Connected pore

Intraparticle convection can also occur in packed beds when the adsorbent particles have very large and well-connected pores. Although, in general, bulk flow through the pores of the adsorbent particles is only a small frac tion of the total flow, intraparticle convection can affec t the transport of veiy slowly diffusing species such as macromolecules. The driving force for convec tion, in this case, is the... 

Specimens of NR ABS/(Octa -I- AO) heat-treated at 350°-400°C developed brittleness of connected pores, whereas VO ABS (Octa -1- AO -I- EPDM), similarly treated, was tougher with large elongated pores about twice the size of the non-treated specimen. Such behavior suggests an intumescent effect of EPDM, i.e. the development of a thick porous surface layer, inhibiting the diffusion of flammable products of plastic degradation towards the gas phase and heat transfer into the plactic mass. 

The quantity of water that can be retrieved from a medium is related to size and shape of the connected pore spaces within that medium. The quantity of water that can be freely drained from a unit volume of porous medium is referred to as the specific yield. The volume of water retained in the medium by capillary and surface active forces is called the specific retention. The sum of specific retention and specific yield is equal to the effective porosity (see Table 3.4). Neither term has a time value attached. Drainage can occur over long periods (i.e., weeks or months). 

Water flow through unsaturated soil is controlled by the same forces as capillary action and water retention (i.e., adhesion, gravity, and surface tension). Flow can occur only when the water phase is continuous from pore to pore. If gravity is the controlling force, downward flow will occur according to Darcy s law in direct proportion to the percentage of water-filled, connected pores. For example, if only half the pores in a cross section are water filled, the flow through that section will be half of that predicted by Q- K1A. 

For a system which consists of a porous matrix which Is purely partitioning, all of the Interstitial capillaries will have connected pores, f 1, and all of the pores will partition particles, ij = 1, thus Equation 26 becomes... 

Highly porous membranes with an inter-connected pore structure were produced using this solvent-casting and particulate-leaching technique (Fig. 4a, b). The porosity of porous PLLA membranes could be controlled by varying the amount of salt used to construct the composite material (Fig. 5a). 

Figure 6.1 Schematic of laminate lay-up. Insert shows serpentine path that matrix resin and voids might take through connected pores formed by the graphite fibers. Each ply is actually many more fibers thick than is shown...

The development of mesoporous materials with more or less ordered and different connected pore systems has opened new access to large pore high surface area zeotype molecular sieves. These silicate materials could be attractive catalysts and catalyst supports provided that they are stable and can be modified with catalytic active sites [1]. The incorporation of aluminum into framework sites of the walls is necessary for the establishment of Bronsted acidity [2] which is an essential precondition for a variety of catalytic hydrocarbon reactions [3], Furthermore, ion exchange positions allow anchoring of cationic transition metal complexes and catalyst precursors which are attractive redox catalytic systems for fine chemicals [4]. The subject of this paper is the examination of the influence of calcination procedures, of soft hydrothermal treatment and of the Al content on the stability of the framework aluminum in substituted MCM-41. The impact on the Bronsted acidity is studied. 

Lens-Type Traps. These form in limestone and sand. In this type of trap the reservoir is sealed in its upper regions by abrupt changes in the amount of connected pore space within a formation. A trap formed in sand is shown in Fig, 7(a). An example is the Burbank Field in Osage County, Oklahoma. This type of trap may occur in sandstones where irregular deposition of sand and shale occurred at the time the formation was laid down. In these cases, oil is confined within the porous parts of the rock hy the nonporous parts of rock surrounding it. A lens-type trap formed in limestone is shown in Fig. 7(b). In limestone formations there are frequent areas of high porosity with a tendency to form traps. Examples of limestone reservoirs of this type are found in the limestone fields of West Texas. 

Pore space a small hole in reservoir rock that contains fluid or fluids a four inch cube of reservoir rock may contain millions of inter-connected pore... 

The figure legend reads Model of the unidirectional diffusion of dye between coupled oligodendrocytes and astrocytes, based on differences in connection pore diameter. Like a fish in a fish trap, dye molecules (black circles) can pass from an astrocyte to an oligodendrocyte (A) but not back in the other direction (B). ... 

The third relaxation process is located in the low-frequency region and the temperature interval 50°C to 100°C. The amplitude of this process essentially decreases when the frequency increases, and the maximum of the dielectric permittivity versus temperature has almost no temperature dependence (Fig 15). Finally, the low-frequency ac-conductivity ct demonstrates an S-shape dependency with increasing temperature (Fig. 16), which is typical of percolation [2,143,154]. Note in this regard that at the lowest-frequency limit of the covered frequency band the ac-conductivity can be associated with dc-conductivity cio usually measured at a fixed frequency by traditional conductometry. The dielectric relaxation process here is due to percolation of the apparent dipole moment excitation within the developed fractal structure of the connected pores [153,154,156]. This excitation is associated with the selfdiffusion of the charge carriers in the porous net. Note that as distinct from dynamic percolation in ionic microemulsions, the percolation in porous glasses appears via the transport of the excitation through the geometrical static fractal structure of the porous medium. 

