Dubinin theory

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). 

In Chapter 2, we discussed the fundamentals of adsorption equilibria for pure component, and in Chapter 3 we presented various empirical equations, practical for the calculation of adsorption kinetics and adsorber design, the BET theory and its varieties for the description of multilayer adsorption used as the yardstick for the surface area determination, and the capillary condensation for the pore size distribution determination. Here, we present another important adsorption mechanism applicable for microporous solids only, called micropore filling. In this class of solids, micropore walls are in proximity to each other, providing an enhanced adsorption potential within the micropores. This strong potential is due to the dispersive forces. Theories based on this force include that of Polanyi and particularly that of Dubinin, who coined the term micropore filling. This Dubinin theory forms the basis for many equations which are currently used for the description of equilibria in microporous solids. 

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.)... 

The adsorption on a solid surface, the types of adsorption, the energetics of adsorption, the theories of adsorption, and the adsorption isotherm equations (e.g., the Langmuir equation, BET equation, Dubinin equation, Temkin equation, and the Freundlich equation) are the subject matter of Chapter 2. The validity of each adsorption isotherm equation to the adsorption data has been examined. The theory of capillary condensation, the adsorption-desorption hysteresis, and the Dubinin theory of volume fllhng of micropores (TVFM) for microporous activated carbons are also discussed in this chapter. 

The Myers-Prausnitz-Dubinin Theory and Non-ideal Adsorption in Microporous Solids,... 

Lavanchy A, Stoeckli E Dynamic adsorption of vapour mixtures in active carbon beds described by the Myers-Prausnitz and Dubinin theories. Carbon 1997 35(10-11) 1573-1579. 

Marsh H, Siemieniewska T. Adsorption of carbon dioxide on carbonised anthracite. Interpretation by Dubinin theory. Fuel 1967 46(6) 441-457. 

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. 

Immersion calorimetry is a useful technique for the characterization of porous materials. The heat evolved in the immersion process is directly related to the integral enthalpy of adsorption if the experiment is carried out at constant pressure and temperature [1]. The experimental data, which are obtained by immersion measurements, are normally used to determine the textural characteristics of the adsorbent, i.e. the micropore volinne or the surface areas accessible to the wetting liquid. In relation to the former Stoeekli et al [2] consider that a thermodynamic consequence of the Dubinin theory is the equation 1. 

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] ... 

Fig. 5 ws the CH4 isotherms measured at 77 K on NTR, LIM, CFC and AC-C03 samples and displayed in a logarithm scale in order to magnify the adsorption range for relative pressure bdow 0.1. Both isotherm step shape and position at F/Pg = 0.5) are different BET and Dubinin theories show, that lower the position of the step, lower the adsorption energy of the adsorbent (2 and respectively). Obviously, the position values are lower for micropotous adsorbents (NTR, LIM, AC-C03) than that of CFC. Isotherm shapes of the mictopcnous adsorbents are dorninated by the absolute pore width and geometry [12]. 

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. 

The main objetive of the work described here is to evaluate the microporosity in a series of activated carbons with increa.sing burn-off and ash (CrjOj) content using the isotherms on non-porous carbon and Cr Oj. samples as references in the< -plot method and the comparison with results obtained from the Dubinin theory and n-nonane preadsorption. 

The adsorption and desorption isotherms of water vapor are drawn at 25°C for dealuminated HY zeolites upon framework Si/Al ratio. The isotherms are compared to that of the parent NaY zeolite. The isotherm changes in shape from the type I to the type IV with an hysteresis loop changing from the type H4 to the type H2, as increases the Si/Al ratio. The POLANYI-DUBININ theory is used to determine the micropore volume accessible to water. It decreases with increasing Si/Al ratios, down to zero at a Si/Al ratio of 35. Such a result is accounted by the adsorption on the hydrophilic centers which are the cations (H ) associated with the structural aluminium ions, each cation being coordinated by 8H2O. 

Adsorption of hydrocarbons or nitrogen reflects the same trend as did water adsorption, with respect to the biporous character of dealuminated samples (structural micropores and secondary mesopores) (refs. 2, 4-6). The non polar character of n-hexane leads to use such a molecule for determining the micropore volume by the POLANYI-DUBININ theory. The study of the pore size distributions from adsorption isotherms and mercury porosimetric measurements characterizes two pore diameters of the secondary pore network, the one between 3 nm and 4 nm and the second to about 20 nm (refs. 7, 8). 

