resonance (DWMR) Imaging is an important tool in diagnostic neuroimaging, but the biophysical basis of the DWMR signal from biological tissue is not entirely understood. Testable, theoretical models relating the DWMR signal to the tissue, therefore, are crucial. This work presents a toy version of such a model of water DWMR signals in brain grey matter. The model is based on biophysical characteristics and all model parameters are directly interpretable as biophysical properties such as diffusion coefficients and membrane permeability allowing comparison to known values. In the model, a computer generated Diffusion Limited Aggregation (DLA) cluster is used to describe the collected membrane morphology of the cells in cortical grey matter. Using credible values for all model parameters model output is compared to experimental DWMR data from normal human grey matter and it is found that this model does reproduce the observed signal. The model is then used for simulating the effect on the DWMR signal of cellular events known to occur in ischemia. These simulations show that a combination of effects is necessary to reproduce the signal changes observed in ischemic tissue and demonstrate that the model has potential for interpreting DWMR signal origins and tissue changes in ischemia. Further studies are required to validate these results and compare them with other modeling approaches. With such models, it is anticipated that sensitivity and specificity of DWMR in tissues can be improved, leading to better understanding of the origins of MR signals in biological tissues, and improved diagnostic capability.

Diffusion coefficients obtained from weighted mean square displacements along probe molecule trajectories within ultrathin liquid TEHOS films show a correlation with film thickness. By studying cumulative distributions obtained with a time resolution of 20 ms, we could show that the diffusion is heterogeneous within our liquid films which consist of a few molecular layers only. We detected two components of the diffusion process, a slower and a faster one. Thinning of the film due to evaporation caused a slowdown of the whole diffusion process. But this resulted not from a slowdown in the two contributing components itself. Instead their relative contributions changed in favor for the slow component. We conclude that there is no pronounced difference in the diffusion coefficients attributed to the molecular layers 3 to 5 vertically above the substrate, but with the loss of upper layers along with the thinning process the concentration of probe molecules in the near surface region containing only one or two molecular layers is increased.

Single particle tracking with a wide field microscope is used to study the solid liquid interface between the viscous liquid tetrakis(2 ethylhexoxy)-silane and a silicon dioxide surface. Silicon dioxide nanoparticles (5 nm diameter) marked with the fluorescent dye rhodamine 6G are used as probes. The distributions of diffusion coefficients, obtained by mean squared displacements, reveal heterogeneities with at least two underlying diffusion components. Measurements on films with varying film thicknesses show that the slower component is independent of the film thickness, while the faster one increases with the film thickness. Additionally, we could show that the diffusion behavior of the particles cannot be sufficiently described by only two diffusion coefficients.

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