Pore networks

The size of the crystallites forming the network of membrane pores and the porous nature of the network affect the permeation and separation properties of porous inorganic membranes. These features will be discussed below. 

From the mercury porosimetry data, porosity can be calculated. A higher porosity means a more open pore structure, thus generally providing a higher permeability of the membrane. Porous inorganic membranes typically show a porosity of 20 to 60% in the separative layer. The porous support layers may have higher porosities. 

The internal surface area of a porous inorganic membrane is often significantly affected by the heat treatment temperature. Leenaars, Keizer and Burggraaf (1984) have shown that, even if the crystallite size of the membrane precursor particles remains essentially the same (from the X-ray line-broadening measurements), the surfaee area of a transition-phase alumina membrane decreases with increasing calcination temperature. Con- 

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To be specific let us have in mind a picture of a porous catalyst pellet as an assembly of powder particles compacted into a rigid structure which is seamed by a system of pores, comprising the spaces between adjacent particles. Such a pore network would be expected to be thoroughly cross-linked on the scale of the powder particles. It is useful to have some quantitative idea of the sizes of various features of the catalyst structur< so let us take the powder particles to be of the order of 50p, in diameter. Then it is unlikely that the macropore effective diameters are much less than 10,000 X, while the mean free path at atmospheric pressure and ambient temperature, even for small molecules such as nitrogen, does not exceed... 

It appears that a loose interpretation of this type may be the origin of a discrenancy found by Otanl and Smith [59] in attempting to apply effective diffusivities from Wakao and Smith s [32] isobaric diffusion data to measurements on a chemically reacting system. This was pointed out by Steisel and Butt [60], and further pursued to the point of detailed computer modeling of a particular pore network by Wakao and Nardse [61]. 

Fig. 3J4 Entrapment of mercury in a pore network. (Courtesy Androutsopoulos and Mann." )...

Dehydration or Chemical Stabilization. The removal of surface silanol (Si—OH) bonds from the pore network results in a chemically stable ultraporous soHd (step F, Fig. 1). Porous gel—siHca made in this manner by method 3 is optically transparent, having both interconnected porosity and sufficient strength to be used as unique optical components when impregnated with optically active polymers, such as fiuors, wavelength shifters, dyes, or nonlinear polymers (3,23). 

Reaction kinetics at phase houndaiies. Rates of adsorption and desorption in porous adsorbents are generally controlled by mass transfer within the pore network rather than by the kinetics of sorption at the surface. Exceptions are the cases of chemisorption and affinity-adsorption systems used for biological separations, where the kinetics of bond formation can be exceedingly slow. 

In these equations, D, is the diffusivity in the subparticles, and Dp is the diffusivity in the pore network formed by the subparticles. 

Permeability is defined as a measure of a rock s ability to transmit fluids. In addition to a rock s being porous, sedimentary rock can also be permeable. Permeability refers to the property of a rock that allows fluids to flow through its pore network at practical rates under reasonable pressure differentials. The quantitative definition of permeability was first given in an empirical relationship developed by the French hydrologist Henry D Arcy who studied the flow of water through unconsolidated sands [31]. 

Figure 10.1 Framework types of some well-known zeolites with their specific pore size and pore network dimensions [5].

Figure 4.1. Representation of the pore structure of HZSM5, one of the most important zeolites industrially. The vertical cylinders represent one pore network, and the other cylinders an interconnecting network. The narrow pores, and their almost complete uniformity, means that only some molecules can enter. Others are excluded, and cannot react at the active sites, which are found within the structure. Thus, the reactivity of a molecule is determined by its shape and size, rather than by its electronic properties. Such a situation is almost unique, with the only exception being enzymes, where molecules must fit into the enzyme active site in order to react.

The advantages of this type of system are obvious the pore space is of sufficient complexity to represent any natural or technical pore network. As the model objects are based on computer generated clusters, the pore spaces are well defined so that point-by-point data sets describing the pore space are available. Because these data sets are known, they can be fed directly into finite element or finite volume computational fluid dynamics (CFD) programs in order to simulate transport properties [7]. The percolation model objects are taken as a transport paradigm for any pore network of major complexity. 

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]. 

The situation is completely different for mass transfer within the pore network of monolithic compounds. Here mass transfer can occur both on the pore surface or in the pore volume and molecular exchange between these two states of mobility can occur anywhere within the pore system, being completely uncorrelated with the respective diffusion paths. As a consequence, Eq. (3.1.11) is applicable, without any restrictions, to describing long-range diffusion in the pore space. Equation (3.1.14) is thus obtained,... 

