© 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.

biL  biLangmuir  ideal bulk and surface phase; monolayer; two types of surface sites (special case of multisite Langmuir equation.

FG  FowlerGuggenheim: as Langmuir + meanfield lateral interactions in surface phase (formally the same as Frumkin isotherm)

Kis  Kiselev (simplified equation): as Langmuir + lateral associative interactions in surface phase.
fullKis  full Kiselev: as Langmuir + lateral associative interactions in surface phase, may also involve lateral interactions of FGtype (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  LangmuirFreudlich  Langmuir + symmetrical quasigaussian 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 quasigaussian 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

GFKis  as GF but with associative interactions (Kiselev)

GFBET  as GF but with BET multilayer buildup

Jov  Jovanovic  homogeneous surface with vertical interactions bulksurface phase

Jovm  JovanovicFreundlich (JF/Jovm)  Jovanovic + surface heterogeneity

RP  RadkePrausnitz (aka. RedlichPeterson)  nonmonolayer experimental equation, contains Henry region, for higher adsorptions behaves like Freundlich eqn.
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