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.