© 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): Volmer
(see global heterogeneity calc. plot)
Local heterogeneity function, h(θ), for Volmer isotherm (mobile physical adsorption) compared with Langmuir equation (localised physical adsorption) - both on in the absence of surface heterogeneity (energetically homogeneous surface).
We always have (in the absence of surface heterogeneity) :
hVol(θ) ≥ hL(θ) .
Similarity of Volmer to Langmuir equation for very low coverages:
hVol(θ → 0) = hL(θ) = 1 ,
and complete incompatibility for high covarages:
hVol(θ → 1) → ∞
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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