© A.W.Marczewski 2002

A Practical Guide to Isotherms of ADSORPTION on Heterogeneous Surfaces

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Global Heterogeneity, H: calculation plot: Volmer
(see local heterogeneity h(θ) function)

Global heterogeneity plot θ(1-θ) vs. ln(p). The mobile adsorption (Volmer) is similar to the localized adsorption (Langmuir) for low coverages (θ < 0.5). For higher coverages localized layer is relatively quickly completed, whereas this process is much harder in mobile adsorption (screening effect of molecules that may change their positions smoothly and not discretely - some "free" sites may be too small to receive and "anchor" adsorbate on the surface).

Global heterogeneity calc. - Volmer mobile adsorption vs. Langmuir localized a.

Similarity of Volmer to Langmuir equation for very low coverages and complete incompatibility for high covarages are clearly visible.
Volmer behaviour is in some way similar to that of localised physical adsorption on heterogeneous surfaces of energy distribution strongly extended towards small and negative energies (molecules are repelled from the surface at high coverages - screening effect).

θ=1 is reached for p→∞ or [p/(1-x)]→∞ (for vapors x=p/ps).
NOTE 1. Replace p with c for dilute solute adsorption.
NOTE 2. There is not much sense in employing mobile adsorption model (e.g. Volmer) to adsorption in solution.

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