Pore shape Influence

The pore shape influences the mass transfer rate and thus the efficiency of separation. The effective diameter of pores determines the range of separated molar masses. The pore size distribution and the pore volume are decisive for selectivity of separation (section 4.6.2.3). The pore sizes of commercially available gels cover the region necessary for separation of the wide spectrum of substances — from low molecular samples to very high polymers, colloidal particles and viruses. The mean values of pore diameters range from few nanometers to about 2.5 /xm. Gels with various pore sizes, but of the same type, can be combined within the same column. 

In concluding this section we would like to emphasize that of course all semi-empirical relations presented for the relative tensile modulus can be used for fitting experimentally measured data for any kind of elastic modulus (and many other properties as well). Also it may be attempted to interpret the values obtained for the intrinsic properties by fitting in terms of a pore shape influence. However, the intrinsic value of 2 in the case of porous materials with spherical pores and Vq = 0.2 is specific to the tensile modulus (where... 

The size and shape of pores, and their distribution also contribute to the separation process. It is obvious that the pore size and pore volume influence markedly the specific surface area. 

Several factors, including molecular size, charge, and shape, influence the glomerular filtration of large molecules. The restricted passage of macromolecules can be thought of as a consequence of the presence of a glomerular capillary wall barrier with uniform pores. 

Brunauer et alP have developed a means of determining the pore volume distribution wherein the pore shape has a negligible influence. 

The specific surface area depends on both the size and shape and is distinctively high for colloidal-sized species. This is important in the catalytic processes used in many industries for which the rates of reactions occurring at the catalyst surface depend not only on the concentrations of the feed stream reactants, but also on the surface area of catalyst available. Since practical catalysts are frequently supported catalysts, some of the surface area is more important than the rest. Also, given that the supporting phase is usually porous, the size and shapes of the pores may influence the reaction rates as well. The final rate expressions for a catalytic process may contain all of these factors surface area, porosity, and permeability. 

Shape selective reactions are typically carried out over zeolites, molecular sieves and other porous materials. There are three major classifications of shape selectivity including (1) reactant shape selectivity where reactants of sizes less than the pore size of the support are allowed to enter the pores to react over active sites, (2) product shape selectivity where products of sizes smaller than the pore dimensions can leave the catalyst and (3) transition state shape selectivity where sizes of pores can influence the types of transition states that may form. Other materials like porphyrins, vesicles, micelles, cryptands and cage complexes have been shown to control product selectivities by shape selective processes. 

These limits are to some extent arbitrary since the pore filling mechanisms are dependent on the pore shape and are influenced by the properties of the adsorptive and by the adsorbent-adsorbate interactions. The whole of the accessible volume present in micropores may be regarded as adsorption space and the process which then occurs is micropore filling, as distinct from surface coverage which takes place on the walls of open macropores or mesopores. Micropore filling may be regarded as a primary physisorption process (see Section 8) on the other hand, physisorption in mesopores takes place in two more or less distinct stages (monolayer-multilayer adsorption and capillary condensation). 

In order to correct these discrepancies, Broekhoff and de Boer [5] generalized Kelvin s equation by taking pore shape into account, as well as the influence of surface curvature on the thickness of the adsorbed layer. The BdB method can be applied to both adsorption and desorption isotherms using four different pore models defined by a shape factor. Unfortunately, owing to computational difficulties, this last method, although more general, has been far less applied than the first two. 

Parameters which influence transport properties are porosity, pore size distribution, pore shape, interconnectivity and orientation. Indirectly particle size distribution and shape are important in the way they affect the uniformity of the pore size distribution, the pore shape and the roughness of the internal surface area. 

There are two main and important typologies of pores closed and open pores. Closed pores are completely isolated from the external surface, not allowing the access of external fluids in neither liquid nor gaseous phase. Closed pores influence parameters like density and the mechanical and thermal properties. Open pores are connected to the external surface, and are therefore accessible to fluids, depending on the pore nature/size and the nature of fluid. Open pores can be further divided into dead-end or interconnected pores. Further classification is related to the pore shape, whenever is possible to determine it. The characterization of solids in terms of porosity consists in determining the following parameters ... 

Pore size and wall structure could be varied by using different additives. Hydrochloric acid, as an additive, considerably reduced the elementary branches in the structure thus influencing the pore shape. The influence of temperature on pore structure is shown in Eig. 14.12. The pore size increased considerably by increasing the electrolyte temperature from 20°C to 65°C. The dendritic branches comprised nano-sized grains between 10 and 20 mn. The electrical resistance decreased from 0.23 to 0.01 ohm after annealing at 500°C for 5 h [57]. 

The equations and plots presented in the foregoing sections largely pertain to the diffusion of a single component followed by reaction. There are several other situations of industrial importance on which considerable information is available. They include biomolecular reactions in which the diffusion-reaction problem must be extended to two molecular species, reactions in the liquid phase, reactions in zeolites, reactions in immobilized catalysts, and extension to complex reactions (see Aris, 1975 Doraiswamy, 2001). Several factors influence the effectiveness factor, such as pore shape and constriction, particle size distribution, micro-macro pore structure, flow regime (bulk or Knudsen), transverse diffusion, gross external surface area of catalyst (as distinct from the total pore area), and volume change upon reaction. Table 11.8 lists the major effects of all these situations and factors. 

