© 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): GL
(see global heterogeneity calc. plot)

Local heterogeneity - model lines for GL equation Local heterogeneity function, h(θ), for Generalized Langmuir (GL) isotherm and its special cases (Langmuir-Freundich, LF, Generalized Freundlich /Sips, GF, and Langmuir-Freundlich, LF) compared with Langmuir equation.

Local covergence of hGL(θ) to limiting values:
hGL(θ → 0) = 1/m
and
hGL(θ → 1) = 1/n
for all cases is clearly visible.
Systems characterized by heterogeneity parameters corresponding to energy distributions extended towards higher adsorption display higher local heterogeneity h(θ) for low coverages and those with energy distribution extended towards small energies display lower local heterogeneity h(θ) for high coverages.
However, the values of local heterogeneity function for heterogeneous surfaces (if lateral interactions are absent):
hGL(θ) ≥ hL(θ) = 1
It also means that the slope of adsorption isotherm on heterogeneous surfaces is always smaller than on homogeneous surface (for a fixed coverage), i.e. adsorption on homogeneous surfaces reacts stronger to the changes of adsorbate pressure than that on heterogeneous surfaces.

θ=1 is reached for p→∞ or [p/(1-x)]→∞ (for vapors x=p/ps) or for solute adsorption c→∞ or [c/(1-x)]→∞ (for weakly soluble solutes; x=c/cs).
NOTE. Replace p with c for dilute solute adsorption.

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