Dubinin-Astakhov equation

The original DR equation is thus a special case of the Dubinin-Astakhov equation, with m = 2 parameter of Equation (4.18) for m = 2 is related to the structural constant B of the DR treatment through the simple expression... 

Dubinin-Kadushkevich. This model (29) is the same as the more general Dubinin-Astakhov equation (30) (see below), with n = 2. Dubinin-Astakhov ... 

Stoeckli (1993) has pointed out that the Dubinin-Astakhov equation (Equation (4.45)) can be derived from Equation (4.52), but McEnaney (1988) and others (e.g. Jaroniec et al. 1997) have drawn attention to the difficulty in arriving at an unambiguous interpretation of the energy distribution function. Indeed, Stoeckli et al. (1998) have now pointed out that Equation (4.45) can be usefully applied to a number of adsorption isotherms on non-porous solids. A comprehensive review of the significance and application of Equation (4.52) is given by Rudzinski and Everett (1992). 

Textural parameters derived from the Dubinin-Astakhov equation applied to CO2... 

Specific micropore volumes derived from the Horvath-Kawazoe (HK) and Dubinin-Astakhov (DA) methods. Characteristic energies from the Dubinin-Astakhov equation. 

The pore volumes of the obtained hard carbons were measured using the molecular probe method [3]. Adsorption isotherms of the probe molecules were measured at 298 K using an adsorption apparatus (Bel Japan, Belsorp 28). The employed probe molecules were CO2, C2H6> n-C4H o and (-C4H10 (minimum molecular dimensions 0.33, 0.40, 0.43 and 0.50 nm, respectively). By applying the Dubinin-Astakhov equation (n=2) [1] to the measured isotherms, the limiting micropore volumes corresponding to the minimum size of the adsorbed molecules were determined. 

Chen, S.G. and Yang, R.T. (1994). Theoretical basis for the potential theory adsorption isotherms. The Dubinin-Radushkevich and Dubinin-Astakhov equations. Langmuir, 10, 4244-9. 

Stoeckli, F., L6pez-Ram6n, M.V., and Moreno-Castilla, C. (2001). The adsorption of phenolic compounds from aqueous solutions by activated carbons described by the Dubinin—Astakhov equation. Langmuir, 17, 3301-6. 

Langmuir and Freundlich models assume an adsorption mechanism of surface coverage-type. A useful model for correlating experimental data with adsorption phenomena based on a pore filling-type mechanism, is the Dubinin-Astakhov equation ... 

Adsorption equilibrium data of SO2, NH3 and CO2 were analyzed by the linearized forms of the Langmuir and Freundlich equations (see Eqns. 2 and 4). The water vapour isotherm was analyzed by the linearized forms of the Dubinin-Astakhov equation (6), because of the above mentioned condensation phenomena. 

As the Freundlich equation is an empirical relationship, the parameters p and n are not connected to quantities of physical significance. On the contrary, Irom the parameter Qo of the Dubinin-Astakhov equation an estimation of the volume Vt of microporous system may be obtained. In fact, the adsorbed amount at the saturation pressure P , Qo, can be converted in microporous volumes Vt, dividing it by the density of water at 25 °C (see Section 2). The obtained value of 0.116 cm /g of dry tuff is in reasonable agreement with analogous values (0.101-0.136 cm /g), estimated for clinoptilolite-rich rocks from Cuba (Roque-Malherbe et ai. 1995). 

Langmuir model is an excellent fit for the adsorption of SO2 and NH3 on Pentalofos tuff and a fairly good representation in the case of CO2. In the latter case, the Freundlich model appears, however, to be more suitable. On the contrary, as expected, in the fitting of the water vapour adsorption isotherm, best results are obtained using the Dubinin-Astakhov equation. 

A brief review of methods based on the integral adsorption Eq, (73) showed that they are attractive to evaluate the pore volume distribution. The analytical solution of this integral for sub-integral functions represented by the Dubinin-Astakhov equation and gamma-type... 

Equation parameter in Dubinin-Astakhov equation Number of adsoibed molecule layers Avogadro constant... 

The exponent 2 in the D-R equation can be replaced by n, which is called the Dubinin-Astakhov equation (or D-A equation). The value of n empirically ranges from below 1 to about 14 (Kapoor and Yang, 1988 Kapoor et al., 1989a). The parameter n can be related to heterogeneity (Jaroniec and Madey, 1988 Rudzinski and Everett, 1992). The theoretical basis given by Chen and Yang (1994) is also valid for the D-A equation. 

Siemieniewska, T., et ah. Application of the Dubinin-Astakhov equation to evaluation of benzene and cyclohexane adsorption isotherms on steam gasified humic acid chars from brown coal. Energy Fuels, 4(1), 61-69(1990). 

Rudzinski, W. Nieszporek, K., and Dabrowski, A Application of the Dubinin-Astakhov equation to the study of the geometric structure, energetic surface heterogeneity and surface topography of carbonaceous adsorbents, Adsorpt. Sci. Technol., 10, 35-62 (1994). 

On the correct use of the Dubinin-Astakhov equation to study the mixed-gas adsorption equilibria. 

Dubinin-Astakhov equation was originally considered to have integer value, and n =, 2 and 3 respectively corresponds to adsorption on the surface, in micropores and ultramicropores where adsorbed molecules lose one, two or three degrees of freedom. For nonpolar adsorbates, the simplified estimates given in Table 3.1 have been proposed. 

Table 3 I Parameters of Dubinin-Astakhov Equations in Relation to ratio of pore size, D, and molecular size, d AHd represents heat of vaporization... 

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