Macropores, definition

As surface area and pore structure are properties of key importance for any catalyst or support material, we will first describe how these properties can be measured. First, it is useful to draw a clear borderline between roughness and porosity. If most features on a surface are deeper than they are wide, then we call the surface porous (Fig. 5.16). Although it is convenient to think about pores in terms of hollow cylinders, one should realize that pores may have all kinds of shapes. The pore system of zeolites consists of microporous channels and cages, whereas the pores of a silica gel support are formed by the interstices between spheres. Alumina and carbon black, on the other hand, have platelet structures, resulting in slit-shaped pores. All support materials may contain micro, meso and macropores (see text box for definitions). 

According to their diameter, pores are conventionally classified as macropores (J>50nm), mesopores (2< J<50nm) and micropores (J<2nm). For nanometer-sized pores the term nanopores has been also used for some time (Handbook of Porous Solids, F. Schiith, K. Sing, J. Weitkamp (eds.), Wiley-VCH, Berlin, 2002) but the definition of nanopores is not fully established. In this chapter the term nanopore will be used for pores with 1 < J < 10 nm. 

The terminology is not yet homogeneous. The use of the prefix nano spread out in the 1990s. Until then, the common term used to be mesoscopic structures, which continues to be used. According to a definition by IUPAC of 1985, the following classification applies to porous materials microporous, < 2 nm pore diameter mesoporous, 2-50 nm macroporous, > 50 nm. 

Fig. 7. Size scale associated with soil mineral particles, organic components, pores and aggregations of mineral and organic components (Baldock 2002). The definitions of pore size have used those developed by IUPAC (micropores < 2 nm, mesopores 2-50 nm and macropores > 50 nm). Alternatively, the pore sizes corresponding to the lower ( /m = - 1500 kPa) and upper ( /m = - 100 kPa) limits of water availability to plants may be used to define the boundaries between the different classes of pore size. /m is soil water metric potential.

Pores are found in many solids and the term porosity is often used quite arbitrarily to describe many different properties of such materials. Occasionally, it is used to indicate the mere presence of pores in a material, sometimes as a measure for the size of the pores, and often as a measure for the amount of pores present in a material. The latter is closest to its physical definition. The porosity of a material is defined as the ratio between the pore volume of a particle and its total volume (pore volume + volume of solid) [1]. A certain porosity is a common feature of most heterogeneous catalysts. The pores are either formed by voids between small aggregated particles (textural porosity) or they are intrinsic structural features of the materials (structural porosity). According to the IUPAC notation, porous materials are classified with respect to their sizes into three groups microporous, mesoporous, and macroporous materials [2], Microporous materials have pores with diameters < 2 nm, mesoporous materials have pore diameters between 2 and 50 nm, and macroporous materials have pore diameters > 50 nm. Nowadays, some authors use the term nanoporosity which, however, has no clear definition but is typically used in combination with nanotechnology and nanochemistry for materials with pore sizes in the nanometer range, i.e., 0.1 to 100 nm. Nanoporous could thus mean everything from microporous to macroporous. 

Fond et al. [84] developed a numerical procedure to simulate a random distribution of voids in a definite volume. These simulations are limited with respect to a minimum distance between the pores equal to their radius. The detailed mathematical procedure to realize this simulation and to calculate the stress distribution by superposition of mechanical fields is described in [173] for rubber toughened systems and in [84] for macroporous epoxies. A typical result for the simulation of a three-dimensional void distribution is shown in Fig. 40, where a cube is subjected to uniaxial tension. The presence of voids induces stress concentrations which interact and it becomes possible to calculate the appearance of plasticity based on a von Mises stress criterion. 

Relatively straightforward is the definition of nanoscopic voids. Nanopores and nanocavities are elongated voids or voids of any shape, and nanomaterials can incorporate especially nanopores in an ordered or disordered way. The former is of crucial importance for many of the hybrid materials discussed in the book (e.g., in Chapters 16 or 18). Nanochannel is also frequently used instead of nanopore, often in biological or biochemical contexts. Besides nanoporous, the term mesoporous is often found in hybrid materials research. Interestingly, the IUPAC has defined the terms mesoporous (pores with diameters between 2 and 50 nm), microporous (pores with diameters <2 nm) and macroporous (pores with diameters >50 nm), yet has not given a definition of nanoporous in the IUPAC Recommendations on the Nomenclature of Structural and Compositional Characteristics of Ordered Microporous and... 

According to the IUPAC definition, porous materials ate divided into three different classes, depending on their pore sizes. Mesoporous materials are described as materials whose pore diameters lie in the range between 2 and 50 nm. Solids with a pore diameter below 2 nm or above 50 nm belong to the class of micro- and macroporous materials, respectively. 

PSD in the mesopore (2-50 nm) and macropore (>50nm) regions can be reasonably obtained by different methods based on the Kelvin equation (like BJH, see below), since this equation describes rather well the equilibrium adsorption in these pores. However, there are no definitive methods for... 

Silica is one of the most abundant chemical substances on earth. It can be both crystalline or amorphous. The crystalline forms of silica are quartz, cristobalite, and tridymite [51,52]. The amorphous forms, which are normally porous [149] are precipitated silica, silica gel, colloidal silica sols, and pyrogenic silica [150-156], According to the definition of the International Union of Pure and Applied Chemistry (IUPAC), porous materials can be classified as follows microporous materials are those with pore diameters from 3 to 20 A mesoporous materials are those that have pore diameters between 20 and 500 A and macroporous materials are those with pores bigger than 500 A [149],... 

The definitions of the moments and their relationship to the system parameters for a biporous (macropore-micropore) adsorbent such as a commercial pelleted molecular sieve are given by the following equations(15,16) ... 

The available transport models are not reliable enough for porous material with a complex pore structure and broad pore size distribution. As a result the values of the model par ameters may depend on the operating conditions. Many authors believe that the value of the effective diffusivity D, as determined in a Wicke-Kallenbach steady-state experiment, need not be equal to the value which characterizes the diffusive flux under reaction conditions. It is generally assumed that transient experiments provide more relevant data. One of the arguments is that dead-end pores, which do not influence steady state transport but which contribute under reaction conditions, are accounted for in dynamic experiments. Experimental data confirming or rejecting this opinion are scarce and contradictory [2]. Nevertheless, transient experiments provide important supplementary information and they are definitely required for bidisperse porous material where diffusion in micro- and macropores is described separately with different effective diffusivities. 

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. 

The irony is that both velocities are derived directly from data easily acquired using the conventional methods of the field in which they are used but that, unfortunately, neither informs well on the actual kinetics of the band convection, which is the primary concern in mass transfer investigations. Since, for all practical purposes, the stream of mobile phase flows only through the macropores, a more useful definition of the velocity is the interstitial velocity... 

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. 

An important type of porous carbons is activated carbons. Granular activated carbons are prepared from different precursors and used in a wide range of industries. Their preparation, structure and applications were reviewed in different books and reviews [3,4,71-75]. In Table 8, some properties of different adsorbents (activated carbons, silica gel, alumina gel and zeolite) are compared with each other. High BET surface area and light weight are the main advantages of activated carbons. Usually activated carbons have a wide ran of pore sizes from micropores to macropores, which shows a marked contrast to the definite pore size of zeolites. 

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). 

Some important critical remarks to the very definitions of these terms, as well as to their experimental measurements, will be given in Chapter 7, Section 5.1.) The true density of macroporous polymers is usually estimated by helium or nitrogen densitometry, while the apparent density can be determined by measuring the diameters of a sufficient number of spherical beads and weighing them. 

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