Three-dimensional network of pores

Another catalytically important zeohte is ZSM-5 (81). There is a three-dimensional network of pores in this zeohte, represented in Figure 16. A set of straight parallel pores is intersected by a set of perpendicular zigzag pores. These pores are smaller than those of the faujasites (Fig. 15). ZSM-5 is classified as a medium pore zeohte, the faujasites ate large pore zeohtes, and zeohte A (Table 2) is a small pore zeohte. 

Pore structures of typical polymeric ultrafiltration membranes, produced by so called "phase inversion methods," consist of interconnected, irregular, three-dimensional networks of pores, interstices and voids in their skin layers. 

The hydrogel formed has a continuous structure, giving a three-dimensional network of pores filled with water. The total volume of pores per mass-unit is called the pore volume and is a specific characteristic of the gel type. It is a main characteristic of sihca hydrogels, that mechanical treatment like milling does not affect the pore structure. Even after ball-milling the hydrogel into submicron particles the structure is maintained [61]. 

H-BEA (H-BETA) a proton exchanged BEA zeolite specimen, characterized by a three-dimensional network of pores consisting of three families of 12-ring interconnected channels [57]. The specimen here illustrated was characterized by a silica-to-alumina ratio = 4.9, corresponding to a distribution of A1 atoms per unit... 

Properties. SUica gel (see Eig. 8) is a coherent, rigid, continuous three-dimensional network of spherical particles of coUoidal sUica. Both sUoxane, —Si—O—Si—, and sUanol, —Si—O—H, bonds are present in the gel stmcture. The pores are intercoimected and fUled with water and/or alcohol from the hydrolysis and condensation reactions (40). A hydrogel is a gel in which the pores are filled with water. A xerogel is a gel from which the hquid medium... 

Normally, an exchanger has many open areas of variable size and shape that are altogether called pores. Only a few inorganic exchangers contain pores of uniform cross section. So, the exchangers exhibit a three-dimensional network of channels with irregular size. 

The pore geometry of the majority of catalysts consists of an interconnected three-dimensional network of... 

The pore space is treated as a lattice of voids interconnected by necks in a three-dimensional network. The pore volume and surface are assumed to be concentrated either in voids (46) or in necks (44,45). Active sites are uniformly distributed on the catalyst surface. 

Further, Imdakm and Matsuura [61] have developed a Monte Carlo simulation model to smdy vapor permeation through membrane pores in association with DCMD, where a three-dimensional network of interconnected cylindrical pores with a pore size distribution represents the porous membrane. The network has 12 nodes (sites) in every direction plus boundary condition sites (feed and permeate). The pore length / is assumed to be of constant length (1.0 p,m), however, it could have any value evaluated experimentally or theoretically [62]. 

The OMC structure also depends on the polymerization step. As mentioned above, the polymerization of the precursor adsorbed in the pore system of the matrix is catalyzed by acids. Different synthesis procedures were developed. For example, an acid solution can be added to the reaction mixture. In this case, the polymerization will take place throughout the entire pore system of the matrix. The resulting OMC can be described as a three-dimensional network of interconnected carbon rods. An example is CMK-3, already presented in Fig. 18.1. In this OMC, parallel-arranged carbon rods with a diameter of approximately 5 nm are connected by narrower carbon rods. The narrow carbon rods were formed in micropores that connect the mesopores of the SBA-15 silica matrix [21]. In an alternative synthesis procedure, a matrix with acid sites on the pore walls (e.g., an aluminosilicate) can be used. In this case, the polymerization of the precursor takes place on the mesopore walls and a carbon film is formed there, whereas the much narrower micropores are entirely filled with the polymerization product. Thus, after pyrolysis and removal of the matrix, the OMC consists of interconnected nanopipes, as opposed to interconnected carbon rods. An example is CMK-5. This OMC is synthesized in an acid form of the matrix used for the synthesis of CMK-3. Thus, CMK-5 consists of interconnected carbon nanopipes, arranged in the same fashion as the carbon rods of CMK-3 (Fig. 18.2) [22]. However, the pore system of these two OMCs differs. The pore system of CMK-3 consists of the voids in between the carbon rods, whereas in addition to these pores CMK-5 also has pores inside the nanopipes. 

In each of the above analyses, the pores were considered as parallel sets of large and small pores without interconnection between the separate sets. However, most void structures comprise a network in interconnected void spaces and "network effects" will diaate the potential implications of changes in pore structure. The generic influence of pore networks were analyzed by Beeckman and Froment22 based on modified Bethe tree two-dimensional networks. Based on this simulated analyses, the authors concluded that the nature of the deactivation does depend on the nature of the network structure. Sahami and Tsotsis employed percolation theory to analyze a three-dimensional network of interconnected pores and concluded that the void interconnectivity is crucial in determining the influence of network structure on the deactivation phenomena. 

After a significant amount of hydrolysis and condensation has taken place, a three-dimensional network of metal and oxygen forms within the sol (metal-oxygen colloids suspended in a liquid) and the viscosity of the sol increases. As condensation continues, the sol transforms into a nonfluid gel and an interconnected and fairly rigid 3-D network extends throughout the entire sample container. The resulting wet gel is an amorphous, porous metal oxide with water and alcohol in its mesoscopic pores. Typically, the solid phase is between 5 and 10% of the total volume. 

In contrast to MCM-41, the pore network of MCM-48 silica is three dimensional and highly interconnected. The strucmre of MCM-48 sdica belongs to the la 3 d space group, which also exists in the binary water/CTAB system (155). This interesting structure is viewed as a bicontinuous system which consists of two mutually intertwined three-dimensional networks of channels (Fig. 9.20 Reference 156). MCM-48 silica can be prepared in high phase purity via hydrothermal synthesis by mning the silica to CTAB ratio and other synthesis parameters, or at room temperamre... 

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