Pore Size distribution: relation

The relation between the dusty gas model and the physical structure of a real porous medium is rather obscure. Since the dusty gas model does not even contain any explicit representation of the void fraction, it certainly cannot be adjusted to reflect features of the pore size distributions of different porous media. For example, porous catalysts often show a strongly bimodal pore size distribution, and their flux relations might be expected to reflect this, but the dusty gas model can respond only to changes in the... 

Che pore size distribution and Che pore geometry. Condition (iil). For isobaric diffusion in a binary mixture Che flux vectors of Che two species must satisfy Graham s relation... 

Of course, these shortcomings of the Wakao-Smith flux relations induced by the use of equations (8.7) and (8.8) can be removed by replacing these with the corresponding dusty gas model equations, whose validity is not restricted to isobaric systems. However, since the influence of a strongly bidisperse pore size distribution can now be accounted for more simply within the class of smooth field models proposed by Feng and Stewart [49], it is hardly worthwhile pursuing this."... 

The pore size distribution function (a) appears parametrically in the flux relations of Feng and Stewart, so their models certainly cannot be completely predictive in nature unless this distribution is known. It is... 

In the pioneer work of Foster the correction due to film thinning had to be neglected, but with the coming of the BET and related methods for the evaluation of specific surface, it became possible to estimate the thickness of the adsorbed film on the walls. A number of procedures have been devised for the calculation of pore size distribution, in which the adsorption contribution is allowed for. All of them are necessarily somewhat tedious and require close attention to detail, and at some stage or another involve the assumption of a pore model. The model-less method of Brunauer and his colleagues represents an attempt to postpone the introduction of a model to a late stage in the calculations. 

A microscopic description characterizes the structure of the pores. The objective of a pore-structure analysis is to provide a description that relates to the macroscopic or bulk flow properties. The major bulk properties that need to be correlated with pore description or characterization are the four basic parameters porosity, permeability, tortuosity and connectivity. In studying different samples of the same medium, it becomes apparent that the number of pore sizes, shapes, orientations and interconnections are enormous. Due to this complexity, pore-structure description is most often a statistical distribution of apparent pore sizes. This distribution is apparent because to convert measurements to pore sizes one must resort to models that provide average or model pore sizes. A common approach to defining a characteristic pore size distribution is to model the porous medium as a bundle of straight cylindrical or rectangular capillaries (refer to Figure 2). The diameters of the model capillaries are defined on the basis of a convenient distribution function. 

Permeability is the conductance of the medium and has direct relevance to Darcy s law. Permeability is related to the pore size distribution, since the distribution of the sizes of entrances, exits and lengths of the pore walls constitutes the primary resistance to flow. This parameter reflects the conductance of a given pore structure. 

Another property of importance is the pore volume. It can be measured indirectly from the adsorption and/or desorption isotherms of equilibrium quantities of gas absorbed or desorbed over a range of relative pressures. Pore volume can also be measured by mercury intrusion techniques, whereby a hydrostatic pressure is used to force mercury into the pores to generate a plot of penetration volume versus pres- sure. Since the size of the pore openings is related to the pressure, mercury intrusion techniques provide information on the pore size distribution and the total pore volume. 

The selectivity of a gel, defined by the incremental increase in distribution coefficient for an incremental decrease in solute size, is related to the width of the pore size distribution of the gel. A narrow pore size distribution will typically have a separation range of one decade in solute size, which corresponds to roughly three decades in protein molecular mass (Hagel, 1988). However, the largest selectivity obtainable is the one where the solute of interest is either totally excluded (which is achieved when the solute size is of the same order as the pore size) or totally included (as for a very small solute) and the impurities differ more than a decade in size from the target solute. In this case, a gel of suitable pore size may be found and the separation carried out as a desalting step. This is very favorable from an operational point of view (see later). 

