Porous solids, definition

Use of the term mean-bulk temperature is to define the model from which temperatures are computed. In shock-compression modeling, especially in porous solids, temperatures computed are model dependent and are without definition unless specification of assumptions used in the calculations is given. The term mean-bulk temperature describes a model calculation in which the compressional energy is uniformly distributed throughout the sample without an attempt to specify local effects. In the energy localization case, it is well known that the computed temperatures can vary by an order of magnitude depending on the assumptions used in the calculation. 

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. 

Although, the true density of solid phase p=m/Vp (e.g., g/cm3) is defined by an atomic-molecular structure (/ ), it has become fundamental to the definition of many texture parameters. In the case of porous solids, the volume of solid phase Vp is equal to the volume of all nonporous components (particles, fibers, etc.) of a PS. That is, Vp excludes all pores that may be present in the particles and the interparticular space. The PS shown in Figure 9.17a is formed from nonporous particles that form porous aggregates, which, in turn, form a macroscopic granule of a catalyst. In this case, the volume Vp is equal to the total volume of all nonporous primary particles, and the free volume between and inside the aggregates (secondary particles) is not included. 

For porous solids such as coal, there are five different density measurements true density, apparent density, particle density, bulk density, and in-place density. The true density of coal is the mass divided by the volume occupied by the actual, pore-free solid in coal. However, determining mass of coal may be deemed as being rather straightforward, but determining volume presents some difficulties. Volume, as the word pertains to a solid, cannot be expressed universally in a simple definition. Indeed, the method used to determine volume experimentally, and subsequently, the density, must be one that applies measurement rules consistent with the adopted definition. 

Unsteady state diffusion in monodisperse porous solids using a Wicke-Kallenbach cell have shown that non-equimolal diffusion fluxes can induce total pressure gradients which require a non-isobaric model to interpret the data. The values obtained from this analysis are then suitable for use in predicting effectiveness factors. There is evidence that adsorption of the non-tracer component can have a considerable influence on the diffusional flux of the tracer and hence on the estimation of the effective diffusion coefficient. For the simple porous structures used in these tests, it is shown that a consistent definition of the effective diffusion coefficient can be obtained which applies to both the steady and unsteady state and so can be used as a basis of examining the more complex bimodal pore size distributions found in many catalysts. 

In the case of powders, if the particles are of fairly simple form, the surface area (excluding submicroscopic cracks) can be estimated from microscopic measurement of the size of the particles.5 Powders, or porous solids composed of aggregations of small particles, can have the particle size approximately estimated by the width, and imperfection of definition, of the lines in an X-ray diffraction photograph.6 This method has been used by Levi and others7 for finely divided metal such as platinum black the particles were usually extremely small, of the same order of size as the particles in a colloidal sol of the metal. For the platinum group, the size of crystalline particles was estimated as from 20 to 120 A. across only. 

Some of the principal terms and properties associated with adsorption, powders and porous solids are defined in Tables 1.1, 1.2 and 1.3. These definitions are consistent with those proposed by the International Union of Pure and Applied Chemistry (IUPAC) (see Sing el al. 1985 Haber, 1991 Rouquerol et al., 1994) and by the British Standards Institution (1958, 1992) and other official organizations (see Robens and Krebs, 1991). 

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 focus of this chapter is on electron-transfer processes occmring in porous media, with particular emphasis on zeolitic, mesoporous materials and sol-gel-derived materials. The definition of different classes of porous solids as specified by lUPAC is based on the pore diameter ... 

Alternative fuels should be substantially non-petroleum in order to provide energy security and environmental benefits, and to substitute for conventional fuels such as gasoline and diesel. Natural gas consisting mainly of methane fits this definition, and the natural gas is mainly stored as compressed natural gas in pressure vessels or as adsorbed gas that can be stored in a porous solid at a low pressure. An important advantage of zeolites over activated... 

Table 1.2 Definitions associated with adsorption, powders and porous solids...

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). 

Equation 12.5.b-8 is the same as Eq. I2.5.b-4 except for the term in the latter with D 2, representing direct effective particle-to-particle transport. For several types of situations, this term may be of definite importance mass transfer in highly porous solids at low Reynolds numbers (Wakao [63]) and the heat transfer situation discussed by Littman and Barile [61], which is analogous to the model for radial heat transfer proposed by De Wasch and Froment [62]. 

The type IV isotherms displayed by most clays are, in gena-al, amenable to surface area measurements using BET analysis, as long as attention is paid to catain constants in the BET equation (49). Furthermore, only the adsorption branch of the isotherm is reliably used to measure pore size distributions, which in most cases is quite broad. Finally, for the interested reader, guidelines for the charactCTization of porous solids containing both definitions and appropriate method selection are provided by Rouquerol et al. (54). 

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 ... 

In network colloids the definition of colloids in terms of dispersed phase and dispersion medium breaks down since the networks consist of interpenetrating continuous channels. Examples include porous solids, where a solid labyrinth contains a continuous gas phase. There are also examples of colloids where three or more phases coexist, two or more of which can be finely divided. These are called multiple colloids. An example is an oilbearing porous rock, since both oil and water will be present within the solid pores. 

Equations (2.3.20) and (2.3.21) merely serve as definitions of t and Kq and are based on the presumption (not necessarily correct) that as defined, these two quantities have the same value for different gases (but the same porous solid). 

In this section we considered the gasification of porous solids by definition this means systems where there is no solid reaction product, so that (in the absence of inerts) upon completion of the reaction all the solid will disappear. As illustrated in Fig. 4.1 the gasification process may be classified into the following three regimes. 

Adsorption by definition is the process whereby specific molecules (the adsorbate) adhere to the surface of a porous solid (the adsorbent). It is generally agreed that the phenomenon of adsorption occurs in stages. First a single laya of adsorbate molecules attaches itself to the surface of the adsorbent then multiple layers form and fill the finer pores in the surface and finally the coarser pores become filled by capillary condensation. The nature of the solid surface is thus of critical importance, and it is the process of activation that gives the required high specific surface. 

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