Description of the Porous Structure

If the C-face (0001) is anodized, conical pores with triangular cross-sections are observed, but the pores are not arranged into arrays of planes (images not shown). The conical pores intersect, forming an overall spongy network. Even though their typical size is very similar to that 

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When modeling phenomena within porous catalyst particles, one has to describe a number of simultaneous processes (i) multicomponent diffusion of reactants into and out of the pores of the catalyst support, (ii) adsorption of reactants on and desorption of products from catalytic/support surfaces, and (iii) catalytic reaction. A fundamental understanding of catalytic reactions, i.e., cleavage and formation of chemical bonds, can only be achieved with the aid of quantum mechanics and statistical physics. An important subproblem is the description of the porous structure of the support and its optimization with respect to minimum diffusion resistances leading to a higher catalyst performance. Another important subproblem is the nanoscale description of the nature of surfaces, surface phase transitions, and change of the bonds of adsorbed species. 

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). 

The dual site-bond description (DD) of disordered stmctures [3] allows a proper modeling of the porous structure. In the context of this treatment, two kinds of alternately intercormected void entities are thought to conform the porous network, i.e. the sites (cavities) and the bonds (capillaries, necks). C bonds meet into a site and each bond is the link between two sites. Thus a twofold distribution of sites and bonds is required to construct a porous network. For simplicity, the size of each entity can be measured in terms of a quantity, R, defined as follows for sites, considered as hollow spheres, R is the radius of the sphere while for bonds, idealized as hollow cylinders open at both ends, R is the radius of the cylinder. Under the DD scheme, FgfR) andFg(R)are the size distribution density functions, for sites and bonds respectively, on a number of elements basis and normalized so that the probabilities to find a site or a bond having a size R or smaller are ... 

Except for the fullerenes, carbon nanotubes, nanohoms, and schwarzites, porous carbons are usually disordered materials, and cannot at present be completely characterized experimentally. Methods such as X-ray and neutron scattering and high-resolution transmission electron microscopy (HRTEM) give partial structural information, but are not yet able to provide a complete description of the atomic structure. Nevertheless, atomistic models of carbons are needed in order to interpret experimental characterization data (adsorption isotherms, heats of adsorption, etc.). They are also a necessary ingredient of any theory or molecular simulation for the prediction of the behavior of adsorbed phases within carbons - including diffusion, adsorption, heat effects, phase transitions, and chemical reactivity. 

In view of evidence such as that in Fig. 8-5, it is unlikely that detailed quantitative descriptions of the void structure of solid catalysts will become available. Therefore, to account quantitatively for the variations in rate of reaction with location within a porous catalyst particle, a simplified model of the pore structure is necessary. The model must be such that diffusion rates of reactants through the void spaces into the interior surface can be evaluated. More is said about these models in Chap. 11. It is sufficient here to note that in all the widely used models the void spaces are simulated as cylindrical pores. Hence the size of the void space is interpreted as a radius 2 of a cylindrical pore, and the distribution of void volume is defined in terms of this variable. However, as the example of the silver, catalyst indicates, this does not mean that the void spaces are well-defined cylindrical pores. 

Polyamino acids can be considered as models for conformational studies, providing an atomistic description of the secondary structural motifs typically found in proteins [30-39]. Two-dimensional hydrogen-bonded layers and columns in the structures of crystalline amino acids can mimic S-sheets and helices in proteins and amyloids [40 5], and can be compared with two-dimensional crystalline layers at interfaces [46-58]. Nano-porous structures of small peptides can mimic cavities in proteins [24, 59-63]. One can also prepare crystals in which selected functional groups and side chains are located with respect to each other in the same way, as at recognition sites of substrate-receptor complexes, and use the systems to simulate the mutual adaptation of components of the complex responsible for recognition. 

