Freundlich's Isotherm Extended by Statistical Mechanics

Area of Science:

• Physical Chemistry
• Surface Science
• Materials Science

Background:

• Freundlich's isotherm is widely used to describe gas and solute adsorption.
• Heterogeneous surfaces present challenges in accurately modeling adsorption behavior.
• Existing models may lack analytical solutions for complex adsorption systems.

Purpose of the Study:

• To derive a new analytical expression for the Freundlich isotherm.
• To provide a theoretical framework compatible with heterogeneous surface theory.
• To facilitate the accurate identification of Freundlich parameters from experimental data.

Main Methods:

• Developed an asymptotic expansion for the adsorption isotherm.
• Assumed an exponential distribution of adsorption sites.
• Incorporated the Langmuir homogeneous isotherm for individual sites.
• Solved the fundamental integral equation for adsorption.

Main Results:

• Obtained an analytical expression for the Freundlich isotherm (θ = KCm).
• Successfully identified the Freundlich parameters K and m from the derived expression.
• The expression is an analytical solution within correct integration limits.
• The model aligns with heterogeneous surface theory.

Conclusions:

• The derived expression offers a robust method for analyzing adsorption on heterogeneous surfaces.
• This approach provides a clear pathway to determine Freundlich parameters.
• Validated the model by fitting experimental data for CO2 adsorption on BPL-activated carbon.