Heterogeneous microporous solid

To overcome these difficulties, Stoeckli (Stoeckli, 1977 Stoeckli et al., 1979) suggested that the original DR equation only holds for those carbons with a narrow micropore size distribution. According to this view, the overall isotherm on a heterogeneous microporous solid is made up of the sum of the contributions from the different groups of pores. Thus,... 

Dubinin and Astakhov [117] put forward a more general form of Eq. (38), termed the DA equation, in which the square exponent is replaced with an empirical constant with a value between 2 and 6. No physical basis was identified, however, for selecting the value of the exponent. To cast the DR equation into a form more suitable for PSD analysis of heterogeneous microporous solids, Stoeckli [118] suggested an integral form of Eq. (38) involving a structure distribution function 7(B) for the micropore PSD,... 

General integral equation [similar to Eq. (44)] for the adsorption isotherm on heterogeneous microporous solids can be written as follows ... 

Ding, L.P. 2002. Multicomponent Adsorption in Heterogeneous Microporous Solids. St. Lucia, Queensland, Austraha. 

To overcome this problem Dubinin, McEnaney, Stoeckli and Kadlec have proposed generalised forms of the DR equation which in principle should be applicable to heterogeneous microporous solids. In practice, the main problem in adopting this approach is to arrive at a unique solution for the probability density function of E and hence the micropore size distribution. These aspects are discussed in Sme detail by McEnaney and Mays. 

The generalised adsorption isotherm (GAI) for heterogeneous, microporous solids (ref. 36) may be written as... 

Microporous solids, zeolites in particular, are widely used in heterogeneous catalytic processes, separations, oil recovery, and other industrial processes (i). A microscopic... 

On the other hand, it is impossible to apply the SP method to the correct description of gas adsorption in the micropores, since the adsorption in the micropores does not occur by multilayer adsorption but by micropore volume filling process. In this case, the pore fractal dimension gives a physical importance for the description of structural heterogeneity of the microporous solids. Terzyk et al.143"149 have intensively investigated the pore fractal characteristics of the microporous materials using gas adsorption isotherms theoretically simulated. 

According to second and third observations, it is difficult to appreciate the maximum value of the surface free energy and surface enthalpy of a solid, especially in the case of microporous materials which are widely efficient adsorption properties of the surface (sample V). Therefore, for this material, more works may be needed on the adsorption isotherm, spreading pressure, isosteric heat of adsorption, and even heterogeneities of solid surfaces. They are concerned with the finite concentration technique with increasing amount adsorbed, which will be dealt to some extent in the next section. 

Several methods have been proposed for the characterisation of the Micropore Size Distribution (MPSD) that take into account the energetic heterogeneity of solid surfaces [9,10]. The Dubinin-Radushkevich (DR) and Dubinin-Astakhov (DA) equations have been used to describe the adsorption process on structurally heterogeneous solids [11,12]. From these equations, the adsorption isotherm can be expressed as follows ... 

The heterogeneous system gas-microporous solid is considered as a homogeneous gas-solid mixture. In this ease, the following assumptions are made. 

We have carried out methane radiolysis experiments under widely varying conditions (9). The most important results are obtained either by homogeneous gamma ray irradiations with a Co source or by heterogeneous irradiations with this same gamma ray source or with fission fragments. Alumina (CAU), silica (CSU), and uranium impregnated charcoal (ECU) have been used as microporous solids. 

Ding, L.P. and Bhatia, S.K. (2001). Apphcation of heterogeneous vacancy solution theory to characterization of microporous solids. Carbon, 39, 2215—29. 

Based on the quite remarkable results obtained with TS-1 we expect that many more examples of microporous solids modified by isomorphous substitution with redox metal ions in the crystal lattice will be described in the future (see Fig. 12). Indeed, the scope for developing unique oxidation catalysts based on the concept of site-isolation in zeolites, silicalites, alpos and sapos is enormous [37], In addition to varying the redox metal the size and hydrophobicity of the cavity can be tuned by, for example, varying Si/Al ratios to provide a variety of unique heterogeneous catalysts for liquid phase oxidation. 

Most heterogeneous catalysts exist in the form of microporous solids. The catalysts are usually produced in the shape of spheres, cylinders, or monoliths, such as those shown in Figure 1. The internal surface area is typically 10-10 m /g. Catalysis occurs either on the surface of the microporous solid, as in the case of zeolites, or on the surface of microdomains of active material dispersed inside the microporous solid, as in supported metals, oxides, sulfides, etc. In either case, the high internal surface area of the microporous solid is used to obtain a high concentration per unit volume of catalytically active centers. 

The distribution function F(z) together with the quantities Zmax, z and are used to characterize the structural heterogeneity of microporous solids. 

Energetic heterogeneity of a microporous solid generated by the overlapping of adsorption forces from the opposite micropore walls can be descaibed by the adsorption potential distribution in micropores This distribution associated with Eq. (62) is given by ... 

This book will address the various fundamental aspects of adsorption equilibria and dynamics in microporous solids such as activated carbon and zeolite. The treatment of equilibria and kinetics, when properly applied, can be used for solids other than microporous solid, such as alumina, silica gel, etc. Recognizing that practical solids are far from homogeneous, this book will also cover many recent results in dealing with heterogeneous media. 

Adsorption isotherms of many microporous solids do not usually conform to the simple DR equation. Even with the adjustable parameter n in the DA equation, it also can not describe well many experimental data. This inability to fit the data is attributed to the heterogeneity of the system, that is the characteristic energy varies with the different regions in the solid. 

---