The pore geometry described in the above section plays a dominant role in the fluid transport through the media. For example, Katz and Thompson [64] reported a strong correlation between permeability and the size of the pore throat determined from Hg intrusion experiments. This is often understood in terms of a capillary model for porous media in which the main contribution to the single phase flow is the smallest restriction in the pore network, i.e., the pore throat. On the other hand, understanding multiphase flow in porous media requires a more complete picture of the pore network, including pore body and pore throat. For example, in a capillary model, complete displacement of both phases can be achieved. However, in real porous media, one finds that displacement of one or both phases can be hindered, giving rise to the concept of residue saturation. In the production of crude oil, this often dictates the fraction of oil that will not flow. 

On this basis the porosity and surface composition of a number of silicas and zeolites were varied systematically to maximize retention of the isothizolinone structures. For the sake of clarity, data is represented here for only four silicas (Table 1) and three zeolites (Table 2). Silicas 1 and 3 differ in their pore dimensions, these being ca. 20 A and 180 A respectively. Silicas 2 and 4, their counterparts, have been calcined to optimise the number and distribution of isolated silanol sites. Zeolites 1 and 2 are the Na- and H- forms of zeolite-Y respectively. Zeolite 3 is the H-Y zeolite after subjecting to steam calcination, thereby substantially increasing the proportion of Si Al in the structure. The minimum pore dimensions of these materials were around 15 A, selected on the basis that energy-minimized structures obtained by molecular modelling predict the widest dimension of the bulkiest biocide (OIT) to be ca. 13 A, thereby allowing entry to the pore network. 

This encapsulation procedure gives the highest activity for the lipases. The lecithin/ amines mixture structuring the pore network leads to a suitable phospholipids bilayer-like environment, which avoids the necessity to create an interface by substrate assembly. Monduzzi and coworkers compared the activity of lipase that was immobilized on SBA-15 physically, or chemically with glutardialdehyde [200]. 

The first phase in the process is the formation of the sol . A sol is a colloidal suspension of solid particles in a liquid. Colloids are solid particles with diameters of 1-100 nm. After a certain period, the colloidal particles and condensed silica species link to form a gel - an interconnected, rigid network with pores of submicrometer dimensions and polymeric chains whose average length is greater than one micrometer. After the sol-gel transition, the solvent phase is removed from the interconnected pore network. If removed by conventional drying such as evaporation, so-called xerogels are obtained, if removed via supercritical evacuation, the product is an aerogel . 

The above behavior of narrow-pore supported cobalt catalysts toward co-fed water can also be explained in terms of relative size of cobalt clusters, pore network of support, expected location of cobalt clusters within the pore network, and relative differences in the residence time of water vapor within and outside the... 

A very convenient method to quantitatively determined the number of Bronsted add sites in the often used photochemical nano-vessels, zeolites X and Y, is available.28 This method take advantage of indicator/probe molecules which undergo an intense color change upon protonation within the zeolite pore network. The amount of a base necessary to quench the color change gives a direct measure of the concentration of acidic sites. The base used to titrate the Bronsted sites must be more basic than the probe molecule and sufficiently basic to be completely protonated. 

Catalysis by sol gel doped silica-based materials has become in the last 20 years a prominent tool to synthesize a vast number of useful molecules both in the laboratory and in industrial plants.12 The underlying basic concept of all sol-gel applications is unique one or more host molecules are entrapped by a sol-gel process within the cages of an amorphous metal oxide where they are accessible to diffusible reactants through the inner pore network, which leads to chemical interactions and reactions (Figure 5.3). 

It is evident that the pore network is modified only by the presence of PNPs in the structure, since the light dispersion becomes so... 

Zeolite structures are designated by a three capital-letter code, for example, FAU stands for the faujasite structure, to which the well-known X and Y zeolites belong. A very useful short notation is used for the description of the pore system(s) each pore network is characterized by the channel directions, the number of atoms (in bold type) in the apertures, the crystallographic free diameter of the apermre (in A), asterisks (1, 2, or 3) indicating whether the systems is one-, two-, or three-dimensional. To completely specify the pore system, the eventual presence of cages (or channel intersections) should be indicated, along with their... 

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