Dubinin-Stoeckli theory

However a recent study has shown that the Stoeckli method (based on the Dubinin-Astakhov theory) [6] gave results similar to those obtained from the molecular simulation methods [9]. On the other hand, the H-K and the MP methods are known to be rather inconsistent. 

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. 

Figure 3 Comparison of PSDs obtained using the Dubinin-Stoeckli (DS), Horvalh-Kawazoe (HK), and density fitnctional theory (DFT) methods to interpret an isotherm generated from molecular simulation of nitrogen adsorption in a model carbon that has an Gaussian distribution of slit pore widths (18]. Results are shown for mean pore widths of 8.9 A (left) and 16.9 A (right).

Stoeckli and Kraehenbuehl [42] discussed the derivation of an exact expression for the enthalpy of immersion of activated carbons using Dubinin s theory as a starting point They tested this expression with experimental data for 10 different carbons immersed in benzene and -heptane. In a subsequent paper, Kraehenbuehl et al. [43] reported the use of immersion calorimetry to determine the micropore size distribution of carbons in the course of then-activation. Later on, Stoeckli and Centeno [44] pointed out that immersion calorimetiy is a useful tool for characterizing solid surfaces in general, but in the case of microporous solids it usually requires complementary information obtained from the adsorption isotherms. They also discussed the limitations and possibilities of the technique and recommended that at least one adsorption isotherm from the vapor phase (e.g., CH2CI2 or CsH ) be determined to remove all the uncertainties. 

Stoeckli, F., Dubinin s theory for the volume filling of micropores An historical approach, Adsorpt. Sci. Technol., 10, 3-16(1994). 

The low partial pressure regions of an isotherm are also where micropore filling occurs. Micropores, with widths less than 2 nm, are easily filled by a few monolayers of most adsorbents, and the second group of equations or theories attempt to extract micropore characteristics from the initial stages of the isotherm. These are similar to the surface area techniques and include Henry s Law based interpretations, the Langmuir-Brunauer equation [IS], and the Dubinin-Stoeckli based theories [16,17]. 

NTR suggest that these mesopores are probably closed. In order to confort this hypothesis, it could be interesting to p orm experimental methods such as liquid intrusion and thermoporosity [17], Gas adsorption study has revealed a TS deposits microporosity and its quantitative characterization has been done using Dubinin-Asthakov and Stoeckli theory. To valid these results, we will extend the number of probe molecules and compare our experimental results with DFT a statistical method [18]. Finally, this observed multiscale porosity can play a role in diffusion and retention of hydrogen, studies are on progress to put in evidence this effect. 

Dubinin-Stoeckli, DS). These methods are based on Dubinin s theory of the volxmie filling of micropores (TVFM), the density functional theory (DFT) and the Horvath-Kawazoe method. However, CO2 provides a complement to N2 adsorption for the assessment of the narrow microporosity [19]. A frequently observed disagreement between the PSD obtained finm adsorption isotherms of different gases is mostly attributed to molecular sieving and networking effects [20], and to specific adsorbate-carbon interactions [9, 21]. Although these factors are important, possible inconsistencies in the PSD may also be caused by the choice of parameters for intermolecular interactions [9]. 

II. MODELS BASED ON THEORY OF VOLUME FILLING A. Dubinin-Stoeckli Method... 

Sorption in micropores can be described by the Dubinin-Radushkevic formalism that has been adapted by Stoeckli et al. This is a largely empirical approach and it should be emphasized that the use of a combination of Langmuir types isotherm leads to similar quantitative results. For evaluation of the distribution of micropores, one can either rely on high-resolution measurements of mostly nitrogen adsorption as suggested by Horvath and Kawazoe or use a combination of probe molecules of different minimum kinetic diameter. More recently, approaches based on density functional theory are put forward. 

When the micropore size is used as the distributed variable, a relationship between the interaction energy and the micropore size has to be known, and this can be determined from the potential energy theory, or if the local isotherm used is the DR or DA equation, the relationship between the characteristic energy and the micropore size proposed by Dubinin and Stoeckli could be used (see Section 4.5). 

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... 

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.)... 

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. 

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. 

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