Pore-shape distributions

There is a demand for rational methods for the development of new catalysts. Strong efforts in this direction have led to a deeper insight into catalytic phenomena on a molecular level. A key design consideration in catalysis is the optimum pore structure of catalyst particles. Design parameters may be distribution of pore radii, distribution of pore length, pore shape, distribution of catalyst crystallites (active centers) within the pores or connectivity. The variable design parameters are constrained between upper and lower bounds due to physical limitations. 

Pore-shape Distributions by Davies and Seaton (1998), Figure 3.24... 

Brunauer and co-workers [211, 212] proposed a modelless method for obtaining pore size distributions no specific capillary shape is assumed. Use is made of the general thermodynamic relationship due to Kiselev [213]... 

The f-curve and its associated t-plot were originally devised as a means of allowing for the thickness of the adsorbed layer on the walls of the pores when calculating pore size distribution from the (Type IV) isotherm (Chapter 3). For the purpose of testing for conformity to the standard isotherm, however, a knowledge of the numerical thickness is irrelevant since the object is merely to compare the shape of the isotherm under test with that of the standard isotherm, it is not necessary to involve the number of molecular layers n/fi or even the monolayer capacity itself. 

The large majority of activated alumina products are derived from activation of aluminum hydroxide, rehydrated alumina, or pseudoboehmite gel. Other commerical methods to produce specialty activated aluminas are roasting of aluminum chloride [7446-70-0], AIQ calcination of precursors such as ammonium alum [7784-25-0], AlH2NOgS2. Processing is tailored to optimize one or more of the product properties such as surface area, purity, pore size distribution, particle size, shape, or strength. 

Rehydration Bonded Alumina. Rehydration bonded aluminas are agglomerates of activated alumina, which derive their strength from the rehydration bonding mechanism. Because more processing steps are involved in the manufacture, they are generally more expensive than activated aluminum hydroxides. On the other hand, rehydration bonded aluminas can be produced in a wider range of particle shape, surface area, and pore size distribution. 

In addition to surface area, pore size distribution, and surface chemistry, other important properties of commercial activated carbon products include pore volume, particle size distribution, apparent or bulk density, particle density, abrasion resistance, hardness, and ash content. The range of these and other properties is illustrated in Table 1 together with specific values for selected commercial grades of powdered, granular, and shaped activated carbon products used in Hquid- or gas-phase appHcations (19). 

Important physical properties of catalysts include the particle size and shape, surface area, pore volume, pore size distribution, and strength to resist cmshing and abrasion. Measurements of catalyst physical properties (43) are routine and often automated. Pores with diameters <2.0 nm are called micropores those with diameters between 2.0 and 5.0 nm are called mesopores and those with diameters >5.0 nm are called macropores. Pore volumes and pore size distributions are measured by mercury penetration and by N2 adsorption. Mercury is forced into the pores under pressure entry into a pore is opposed by surface tension. For example, a pressure of about 71 MPa (700 atm) is required to fill a pore with a diameter of 10 nm. The amount of uptake as a function of pressure determines the pore size distribution of the larger pores (44). In complementary experiments, the sizes of the smallest pores (those 1 to 20 nm in diameter) are deterrnined by measurements characterizing desorption of N2 from the catalyst. The basis for the measurement is the capillary condensation that occurs in small pores at pressures less than the vapor pressure of the adsorbed nitrogen. The smaller the diameter of the pore, the greater the lowering of the vapor pressure of the Hquid in it. 

Transition aluminas are good catalyst supports because they are inexpensive and have good physical properties. They are mechanically stable, stable at relatively high temperatures even under hydrothermal conditions, ie, in the presence of steam, and easily formed in processes such as extmsion into shapes that have good physical strength such as cylinders. Transition aluminas can be prepared with a wide range of surface areas, pore volumes, and pore size distributions. 

The models of Matranga, Myers and Glandt [22] and Tan and Gubbins [23] for supercritical methane adsorption on carbon using a slit shaped pore have shown the importance of pore width on adsorbate density. An estimate of the pore width distribution has been recognized as a valuable tool in evaluating adsorbents. Several methods have been reported for obtaining pore size distributions, (PSDs), some of which are discussed below. 

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. 

The shape of the pore size distribution curve strongly depends on the molecular weight distribution of the linear polymer. The narrowest pore size distributions were obtained with the linear polymers having the lowest polydisper-sity indices. 

The physicochemical properties of carbon are highly dependent on its surface structure and chemical composition [66—68], The type and content of surface species, particle shape and size, pore-size distribution, BET surface area and pore-opening are of critical importance in the use of carbons as anode material. These properties have a major influence on (9IR, reversible capacity <2R, and the rate capability and safety of the battery. The surface chemical composition depends on the raw materials (carbon precursors), the production process, and the history of the carbon. Surface groups containing H, O, S, N, P, halogens, and other elements have been identified on carbon blacks [66, 67]. There is also ash on the surface of carbon and this typically contains Ca, Si, Fe, Al, and V. Ash and acidic oxides enhance the adsorption of the more polar compounds and electrolytes [66]. 

