Characterization of the Pore Structure of Membranes
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Description of Porous Materials—Definitions Origins of Pore Structure Porous materials can be formed in sev
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eral ways, although the following three are most important in the synthesis of membrane structures. In the first method, the pores may be an inherent feature of crystalline structures (e.g., zeolites and clay minerals). Such intracrystalline pores are generally of molecular dimensions and result in very regulär networks. In the second instance, the pores may be formed by the packing and subsequent consolidation of small particles, as may occur in some inorganic gels and ceramics. In the third route, certain elements of an original structure are selectively removed to create pores.4 Examples include the formation of porous metal oxides by thermal decomposition of hydroxides, of porous glasses by chemical etching, of activated carbons by controlled pyrolysis, and of alumina by anodic oxidation of aluminum to give oriented, cylindrical pores. A quantitative description of pore struc tures is generally made with reference to an idealized model. In such model Sys tems, the pore geometry can be defined precisely in terms of pore size, shape, Con nectivity, etc. An insight into the origin of porosity can therefore provide confidence in the reality of the model used.
Quantitative Description of Pore Structures To define pore structure, IUPAC has recently made the following recommendations: 4 Porosity is defined as the fraction e of the total volume of the sample that is attributed to the pores detected by the method used, viz., e = Vp/V. Note that e depends on the method used to determine the apparent volume V (e.g., geometrical or fluid displacement) and on that used to assess the pore volume Vp. Some methods (e.g., using a gas or a fluid) have access only to "open" pores, whereas others may have access to "closed" pores
also (e.g., methods using radiation scatter ing). Furthermore, for any given method, e will depend on the size of the molecu lar probe (in fluid displacement or adsorption) or on the scale of measurement (in stereology). This concept is developed in the theory of fractal analysis. 5 The specific surface area is defined as the accessible area of solid surface per unit mass of material. It is also dependent on the method employed and the size of the probe used (e.g., adsorbate molecular probe, wavelength of radiation, etc.) and is of particular significance for materials containing micropores. 6 The pore size, or more precisely, pore width, is the distance between two opposite walls of the pore. The following Classification of pore sizes, based on width, has been recommended by IUPAC:4 micropores, width < 2 nm; mesopores, 1 nm < width < 50 nm; mncropores, width > 50 nm. Precise definition is often complicated because pore shape is generally ir regulär, leading to a variety of definitions of "size." Moreover, porous Systems gen erally consist of interconnected net works, and results will depend on the sequence in which pores are accessed by the method (e.g., mercury intrusion).
Model Por
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