Equation Dubinin-Radushkevich

The porosity of the samples is characterised by N2 adsorption at 77 K, and CO2 adsorption at 273 K, using an automated volumetric system (Quantachrome Autosorb-6). From N2 adsorption the DR (Dubinin-Radushkevich) equation is applied for calculating the total micropore volumes, and the BET... 

Porous texture characterization of all the samples was performed by physical adsorption of N2 at 77K. and CO2 at 273K, using an automatic adsorption system (Autosorb-6, Quantachrome). The micropore volume, Vpp (N2), was determined by application of Dubinin-Radushkevich equation to the N2 adsorption isotherm at 77K up to P/Po< 0.1. The volume of narrow micropores, Vnpp (DR,C02>, (mean pore size lower than 0.7 nm) was calculated from CO2 adsorption at 273 K. 

The fresh and spent catalysts were characterized with the physisorption/chemisorption instrument Sorptometer 1900 (Carlo Erba instruments) in order to detect loss of surface area and pore volume. The specific surface area was calculated based on Dubinin-Radushkevich equation. Furthermore thermogravimetric analysis (TGA) of the fresh and used catalysts were performed with a Mettler Toledo TGA/SDTA 851e instrument in synthetic air. The mean particle size and the metal dispersion was measured with a Malvern 2600 particle size analyzer and Autochem 2910 apparatus (by a CO chemisorption technique), respectively. 

Comparison Between the Cohen-Kisarov and Dubinin-Radushkevich Equations. In a plot of log q vs. e2 the experimental points for one adsorption isotherm on zeolite frequently do not give a straight line, which would verify the Dubinin-Radushkevich equation. In this case, two distinct lines of different slopes are found (4). 

Let us assume that an experimental isotherm is perfectly described by the Cohen-Kisarov equation. When plotting the experimental points with the previous coordinates, three different cases may occur (1) if cmlA < 2, a case which was not yet found ((4) and Table I), the curve exhibits a constant convex curvature towards the ordinate axis (2) if cm /A > 2, the curve exhibits two distinct inflection points (Figure 3) where the experimental curve may easily be confused with the tangent to the inflection point, thus explaining the previous observations (3) if cm /A decreases to a value of 2, these inflection points are unified to give a large linear section, and the Dubinin-Radushkevich equation behaves as a limiting case of the Cohen-Kisarov equation. 

By combining Equations 4.12 and 4.15, and for plotting purposes, the well-known Dubinin-Radushkevich equation (DR) is obtained ... 

Stoeckli HF. Generalization of Dubinin-Radushkevich equation for filling of heterogeneous micropore systems./. Colloid Interface Sci., 1977 59(1) 184-185. 

At this point, it is feasible to correlate the liquid-phase adsorption equilibrium single component data, with the help of isotherm equations developed for gas-phase adsorption, since, in principle, it is feasible to extend these isotherms to liquid-phase adsorption by the simple replacement of adsorbate pressure by concentration [92], These equations are the Langmuir, Freundlich, Sips, Toth, and Dubinin-Radushkevich equations [91-93], Nevertheless, the Langmuir and Freudlich equations are the most extensively applied to correlate liquid-phase adsorption data. [2,87],... 

The micropore volume is defined as the pore volume of the pores < 2 nm. Microporous volumes calculated from the application of the Dubinin-Radushkevich equation to the N2 adsorption isotherms at 77 K. The mean pore size of each sample obtained from N2 adsorption was determined by applying Dubinin-Radushkevich equation. The hydrogen sorption isotherms were measured with the High Speed Gas Sorption Analyser NOVA 1200 at 77 K in the pressure range 0-0.1 MPa. 

Physisorption on microporous carbons can be described with the Dubinin-Radushkevich equation [13]... 

As a results of the experiments, we obtained hydrogen sorption isotherms for different carbon materials and empirical coefficients for the Dubinin-Radushkevich equation (5), presented in Table 3. 

TABLE 3. The empirical coefficients of Dubinin-Radushkevich equation for hydrogen sorption on the carbon materials... 

The influence of temperature can be seen on Figs. 8-9. The storage capability is increasing for lower temperatures. Figure 9 compares the behaviour of the adsorption isotherms at different temperature levels for two of the more promising samples steam activated Busofit-M8 and wood-based carbon WAC 3-00 . The shape of the isotherms in the two cases is dissimilar. The isotherms for the 77 and 153 K exhibit a classical type 1 isotherm shape indicating a microporous material. The isotherms at room temperature exhibit a much less pronounced curvature (more like type II isotherm). As is seen from plots (Fig. 9) experimental data fit the calculated adsorption values (Dubinin-Radushkevich equation) with an error sufficient for practical purposes. 

Figure 9. Hydrogen adsorption isotherms for active carbon fiber Busofit-M8 (a), wood-based cardon WAC 3-00 (b) and different temperatures (1 - 77, 2 -153, 3 - 193, 4 - 293 K) experimental data - points, calculated data (Dubinin-Radushkevich equation) - lines.

Two kinetic (CMS-Kl, CMS-K2) and one equilibrium (CMS-R) carbon molecular sieves, used originally for separation of gaseous mixtures, were investigated. The adsorption Nj isotherms at 77 K, in static conditions where obtained. In the case of the two first sieves the adsorption was so low that the calculation of parameters characterizing the texture was impossible. The volume of nitrogen adsorbed on the sieve CMS-R is remarkable From obtained results parameters characterizing micropore structure according to Dubinin -Radushkevich equation and Horvath - Kawazoe method were determined. 

