Pore width, definition

In Figure lb, each figure is considered as a unique stracture, which is repeated to form the porous solid. In each model, the variation of the micropore volume with the pore width (w) has been calculated. (It must be noted that w is the effective pore width, according to definition of Kaneko et al [5]). 

The integral is defined with respect to logarithm of the pore width. Such a definition is preferable as the pore size usually varies over a wide range. Equation (11.38) is the Fredholm integral equation of the first kind, with p(p, H) being the kernel. The numerical inversion for determining PSD function fi) is achieved by discretizing the Fredholm equation as follows ... 

Initially, porous materials were defined in terms of their adsorption properties and thus distinguished by the pore size range. Pore size usually refers to pore width, that is, the diameter or distance between opposite walls in a solid. According to the lUPAC definition (13), porous solids are then divided into three classes microporous (<2 nm), mesoporous (2 to 50nm) and macroporous (>50nm) materials (Fig. 9.2). 

The total surface area of a porous material is given by the sum of the internal and external surface areas. Pores are classified as micropores (pore width less than 2 nm), mesopores (pore width between 2 and 50 nm), and macropores (pore width greater than 50 nm) according to the definitions proposed by lUPAC (6). The specific pore volume, pore widths, and pore size distributions for micro-and mesopores are determined by gas adsorption. In the case of mesopores, the method is based on the relationship between the pressure of capillary condensation and the radius of a cylindrical pore in which condensation takes place, given by the Kelvin equation ... 

The definition of the different types of pores is based on their width, which represents the distance between the walls of a slit-shaped pore or the radius of a cylindrical pore. This classification, which is not entirely arbitrary, is now widely accepted and used. It takes into account differences in the behaviour of molecules adsorbed in micropores and in mesopores. It appears that for pore widths exceeding 1.5-2.0 nm, the gaseous adsorbate condenses in a liquid-like state and a meniscus is formed. As a consequence, a hysteresis loop appears on desorption and its interpretation can lead to the distribution of the mesopores in the adsorbent [23]. The limit between mesopores and macropores at 50 nm is more artificial, and corresponds to the practical limit of the method for pore-size determination based on the analysis of the hysteresis loop. As a rule, the porous structure of the usual types of activated carbons is tridisperse, i.e. they contain micropores, mesopores and macropores. Micropores are of the greatest significance for adsorption owing to their very large specific surface area, and their large specific volume. At least 90-95% of the total surface area of an activated carbon can correspond to micropores. 

In addition to the total porosity, Figure 4 reveals qualitative infonnation about the pore structures in die different films, b the MSQ film widi 1 % by mass porogen, the iqitake saturates at low partial pressures and die adsorption and desorption branches coincide. This is characteristic of the lUPAC definition of micropore filling (pores widths less than 2 nm [9,10]), and consistent with die fectdiat MSQ materials should be inherendymicroporous. 

Adsorbents such as some silica gels and types of carbons and zeolites have pores of the order of molecular dimensions, that is, from several up to 10-15 A in diameter. Adsorption in such pores is not readily treated as a capillary condensation phenomenon—in fact, there is typically no hysteresis loop. What happens physically is that as multilayer adsorption develops, the pore becomes filled by a meeting of the adsorbed films from opposing walls. Pores showing this type of adsorption behavior have come to be called micropores—a conventional definition is that micropore diameters are of width not exceeding 20 A (larger pores are called mesopores), see Ref. 221a. 

The International Union of Pure and Applied Chemistry has adopted the following definitions of pores by width micropores, < 2nm mesopores, 2-50 nm macropores. > 50 nm. 

For the five mixtures, the cumulative mesoporous volume, Feds, and mesoporous surface area, S edB, and are both linear decreasing functions of the micropore content y (Figure 2b). The cumulative specific surface area SedB is definitely a better estimator of the mesoporous surface than the specific surface S xt computed Ifom the t-plot. The lUPAC classification states that mesopores are pores whose width is larger that 2 nm. In the case of the cylindrical pore model retained for the pore size distribution, this is equivalent to radii larger than 1 nm. It should however be stressed that the calculation of the cumulative surface and volume of the mesopores must not be continued at lower pressures than the closing of the hysteresis loop (gray zones of Figures 3a and 3b). If a black box analysis tool is used and if the calculation is systematically continued down to 1 nm, severe overestimation of the mesopores surface and volume may occur. 

Usually the pores in a material do not have the same size but exist as a distribution of size which can be wide or sharp. We can characterise a film by a nominal or an absolute pore size. In fact this definition rather characterises the size of the particles or molecules retained by the layer. Pore size distribution is classically represented by the derivatives dSp/dfp or dUp/drp as a function of Fp (pore radius) where Sp and Vp are respectively the wall area and volume of the pores. The size in question is here the radius, which implies that the pores are known to be, or assumed to be, cylindrical. In other cases, Fp should be replaced by the width. 

Three groups of pores of different width, tv, were defined by Dubinin [9]. The classification, which was adopted in a revised form by the lUPAC [10], is as follows in micropores tv< 2nm in mesopores w 2-50nm in macropores IV > 50 nm. It also expedient [11] to subdivide the micropores into ultramicropores (iv < 1 nm) and supermicropores (iv 1—2 nm). However, all these dimensions are somewhat arbitrary and imprecise because the stages of pore filhng are dependent on the gas-solid system as well as the pore geometry [11]. Similarly, there is no precise definition of the currently popular term nanopore, which is often applied to a pore in the supermicropore or narrow mesopore range. 

Membrane technologists are well aware that the most permeable glassy polymers are those which possess a very high free volume, where the term free volume refers to the intermolecular voids within a material [1], Scientists who work with molecular sieves, such as zeolites, commonly use the term microporous material to describe those materials which contain pores or channels less than 2nm in width, a definition that arises in the context of gas adsorption studies [2],... 

The lUPAC deflnes a porous solid as any solid material that contains cavities, channels, or interstices, but goes on to state that in a particular context, a more restrictive definition may be appropriate. Nanoporous refers to a material consisting of a regular framework having pores with widths in the range 2 to 1000 nm. These materials can further be subdivided into three categories ... 

Microporosity is defined by lUPAC as pore sizes (diameter or sht width) of 2 nm or less. Although this is the official definition, the practical definition would be in terms of the isotherm produced. The type of isotherm that is produced is usually a type I isotherm, although this could be misleading. The chi (x) feature associated with microporosity is feature 2 in the absence of feature 3, that is a negative curvature in the x plot without any preceding high-pressure positive curvature. 

The ubiquity of porous materials has led to confusion in the usage of such terms as micropore, macropore, total pore volume and internal area. In the lUPAC classification of pore size, the micropore width is taken to not exceed about 2 nm (20 ), the mesopore width to be in the range 2-50 nm and the macropore width to be above about 50 nm (0.05 pm). In recent years these definitions have served us well, especially in the context of gas adsorption and mercury porosimetry, but it is becoming increasingly clear that some refinements are required and that account should be taken of pore shape. 

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