A. Elm Chaouri, M.H. Simonot-Grange, Hydration thermodynamic functions of hectorite and montronite from experimental Isotherms and the Polanyi-Dubinin theory, 9th International Clay Conference, Strasbourg, France, August 28 September 1, 1989. 

No current theory is capable of providing a general mathematical description of micropore fiUirig and caution should be exercised in the interpretation of values derived from simple equations. Apart from the empirical methods described above for the assessment of the micropore volume, semi-empirical methods exist for the determination of the pore size distributions for micropores. Common approaches are the Dubinin-Radushkevich method, the Dubinin-Astakhov analysis and the Horvath-Kawazoe equation [79]. 

H.H. Dubinin, V.V. Serpinsky and K.O. Murdmaa (Eds.), Adsorption and Adsorbents (Russ.) (Proc. 6th Allunion Conf. Adsorption Theory, Moscow, November 18-21, 1985), Nauka, Moscow, 1987. 

Mikhail, Brunauer, and Bodor proposed an extension of deBoer s r-method for the analysis of micropores which offers several advantages. These include the ability to obtain the micropore volume, surface, and their distributions from one experimental isotherm. Data for the MP (micropore analysis) method need not be measured at the very low pressures needed for the Dubinin and Kaganer theories. The method... 

An analytical method for applying Polanyi s theory at temperatures near the critical temperature of the adsorbate is described. The procedure involves the Cohen-Kisarov equation for the characteristic curve as well as extrapolated values from the physical properties of the liquid. This method was adequate for adsorption on various molecular sieves. The range of temperature, where this method is valid, is discussed. The Dubinin-Rad/ush-kevich equation was a limiting case of the Cohen-Kisarov s equation. From the value of the integral molar entropy of adsorption, the adsorbed phase appears to have less freedom than the compressed phase of same density. 

The method proposed here for applying Polanyi s theory analytically agrees well with experiments at temperatures not too far above the critical temperature of the adsorbate. In this domain, the Dubinin-Radushkevich... 

Experimental isotherms from Barrer and Stuart (15) are used as a check on the present theory. Following the liquid filling theory of Dubinin (ll) and other (12, 13, lU), saturation values of for Argon on LiX at the various experimental temperatures are as follows ... 

Now let us overview the theoretical adsorption models for characterization of the pore structures according to the pore size range. For physical adsorption of the gas molecules on such microporous solids as activated carbons and zeolites, Dubinin and Radushkevich95 developed an empirical equation, which describes the volume filling process in the micropores. Their theory incorporates earlier work by Polanyi96 in regard to the adsorption potential Ad defined as... 

Peculiarities of Adsorption in Microporous Carbons (the Polanyi Potential Theory Dubinin and Related)... 

The temperature invariance of the adsorption potential (fundamental postulate of Polanyi s theory) has been widely proved, especially, by the extensive work led by Dubinin [31-34],... 

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 ... 

FIGURE 4.6 PSDs obtained from the high-resolution N2 adsorption isotherms at 77 K (Figure 4.4) by applying different theories (a) Horvath-Kawazoe (b) Dubinin-Astakhov, and (c) DFT method. 

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

Dubinin MM. The potential theory of adsorption of gases and vapors for adsorbents with energetically nonuniform surfaces. Chem. Rev., 1960 60 235-241. 

The Dubinin adsorption isotherm equation is a good tool for the measurement of the micropore volume. This isotherm can be deduced with the help of Dubinin s theory of volume filling, and Polanyi s adsorption potential [11,26], The Dubinin adsorption isotherm equation has the following form [11]... 

The theory of microporous volume filling, worked out by Dubinin, is widely used for quantitative characteristic of adsorptive properties and basic varieties of porous structure. Equilibrium state equation (3) includes the saturation pressure Psal. Since the hydrogen sorption isotherms are measured within the temperature and pressure intervals comprising the regions of supercritical states of the adsorptive (Tcr — 33.24 K Pcr— 1.298 MPa), the notion of saturation pressure... 

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