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.
Separation of the First Adsorbed Layer from Others and Calculation of the BET Compatible Surface Area from Type II Isotherms.
In the previous paper it has been proven that a BET compatible specific surface area, asc(N2, 77), can be calculated from any Type I isotherm measured below the critical temperature. In this paper it is proven that the same calculation can be performed from any Type II isotherms if the isotherm has a pure monolayer domain. In order to distinguish the mono- and multilayer adsorption the relative free energy of the surface as a function of the adsorbed amount, pir(ns), and the functions psi(pr) and psi(ns) are applied, both defined by the differential expression (ns/pr)(dpr/dns). When the multilayer adsorption becomes the dominant process then the function pir(ns) has a point of inflexion and functions psi(pr) and psi(ns) have maximum values. It has been demonstrated that in most of the Type II isotherms the mono- and multilayer domains can be separated, so the monolayer component isotherm can be calculated by the T (Tóth) equation. Therefore, it is possible to calculate the BET compatible specific surface area discussed in detail in the previous paper. It has also been proven that there are Type II isotherms which describe only multilayer adsorption; i.e., the functions psi(pr) and psi(ns) do not have maximum values. In these cases the Harkins-Jura equation should be applied. Copyright 1999 Academic Press.
Thorium in monazite sand; separation and determination by precipitation from homogeneous solution
A new method is described which consists of three steps: (1) decomposition of the monazite sand with perchloric acid; (2) separation of thorium and the rare earths by hydrolysis of methyl-oxalate in acid solution; and (3) separation of thorium from the rare earths by hydrolysis of urea in the presence of formic acid. The authors consider the method to be accurate and rapid.