Pore space topology

The use of fractal and percolation concepts to characterize pore-space topology (Sahimi, 1993) is a notable exception. 

In materials of infinite extent, the above definitions remain valid. As noted previously (Chapter 4), for pore space topologies with a given coordination number, there exists a critical filling probability (porosity). In materials with filling probabilities above this critical value, the size of the largest cluster is comparable to the size of the lattice. The presence of this lattice spanning cluster does not require that the material be finite in extent in fact, most analytical results in percolation theory assume that the lattice is infinite. For... 

Taking into account that E,0 0 (since topologically Dy < 3, and d = 3), we obtain a simple approximate relationship between the average porosity of a glass and the fractal dimension of the pore space, which reads... 

Vi >gel, H.J., and A. Krelzschmar. 1996. Topological characterization of pore space in soil—sample preparation and digital image-processing. Geoderma 73 23-38. 

We now study the morphological and topological characteristics of site-bond-site 3D cubic network model. The following additional assumptions are made about the pore space i. The pore space is a lattice of spherical cavities interconnected by cylindrical channels. The catalytic surface mainly belongs to the voids of the lattice, ii. Active sites are uniformly... 

The function h r, r ) accounts for the possibility that due to hysteresis effects, the interface does not advance completely to pores with capillary radius with increasing S, it depends on the detailed topology of the pore space and, thus, demands more detailed microstructure characterization. T is a factor of order 1, depending on pore geometry and wetting properties. 

There is also the effect of the structure of the porous material. For a nonequilibrium measurement of diffusion, one can consider that there is no straight path for solutes to travel in the direction of the flux. In an equilibrium measurement of intradiffusion, this represents the fact that solutes are not longer subject to a purely random walk. When a solute is near a pore surface, the probabilities for moving in each direction are no longer uniform certain directions are prohibited by the pore wall. For technical precision, then, one should differentiate between a structure factor and a tortuosity. A tortuosity, t, quantitatively describes experimental results in which multiple interactions affect the diffusion. A structure factor, q, quantitatively describes only the effect of pore space geometry and topology on diffusion. Note that for limited conditions—when studying diffusion of small molecules and a passive pore surface—this allows for x cj. 

Intrinsically, a pore network contains the pore space s cormectivity data, where the term coordination number represents the number of throat comiections at each pore. In addition to this topological information, the size and shape of each element can be incorporated. A pore network model can be tuned to have the... 

Once a pore space is known, a pore network can be created through a variety of methods. Methods that reduce the pore space into a topologically equivalent skeleton involve either a thiiming algorithm or, in the case of the 2D models " -a Voronoi diagram around the material locations. An alternative method to determine the representative pore network for a pore space is the maximal ball method, which is a computationally inexpensive techniqne that has been demonstrated for GDL-like structures. ... 

It is therefore reasonable to postulate that the confinement of carbene 46, perhaps within the nanoscopic pores of CyDs and FAUs, would inhibit the fragmentation reaction and foster the 1,3-CH insertion. This reasoning is twofold (1) there may not be enough space within the hosts cavities for the unraveling process, 46—>47, and (2) distortion of the carbene s topology might concomitantly disfavor the coarctate TS and allow the 1,3-CH insertion, 46->48, to finally occur. 

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