© 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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local heterogeneity function h(θ): Jovanovic

(see global heterogeneity calc. plot)

Local heterogeneity function, h(θ), for Jovanovic and Jovanovic-Freundlich (JF, aka. Jov-m, i.e. Jovanovic + heterogeneity) compared with Langmuir, Generalized Freundlich (GF)/Sips and Freundlich (F) equations.

All equations (JF/Jov-m, GF and F) corresponding to heterogeneous surfaces and characterized by the same value of heterogeneity parameter m for low surface coverages θ behave in the same way :

h_{het}(θ → 0) = 1/m

However, for medium and high coverages θ) the differences become clear. For Freundlich and Jovanovic-derived isotherms:

h_{het}(θ → 1) = 0

as opposed to Langmuir-based GF isotherm:

(h_{GF}(θ → 1) = h_{L}(θ) = 1).

*For other Langmuir-based isotherms (see model picture for GL): h _{GL}(θ) ≥ h_{L}(θ) = 1
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Those differences result partially from their implied local isotherms, i.e. different adsorption/interaction models (Langmuir, Jovanovic, Freundlich), partially from the magnitude of heterogeneity effects (heterogeneous or homogeneous: JF (Jov-m) / Jov; GF / L) or shape of energy distribution function corresponding to apparently identical heterogeneity parameters or other factors (e.g. Freundlich should be used for weakly soluble substances with c ≤ c

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