© A.W.Marczewski 2002

A Practical Guide to Isotherms of ADSORPTION on Heterogeneous Surfaces

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

Local heterogeneity - model lines for F,DR and DA equations Local heterogeneity function, h(θ), 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 Bn(RT)n (here denoted as B) is visible. Smaller Bn(RT)n give higher h(θ). 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, hL(θ) = 1, and Langmuir-derived isotherms, hGL(θ) ≥ 1 (GL), emphasizes the difference of the underlying adsorption model of all DA equations (F,DR,DA), where :
hF,DR,DA(θ → 1) = 0
for F (DA with n=1):
hF(θ → 0) = 1/m > 0
for DR and DA (i.e. DA with n > 1)
hDR,DA(θ → 0) = 0
All those cases reflect inconsistency with the Henry model for very low adsorptions.

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

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

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