Pore concept

Type 1 isotherms, as will be demonstrated in Chapter 4, are characteristic of microporous adsorbents. The detailed interpretation of such isotherms is controversial, but the majority of workers would probably agree that the very concept of the surface area of a microporous solid is of doubtful validity, and that whilst it is possible to obtain an estimate of the total micropore volume from a Type I isotherm, only the crudest guesses can be made as to the pore size distribution. 

As already indicated in Section 3.1, the study of mesoporous solids is closely bound up with the concept of capillary condensation and its quantitative expression in the Kelvin equation. This equation is, indeed, the basis of virtually all the various procedures for the calculation of pore size... 

In very small pores the molecules never escape from the force field of the pore wall even at the center of the pore. In this situation the concepts of monolayer and multilayer sorption become blurred and it is more useful to consider adsorption simply as pore filling. The molecular volume in the adsorbed phase is similar to that of the saturated Hquid sorbate, so a rough estimate of the saturation capacity can be obtained simply from the quotient of the specific micropore volume and the molar volume of the saturated Hquid. 

This division is somewhat arbitrary siace it is really the pore size relative to the size of the sorbate molecule rather than the absolute pore size that governs the behavior. Nevertheless, the general concept is useful. In micropores (pores which are only slightly larger than the sorbate molecule) the molecule never escapes from the force field of the pore wall, even when ia the center of the pore. Such pores generally make a dominant contribution to the adsorptive capacity for molecules small enough to penetrate. Transport within these pores can be severely limited by steric effects, leading to molecular sieve behavior. 

During the adsorption or occlusion of various molecules, the micropores fill and empty reversibly. Adsorption in zeoHtes is a matter of pore filling, and the usual surface area concepts are not appHcable. The pore volume of a dehydrated zeoHte and other microporous soHds which have type 1 isotherms may be related by the Gurvitch rule, ie, the quantity of material adsorbed is assumed to fill the micropores as a Hquid having its normal density. The total pore volume D is given by... 

Chemical Potential. Equilibrium calculations are based on the equaHty of individual chemical potentials (and fiigacities) between phases in contact (10). In gas—soHd adsorption, the equiHbrium state can be defined in terms of an adsorption potential, which is an extension of the chemical potential concept to pore-filling (physisorption) onto microporous soHds (11—16). 

Process Concept The application of a direct elecdric field of appropriate polarity when filtering should cause a net charged-particle migration relative to the filter medium (electrophoresis). The same direct electric field can also be used to cause a net fluid flow relative to the pores in a fixed filter cake or filter medium (electroosmosis). The exploitation of one or both of these phenomena form the basis of conventional electrofiltration. 

The principal cathodic reaction on the upper surface of the membrane is the reduction of Cu " that is formed by the reaction of Cu with dissolved oxygen in the water these Cu ions are provided partly from the diffusion through the pores in the oxide membrane from within the pit and partly from those produced by cathodic reduction (equation 1.154). Lucey s theory thus rejects the conventional large cathode small anode relationship that is invoked to explain localised attack, and this concept of an electronically conducting membrane has also been used by Evans to explain localised attack on steel due to a discontinuous film of magnetite. 

This concept may be invoked to account for electrolyte formation in microcracks in a metal surface or in the re-entrant angle formed by a dust particle and the metal surface. More importantly, it can also explain electrolyte formation in the pores of corrosion product and hence the secondary critical humidity discussed earlier. Ferric oxide gel is known to exhibit capillary condensation characteristic and pore sizes deduced from measurements of its adsorptive capacity are of the right order of magnitude to explain a secondary critical relative humidity as70 7o for rusted steel . 

Equation 1 has as its basis the concept that diffusion, either through pores or to the gross surface of the catalyst particle, controls the reaction rate. When the control is strictly by the gas film surrounding the catalyst, one would have to convert Equation 1 to... 

The second case study. This involves all silica micro- and mesoporous SBA-15 materials. SBA-15 materials are prepared using triblock copolymers as structure-directing templates. Typically, calcined SBA-15 displays pore sizes between 50 and 90 A and specific surface areas of 600-700 m g with pore volumes of 0.8-1.2cm g h Application of the Fenton concept to mesoporous materials looks simpler since mass transfer would be much less limited. However, it is not straightforward because hydrolysis can take place in the aqueous phase. 

The concept of a T2 cut-off that partitions the relaxation time distribution between the pores which can be displaced and those that cannot does not always apply. An exception is when there is significant diffusional coupling between the micropores that retain water at a high capillary pressure and the macropores in close proximity to the microporous system [26, 27]. A spectral BVI model or a forward model has been suggested to interpret these systems [30, 31, 53]. 

Since it was proposed in the early 1980s [6, 7], spin-relaxation has been extensively used to determine the surface-to-volume ratio of porous materials [8-10]. Pore structure has been probed by the effect on the diffusion coefficient [11, 12] and the diffusion propagator [13,14], Self-diffusion coefficient measurements as a function of diffusion time provide surface-to-volume ratio information for the early times, and tortuosity for the long times. Recent techniques of two-dimensional NMR of relaxation and diffusion [15-21] have proven particularly interesting for several applications. The development of portable NMR sensors (e.g., NMR logging devices [22] and NMR-MOUSE [23]) and novel concepts for ex situ NMR [24, 25] demonstrate the potential to extend the NMR technology to a broad application of field material testing. 

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. 

S. Anferova, V. Anferov, D. G. Rata, B. Bliimich, J. Arnold, C. Clauser, P. Blunder, H. Raich 2004, (A mobile NMR device for measurements of porosity and pore size distribution of drilled core samples), Concepts Magn. Reson. Part B 23B (1), 26-32. 

This section specifically concerns itself with filters that must be used that do release fibers. It is noted that an additional filter with a maximum pore size of either 0.2 or 0.45 pm must also be used to finish the filtration. This is an absolute requirement with asbestos filters used because of the total concept of safety and effectiveness of the drug. This section simply sets the time limit for instituting good filtration procedures for parenteral products. 

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