Gel filtration chromatography has been extensively used to determine pore-size distributions of polymeric gels (in particle form). These models generally do not consider details of the shape of the pores, but rather they may consider a distribution of effective average pore sizes. Rodbard [326,327] reviews the various models for pore-size distributions. These include the uniform-pore models of Porath, Squire, and Ostrowski discussed earlier, the Gaussian pore distribution and its approximation developed by Ackers and Henn [3,155,156], the log-normal distribution, and the logistic distribution. 

Using the formalism of statistical mechanics, Giddings et al. [135] investigated the effects of molecular shape and pore shape on the equilibrium distribution of solutes in pores. The equilibrium partition coefficient is defined as the ratio of the partition function in the pore... 

SEM micrographs (Figure 4) show the deposition on the a-Al203 grains of small crystallites with the typical hexagonal shape of silicalite. The pore size distribution, as deduced from N2 adsorption, presents a very narrow peak centred on 0.5 nm, also in good agreement with the pore diameter of silicalite-type zeolites. 

Such a choice of pore shape and distribution leads to a relatively simple mathematical formulation without loss of generality. 

The nitrogen adsorption isotherms for the onion-like Fe-modified MLV-0.75 materials are of type IV, although their hysteresis loops are of complex types, HI, H2, and H3. The H2-type hysteresis loop indicates the presence of bottle-shaped pores. The pore sizes obtained with the BJH method can be assigned to entry windows of mesopores. For pure MLV-0.75 and Fe-modified MLV-0.75 (x = 1.25), the pore size distributions exhibit two peaks (Fig. Id). The first peak appears at 9.0 and ca. 6 nm for MLV-0.75 and Fe-MLV-0.75, respectively. The shift of the broad peak maximum of the distribution curve... 

The mesopores are with regular and well-defined shapes and have a broad pore size distribution. N2 adsorption analysis revealed also a broad pore size distribution centered around 28 nm. The... 

Besides the 29Si and 27 A1 NMR studies of zeolites mentioned above, other nuclei such as H, 13C, nO, 23Na, 31P, and 51V have been used to study physical chemistry properties such as solid acidity and defect sites in specific catalysts [123,124], 129Xe NMR has also been applied for the characterization of pore sizes, pore shapes, and cation distributions in zeolites [125,126], Finally, less common but also possible is the study of adsorbates with NMR. For instance, the interactions between solid acid surfaces and probe molecules such as pyridine, ammonia, and P(CH3)3 have been investigated by 13C, 15N, and 31P NMR [124], In situ 13C MAS NMR has also been adopted to follow the chemistry of reactants, intermediates, and products on solid catalysts [127,128],... 

The catalyst activity depends not only on the chemical composition but also on the diffusion properties of the catalyst material and on the size and shape of the catalyst pellets because transport limitations through the gas boundary layer around the pellets and through the porous material reduce the overall reaction rate. The influence of gas film restrictions, which depends on the pellet size and gas velocity, is usually low in sulphuric acid converters. The effective diffusivity in the catalyst depends on the porosity, the pore size distribution, and the tortuosity of the pore system. It may be improved in the design of the carrier by e.g. increasing the porosity or the pore size, but usually such improvements will also lead to a reduction of mechanical strength. The effect of transport restrictions is normally expressed as an effectiveness factor q defined as the ratio between observed reaction rate for a catalyst pellet and the intrinsic reaction rate, i.e. the hypothetical reaction rate if bulk or surface conditions (temperature, pressure, concentrations) prevailed throughout the pellet [11], For particles with the same intrinsic reaction rate and the same pore system, the surface effectiveness factor only depends on an equivalent particle diameter given by... 

The first task was to produce carriers from different recipes and in different shapes as shown schematically in Fig. 8. The raw materials diatomaceous earth, water and various binders are mixed to a paste, which is subsequently extruded through a shaped nozzle and cut off to wet pellets. The wet pellets are finally dried and heated in a furnace in an oxidising atmosphere (calcination). The nozzle geometry determines the cross section of the pellet (cf. Fig. 3) and the pellet length is controlled by adjusting the cut-off device. Important parameters in the extrusion process are the dry matter content and the viscosity of the paste. The pore volume distribution of the carriers is measured by Hg porosimetry, in which the penetration of Hg into the pores of the carrier is measured as a function of applied pressure, and the surface area is measured by the BET method, which is based on adsorption of nitrogen on the carrier surface [1]. 

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