From obtained isotherm were determined parameters characterizing micropore structure according to Dubinin - Radushkevich equation [6] and Horvath - Kawazoe method [7] which are presented below ... 

The applicability of the Dubinin-Radushkevich equation to the very low pressure region of isotherms of various microporous solids. 

Over the years there has been a lot of debate concerning the applicability of the Dubinin-Radushkevich equation on the very low pressure region of isotherms of microporous solids. The experimental downward deviation of the DR-plot for very low pressures is generally attributed to kinetic barriers, especially in the case of nitrogen adsorption at 77K. This low pressure region of isotherms of various adsorbents can be fitted with the Langmuir equation. Hence it is shown that the downward deviation is not due to experimental factors but reflects a different adsorption mechanism. 

All the nitrogen and argon isotherms could be fitted with the Dubinin-Radushkevich equation between, typically, 10 and p/po 10. At higher pressures capillary condensation causes the isotherm to diverge. At lower pressures the typical deviation described in Fig 1 was observed. The carbon dioxide isotherm showed only a minor deviation from the DR-plot (one point) and was hence excluded from this study. 

Specific surface areas of various carbonized materials were measured by nitrogen gas adsorption with BET methods using an automated surface area analyzer (micro-track type 4200, Nikkiso, Japan). For mesopores whose diameter were less than SO nm, the surface areas and pore volumes were measured by carbon dioxide adsorption. The carbon dioxide adsorption at 298 K was measured with Bellsorp 28 (BEL Japan). The pore volume was determined using Dubinin-Radushkevich equation [4], and the surface area was determined by Medek s method [S]. 

A similar technique is based on the theory of micropore volume filling. It states that the total microporous volume accessible to a given adsorbate can be obtained from the Dubinin-Radushkevich equation as a function of the temperature, relative pressure, and characteristic energy of adsorption. When this procedure is applied to a few linear or spherical molecules (as probes) of different but known sizes, the adsorption isotherms of these gases at the same temperature can be employed in combination with their... 

The main porous structure characteristics (Table 2) were determined on the basis of benzene vapor adsorption isotherms using McBain-Baker sorption balances at 20°C (293 K), i.e., the specific BET surface area (5bht) [39], the surface area of mesopores (5 ,e), and the parameters of the Dubinin-Radushkevich equation (the volumes of the micropores and supermicropores. Woi and W 2, and the characteristic energies of adsorption, E, and o ) 136,37). In addition, the total micropore volume (ZVT, ) and geometric micropore surface area (5J 1168] were calcu-... 

Table 4 Surface properties of the lignocellulosic wastes and derived chars, as estimated from Nj and CO2 adsorption data applying BET and Dubinin-Radushkevich equations.

The benzene adsorption/desorption data were used to analyze the porous structure of activated carbons. The BET specific surface area, Sbet, was estimated from the linear BET plot. The adsorption process in microporous materials is well described by the pore filling model. Taking into account the heterogeneity of micropore structure, a special form of Dubinin-Radushkevich equation, the two-term DR isotherm was applied [6,7] allowing for determination of micropore volumes and adsorption energies ... 

N2 and CO2 adsorption isotherms at 77 K and 273K, respectively, were carried out with an Autosorb-6 equipment at subatmospheric pressures. The densities used for liquid N2 at 77K and adsorbed CO2 at 273 K were, respectively, 0.808 g/ml and 1.023 g/ml [4,9,10]. The density of the CO2 adsorbed in microporous carbons was determined in previous studies [4,8-10]. This value at 273K is 1.023g/cc and it is between the value of the liquid CO2 at this temperature and the estimated by Dubinin considering the b constant of the Van der Waals equation of the C02[24]. Dubinin-Radushkevich equation [24,25] was used to assess the micropore volume from gas adsorption. 

A proper comparison of the N2 and CO2 adsorption experiments as well as the differences between samples is conducted by using the characteristic curves plots [9,10]. The characteristic curves have been calculated by applying the Dubinin-Radushkevich equation [24-25] (eq. 1) to the different adsorption isotherms. 

Table 1 contains the micropore volumes obtained by applying the Dubinin Radushkevich equation [22] to the N2 and CO2 isotherms adsorption at 77K and 273K, respectively. For comparison purposes, the table also includes the BET surface area [23],... 

The volumes of mesopores (Vmes) and benzene accessible micropores (Vmic.c6H6) were calculated, as described before [12], from benzene sorption isotherms, taking account of the mesopore size distribution and of the Gurvitsch mle. Submicropore volumes (Vs-mic) were calculated as differences between the values of Vo.dr,co2 (parameter from the Dubinin-Radushkevich equation applied to CO2 adsorption) and respective volumes of benzene accessible micropores. In cases where these latter volumes were higher than Vo,dr,co2, the volumes of submicropores were assumed to be zero. 

Tables la and lb show the quantitative results of the nitrogen adsorption-desorption isotherm analysis, i.e., BET specific surface area (Sbet), pore volume (Vp) calculated from the adsorbed volume at saturation, and total micropore volume (Vdub) calculated by the Dubinin-Radushkevich equation [19]. Bulk density of each sample is also displayed.

Wo, micropore volume from the Dubinin-Radushkevich equation apphed to CO2 adsorption at 77 K Lo, mean micropore width from CO2 adsorption at 77 K V2, pores with diameter between 3.7 and 50 nm V3, pores with diameter wider than 50 nm. 

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