The pore size distribution in the carbon support is an important factor for a well performance of the catalyst. Pores in the nanometric scale are classified by lUPAC in three groups the micropores are those with diameters lower than 2 nm, the mesopores with diameters between 2 and 50 nm and the macropores with diameters larger than 50 run. Each pores size offers different benefits, the micropores produce materials with high surfaces area but could be inaccessible to liquid solutions or have slow mass transport. A material with mesopores has a lower surface area but better accessibility than those with micropores. FinaUy, materials with macropores show the lowest surface area, but they are easily accessible to liquid fuel. For this reason, the structured carbons, principally mesoporous carbon, have attracted considerable attention due to their potential application in the catalyst area, where the challenging is to favour the dispersion of catalyst and allow the accessibility of liquids that feed the anode side of a DMFC. In the following sections a description of different carbons support wdl be discussed stressing on the effect of the porous structure. 

Abstract The polymer electrolyte fuel cell (PEFC) consists of disparate porous media microstructures, e.g. catalyst layer, microporous layer, gas diffusion layer, as the key components for achieving the desired performance attributes. The microstmcture-transport interactions are of paramount importance to the performance and durability of the PEFC. In this chapter, a systematic description of the stochastic micro structure reconstmction techniques along with the numerical methods to estimate effective transport properties and to study the influence of the porous structures on the underlying transport behavior is presented. 

In brief, we have observed the scale-dependent diffusion of a tracer particle in a porous silica gel, although the explored medium is probably not fractal. At small scales, the diffusion is free at large scales it is slowed due to the tortuous paths of the porous structure. The crossover region corresponds to sizes comparable with the mesh size of the silica gels. The data support a structural description in terms of double porosity. 

Quantitative, nonempirical models of transport in porous materials require a more sophisticated description of the porous microstructure. For many materials the pore structure is stochastic, consisting of an ensemble of individual pores of random size distributed randomly throughout the material. Useful models of transport in these polymers can be based on percolation descriptions of porous media. Percolation descriptions have been used to describe fluid flow, electrical conduction, and phase transitions in random systems [26, 38]. 

The structure of the so-called "composite" membranes used in reverse osmosis is also much more complex than the conventional, simplistic description of the ultrathin semipermeable film deposited on and supported by a porous substrate. Most of these membranes which exhibit high flux and separation are composed of an anisotropic, porous substrate topped by an anisotropic, ultrathin permselective dense layer which is either highly crosslinked, or exhibits a progressively decreased hydrophilicity toward the surface. The basic difference between the conventional anisotropic (asymmetric) membrane and the thin film composite is that the latter might be... 

A model Is presented for char gasification with simultaneous capture of sulfur In the ash minerals as CaS. This model encompasses the physicochemical rate processes In the boundary layer, In the porous char, and around the mineral matter. A description of the widening of the pores and the eventual collapse of the char structure Is Included. The modeling equations are solved analytically for two limiting cases. The results demonstrate that pore diffusion effects make It possible to capture sulfur as CaS In the pores of the char even when CaS formation Is not feasible at bulk gas conditions. The model predictions show good agreement with experimentally determined sulfur capture levels and reaction times necessary to complete gasification. 

In porous media, in addition to the intrinsic properties of the diffusing species, the structure of the solid has an important Influence on the transport mechanisms. Any description of the pro-cesses taking place should account for these features and the... 

The effective-scale models have been most often used in the description of transport and reaction processes within the porous structure of catalysts. Such models are based on the introduction of an effective diffusion coefficient De, that is used in the analogy to the Fick s law for the description of diffusion... 

The diameter or the radius of the pores is one of the most important geometric characteristic of porous solids. In terms of lUPAC nomenclature, we can have macropores (mean pore size greater than 5 x 10 m), mesopores (between 5 x 10 and 2 x 10 m) and micropores (less than 2 x 10 m). The analysis of species transport inside the porous structure is very important for the detailed description of many unit operations or applications among them we can mention suspension filtration, solid drying and humidification, membrane processes (dialysis, osmosis, gaseous permeation. ), flow in catalytic beds, ion exchange, adsorp-... 

For pores smaller than 10 m, a molecular sieving effect can be present and the movement of one or more species inside the porous solid occurs due to the molecular interactions between the species and the network of the porous body here, for the description of species displacement, the theory of molecular dynamics is frequently used. The affinity between the network and the species is the force that controls the molecular motion at the same time, the affinity particularities, which appear when two or more species are in motion inside the porous structure, explain the separation capacity of those solids. We can use a diffusive characterisation of species motion inside a porous solid by using the notion of conformational diffusion. 

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