Adsorption Theory and Models of Aerogel

1. Difference in Adsorption Layers

• Langmuir Theory: Adsorption occurs only on a single molecular layer on the surface of a solid and stops once the layer is formed.
• BET Theory: Extends to multi-layer adsorption. The first layer is held by chemical bonds or strong van der Waals forces, while subsequent layers are dominated by intermolecular forces. Suitable for medium and low-pressure physical adsorption, such as multi-layer adsorption within aerogel pores.

2. Essence of the Adsorption Mechanism

• Langmuir Theory: Based on chemisorption. Adsorption sites are uniform and irreversible, with dynamic equilibrium between adsorption and desorption.
• BET Theory: Based on physical adsorption. The first layer has strong surface interaction; subsequent layers have weaker intermolecular forces. Applicable for specific surface area and pore size analysis of porous materials like aerogels.

3. Comparison of Applicable Scenarios

• Langmuir Theory: Suitable for single-layer adsorption systems (e.g., chemical bonding or low site-density materials), but cannot describe complex adsorption in porous structures.
• BET Theory: Designed for multi-layer adsorption. Ideal for high-specific-surface-area materials such as aerogels. Works best at medium relative pressure (P/P₀ = 0.05–0.35), enabling accurate specific surface area calculation and pore distribution analysis.

4. Comparison of Core Assumptions

• Langmuir Theory:
• Uniform surface with equivalent adsorption sites
• No interaction between adsorbed molecules
• Only applicable to single-layer reversible adsorption
• BET Theory:
• First layer similar to Langmuir model, subsequent layers dominated by intermolecular forces
• Adsorption heat remains constant from the second layer onward (equal to heat of liquefaction)
• Monolayer adsorption capacity obtained via linear fitting p/V(p0−p)vs.p/P0p / V(p₀ - p) vs. p/P₀p/V(p0​−p)vs.p/P0​, from which specific surface area is derived

5. Practical Applications in Aerogels

The high specific surface area and porous structure of aerogels make their adsorption behavior more consistent with BET theory:

• Specific Surface Area Calculation: BET equation fits nitrogen or CO₂ adsorption isotherms; results are derived using molecular cross-sectional area—key for material characterization.
• Pore Distribution Analysis: BET is often combined with BJH, DFT, and other models to reveal micropores (<2 nm) and mesopores (2–50 nm).
• Experimental Optimization: Recommended pressure range is 0.05–0.35 to avoid unsaturation at low pressure or capillary condensation at high pressure.

6. Langmuir in Special Scenarios

Despite the dominance of BET theory, Langmuir still applies in:

• Low-pressure adsorption (single-layer unsaturated)
• Functionalized surfaces (uniform adsorption sites)
• Weak intermolecular interactions (primarily physical adsorption)