Dubinin/Radushkevich adsorption isotherm

Dual nickel, 9 820—821 Dual-pressure processes, in nitric acid production, 17 175, 177, 179 Dual-solvent fractional extraction, 10 760 Dual Ziegler catalysts, for LLDPE production, 20 191 Dubinin-Radushkevich adsorption isotherm, 1 626, 627 Dubnium (Db), l 492t Ductile (nodular) iron, 14 522 Ductile brittle transition temperature (DBTT), 13 487 Ductile cast iron, 22 518—519 Ductile fracture, as failure mechanism, 26 983 Ductile iron... 

Cerofolini GE (1975) A model which allows for the Freundlich and the Dubinin-Radushkevich adsorption isotherms. Surface Sci 51 333-335... 

Fe Oj, FejO, nanocomposites, oxidation polymerization, Langmuir adsorption isotherm, Freundlich adsorption isotherm, Dubinin-Radushkevich adsorption isotherm, Tempkin adsorption isotherm, pseudo-first-order kinetic. Pseudo-second-order kinetic, removal efficiency, adsorption capacity... 

Dubinin and his co-workers [156-158] as well as Radushkevich [159] found that the characteristic adsorption curve is related to the porous structure of the adsorbent. Radushkevich [159] proved theoretically the equations of the characteristic adsorption curves for the two extreme types of adsorbents with narrow and wide pores. Based on this Dubinin proposed the expression known in literature as the Dubinin-Radushkevich (DR) isotherm equation [136]. 

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. 

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). 

Semiernpirical Isotherm Models. Some of these models have been shown to have some thermodynamic inconsistencies and should be used with due care. They include models based on the Polanyi adsorption potential (Dubinin-Radushkevich, Dubinin-Astakhov, Radke-Prausnitz, Toth, UNI LAN. and BET). 

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. 

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. 

The methods depend on the theoretical treatment which is used. A majority of them are based on the Generalised Adsorption Isotherm (GAI) also called the Integral Adsorption Equation (LAE). The more recent approaches use the Monte Carlo simulations or the density functional theory to calculate the local adsorption isotherm. The analytical form of the pore size distribution function (PSD) is not a priori assumed. It is determined using the regularization method [1,2,3]. Older methods use the Dubinin-Radushkevich or the Dubinin-Astakhov models as kernel with a gaussian or a gamma-type function for the pore size distribution. In some cases, the generalised adsorption equation can be solved analytically and the parameters of the PSD appear directly in the isotherm equation [4,5,6]. Other methods which do not rely on the GAI concept are sometimes used the MP and the Horvath-Kawazoe (H-K) methods are the most well known [7,8]. 

Table 2 Parameters of Dubinin-Radushkevich Isotherm for Phe Adsorption on CA-3 Sample at Different Steam Percentages.

For a carbonaceous material, the higher the steam percentage (in volume) in the gas stream, the lower its Phe adsorption capacity. The isotherms shape suggests that the presence of moisture in the gas stream seems to avoid the multilayer adsorption. The best model to fit the Phe adsorption capacities on carbonaceous materials is the Dubinin-Radushkevich model. 

Several methods have been proposed for the characterisation of the Micropore Size Distribution (MPSD) that take into account the energetic heterogeneity of solid surfaces [9,10]. The Dubinin-Radushkevich (DR) and Dubinin-Astakhov (DA) equations have been used to describe the adsorption process on structurally heterogeneous solids [11,12]. From these equations, the adsorption isotherm can be expressed as follows ... 

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. 

Sorption of nitrogen Nitrogen isotherms were measured using a ASAP 2010 (Micromeritics) at —196 °C. Before the experiment the samples were heated at 120 °C and then outgassed overnight at this temperature under a vacuum of 10 Torr to constant pressure. The isotherms were used to calculate the surface area and pore (DFT [10]) and characteristic enei of adsorption, (Eg) (Dubinin-Radushkevich method [11]). 

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-... 

Micropores in the lignocellulosic wastes and resulting chars were analysed from CO2 adsorption isotherms by applying the Dubinin-Radushkevich (DR) equation (14). DR plots... 

Figure 2 presents the CO2 adsorption isotherms obtained at 273 K for samples of series CS (a) and CW (b). The amount of carbon dioxide adsorbed increases, for both series, with bum-off. Isotherms are rather similar for samples with low burn-off (CS-2 to CS-8 on one hand, CW-1 and CW-2 on the other) what makes it difficult to distinguish them only with these measurements. When plotted in Dubinin-Radushkevich (D-R) coordinates, these isotherms become straight lines as corresponds to samples with a narrow and uniform homogeneous microporosity. The micropore volumes of the different samples, obtained by application of the D-R equation to the CO2 adsorption data are reported in Table 1. Micropore volumes increase from 0.22-0.23 cm g- in the less activated CMS to 0.32 cm g- in samples with the highest burn-off in each series although, due to the different reactivity of the starting materials, they are obtained after very different activation times (16 h for CW series and 70 h for CS series). 

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 ... 

We turn now to the analysis of pore structure. For this purpose, various optional computational procedures are incorporated in the software, which is now provided with most commercial adsorption equipment. For example, for micropore size analysis the isotherm can be converted into a t-plot and also displayed in either the Dubinin-Radushkevich (DR) or the Dubinin-Astakov (DA) coordinates. With some packages it is also possible to apply the MP method of Brunauer, the Horvath-Kawazoe (HK) method and/or density functional theory... 

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],... 

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