Random flights in confining interfacial systems

Porous materials, concentrated colloidal suspensions are examples of confining systems developing large specific surface and presenting a rich variety of shapes. Such an interfacial confinement strongly influences the molecular dynamics of embedded fluids and the diffusive motion of entrapped Brownian particles. An individual trajectory near the interface can be described as an alternate succession of adsorption steps and random flights in the bulk. Statistical properties of these random flights in various interfacial confining systems are needed as prerequisites in order to understand the full transport process. Related to first passage processes, these properties play a central role in numerous problems such as the mean first exit time in a bounded domain, heterogeneous catalytic reactivity and nuclear magnetic relaxation in complex and biological fluids. In the present work, we first consider the various possibilities of connecting two points of a smooth interface by a random flight in the bulk. Second, we analyse from the theoretical and experimental points of view a way to probe Brownian flight statistics. From the experimental point of view, we investigate the slow fluid dynamics near some colloidal interfaces by field-cycling NMR relaxometry. This is a way to follow slow dynamical correlations from 1 ns to 10 μs. This spectroscopy appears to be a good choice, considering that the algebraic nature of the probability of the first return to a surface builds a long-time memory. The experimental part confirms that the embedded fluid dynamics is sensitive to possible morphologic crossover and provides information about interface geometry. We also believe that such an approach can be used to probe interfacial dynamics by itself, for example in the case of a colloidal system undergoing a phase transition (dynamical arrest, rotational blockage,...)