Cluster porosity

The values of the mass fractal dimension (obtained from SAXS [16]) show how the structure of the silicate polymers in the sol varies with the different routes these sols take to the same final dilution, H20/Si ratio and pH. The mass fractal dilnensions are considerably different. We would expect AAB, which is right at the borderline of D = 1.5 for Equation 2, to exhibit different behavior than B2 with D = 2.3. However, Table I shows that both sols exhibit an increase in porosity with sol age (once the pore-plugging species are burned out of B2). The reason for this is the tradeoff between cluster porosity and cluster interpenetration. B2 clusters are less porous but pack less efficiently than AAB clusters. This tradeoff is illustrated schematically in Figure 1. 

F ure 1. Schematic illustrating the tradeoff between cluster porosity and porosity between clusters with D. B2 clusters have high D (a) individual cluster porosity is low but (b) porosity between clusters is high. AAB clusters have low D (c) individual cluster porosity is high but (d) porosity between clusters is low. 

Figure 2.9.3 shows typical maps [31] recorded with proton spin density diffusometry in a model object fabricated based on a computer generated percolation cluster (for descriptions of the so-called percolation theory see Refs. [6, 32, 33]).The pore space model is a two-dimensional site percolation cluster sites on a square lattice were occupied with a probability p (also called porosity ). Neighboring occupied sites are thought to be connected by a pore. With increasing p, clusters of neighboring occupied sites, that is pore networks, begin to form. At a critical probability pc, the so-called percolation threshold, an infinite cluster appears. On a finite system, the infinite cluster connects opposite sides of the lattice, so that transport across the pore network becomes possible. For two-dimensional site percolation clusters on a square lattice, pc was numerically found to be 0.592746 [6]. 

Fig. 2.9.13 Qu asi two-dimensional random ofthe percolation model object, (bl) Simulated site percolation cluster with a nominal porosity map of the current density magnitude relative p = 0.65. The left-hand column refers to simu- to the maximum value, j/jmaK. (b2) Expedited data and the right-hand column shows mental current density map. (cl) Simulated NMR experiments in this sample-spanning map of the velocity magnitude relative to the cluster (6x6 cm2), (al) Computer model maximum value, v/vmax. (c2) Experimental (template) for the fabrication ofthe percolation velocity map. The potential and pressure object. (a2) Proton spin density map of an gradients are aligned along the y axis, electrolyte (water + salt) filling the pore space...

Full catalyst formulations consist of zeolite, metal and a binder, which provides a matrix to contain the metal and zeolite, as well as allowing the composite to be shaped and have strength for handling. The catalyst particle shape, size and porosity can impact the diffusion properties. These can be important in facile reactions such as xylene isomerization, where diffusion of reactants and products may become rate-limiting. The binder properties and chemistry are also key features, as the binder may supply sites for metal clusters and affect coke formation during the process. The binders often used for these catalysts include alumina, silica and mixtures of other refractory oxides. 

A model has been developed to describe the penetration of polydimethylsi-loxane (PDMS) into silica agglomerates [120]. The kinetics of this process depend on agglomerate size and porosity, together with fluid viscosity. Shearing experiments demonstrated that rupture and erosion break-up mechanisms occurred, and that agglomerates which were penetrated by polymer were less readily dispersed than dry clusters. This was attributed to the formation of a network between sihca aggregates and penetrated PDMS, which could deform prior to rupture, thereby inhibiting dispersion. 

The stable porosity of such MOFs is attributable to the structural properties of the metalcarboxylate clusters, where each metal ion is locked into place by the carboxylates, to create rigid units of simple geometry, referred to as SBUs [232], similarly to the case of inorganic zeolites. 

Shrinkage porosity Gas porosity Appears as a localized honeycomb or mottled pattern due to improper pouring temperature or alloy composition (e.g., A1 alloys) Round or elongated smooth, dark spots located individually or in clusters distributed randomly in the casting due to release of gas during solidification or evaporation of moisture from volatiles from the mold surface... 

Note that the fractal dimensions discussed here are the fractal dimensions of the excitation transfer paths connecting the hydration centers located on the inner surface of the pores. Due to the low humidity, all of the water molecules absorbed by the materials are bound to these centers. The paths of the excitation transfer span along the fractal pore surface and depict the backbone of clusters formed by the pores on a scale that is larger than the characteristic distance between the hydration centers on the pore surface. Thus the fractal dimension of the paths Dp approximates the real surface fractal dimension in the considered scale interval. For random porous structures, Dp can be also associated with the fractal dimension D, of the porous space Dp = Dr. Therefore, the fractal dimension Dp can be used for porosity calculations in the framework of the fractal models of the porosity. 

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