Calculation of the BET-Compatible Surface Area from Any Type I Isotherms Measured above the Critical Temperature.
In our previous papers [Tóth, J., et al., J. Colloid Interface Sci. 212, 402 (1999); 212, 411 (1999)] it has been proven that a BET-compatible specific surface area, a(s)(c)(N(2), 77), can be calculated from any Type I monolayer isotherms and from the monolayer domain of Type II isotherms, both measured below the critical temperature. In this paper, the calculation of a(s)(c)(N(2), 77) from Type I isotherms at temperatures above the critical temperature is discussed. These calculations are also based on the thermodynamical consistent form of the Tóth (T) equation. This relationship can be derived from the differential equation dn(s)/n(s)=[psi(p)](-1)dp/p, where the function psi(p) is calculable from the measured isotherms and includes the change in the surface free energy. The basic problem of the calculation of a(s)(c)(N(2), 77) is the determination of the upper limit of integration (p(u)) required to solve this differential equation. It is demonstrated that p(u) can be calculated from the equation ln(p(u))=-alphaT(-1)+beta. The constants alpha and beta are independent of the temperature of the isotherms but they are very sensitive to the structure of adsorbents and to the quality of adsorptives. This fact also makes it possible to characterize exactly the nanostructure of solids and the state of adsorptives. Copyright 2000 Academic Press.
Modeling of adsorption isotherms of phenol and chlorophenols onto granular activated carbon. Part II. Models with more than two parameters.
The adsorption equilibrium isotherms of five phenolic compounds, phenol, 2-chlorophenol, 4-chlorophenol, 2,4-dichlorophenol, and 2,4,6-trichlorophenol, from aqueous solutions onto granular activated carbon were studied and modeled. In order to determine the best-fit isotherm, the experimental equilibrium data were analyzed using thirteen adsorption isotherm models with more than two-parameter; nine three-parameter equations - the Redlich-Peterson, Sips, Langmuir-Freundlich, Fritz-Schlunder, Radke-Prasnitz (three models), Tóth, and Jossens isotherms - three four-parameter equation - the Weber-van Vliet, Fritz-Schlunder, and Baudu isotherms - and one five-parameter equation - the Fritz-Schlunder isotherm. The results reveal that the adsorption isotherm models fitted the experimental data in the order: Baudu (four-parameter)>Langmuir-Freundlich (three-parameter)>Sips (three-parameter)>Fritz-Schlunder (five-parameter)>Tóth (three-parameter)>Fritz-Schlunder (four-parameter)>Redlich-Peterson (three-parameter). The influence of solution pH on the adsorption isotherms of 4-CP was investigated. It was shown that the solution pH has not an effect on the adsorption isotherms for pH
Diagnosis of the σ-, π- and (σ+π)-Aromaticity by the Shape of the NICSzz-Scan Curves and Symmetry-Based Selection Rules
The NICSzz-scan curves of aromatic organic, inorganic and “all-metal” molecules in conjunction with symmetry-based selection rules provide efficient diagnostic tools of the σ-, π- and/or double (σ + π)-aromaticity. The NICSzz-scan curves of σ-aromatic molecules are symmetric around the z-axis, having half-band widths approximately less than 3 A with the induced diatropic ring current arising from Tx,y-allowed transitions involving exclusively σ-type molecular orbitals. Broad NICSzz-scan curves (half-band width approximately higher than 3 A) characterize double (σ + π)-aromaticity, the chief contribution to the induced diatropic ring current arising from Tx,y-allowed transitions involving both σ- and π-type molecular orbitals. NICSzz-scan curves exhibiting two maxima at a certain distance above and below the molecular plane are typical for (σ + π)-aromatics where the π-diatropic ring current overwhelms the σ-type one. In the absence of any contribution from the σ-diatropic ring current, the NICSzz(0) value is close to zero and the molecule exhibits pure π-aromaticity.