© A.W.Marczewski 2002

A Practical Guide to Isotherms of ADSORPTION on Heterogeneous Surfaces

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Global Heterogeneity, H:
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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).

Changing properties with the change of parameter n as well as B_{n}(RT)^{n} (here denoted as B) is visible. Smaller B_{n}(RT)^{n} give higher "peak" widths (of the same shape/symmetry type) i.e. global heterogeneity H. Changes of n and B_{n}(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, H_{GL} ≥ 1 (GL), emphasizes the difference of the underlying adsorption model of all DA equations (F,DR,DA), where for some pressure p = p_{o} 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=p _{s} .*

Legend:

In the picture "B" denotes B_{n}(RT)^{n} value.

Send a message to *Adam.Marczewski AT@AT umcs.lublin.pl*