A Practical Guide to Isotherms of ADSORPTION on Heterogeneous Surfaces

Linear Langmuir plot - model pictures

Model picture: L (Langmuir), bi-Langmuir (bi-L), LF (Langmuir-Freudlich), T (Tóth), Radke-Prausnitz aka. Redlich-Peterson (RP), F-G (Fowler-Guggenheim), Kis (Kiselev), GF (Generalized Freudlich), GF-Kis (GF with associative interactions), full Kiselev (full Kis), full Kiselev with non-specific interactions (full Kis+FG), Jovanovic (Jov), Jovanovic-Freundlich ( (Jovanovic + heterogeneity JF/Jov-m) - dilute solute adsorption (for gas adsorption replace concentration, c, with pressure, p).
Large circles, triangles and squares with corresponding thin dotted lines show why the 2-point Langmuir-plot estimation of isotherm adsorption capacity should be avoided when lateral interactions are involved.

Parameters: am=1, K=1, Kn=1 (Kiselev), α=0.5 (FG), m=0.9 (GF,LF,Tóth), Cs=100 (solubility limit for multilayer buildup). See below for higher heterogeneity. (legend) legend

Parameters: am=1, K=1, Kn=3 (Kiselev), α=2 (FG), m=0.9 (GF,LF,Tóth), Cs=100 (solubility limit for multilayer buildup). See below for higher heterogeneity. (legend) legend

Parameters: am=1, K=1, Kn=3 (Kiselev), α=2 (FG), m=0.7 (GF,LF,Tóth), Cs=100 (solubility limit for multilayer buildup). See above for lower heterogeneity (Legend is at the top). legend

Parameters: am=1, K=1 (all except for bi-Langmuir), Kn=1 (Kiselev), Kn=0.5 (full Kiselev) (equiv. to Kn=1 for simplified Kiselev), α=0.5 (FG, full Kiselev+FG), m=0.9 (GF,LF,Tóth,JF/Jov-m). For bi-Langmuir (two sites): am=1 = am1 + am2 (am1=0.9, K1=1, am2=0.1, K2=10). See other picture for stronger lateral interactions or above for higher heterogeneity. (legend) legend

Parameters: am=1, K=1 (all except for bi-Langmuir), m=0.9 (GF,LF,Tóth,RP,JF/Jov-m). For bi-Langmuir (two sites): am=1 = am1 + am2 (am1=0.9, K1=1, am2=0.1, K2=10). See other picture for stronger lateral interactions or above for higher heterogeneity. (legend) legend

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