Volume filling of micropores

Virial Isotherm Equation. No isotherm equation based on idealized physical models provides a generally valid description of experimental isotherms in gas-zeolite systems (19). Instead (6, 20, 21, 22) one may make the assumption that in any gas-sorbent mixture the sorbed fluid exerts a surface pressure (adsorption thermodynamics), a mean hydrostatic stress intensity, Ps (volume filling of micropores), or that there is an osmotic pressure, w (solution thermodynamics) and that these pressures are related to the appropriate concentrations, C, by equations of polynomial (virial) form, illustrated by Equation 3 for osmotic pressure ... 

Dubinin and coworkers, during the course of their extensive studies on activated carbons, have developed the so-called theory of volume filling of micropores. Based on numerous experimental data, Dubinin and collaborators have added a second postulate to the Polanyi theory, which complements it. For an identical degree of filling of the volume of adsorption space, the ratio of adsorption potentials for any two vapors is constant ... 

Dubinin MM. Generalization of the theory of volume filling of micropores to nonhomogeneous microporous structures. Carbon, 1985 23(4) 373-380. 

Benzene was the most popular adsorptive in many early studies of the pore structure of activated carbons (Dubinin, 1958,1966 Cadenhead and Everett, 1958 Smisek and Cemy, 1970). Indeed, in order to construct the characteristic curve for a given micro-porous carbon, Dubinin and his co-workers (Dubinin, 1966) originally adopted benzene as the standard adsorptive thus, in the context of the Dubinin theory of the volume filling of micropores (TVFM), the scaling factor p (C6H6) = 1 (see Chapter 8). 

Based on the Dubinin s theory of volume filling of micropores, a modified Dubinin-Stoeckli (DS) equation was used to estimate micropore contribution with correction related to adsorption in mesopores [7]. The Sps, Vds and other parameters with the DS subscript (Table 1) were calculated over the pore range at the half-widA xds = 0.2-1.0 nm. 

The concept of volume filling of micropores under review is based on a radical difference of adsorption in micropores as a limiting case as compared with the opposite limiting case of adsorption on the surface of nonporous adsorbents of identical chemical nature. The concept of adsorption in micropores is of a thermodynamical nature, and its main initial principle, which has the meaning of a rational approximation, con-... 

Naturally, the concept of volume filling of micropores does not replace, but merely supplements the concepts of adsorption developed at the so-called molecular level, using, in particular, the molecular-statistical approach. We believe that further development of both approaches will in the long run result in the substantiation of the initial approximate propositions regarding volume filling of micropores, since they express the principal experimental facts. 

Generalization of the Concept of Volume Filling of Micropores to Adsorption of Gases and Vapors on XeoUtes... 

The examples above demonstrate satisfactory agreement between the calculated results and the experimental data. This shows that the initial approximate assumptions are reasonable. In most cases, the one-term Equation 5 is applicable for the description of adsorption equilibria on zeolites, particularly for zeolites with small voids (zeolite L, chaba-site, erionite, mordenite) for which, in adsorption of hydrocarbons, n = 3 as a rule. The concept of the volume filling of micropores makes it possible to describe adsorption equilibria over sufficiently wide ranges of temperatures and pressures (using fs instead of Ps) with the use of only 3 experimentally determined (usually from 1 adsorption isotherm for the average temperature) constants. Wo, A, and n. The constant n requires only a tentative estimation, since it is expressed by an integer. 

If we neglect the difference between electrostatic and dispersion interaction energies, then, in accordance with the concept of volume filling of micropores described previously, the equation of adsorption of methane on zeolite L will be expressed by Ref. 3 as... 

G. V. Tsitsishvili (Academy of Sciences of the Georgian SSR, Tbilisi, USSR) The nev method of description of the adsorption isotherms allows one, on the basis of the theory of volume filling of micropores, to characterize adsorption on the microporous adsorbent containing adsorption sites of different nature. For zeolites, there are approximately two adsorption sites cations and framework. The existence of cations in different positions must be taken into account. It is important to use the Dubinin approach to desorption-adsorption equilibrium on decationized and other forms of zeolites. We have already obtained some good results in this direction. 

It is shown that the position of PSDs calculated by the HK method depend strongly on the A(w)-relationship used. For instance, the pore widths at the maxima of PSDs obtained by the HK method with the Saito-Foley expression for cylindrical pores are underestimated about 1.4 nm. However, the HK method with the relationship between A and w established on the basis of good-quality MCM-41 materials [26] provides an accurate estimation of the pore widths of mesoporous silicas. While the position of PSD may be improved by a proper selection of the A(w)-relation, its unphysical features remain. The height of main peak is significantly reduced in order to compensate the appearance of an artificial small peak and tail in the micropore-mesopore transition range. These artifacts arise from the condensation approximation used in the HK method, which does not provide a good representation for the volume filling of micropores. 

A. Kiselev developed the adsorption-structural method of investigation (129), which made possible a rational classification of adsorbents (130-132). Dubinin, Radushkevitch, Bering, Serpinsky, and others have developed on the basis of their experimental results a theory on the physical adsorption of gases and vapors in microporous adsorbents that they call the theory of volume filling of micropores. The theory is applicable to almost all the adsorption systems, including microporous silica gels and porous glasses (133, 134). 