A range of individual pore size PLgel packing materials is produced and their pore size distribution is conveniently represented by a SEC calibration curve as illustrated in Fig. 12.1. It should be pointed out that the descriptors used for the different pore sizes, 50 A, 100 A, and so on, are not the actual pore sizes of the beads but relate to the size of a polystyrene molecule just excluded from the packing material. This nomenclature comes from the original work carried out by Moore (3) and should only be viewed in the context of differentiating... 

Most size exclusion chromatography (SEC) practitioners select their columns primarily to cover the molar mass area of interest and to ensure compatibility with the mobile phase(s) applied. A further parameter to judge is the column efficiency expressed, e.g., by the theoretical plate count or related values, which are measured by appropriate low molar mass probes. It follows the apparent linearity of the calibration dependence and the attainable selectivity of separation the latter parameter is in turn connected with the width of the molar mass range covered by the column and depends on both the pore size distribution and the pore volume of the packing material. Other important column parameters are the column production repeatability, availability, and price. Unfortunately, the interactive properties of SEC columns are often overlooked. 

Porous packed systems represent in addition to the hydrodynamic effect, the possibility for separation due to size-related exclusion of particles from the pores, essentially LEG. In this section a brief overview of some of o ir more recent results pertaining to the question of pore size distribution effects will be given, fore detailed discussions are presented elsewhere (23>2U). 

Hydraulic conductivity is one of the characteristic properties of a soil relating to water flow. The movement of water in soil depends on the soil structure, in particular its porosity and pore size distribution. A soil containing more void space usually has a higher permeability. Most consolidated bedrocks are low in permeability. However, rock fractures could create a path for water movement. 

High porosity carbons ranging from typically microporous solids of narrow pore size distribution to materials with over 30% of mesopore contribution were produced by the treatment of various polymeric-type (coal) and carbonaceous (mesophase, semi-cokes, commercial active carbon) precursors with an excess of KOH. The effects related to parent material nature, KOH/precursor ratio and reaction temperature and time on the porosity characteristics and surface chemistry is described. The results are discussed in terms of suitability of produced carbons as an electrode material in electric double-layer capacitors. 

Studies have shown that the pore size distribution can influence liquid penetration into tablets [28,29,52]. The accessibility of water vapor to tablet components has been related to chemical stability, especially in the case of hydrolyzable drugs [28]. Solvent penetration, which can affect tablet disintegration and dissolution, has been related to pore size [52]. 

The silica carrier of a sulphuric acid catalyst, which has a relatively low surface area, serves as an inert support for the melt. It must be chemically resistant to the very corrosive pyrosulphate melt and the pore structure of the carrier should be designed for optimum melt distribution and minimum pore diffusion restriction. Diatomaceous earth or synthetic silica may be used as the silica raw material for carrier production. The diatomaceous earth, which is also referred to as diatomite or kieselguhr, is a siliceous, sedimentary rock consisting principally of the fossilised skeletal remains of the diatom, which is a unicellular aquatic plant related to the algae. The supports made from diatomaceous earth, which may be pretreated by calcination or flux-calcination, exhibit bimodal pore size distributions due to the microstructure of the skeletons, cf. Fig. 5. 

These correlations are applicable to all the systems employed, provided that the initial maximum values of the transfer coefficients are used. This suggests that the extrapolation gives the true gas-film coefficient. This is borne out by the fact that the coefficient remained unchanged for a considerable period when the pores were large, though it fell off extremely rapidly with solids with a fine pore structure. It was not possible, to relate the behaviour of the system quantitatively to the pore size distribution however. 

Thermoporometry [107] has also been used in evaluating resin porosity [108] and in effect gives information on the solvent wetted state of resins. The technique exploits the phenomenon that the freezing point of a liquid is depressed when it is confined in pores of small radius. Calorimetric measurements on solvent imbibed resins at increasingly reduced temperatures allows a distribution curve to be generated. This in turn can be related to a pore size distribution. The technique is not routine nor widely practiced and more information is available in reference [17]. 

Maceral behaviour and interaction on carbonization Mesophase development during carbonization Relation of coke strength (stability) to coke texture, pore size distribution, pore wall thickness... 

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