© A.W.Marczewski 2002

A Practical Guide to Isotherms of ADSORPTION on Heterogeneous Surfaces

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Global Heterogeneity, H: calculation plot: F, DR, DA
(see local heterogeneity h(θ) function)

Global heterogeneity plot θ(1-θ vs. ln(p) for Freundlich (F), Dubinin-Radushkevich (DR or DA with n=2) and Dubinin-Astakhov (DA) equations (adsorption in micropores) compared with Langmuir (L) isotherm (homogeneous flat surface).

Global heterogeneity calc. - model lines for F,DR and DA equations

Changing properties with the change of parameter n as well as Bn(RT)n (here denoted as B) is visible. Smaller Bn(RT)n give higher "peak" widths (of the same shape/symmetry type) i.e. global heterogeneity H. Changes of n and Bn(RT)n result also in changes of equation symmetry (compare e.g. 2 lines for the DR as well 2 lines for DA with n=3).
Comparison with Langmuir, H = 1, and Langmuir-derived isotherms, HGL ≥ 1 (GL), emphasizes the difference of the underlying adsorption model of all DA equations (F,DR,DA), where for some pressure p = po the adsorption must be completed, whereas for all Langmuir derived equations this process does not end at finite pressure, unless multilayer is introduced. At the same time all DA-group equations (with the exception of Freundlich and B=1) are not consistent with the Henry model for very low adsorptions (the same applies to GF, LF and GL if m < 1).

For all DA-group equations (with the exception of Langmuir) point θ=1 corresponds to p=ps .
NOTE. Replace p with c for dilute solute adsorption.

In the picture "B" denotes Bn(RT)n value.

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