© A.W.Marczewski 2002

A Practical Guide to Isotherms of ADSORPTION on Heterogeneous Surfaces

Reload Adsorption Guide

Generalized Langmuir eq. Generalized Langmuir (GL) isotherm equation [Marczewski-Jaroniec (MJ) isotherm]

see also: GL energy distribution, General Integral Equation and energy dispersion
see also: all discussed isotherm equations

GL references | GL isotherm (GL special cases: L | LF | GF | Tóth )
GL with: lateral interactions ( specific | non-specific ) | BET multilayer

GL: First introduced by myself (AWM) and M. Jaroniec
  1. "A New Isotherm Equation for Single-Solute Adsorption from Dilute Solutions on Energetically Heterogeneous Solids", A.W.Marczewski and M.Jaroniec, Mh.Chem., 114, 711-715 (1983), (doi).
In this paper a GL linear plot - a generalization of linear Langmuir plot - was also introduced.

GL was later discussed and used to analyse adsorption data in a series of papers, e.g.:

  1. "Physical Adsorption on Energetically Heterogeneous Solids. I. Generalized Langmuir Equation and Its Energy Distribution", M.Jaroniec and A.W.Marczewski, Mh.Chem., 115, 997-1012 (1984), (doi).
  2. "Physical Adsorption on Energetically Heterogeneous Solids. II. Theoretical Extension of a Generalized Langmuir Equation and Its Application for Analysing Adsorption Data", M.Jaroniec and A.W.Marczewski, Mh.Chem., 115, 1013-1038 (1984), (doi).
  3. "Adsorption from Solutions of Nonelectrolytes on Heterogeneous Solid Surfaces: A Four-Parameter Equation for Excess Adsorption Isotherm", M.Jaroniec and A.W.Marczewski, Mh.Chem., 115, 541-550 (1984), (doi).
  4. "Relationships Defining Dependence Between Adsorption Parameters of Dubinin-Astakhov and Generalized Langmuir Equations", M.Jaroniec and A.W.Marczewski, J. Colloid Interface Sci., 101, 280-281 (1984), (doi).
  5. "A New Method for Characterizing the Global Adsorbent Heterogeneity by Using the Adsorption Data", A.W.Marczewski, M.Jaroniec and A.Deryło-Marczewska, Mat.Chem.Phys., 14, 141-166 (1986), (doi).

Note. Almost parallely a similar (but different in formulation) equation was published by J. Tóth as Freundlich-Tóth (FT) isotherm.

NOTE
Equations below are good e.g. for dilute solutions of organics. For gas adsorption replace concentration, c, with pressure, p. If you deal with weakly soluble solutes (or your concentrations are close to solubility limit, cs) or vapours (pressures close to saturation pressure, ps), you should take it into account, e.g. by using "multilayer correction" - see below.

GL - Generalized Langmuir (aka. MJ, M-J: Marczewski-Jaroniec iso.)
Isotherm of localized physical adsorption on energetically heterogeneous solids:
Generalized Langmuir eq.
where: θt is global (overall) adsorption isotherm (overall coverage) obtained from General Integral Equation of Adsorption (see general discussion) for Langmuir local equation.

GL isotherm for specific values of parameters (generally parameter m is responsible for the isotherm behaviour at c → 0 whereas n for the course at c → ∞) reduces to the simpler well known equations:

GL-Kis - GL with lateral interactions of associative type (random topography) (see General Integral Equation in dilute solute adsorption)

Generalized Langmuir eq. with associative (Kiselev) lateral interactions

GL-FG - GL with lateral interactions of FG / Van der Waals type (random topography) (see General Integral Equation in dilute solute adsorption)

Generalized Langmuir eq. with mean-field (FG) lateral interactions

GL-BET - GL with simple "multilayer correction" of BET type (cs is solubility limit and x=c/cs)
(may be treated as a 1st approximation)
Generalized Langmuir eq. with BET multilayer effect

GL references | GL isotherm (GL special cases: L | LF | GF | Tóth )
GL with: lateral interactions ( specific | non-specific ) | BET multilayer

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