Adsorption models and isotherms are key to understanding how molecules stick to surfaces. They show us how much stuff gets adsorbed at different pressures and temperatures, giving us crucial info about surface properties and interactions.

These models help us figure out important things like adsorption capacity and surface area. We'll look at different types of isotherms, compare models like Langmuir and BET, and see how to interpret the data they give us.

Adsorption isotherms and their significance

Graphical representation and information provided

• Adsorption isotherms graphically represent the relationship between the amount of adsorbate adsorbed on an adsorbent surface and the equilibrium pressure or concentration of the adsorbate at a constant temperature
• Provide essential information about:
  • Adsorption capacity
  • Surface properties
  • Interactions between the adsorbent and adsorbate

Classification and factors influencing adsorption isotherms

• IUPAC classification categorizes adsorption isotherms into six main types (I to VI), each corresponding to specific adsorption mechanisms and surface characteristics
• Factors influencing the type of adsorption isotherm:
  • Nature of the adsorbent (pore size, surface chemistry)
  • Nature of the adsorbate (size, polarity)
  • Operating conditions (temperature, pressure)
• Adsorption isotherms are crucial for designing and optimizing adsorption-based processes (gas separation, purification, catalysis) by determining the required amount of adsorbent and optimal operating conditions

Applying adsorption models

Langmuir adsorption model

• Assumes monolayer adsorption on a homogeneous surface with no lateral interactions between adsorbed molecules
• Langmuir equation relates the amount of adsorbed species to the equilibrium pressure or concentration
• Linearized Langmuir equation determines:
  • Maximum monolayer adsorption capacity (qm), related to surface area
  • Langmuir adsorption constant (KL), related to adsorbent-adsorbate interaction strength

BET (Brunauer-Emmett-Teller) adsorption model

• Extends the Langmuir model to multilayer adsorption
• Assumes the first adsorbed layer acts as a substrate for further adsorption
• Adsorption energy is equal to the liquefaction energy for all layers except the first
• BET equation relates the amount of adsorbed species to the equilibrium pressure or concentration and includes a parameter (C) accounting for the difference in adsorption energy between the first and subsequent layers
• Linearized BET equation determines the monolayer adsorption capacity (qm), used to calculate the specific surface area of the adsorbent using the cross-sectional area of the adsorbate molecule
• Pore size distribution of the adsorbent can be derived from the adsorption isotherm using methods like the Barrett-Joyner-Halenda (BJH) method, relating the amount of adsorbate removed during desorption to the pore size

Adsorption model comparisons

Langmuir vs. BET models

• Langmuir model assumes monolayer adsorption, homogeneous surface, no lateral interactions, and equal adsorption energy for all sites
• BET model extends to multilayer adsorption with equal adsorption energy for all layers except the first
• Langmuir model is more suitable for chemisorption or physisorption at low pressures (monolayer coverage dominant)
• BET model is more applicable to physisorption at higher pressures (multilayer adsorption occurs)

Other adsorption models

• Freundlich adsorption model (empirical):
  • Assumes a heterogeneous surface with a distribution of adsorption energies
  • Describes both chemisorption and physisorption
  • Does not provide a physical interpretation of the adsorption process
• Dubinin-Radushkevich (DR) model:
  • Based on the theory of volume filling of micropores
  • Suitable for describing adsorption in microporous materials, particularly for gases and vapors at high pressures
• Temkin adsorption model:
  • Assumes a linear decrease in adsorption energy with surface coverage due to adsorbate-adsorbate interactions
  • Suitable for systems with a uniform distribution of binding energies

Interpreting adsorption isotherms

Insights from isotherm shape

• Shape provides qualitative information about the strength and nature of adsorbent-adsorbate interactions and surface heterogeneity
• Type I isotherms (Langmuir-type):
  • Indicate strong adsorbent-adsorbate interactions
  • Predominantly microporous adsorbent
• Type II and III isotherms:
  • Suggest weaker interactions
  • Non-porous or macroporous adsorbent
• Type IV and V isotherms:
  • Exhibit hysteresis loops associated with capillary condensation in mesopores
  • Provide information about pore size distribution and shape

Additional insights from adsorption isotherms

• Steps or inflections may indicate surface heterogeneity (different types of adsorption sites or pore sizes)
• Slope of the adsorption isotherm at low pressures (Henry's law region) is related to the adsorbent-adsorbate interaction strength (steeper slope indicates stronger interactions)
• Hysteresis loop between adsorption and desorption branches provides insights into pore network connectivity and the presence of pore blocking or cavitation effects
• Comparing adsorption isotherms for different adsorbates on the same adsorbent reveals the effect of adsorbate properties (size, polarity) on adsorption behavior and selectivity