Plachenov (96, 97) estimated the limiting dimensions of the equivalent radii of mesopores. The distribution of the volume of the mesopores calculated from their equivalent radii was compared with capillary condensation measurements. The macroporous and the intermediate mesoporous structure were determined, as were the volume of the micropores and the constant in the equation of the isotherm adsorption theory describing the volume filling of micropores (133, 134). 

The nitrogen adsorption isotherm recorded on ZSM-5 zeolite prepared without carbon displays almost rectangular shape being typical for purely microporous materials (Fig. 3). The isotherms on all samples prepared using carbon template (Fig. 3) posses both micro- and mesoporous features. The almost vertical rise of the adsorbed amount of nitrogen up to ptp = 0.05 corresponds to the volume filling of micropores. The isotherms exhibit hysteresis loops at plpo > 0.4, which are indicative for the capillary condensation in mesopores. The distribution of these... 

The Dubinin-Radushkevich (DR) equation, proposed in 1947 [110], undoubtedly occupies a central position in the theoiy of physical adsorption of gases and vapors on microporous solids (the theoiy of volume filling of micropores TVFM) [93], The amount adsorbed in micropores dm,-is ... 

The potential theory of adsorption was introduced by Polanyi in 1914. Dubinin [48,49] and Stoeckli et al. [50] improved the theory and termed it the theory of volume filling of micropores (TVFM). This theory has been widely used in correlating the effect of temperature on the adsorption isotherms of pure gases. The modern formulationof TVFM is the Dubinin-Astakhov (DA) equation, which is expressed as... 

The key issue from both a practical and a fundamental viewpoint is whether or not the entire adsorbent surface is available for adsorption. (Multilayer adsorption or volume filling of micropores is not considered here, nor is the possibility of molecular sieving.) Its resolution depends on the answers to two questions ... 

This has led to the development of the theory of volume filling of micropores (TVFM theory). The theory provides a satisfactory description of the shapes of adsorption isotherms where the adsorption takes place largely in micropores. It is based on the assumption that the characteristic adsorption equation expressing the degree of filling of micropores (i.e., the volume filling of micropores) is a function of the differential molar work of adsorption. The adsorption process in this case involves dispersion forces as the main component in the adsorption-adsorbent interactions. 

FIGURE 4.16 Comparison of micropore distribution of carbon CEP-59 calculated using Dubinin theory of volume filling of micropores and the experimental data obtained fiom molecular sieve experiments in the region of micropore width less than 0.75 nm. (After Stoeckli, F.H. and Kraehenbeuhl, F., Carbon, 19, 353, 1982. With permission.)... 

Kadlec, O., Mechanisms of volume filling of micropores during adsorption of vapours, Adsorpt, Sci. Technol., 1(2), 133-150(1984). 

Jaroniec, M., Fifty years of the theory of the volume filling of micropores, Adsorption, 3(3), 187-188 (1997). 

Fifty Years ofthe Theory ofthe Volume Filling of Micropores,... 

Stoeckli HR, Krachenbuehl R. The enthalpies of immersion of active carbons, in relation to the Dubinin theory of volume filling of micropores. Carbon 1981 19(5) 353-356. 

In order to characterize the adsorbents micropore syston we used the Dubinin theory of the volume filling of micropores. The isotherm for sUt-shaped micropores of activated carbon was described by the Dubinin-Asthakov (DA) equation in the relative pressure range 10 -0.2 [5] ... 

Another application of the potential theory is adsorption in micropores (the theory of volume filling of micropores), which is illustrated in Fig. 17. In this case, the variable x represents volume, so that the value of A is interpreted as part of the pore voliune filled by the adsorbate. Correspondingly, the surface excesses are substituted by excess amoimts adsorbed per unit volume. Instead of the dependence s(x), the distribution x(e) of the pore volume by potentials is considered. Every so often, this distribution is given by the generalized Dubinin dependence [98-100]. The characteristic parameters of this dependence are the total pore volume Xq, the characteristic adsorption energy Cq. and the exponent... 

FIG. 17 Theory of volume filling of micropores distribution of volmnes (x) by the values of the potential. 

The Oij-method (1,2) provides a useful means to detect the presence of mesoporosity in a porous solid it can also be successfully applied to evaluate the volume of micropores, especially in solids devoid of mesopores. However, the capillary structure of activated carbons is frequently composed of both kinds of porosity and so the evaluation might become more difficult. Attempts were made by various authors to transform experimental isotherms, with the purpose to adapt them to a single kind of porosity. This can be done by elimination of adsorption on the surface of mesopores, as is the case when the Dubinin theory of volume filling of micropores is applied (3). Another interesting approach -the carbon dioxide subtraction method (CDS)- has recently been proposed (4), with the aim to obtain an isotherm for porous systems devoid of micropores. In the present paper some related problems are considered, with particular attention to the evaluation of the carbon dioxide adsorption data. The research was carried out on a suite of progressively activated chars from humic acids. 

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