Pore size distribution, three-dimensional

The physical characterisation of membrane structure is important if the correct membrane is to be selected for a given application. The pore structure of microfiltration membranes is relatively easy to characterise, SEM and AFM being the most convenient method and allowing three-dimensional structure of the membrane to be determined. Other techniques such as the bubble point, mercury intrusion or permeability methods use measurements of the permeability of membranes to fluids. Both the maximum pore size and the pore size distribution may be determined.1315 A parameter often quoted in manufacturer s literature is the nominal... 

This chapter discusses the synthesis, characterization and applications of a very unique mesoporous material, TUD-1. This amorphous material possesses three-dimensional intercoimecting pores with narrow pore size distribution and excellent thermal and hydrothermal stabilities. The basic material is Si-TUD-1 however, many versions of TUD-1 using different metal variants have been prepared, characterized, and evaluated for a wide variety of hydrocarbon processing applications. Also, zeolitic material can be incorporated into the mesoporous TUD-1 to take the advantage of its mesopores to facilitate the reaction of large molecules, and enhance the mass transfer of reactants, intermediates and products. Examples of preparation and application of many different TUD-1 are described in this chapter. 

Besides specific surface area, silicas are also characterised by their porosity. Most of the silica s are made out of dense spherical amorphous particles linked together in a three dimensional network, this crosslinked network building up the porosity of the silica. Where the reactivity of diborane towards the silica surface has been profoundly investigated, little attention has been paid to the effect of those reactions on the pore structure. However different methods are developed to define the porosity and physisorption measurements to characterise the porosity parameters are well established. Adsorption isotherms give the specific surface area using the BET model, while the analysis desorption hysteresis yields the pore size distribution. 

Zeolite-based processes have gradually displaced conventional ones, involving supported H3P04 or A1C13 as catalysts, in the manufacture of cumene, the raw material for phenol production [1, 6, 39]. A three-dimensional dealuminated mordenite (3-DDM) catalyst was developed by Dow Chemical for this purpose [39]. Dealumination, using a combination of acid and thermal treatments, increases the Si/Al ratio from 10-30 up to 100-1000 and, at the same time, changes the total pore volume and pore-size distribution of the mordenite. The... 

Further, Imdakm and Matsuura [61] have developed a Monte Carlo simulation model to smdy vapor permeation through membrane pores in association with DCMD, where a three-dimensional network of interconnected cylindrical pores with a pore size distribution represents the porous membrane. The network has 12 nodes (sites) in every direction plus boundary condition sites (feed and permeate). The pore length / is assumed to be of constant length (1.0 p,m), however, it could have any value evaluated experimentally or theoretically [62]. 

All of the currently used porous packing materials have a three-dimensional network structure, effectively giving rise to a pore size distribution. In these separating media, the dependence of 7 on A will be less sharp compared with the one in Fig. 3. It is desired by chromatographers that the retention time is a linear function of log M. Because the retention time is a linear function of K, the plot of K needs to be a linear function of log M in as broad a range of MWs as possible. A naturally occurring pore size distribution is not sufficient to cause the desired linearity. Therefore, mixed-bed columns, packed with porous materials of different pore-size-distribution ranges, have been developed and used broadly as linear columns. 

Thus, it appears that relative permeability curves follow percolation theory, since they satisfy both the theoretical percolation threshold and the scaling law for three dimensional networks [9]. More importantly, relative permeability curves of different connectivity exhibit the same behavior with as is approached. The same conclusion is valid for different pore size distribution functionsprovided that f.y< 8 [II],... 

Fig. 2. Two-dimensional illustration of the geometric definition of the pore size distribution [25]. Point Z may be overlapped by all three circles of differing radii, whereas point Y is accessible only to the two smaller circles and point X is excluded from all but the smallest circle. The geometric pore size distribution is obtained by determining the size of the largest circle that can overlap each point in the pore volume. (Reproduced with permission from S. Ramalingam, D. Maroudas. and E. S. Aydil. Interactions of SiH radicals with silicon surfaces An atomic-scale simulation study. Journal of Applied Physics, 1998 84 3895-3911. Copyright 1998, American Institute of Physics.)...

As new membranes are developed, methods for characterization of these new materials are needed. Sarada et al. (34) describe techniques for measuring the thickness of and characterizing the structure of thin microporous polypropylene films commonly used as liquid membrane supports. Methods for measuring pore size distribution, porosity, and pore shape were reviewed. The authors employed transmission and scanning electron microscopy to map the three-dimensional pore structure of polypropylene films produced by stretching extended polypropylene. Although Sarada et al. discuss only the application of these characterization techniques to polypropylene membranes, the methods could be extended to other microporous polymer films. Chaiko and Osseo-Asare (25) describe the measurement of pore size distributions for microporous polypropylene liquid membrane supports using mercury intrusion porosimetry. 

Fig. 4.13 Preparation process of three-dimensionally ordered macroporous carbon with controlled pore size distribution by using monodispersed polystyrene and silica beads...

Recent particle tracking simulations in soil network models indicate that solute dispersion is more sensitive to the water retention curve than to the particular combination of pore-size distribution and topology that determine its shape (Vogel, 2000). Numerical particle tracking techniques have also been used to simulate solute dispersion in fractured media. Examples for two-dimensional randomly intersecting fracture networks include the models developed by Hull et al. (1987), Smith and Schwartz (1984), Robinson and Gale (1990), and Clemo and Smith (1997). Recently Nordqvist et al. (1996) and Margolin et al. (1998) have extended this approach to three-dimensional fracture networks. 

Because the longitudinal direction of wood is very marked, it is quite simple to obtain the three-dimensional structure of the material from a cross section. Figure 40.15 depicts the examples of capillary pressure curves calculated from nticroscopic images of cross sections of wood. In this case, the pore-size distribution has been calculated using image processing (Perre, 1997 Perre and Turner, 2002). 

A general problem of the MIP technology—as it had been established during the last decades—is linked to the simultaneous—and widely random—formation of the imprinted receptor sites and the polymer matrix. A certain amount of matrix material is required to host and stabilize the receptor sites. This polymer can form a nonporous or a porous structure in the first case receptor sites on the solid surface determine MIP performance, in the latter case pore size and pore size distribution as well as pore connectivity play an additional role. Random distribution and uneven accessibility of imprinted receptor sites in the (three-dimensional) volume of an MIP material—typically particles—are characteristic for the state of the art. 

Atomic force microscopy (AFM) was first applied to investigate the polymer surfaces in 1988 shortly after its invention [23]. Today, studies by AFM range from simple visualization of morphology to more advanced examination of polymer structure and properties at the nanometer scale. AFM gives three-dimensional pictures of the surfaces, while other methods, SEM and TEM, do not. AFM is frequently applied to polymer surfaces, principally to reveal morphology, nanostructure, chain packing, conformation, pore size, and pore size distribution at the surface. 

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