© A.W.Marczewski 2002

A Practical Guide to Isotherms of ADSORPTION on Heterogeneous Surfaces

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Linear Langmuir plot

Use a linear Langmuir plot (compare other linear plots as well as Graham plot): Ads vs. Ads / Conc in order to find your type of heterogeneity (if any), lateral interactions (if needed) or multilayer buildup "correction". (Ads/Conc vs. Ads plot is known as Scatchard plot).
(Here are model pictures):
NOTE:
   Replace Conc with Pressure for gas adsorption.

• L - Langmuir - ideal bulk and surface phase; monolayer; homogeneous surface
• GL - Generalized Langmuir - ideal bulk and surface (adsorbed) phase; monolayer; heterogeneous surface (it has its own version of linear plot which requires a priori knowledge of heterogeneity parameters). LF, GF and Toth may be considered as special cases of GL isotherm.
• bi-L - bi-Langmuir - ideal bulk and surface phase; monolayer; two types of surface sites (special case of multi-site Langmuir equation.
• F-G - Fowler-Guggenheim: as Langmuir + mean-field lateral interactions in surface phase (formally the same as Frumkin isotherm)
• Kis - Kiselev (simplified equation): as Langmuir + lateral associative interactions in surface phase.
  full-Kis - full Kiselev: as Langmuir + lateral associative interactions in surface phase, may also involve lateral interactions of FG-type (mean field approx.)
• GF - Generalized Freudlich - Langmuir + surface heterogeneity similar to Freudlich (exponentially decreasing distribution of ads. energy), but in contrast to the "true Freundlich" - monolayer; reduces to Freundlich eq. for low adsorption values and to Langmuir at high adsorption values. Special case of GL isotherm
• LF - Langmuir-Freudlich - Langmuir + symmetrical quasi-gaussian surface heterogeneity (exponentially decreasing distribution of ads. energy on both sides); monolayer; reduces to Freundlich (or GF) eq. for low adsorption values, for high adsorptions becomes similar to Toth equation. Special case of GL isotherm
• T - Tóth - Langmuir + asymmetrical quasi-gaussian surface heterogeneity (exponentially decreasing distribution of ads. energy on both sides with bigger tail for low adsorption energies); monolayer; reduces to Henry eq. (a=Kc) for low adsorption values and becomes similar to LF for high adsorption values. Special case of GL isotherm
• GF-Kis - as GF but with associative interactions (Kiselev)
• GF-BET - as GF but with BET multilayer buildup
• Jov - Jovanovic - homogeneous surface with vertical interactions bulk-surface phase
• Jov-m - Jovanovic-Freundlich (JF/Jov-m) - Jovanovic + surface heterogeneity
• RP - Radke-Prausnitz (aka. Redlich-Peterson) - non-monolayer experimental equation, contains Henry region, for higher adsorptions behaves like Freundlich eqn.

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