Adsorption Isotherm (Langmuir-Freundlich)
Also known as: Langmuir isotherm, Freundlich isotherm, sorption equilibrium
Adsorption isotherms describe the equilibrium uptake of a substance on a solid surface as a function of gas or solution phase concentration at constant temperature. The Langmuir isotherm (1918) and Freundlich isotherm (1906) are classical empirical models. The Langmuir model assumes monolayer coverage and is mechanistic; the Freundlich model is empirical and describes multilayer or heterogeneous adsorption. These isotherms are essential for designing separation processes (activated carbon filters, molecular sieves) and understanding pollutant sorption.
Key highlights
- Simple models (Langmuir, Freundlich) are easy to fit and interpret
- Mechanistic basis (Langmuir) provides physical insight
- Widely applicable across gas and liquid phase systems
- Enables quick estimation of column performance without detailed kinetics
Intuition
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How it works
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When to use it
Use adsorption isotherms to design fixed-bed adsorbers for gas or liquid separation. They are essential for predicting breakthrough curves and sizing carbon filters, zeolite beds, and ion exchangers. Apply when the system is at or near equilibrium. Avoid when kinetics (adsorption rate) is rate-limiting or when temperature changes significantly during the process.
Strengths & limitations
- Simple models (Langmuir, Freundlich) are easy to fit and interpret
- Mechanistic basis (Langmuir) provides physical insight
- Widely applicable across gas and liquid phase systems
- Enables quick estimation of column performance without detailed kinetics
- Assumes equilibrium; does not account for mass transfer kinetics or breakthrough transients
- Langmuir assumes monolayer coverage, which is violated at high loadings (especially in liquids)
- Freundlich is purely empirical; parameters lack physical meaning
- Does not capture site heterogeneity well; multilayer or competitive adsorption requires more sophisticated models
Common pitfalls
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Applications
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Frequently asked
What is the difference between Langmuir and Freundlich isotherms?
Langmuir assumes a fixed number of adsorption sites (monolayer saturation); uptake plateaus. Freundlich is empirical; uptake increases indefinitely (at decreasing rate). Langmuir works well for homogeneous surfaces and single-layer coverage; Freundlich fits heterogeneous surfaces and multilayer systems.
How do you choose between isotherm models?
Fit several models (Langmuir, Freundlich, Sips) to your data and compare R² values. Sips (combines both) often fits best. Consider the surface chemistry: homogeneous → Langmuir; heterogeneous → Freundlich or Sips.
What is the relationship between isotherm and breakthrough curve?
The isotherm defines equilibrium, but the breakthrough curve shows the dynamic column performance. Isotherms alone do not predict when breakthrough occurs; you need kinetics and column mass transfer data.
Sources
- 1.Langmuir, I. (1918). The adsorption of gases on plane surfaces of glass, mica, and platinum. Journal of the American Chemical Society, 40(9), 1361-1403.
- 2.Freundlich, H. M. F. (1906). Über die Adsorption in Lösungen. Zeitschrift für Physikalische Chemie, 57(1), 385-470.
- 3.Yang, R. T. (1997). Gas Separation by Adsorption Processes. Butterworth-Heinemann.ISBN 978-0-7506-3897-0
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Cite this page
ScholarGate. (2026, June 3). Adsorption Isotherm (Langmuir-Freundlich). ScholarGate. https://scholargate.app/applied-physics/adsorption-isotherm