Microporous carbons description

Stoeckli HF. On the description of micropore distributions by various mathematical-models. Carbon, 1989 27(6) 962-964. 

Porous carbons were prepared using MCM-48 and SBA-15 mesoporous templates and various carbon precursors (see Chapter 3 for preparation description). Figure 8.11 displays the nitrogen adsorption isotherms at 77 K of SBA-15 and of the corresponding templated carbon obtained by carbonization of sucrose in the template. Both isotherms show a bimodal porosity in the templated carbon, mesopores are generated by the removal of the silica walls, and micropores are present in... 

The thermodynamic approach considers micropores as elements of the structure of the system possessing excess (free) energy, hence, micropore formation processes are described in general terms of nonequilibrium thermodynamics, if no kinetic limitations appear. The applicability of the thermodynamic approach to description of micropore formation is very large, because this one is, in most cases, the result of fast chemical reactions and related heat/mass transfer processes. The thermodynamic description does not contradict to the fractal one because of reasons which are analyzed below in Sec. II. C but the nonequilibrium thermodynamic models are, in most cases, more strict and complete than the fractal ones, and the application of the fractal approach furnishes no additional information. If no polymerization takes place (that is right for most of processes of preparation of active carbons at high temperatures by pyrolysis or oxidation of primary organic materials), traditional methods of nonequilibrium thermodynamics (especially nonequilibrium statistical thermodynamics) are applicable. 

The nonequilibrium statistical thermodynamic approach in the description of microporous materials prepared by pyrolysis of organic materials (active carbons) comprises two principal methods these for systems with regular and random fluxes. These methods comprise steady-state and nonsteady-state models which can be formulated for homo- and heterogeneous systems. 

High separation factors can be obtained with microporous membranes with a pore diameter smaller than 2 nm and are realised with carbon, silica and zeolite membrane systems. The description of these systems is still in its infancy. 

The thermodynamic description of the adsorption isotherm of a supercritical gas was shown in the above subsection. The thermodynamic approach cannot explain a more physical meaning of Wl. The molecular potential theory treats the interaction between an admolecule and the pore surface as a function of the distance, as mentioned before. If we use the model of the two parallel semi-infinite slabs of graphite as the micropore walls of activated carbon, the additive form gr(z) of the 9-3 potentials from both graphite slabs is obtained [43] ... 

Here B is the temperature-independent structural parameter associated with the micropore sizes, and is the similarity coefficient, which reflects the adsorbate properties [93]. Eq. (36) is commonly used for description of gas and vapor adsorption on microporous active carbons [13, 93, 111]. 

Strongly activated carbons possess a broad distribution of micropores because some walls between adjacent micropores burn off. In this case the DR and DA equations cannot give a satisfactoiy representation of adsorption data [115], Based on the postulate that DR Eq. (36) and DA Eq. (37) describe adsorption in uniform micropoies, Izotova and Dubinin [116] proposed the following two-tenn equation for description of adsorption on solids with bimodal microporous structure ... 

It was shown elsewhere [68,105,129] tliat the Jaroniec-Choma (JC) equation, which was obtained ty generalization of the DA Eq. (37) for n = 2 or n = 3, gives good description of gas and vapor adsorption for many microporous active carbons. A general form of the JC equation can be written as [105] ... 

The pore size distribution in the carbon support is an important factor for a well performance of the catalyst. Pores in the nanometric scale are classified by lUPAC in three groups the micropores are those with diameters lower than 2 nm, the mesopores with diameters between 2 and 50 nm and the macropores with diameters larger than 50 run. Each pores size offers different benefits, the micropores produce materials with high surfaces area but could be inaccessible to liquid solutions or have slow mass transport. A material with mesopores has a lower surface area but better accessibility than those with micropores. FinaUy, materials with macropores show the lowest surface area, but they are easily accessible to liquid fuel. For this reason, the structured carbons, principally mesoporous carbon, have attracted considerable attention due to their potential application in the catalyst area, where the challenging is to favour the dispersion of catalyst and allow the accessibility of liquids that feed the anode side of a DMFC. In the following sections a description of different carbons support wdl be discussed stressing on the effect of the porous structure. 

Practical solids are generally heterogeneous, and this subject of heterogeneity is the topic of Chapter 6, where the concept of distribution of the interaction energy between adsorbate molecules and solid atoms is discussed. For systems, such as non-polar hydrocarbons on activated carbon, where the adsorption force is dispersive by nature, the role of micropore size distribution is important in the description of solid heterogeneity. The concept of distribution is not restricted to the interaction energy between adsorbate molecules and solid atoms, it can be applied to the Henry constant, the approach of which has been used by Sircar, and it can be applied to free energy, which was put forward by Aharoni and Evans. 

Swiatkowski, A, Trznadel, B.J., and Zietek, S., Description of active carbon micropore size distribution based on the Horvath-Kawazoe equation adapted to benzene adsorption isotherms, Adsorpt. Sci. Technol., 14(1), 59-68(1996). 

An alternative to the localized theory of adsorption is the so-called potential theory, which has been developed as a slab adsorption theory on a surface and its analog for adsorption in microporous media, the theory of volume filling in micropores (TVFM). The potential theory of adsorption, first formulated by Polanyi [91], is widely used for the description of adsorption of gases on a solid. The TVFM is applied to adsorption in activated carbons, silica gels, and other types of microporous medium. 

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