Dubinin-Radushkevich equation for

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

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

P-20 - Application of adsorption Dubinin-Radushkevich equation for study of -pentane and w-xylene conversion catalysts microporous structure... 

Common evaluation tools that provide quantitative information are the Density Functional Theory (DFT) for micropores and mesopores, Hie Dubinin-Radushkevich equation for the extraction of characteristic parameters on micropores, the t-plot and the oLg-plot for the separation of surface area located in micro- and nonmicropores, the method to calculate the so-called BET surface area and the BJH relationship that provides access to the mesopore size distribution. 

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... 

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). 

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

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],... 

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. 

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. 

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. 

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]. 

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. 

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],... 

Based on the Polanyi potential theory, different approaches to describe the adsorption behavior of a purely microporous material (isotherm type I, Figure 21.25) have been undertaken by Dubinin and Stockli in collaboration with different other scientists. The simplest relationship that can be considered the base for all other variants is the Dubinin-Radushkevich equation [58] ... 

The Dubinin-Radushkevich equation with its numerous modifications is very important for the adsorption methods of characteristics of most industrial adsorbents. These adsorbents have a complex and well developed porous structure including pores of different shapes and widths but micropores play the... 

Activated carbons and CMS were characterized by measuring the adsorption isotherms of N2 at 77 K and of CO2 at 298 K. A low temperature, N2 adsorption apparatus (Quantasorb, by Quantachrome) was used for the determination of N2 adsorption isotherms. CO2 adsorption data were obtained with a laboratory volumetric equipment. Surface areas were estimated from N2 isotherms by using the BET multiple point equation and from CO2 isotherms by using the Dubinin-Radushkevich equation. Prior to the measurement of N2 adsorption, samples were outgassed at 383 K for 12 hours under helium flow. For CO2 adsorption measurements, samples were first oven - dried at 383 K for 24 hours, and then outgassed overnight at 383 K, at a pressure of about 1 Pa. 

Carbon dioxide isotherms at room temperature, and the corresponding surface areas estimated by the Dubinin-Radushkevich equation, are shown in Figures 21 and 22 as a function of reaction time and temperature. CO2 surface areas changed only slightly with CsHe reaction time and ranged between 130 and 170 m /g at 500°C, and 104 to 164 m /g at 700°C. For all samples, no distinct trends are identified on the possible effect of temperature and cracking reaction time on CO2 surface area development. 

Serpinski, V.V., and Jakubov, T.S., Dubinin-Radushkevich equation as the equation for the excess adsorption isotherm, Adsorpt. Sci. Technol., 10, 85-92 (1994). 

---