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Adsorption Isotherms I

Adsorption Isotherms I

Adsorption isotherms are mathematical models that describe how molecules in a gas or liquid phase interact with surfaces. Two of the most common isotherm models are the Langmuir and Freundlich isotherms, which relate to Type I monolayer chemisorption. The Langmuir model is based on four key assumptions:• Adsorption cannot exceed monolayer coverage.• All surface sites are equivalent.• Molecules adsorb only at vacant sites.• There are no interactions between adsorbed molecules.Consider the...

Adsorption Isotherms II

Adsorption Isotherms II

Brunauer, Emmett, and Teller (BET) introduced a theory in 1938 that modified Langmuir's assumptions to explain multilayer physical adsorption. This theory is applicable to Type II isotherms and provides a more realistic picture of adsorption processes. The BET theory assumes a uniform solid surface with localized adsorption sites, where adsorption at one site doesn't affect adsorption at neighboring sites. This theory also allows for the possibility of additional molecules being adsorbed on top...

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Updated: Jun 14, 2026

Synthesis and Characterization of Functionalized Metal-organic Frameworks

Synthesis and Characterization of Functionalized Metal-organic Frameworks

Published on: September 5, 2014

Quantifying Metal-Organic Framework (MOF)-Polymer Adsorption Using Single-Particle Langmuir Isotherm Testing (SPLIT).

Adedire D Adesiji¹, Yihong Xu², Joseph M Palomba³

¹Department of Mechanical Engineering, Boston University, Boston, Massachusetts 02215, United States.

ACS Applied Materials & Interfaces

|December 16, 2025

Summary

This summary is machine-generated.

We developed Single-Particle Langmuir Isotherm Testing (SPLIT) to measure polymer-MOF interactions. This atomic force microscopy method quantifies polymer binding energies and guides composite material design.

Keywords:

adhesion adsorption metal−organic frameworks mixed-matrix membranes polymer single particle

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Area of Science:

Materials Science
Surface Chemistry
Nanotechnology

Background:

Polymer-MOF interactions are crucial for composite materials but are hard to study.
Existing methods often use indirect measurements and average results.

Purpose of the Study:

To introduce a new method, SPLIT, for quantifying single MOF-polymer interactions.
To enable direct measurement of thermodynamic properties and polymer behavior.

Main Methods:

Single-particle Langmuir isotherm testing (SPLIT) using atomic force microscopy (AFM).
Measuring adhesion forces between a MOF-coated AFM probe and a reference surface.
Analyzing adhesion force variations with polymer concentration to determine binding energies.

Main Results:

SPLIT accurately quantifies polymer adsorption onto single MOF particles.
The method provides thermodynamic properties like MOF-polymer binding energies.
SPLIT offers insights into polymer molecular weight effects and solvent interactions.

Conclusions:

SPLIT is a powerful technique for characterizing MOF-polymer interactions at the single-particle level.
This method provides direct relevance for designing advanced composite materials, including mixed-matrix membranes.
SPLIT measurements can predict polymer concentrations that cause MOF aggregation.