© A.W.Marczewski 2002
A Practical Guide to Isotherms of ADSORPTION on Heterogeneous Surfaces
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 was later discussed and used to analyse adsorption data in a series of papers, e.g.:
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, c_{s}) or vapours (pressures close to saturation pressure, p_{s}), 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:
where: θ_{t} 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)
GL-FG - GL with lateral interactions of FG / Van der Waals type (random topography) (see General Integral Equation in dilute solute adsorption)
GL-BET - GL with simple "multilayer correction" of BET type (c_{s} is solubility limit and x=c/c_{s})
(may be treated as a 1st approximation)
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