Description pore structure

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. 

Scanning electron microscopy and other experimental methods indicate that the void spaces in a typical catalyst particle are not uniform in size, shape, or length. Moreover, they are often highly interconnected. Because of the complexities of most common pore structures, detailed mathematical descriptions of the void structure are not available. Moreover, because of other uncertainties involved in the design of catalytic reactors, the use of elaborate quantitative models of catalyst pore structures is not warranted. What is required, however, is a model that allows one to take into account the rates of diffusion of reactant and product species through the void spaces. Many of the models in common use simulate the void regions as cylindrical pores for such models a knowledge of the distribution of pore radii and the volumes associated therewith is required. 

Since we don t usually know enough about pore structure and other matters to assess the relative importance of these modes, we fall back on the phenomenological description of the rate of diffusion in terms of Fick s (first) law. According to this, for steady-state diffusion in one dimension (coordinate x) of species A, the molar flux, NA, in, say, mol m-2 (cross-sectional area of diffusion medium) s-1, through a particle is... 

The separator pore structure is usually very complex. It consists of a porous network of interconnected pores, which are filled with liquid electrolyte. A complete description of the pore structure would require a very intricate model. Simulations are only practically possible if the structure is represented by a simplified quasi-continuum involving a few param-... 

The parameters of the pore structure, such as surface area, pore volume, and mean pore diameter, can generally be used for a formal description of the porous systems, irrespective of their chemical composition and their origin, and for a more detailed study of the pore formation mechanism, the geometric aspects of pore structure are important. This picture, however, oversimplifies the situation because it provides a pore uniformity that is far from reality. Thorough attempts have been made to achieve the mathematical description of porous matter. Researchers discussed the cause of porosity in various materials and concluded that there are two main types of material based on pore structure that can be classified as corpuscular and spongy systems. In the case of the silica matrices obtained with TEOS and other precursors, the porous structure seems to be of the corpuscular type, in which the pores consist of the interstices between discrete particles of the solid material. In such a system, the pore structure depends on the pores mutual arrangements, and the dimensions of the pores are controlled by the size of the interparticle volumes (1). 

On the other hand, it is impossible to apply the SP method to the correct description of gas adsorption in the micropores, since the adsorption in the micropores does not occur by multilayer adsorption but by micropore volume filling process. In this case, the pore fractal dimension gives a physical importance for the description of structural heterogeneity of the microporous solids. Terzyk et al.143"149 have intensively investigated the pore fractal characteristics of the microporous materials using gas adsorption isotherms theoretically simulated. 

For the description of this flow, the Carman-Kozeny expression [16] can be applied, since the Hagen-Poiseuille equation is not valid, given that usually inorganic macroporous and mesoporous membranes are prepared by the sinterization of packed quasispherical particles, which develop a random pore structure [19]. In this case, the Carman-Kozeny factor for a membrane formulated with pressed spherical particles is [74]... 

A = constant descriptive of pore structure chosen to fit data at p/p, = 0.89 (250 Circles, observed rates at 25C Crosses, observed rates at 35C... 

Although the current permeability model properly reflects many of the important features of foam displacement, the authors acknowledge its limitations in several respects. First, the open pore, constricted tube, network model is an oversimplification of true 3-D porous structures. Even though communication was allowed between adjacent pore channels, the dissipation associated with transverse motions was not considered. Further, the actual local displacement events are highly transient with the bubble trains moving in channels considerably more complex than those used here. Also, the foam texture has been taken as fixed the important effects of gas and liquid rates, displacement history, pore structure, and foam stability on in situ foam texture were not considered. Finally, the use of the permeability model for quantitative predictions would require the apriori specification of fc, the fraction of Da channels containing flowing foam, which at present is not possible. Obviously, such limitations and factors must be addressed in future studies if a more complete description of foam flow and displacement is to be realized. 

In the modern chemical and biochemical research porous materials play an irreplaceable role. The mass transport resistance in the pore structure of the porous solids significantly affects rates of transport processes, which take place inside the porous material (Keil [1], Haugaard and Livbjerg [2], Capek and Seidel-Morgernstern [3]). Inclusion of transport processes into the description of the whole process is essential when reliable simulations/predictions have to be made. 

Cylindrical pellets of four industrial and laboratory prepared catalysts with mono- and bidisperse pore structure were tested. Selected pellets have different pore-size distribution with most frequent pore radii (rmax) in the range 8 - 2500 nm. Their textural properties were determined by mercury porosimetry and helium pycnometry (AutoPore III, AccuPyc 1330, Micromeritics, USA). Description, textural properties of catalysts pellets, diameters of (equivalent) spheres, 2R, (with the same volume to geometric surface ratio) and column void fractions, a, (calculated from the column volume and volume of packed pellets) are summarized in Table 1. Cylindrical brass pellets with the same height and diameter as porous catalysts were used as nonporous packing. 

The relevance of the second approach stems from the possibility to use the same pore-structure model as used in description of the process in question (counter-current (isobaric) diffusion of simple gases, permeation of simple gases under steady-state or dynamic conditions, combined diffusion and permeation of gases under dynamic conditions, etc.). 

Today two models are available for description of combined (diffusion and permeation) transport of multicomponent gas mixtures the Mean Transport-Pore Model (MTPM)[21,22] and the Dusty Gas Model (DGM)[23,24]. Both models enable in future to connect multicomponent process simultaneously with process as catalytic reaction, gas-solid reaction or adsorption to porous medium. These models are based on the modified Stefan-Maxwell description of multicomponent diffusion in pores and on Darcy (DGM) or Weber (MTPM) equation for permeation. For mass transport due to composition differences (i.e. pure diffusion) both models are represented by an identical set of differential equation with two parameters (transport parameters) which characterise the pore structure. Because both models drastically simplify the real pore structure the transport parameters have to be determined experimentally. 

The aim of this study is to compare pore structure characteristics of two porous catalysts determined by standard methods of textural analysis (physical adsorption of nitrogen and mercury porosimetry) and selected methods for obtaining parameters relevant to transport processes (multicomponent gas diffusion and permeation of simple gases). MTPM was used for description of these processes. 

Our group has combined the EVB model with a complete atomistic description of the Nafion subphase [76]. The pore structure obtained (see Fig. 4) supports the disordered Nafion model by Yeager and Steck [49] more than the symmetrical one by Gierke [48]. Activation energies obtained for proton transport at A = 5 and A = 10 are similar to the ones discussed above for the simpler pore model. This is not unexpected since the total simulation time... 

In this section these relationships will be explored in more detail with particular emphasis on the porous properties of membranes and their characterisation. Firstly we will present the general definitions and terminology used to describe porous media. The origin of porosity in inorganic materials will also be outlined and related to a quantitative description of pore structures in... 

The measurement of the permeability of non adsorbed gases is classically used to determine the range of pore size in membranes (macro, meso or micropores). Indeed by plotting the permeability as a function of gas pressure, a straight line is usually obtained whose slope gives an indication of the gas transport mechanism in the membrane. A quantitative description of pore structure can be attempted from the results. 

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