© A.W.Marczewski 2002

A Practical Guide to Isotherms of ADSORPTION on Heterogeneous Surfaces

Reload Adsorption Guide

PHI-function definition ADSORPTION: φ-function

General Integral Equation / GL (Generalized Langmuir) / All equations (preview)


Adsorption type ( Linear Langmuir plot / Graham plot / Consistency / Henry constant )
Popular isotherms ( Mono-, Multilayer, Experimental, Micro-, Mesoporous )
Data analysis: ( LSq data fitting / Global heterogeneity / Linear plots / φ-function )
Prediction/Description of Multicomponent adsorption / Wastewater adsorption
Heterogeneity and Molecular Size ( Theory and Prediction / Simple binary isotherm )


PHI-function definition φ-function method:

Use a so-called: φ-function method (where φ = δ log(a)/ δ log(c)) (derivative of adsorption isotherm in logarithmic co-ordinates).
  1. A.W. Marczewski, M. Jaroniec, Mh. Chem, 114, 711, (1983), (doi).
  2. M. Jaroniec, A.W. Marczewski, Mh. Chem. 115, 997 (1984), (doi).
  3. M. Jaroniec, A.W. Marczewski, Mh. Chem. 115, 1013 (1984), (doi).
  4. M. Jaroniec, A.W. Marczewski, J. Colloid Interface Sci., 101, 280 (1984), (doi).

model pictures φ-function is a dimensionless variable (independent of adsorption and concentration/pressure units as well as independent of type of logarithm you use). Various plots of φ-function versus adsorption, pressure/concentration etc. allow to determine isotherm type and isotherm parameters (or sometimes at least to reject some existing choices) (Here are model pictures)
NOTE. This method allows to determine equation type and parameters very precisely, however your data should be very good - evenly spaced, smooth and in a wide range of relative adsorption φ) - method is sensitive to data scatter.


Adsorption type ( Linear Langmuir plot / Graham plot / Consistency / Henry constant )
Popular isotherms ( Mono-, Multilayer, Experimental, Micro-, Mesoporous )
Data analysis: ( LSq data fitting / Global heterogeneity / Linear plots / φ-function )
Prediction/Description of Multicomponent adsorption / Wastewater adsorption
Heterogeneity and Molecular Size ( Theory and Prediction / Simple binary isotherm )


General Integral Equation / GL (Generalized Langmuir) / All equations (preview)

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