Mid-temperature process II This process extends over mid-range temperatures (300-400 K) and over low to moderate frequencies (up to 105 Hz). The mid-temperature process was associated with the percolation of charge excitation within the developed fractal structure of connected pores at low... 

Since these centers are distributed in the pore volume, the excitation transmits through the volume and is not related to the hydration centers located on the pore surface of the connective pores. Due to the large number of hydration centers, and the short distance between the neighboring centers, the path can be approximated by a line with a fractal dimension close to unity (see Fig. 29a). 

In this chapter it will be shown with numerous examples how information on open versus closed porosity, the total porosity, the pore sizes and a measure of the average length of connected pores can be measured with varying degrees of ease. Some of these parameters can be obtained from alternate methods. However, none can provide depth dependent profiles of the parameter without microtoming the sample. No special sample preparation is required. A sample investigated by positrons could easily be reinserted in a device production line to correlate results from positron measurements with device performance. 

A simple fit of the data with the product of an exponential association and an exponential decay to estimate the escape depth, overestimates the escape depth by folding the positron implantation profile and diffusion into the fitting parameters [30], A more appropriate numerical fitting method based on the diffusion equation was used to take both the implantation profile and diffusion into account [31]. When it is applied to the 3-to-2 photon ratio data suitable absorbing boundary conditions need to be included. The results for the escape depth are shown in Figure 7.8 [30]. In addition to the diffusionlike motion of positronium in connected pores, positrons and positronium diffuse to the pores. 

Figure 7.7 Schematic of the behavior of positronium in porous materials from isolated pores (top) to connected pores (middle) and totally open porosity (bottom). Connected pores are linked to the surface from a mean depth (middle left).

At porogen loads above 23% the escape depth rises more rapidly. Pores begin to connect at this porogen load. Percolation, when the first channel of connected pores spans the entire sample thickness, occurs at a higher load. This will be discussed later. In samples with porogen loads in excess of 50% the escape length becomes far greater than the sample thickness. 

At >29% porogen load the large pores feed the network of connected pores and at >40% porogen load the intensity of open porosity levels off because of the fast pick-off at the interface to the substrate, indicating that percolation occurs within the porogen load range of 29 to 40%. 

As well as in terms of their sizes, pores can also be classified on the basis of their shapes (cylinders, cones, slits, etc.) and on their connectivity pores may be open on only one side, but they may also run from one side of the adsorbent to the other and thereby be connected to each other. 

Values of t are obtained from adsorption data of the same adsorptive on a non-porous surface of the same nature, as in fig. 1.28. Substituting bulk values for y and, the pore size distribution a(p) or d(p) is obtainable. The occurrence of hysteresis implies that this gives different results for the two branches (ascending and descending) of the curve. In fact, the difference between the two metastable states is a characteristic of the type of pores. For non-connected pores, usually the downward curve is analyzed, because then the menisci have already been formed but for connected networks the ascending one may be more appropriate. After each stepwise change of p, the radius is calculated and from that the exposed pore volume and pore area. This yields a cumulative distribution which, if so desired, can be differentiated. 

For randomly connected pore networks, some of the supercritical pores (those larger than the molecular size) are connected only through subcritical pores (those smaller than the molecular size) and are therefore not accessible. In a given network, in which not all the pores can accommodate the probe moleeules, the number fraction of the pores that are available is... 

The sizes of the pores in this zone are also between dci and oo. However, some of the connecting pores have size between dci and dc2, and are accessible only to component 1. Zone IV... 

This zone also comprises pores having size between dc2 and oo, but the connecting pores have dimension smaller than dci. Consequently, pores in this zone are inaccessible to both compounds. Therefore, the amount of component 1 adsorbed in zones II-IV can be written... 

As already discussed, for the partial blocking of ZSM-5 by benzene, the experimental data discussed herein will be compared with two cases of an obstacle distribution (1) in the connecting pore segments or (2) in the channel intersections. Figure 33 compares the experimental results and the computer simulations. For pyridine, the self-diffusion data are in satisfactory agreement with the model for obstacles distributed over the channel intersections. One has to conclude, therefore, that the chemisorbed pyridine molecules and, thus, the Brpnsted acid sites, are localized near or even in the channel intersections. That is to say, all catalytically active centers are accessible for a reactant molecule in a channel intersection. 

The measured surface area consists of both external and internal area where internal surface area includes all cracks or connected pores that are deeper than they are wide, varying from subatomic defects to pores of extreme size (Gregg and Sing, 1982). For example, micropores are dehned as pores with radius <2 nm, mesopores as pores with radius from 2 nm to 50 nm, and macropores as those with pores of diameter >50 nm. The main distinction between internal and external surface is that advection can control transport to and away from external surface while diffusion must control transport for internal pore space (Hochella and Banheld, 1995). Porosity may be related to crystallization or replacement processes (Putnis, 2002). 

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