Dipolar Energy Transfer and Knudsen Diffusion Inside Disordered Porous Media: Interfacial Geometry and Chord Distributions.

Abstract

AbstractThe interfacial geometry of a disordered porous medium strongly influences Knudsen diffusion of gases and interfacial dipolar energy transfer. Some interesting comparison can be made between these two transport processes, involving statistical properties of chords belonging either to the solid matrix or to the pore network. A quantitative analysis of these two mechanisms is proposed, based on a chord distribution model. In a first part, we discuss how chord distribution functions contribute to the stastistical characterization of a porous medium. We show that a direct connection between imaging techniques and small angle scattering provides, in many cases, a reliable description of theses functions. In a second part, interfacial direct energy transfer is analyzed. This one step excitation transfer strongly relies on the interfacial autocorrelation function φ2s(r). An analytic expression of φ2s(r) is given and theoretical predictions compared with available experiments. In a third part and following the seminal work of Derjaguin on the Knudsen diffusion, we critically examine how the self diffusion coefficient can be related to the two first moments of the pore chord distribution. A direct comparison with experimental results and numerical simulations is presented in the case of a model porous medium: the random packing of hard spheres. Finally, we analyze a trapping reaction where an excited gas molecule, diffusing in the Knudsen regime, relaxes primarily by wall effects. We show how the chord distribution of the pore network permits to compute the survival probability of the tagged molecules. Two situations are more closely analyzed: the strong and the very weak wall quenching efficiency.