Pore connectivity

High catalytic activity and selectivity of silicalite-l/H-ZSM-5 composites must be caused by the direct pore-to-pore connection between H-ZSM-5 and silicalite-l as revealed by Fe-SEM and TEM [43]. The silicalite-l crystals were epitaxially grown on the surface of the H-ZSM-5 crystals. 

Sel et al.29 demonstrated that the pore shape and pore connectivity play the crucial role in the electrical conductivity of the functionalized silica channels. A sufficient connection between the mesopores is indispensable to allow sufficient functionalization, a facilitated electron hopping in the matrix, and a better accessibility of the electrode surface. 

In many cases the medium in which the molecules move is not homogeneous and the diffusion motion of the molecules is influenced by the structure of the medium. Examples are the diffusion of water and oil in porous rock or in water-oil emulsions. Many publications have shown that the NMR diffusion results can be used to quantitatively study the porous structure, like the determination of pore and droplet sizes, pore connectivity and pore hopping or of the surface to volume ratio of the pores. 

As discussed above, hysteresis loops can appear in sorption isotherms as result of different adsorption and desorption mechanisms arising in single pores. A porous material is usually built up of interconnected pores of irregular size and geometry. Even if the adsorption mechanism is reversible, hysteresis can still occur because of network effects which are now widely accepted as being a percolation problem [21, 81] associated with specific pore connectivities. Percolation theory for the description of connectivity-related phenomena was first introduced by Broad-bent et al. [88]. Following this approach, Seaton [89] has proposed a method for the determination of connectivity parameters from nitrogen sorption measurements. 

However, desorption follows the meniscus receding mechanism, and vaporization occurs only in pores connected to the vapor phase. As a result, pore C remains fiUed until pore B is emptied, and the sequence of evaporation is in fact B and C together followed by A. This mechanism can lead to very steep Type H2 hysteresis loops. Indeed, a common diagnostic feature of many hysteresis loops is that the steep region leading to the lower closure point occurs at nearly the same relative pressure. It is almost independent of the porous adsorbent, but mainly dependent on the adsorptive. In case of nitrogen this happens at a relative pressure p/po 0.4 [21]. 

Figure 11-10. a) Reduction of an oxide crystal, (A,B)0, resulting in internal precipitation. of A (schematic), b) Cross section of a (Ni,Mg)0 single crystal, reduced in H2/H20. Typical morphology of the reaction product if ANi0> 10%. Pores connect the reaction front with the external reducing gas. 

Downward movement of triazines may occur from percolating water carrying them to lower soil depths. Within well-structured soils with abundant macropores, triazines have been reported to move to deeper depths than in nonstructured soils with fewer pores. Increased permeability, percolation, and solute movement can result from increased porosity -especially in no-tillage systems where there is pore connectivity at the soil surface. Triazines can move to shallow ground-water by macropore flow in sandy soil if sufficient rainfall occurs shortly after they are applied (Ritter et al, 1994a, b). 

According to the IUPAC,79 the hysteresis loops are classified into four types from Type HI to Type H4. The Type HI loop in Figure 3 is characteristic of the mesoporous materials consisting of the pores with cylindrical pore geometry or the pores with high degree of pore size uniformity.88,89 Hence, the appearance of the HI loop on the adsorption isotherms for the porous solids generally indicates facile pore connectivity and relative narrow PSD. 

Many porous adsorbents give Type H2 hysteresis loop, but in such systems PSD or pore shape is not well-defined. Indeed, the H2 loop is especially difficult to interpret. In the past it was considered to be a result of the presence of the pores with narrow necks and wide bodies (ink-bottle pores), but it is now recognized that this provides an over-simplified picture and the pore connectivity effects must be taken into account.79... 

In this paper, we will consider only the dynamic aspects of this percolation problem, i.e., the stochastic distribution of velocities between the flow structures. To analyze a percolation process, it is useful to represent the scattering medium (i.e. the packed bed) by a lattice as depicted in Figure 2. The sites of the lattice correspond to the contact points between the particles whereas the bonds correspond to the pores connecting two neighbour contact points. The walls of these pores are delimited by the external surface of the particles. The percolation process is... 

D DM catalysts have a new pore structure consisting of crystalline domains of 8- and 12-ring pores connected by mesopores (5-10 nm). The presence of the latter enhances accessibility to the micropore regions without seriously compromising the shape-selective character of the catalyst. This combination of changes in acidity and pore structure transforms synthetic mordenites into highly active, stable and selective alkylation catalysts. 

Let us postulate that the condensate cannot leave a pore (or segment of a pore) at the Kelvin relative pressure unless there is a continuous channel of vapour leading to the adsorbent surface. It follows that the probability that a portion of the condensate will be trapped will depend on the nature of the pore network and the numerical and spatial distribution of pore size. Thus, a large amount of entrapment - and hence pronounced hysteresis - will be observed if a high proportion of the pore volume is only accessible through narrow channels with a relatively low level of pore connectivity. 

Q. To proceed further at this point one has to specify a pore model for the catalyst, and a model for the active site distribution. Froment and co-workers have examined a variety of cases such as single pore models (single-ended pores and pores open on both sides) with both deterministic and stochastic active site distributions, the bundle of parallel pores model and various tree-like models of the porous structure, which were earlier used by Pismen (40) to describe transport and reaction in porous systems. Such treelike models contain interconnected pores but lack any closed loops and are usually called Bethe networks or lattices. They are completely characterized by their coordination number Z, which is the number of pores connected to the same site of the network. 

For a fixed temperature the diffusion length is constant, while the introduction of pores permits the motion of positronium to the surface from deeper in the sample. For isolated and closed pores this change in range is determined by the size of the pores. When the pores connect, the length of the connected chain becomes the dominant value. As percolation is reached, this length rises sharply. 

The positron lifetime hovers around 0.5 ns ( ). All other lifetimes are due to positronium. The para-positronium (o) with nominally 0.125 ns and the smallest ortho positronium lifetime (A) of about 3.6 ns originate the cages inherent to MSSQ. This result agrees well with measurements on thick samples published earlier by Li et al. [23] The remaining three larger lifetimes originate from positronium in small (B) and large (7) closed pores and pores, connect to channels which link to the surface (Q open porosity). 

The PS micromodel, on the other hand, had fewer pore connections, and the pores were of more uniform size consequently, it was almost completely swept of liquid in the GDS foam flood (Test... 

The macropore diameter decreases by a fector of three from PKlll to PK118 (see Fig. 2). Notably, the nr values decrease from PKlll to PK118 with PK114 as an exception. This means that the pore connectivity diminishes with increasing macropore diameter. 

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