For pores of cylindrical or slit shape, the behaviour of the calculated statistical thickness does not follow that of a flat surface as the pore shape can influence the statistical film thickness. This is explained as follows. For cylindrical pores, the solid will take up more sorbates than a free surface, that is... 

In conventional membrane emulsification, droplets are formed at the membrane surface and detached from it by wall shear stress of the continuous phase (Figure 20.8, middle) [29,45,46]. In addition to tubular membranes made from ceramics such as aluminum oxide, special porous glasses such as SPG (Shiratsu Porous Class) membranes and polymers such as polypropylene (29, 47, 48], flat filter membranes made of PTFE [49, 50], nylon [51] and silicon (30, 51-55] have been used in emulsification. Silicon membranes are produced by microengineering techniques. This technology offers the possibility to influence precisely the structure of a membrane (arrangement of pores, pore shape, size and distance, porosity, surface characteristics, as shown in Figure 20.7). Very thin active layers reduce the pressure drop without losing mechanical stability. 

Pore geometry influences the shape of impedance plots. In what follows, various pore geometries will be presented. First, the ohmic drop in solution only will be taken into account, and later the ohmic drop in solution and in the electrode material will be considered [407]. 

Closed and open pores (Fig. 56) are an important feature of ceramic materials. They exert a strong influence on chemical resistance, strength, thermal conductivity, modulus of elasticity, and thermal shock characteristics. In characterizing a ceramic, it is important to determine not only its total porosity, but also the pore types, pore shapes, pore sizes, and pore size distribution that are present. 

Miscellaneous effects A number of factors can influence the effectiveness factor, some of which are particle size distribution in a mixture of particles/pellets, change in volume upon reaction, pore shape and constriction (such as ink-bottle-type pores), radial and length dispersion of pores, micro-macro pore structure, flow regime (such as bulk or Knudsen), surface diffusion, nonuniform environment around a pellet, dilution of catalyst bed or pellet, distribution of catalyst... 

As speculated in Chapters 4 and 5 it is believed that the shape of the actual pore structure is a secondary influence (the primary influence being the fineness of the screen) on the effective pore diameter. For example, for Dutch Twill meshes, these openings are complex 3D structures. The equilibrium L/V interface shape is complex and it depends on the size and packing of the wires. If it were possible to observe microscopically a L/V interface within a Dutch Twill weave, it might be possible to imderstand why the 450 X 2750 outperforms the 510 x 3600. Meanwhile, it is much more efficacious to look at deeper correlations between the pore diameter and geometrical properties of the mesh like the warp and shute wire diameters. Since the warp and shute diameters are a maj or factor in determining the pore shape it is likely that they have a relationship with the pore diameter. 

Pores in solids have many properties such as shape, location, connectivity and surface chemistry. Perhaps the easiest property of a pore to visualise (though not necessarily to define) is its size, i. e., its extent in one spatial dimension. This is probably one reason why size is often the first or main property used to characterise a pore. However, another more important reason is that pore size has, arguably, the greatest or widest influence on the properties (and hence uses) of solids, compared to other parameters such as pore shape. It is therefore unquestionably useful and conveiuent to use pore size (or pore size distribution) as a means to characterise and compare different porous solids. 

In principle, it can be attempted to interpret deviations of the intrinsic tensile modulus determined by fitting with any of the relations above from the benchmark value 2 in terms of an influence of pore shape. This is possible because usually the deviations in [ ] caused by a variation of the matrix Poisson ratio are in practice negligible. Apart from the obvious advice... 

Influence of the shape of pores on elastic properties was determined on the basis of the theory elaborated by Rossi for concentration of stresses on pores, C53. According to investigations published in C63, for sphericalpores slope of the curve E = fCPD is the least for a given medium and axial ratio a/c=l. Following deviation from spherical shape to prolate spheroid increases also the curve slope, what was confirmed experimentally. On their basis one can determine axial ratio a/c for pores and influence of technological... 

Permeability is a product of four parameters porosity, tortuosity, pore-body radius, and pore shape. The last term in brackets of Eq. (2.56) expresses the influence of the ratio y on permeability. This effect is demonstrated in Fig. 2.28b, where a dramatic decrease of permeability with increasing ratio (—>1) can be observed. For example, a ratio =3 results in a decrease of... 

The adsorption of water vapour has been studied with a range of microporous carbons, zeolites and aluminophosphates in order to elucidate the relative influence of surface chemistry, pore size and pore shape upon the form of the water isotherm. It was possible to separate the adsorbents into three groups on the basis of their affinity and capacity for water vapour. The porous carbons were further examined using the BET and Dubinin-Serpinsky equations. The results show that the adsorption of water vapour at low p/p° is largely dependent upon specific adsorbent-adsorbate interactions whilst at higher relative pressures the micropore size and shape control the extent of adsorption. It is proposed that hydrogen-bonded layers of water can be more readily accommodated in the narrow slit shaped pores (-0.5nm) of molecular sieve carbons than in tubular pores of similar width (e.g. Silicalite/ZSM-5). 

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