Diffusion and Reactive Properties in Disordered Porous Media and in Confining Geometries
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transitions in disordered porous materials. Several problems are not clearly settled down and need to be clarified. We mention just a few: (i) How geometrical disorder and thermodynamics couple, especially in adsorption/desorption processes[ 1]. (ii) What some terms, such as "tortuosity" or "obstruction factor" mean and how the pore network geometry (morphology+topology) influences molecular transport, reactivity, and excitation relaxation. The main purpose of the article deals with the second topic. As it can be seen in Fig 1, one main difficulty is to handle a full 3D geometrical description of a disordered material especially at the mesoscopic scale (5A-lIlgm) and to couple this characterisation with transport or phase transition processes. Several usual characteristics such as the pore size or the pore shape are generally ill-defined. A challenging question is to find a way to reconstruct a realistic 3D configuration from more simple informations such as a 2D random cut, allowing to capture main morphological and topological features of the original medium. As shown elsewhere, there exist some methods which enable to solve such a problem within a reasonable approximation [2-5]. Based on the Berk and Teubner's works [6,7], we have recently proposed an off-lattice reconstruction scheme[5). Critical evaluation of these 3D off-lattice reconstruction using Gaussian random fields were performed for different types of geometrical disorder (cement pastes, soils, Vycor glass, symmetrical sponge phase, mass or surface fractals). We give a brief survey of this method in section II and show an application in the case of the
Vycor porous glass. Properties of the self diffusion propagator are presented in section III. In
Mat. Res. Soc. Symp. Proc. Vol. 543 01999 Materials Research Society
section IV, we discuss how geometrical features influence molecular transport at long time. Two systems are presented. First, we focus on ionic conductivity of an asymmetric sponge phase. We then outline some basic properties of the Knudsen diffusion [8] and show how this basic transport process can be considered as a continuous time random walk [9]. An interesting consequence is that for some specific disordered porous media or "low dimension" geometries, there is a transition from a Gaussian diffusion to a Levy walk [10]. Finally, in section V, we attempt to exhibit connections between confining geometry and excitation relaxation. Some new results concerning the simulation of NMR relaxation of water liquid inside Vycor glass are presented.
Figure 1: 3D off-lattice reconstruction of a Vycor porous glass. The pore network is in white. The edge of the cube is IOOOA long. II/ OFF-LATTICE FIELDS.
RECONSTRUCTION
USING
GAUSSIAN
RANDOM
A biphasic random medium is completely defined by a density field (P(r). This function equals zero inside the pore network and one elsewhere. The autocorrelation of this field, (p2 v(r), can be directly estimated on 2D planar section of an isotropic disordered porous medium. A good approximation can also
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