Analysis of the Derived Curves of Adsorption Isotherms†

The paper aims to provide new insights into the mechanism of adsorption of nitrogen at 77 K in the submonolayer range, by means of analysis of the isotherm derivative d[ N ( p )]/d p . For this purpose, a series of isotherms of adsorption on different types of carbons are analyzed. In order to investigate deterministic isotherms, a series of isotherms of adsorption in slit-shaped micropores, calculated by Lastoskie et al., are analyzed by the same method. It is shown that the derivatives can always be fitted to power laws, i.e., d[ N ( p )]/d p ∝ p ν where −2 ≤ ν ≤ 0. For carbons, several regimes, characterized by different ν values are evidenced. In contrast, for silicas, a single power law (−1 ≤ ν ≤ −0.5) is evidenced over a broad range of relative pressures (10 - 6 −0.2). It yields a Freundlich equation after integration, whereas more than one equation is needed to describe adsorption on carbons. Depending on ν, integration yields Henry, Freundlich, or Temkin equations or a new one (“C-type”), involving a negative exponent for p . Dubinin−Radushkevich plots, largely used for carbons, are also shown. The comparison with the derivatives provides explanation for the usual deviations from the DR equation. The exponent ν is related to a fractal dimension D by means of the following relation: ν = ( D − 4)/2. The physical meaning of D is discussed. When the solid surface is fractal, the upper value of D s, which is deduced from ν, is compared to the ones obtained by other methods. This work also provides a theoretical background for some usual empirical isotherm equations.