Adsorption isotherms are key to understanding how molecules stick to surfaces. They show how much stuff gets adsorbed at different pressures or concentrations, helping us figure out surface properties and design better materials.

These models, like Langmuir and BET, help us predict how gases and liquids interact with solids. This knowledge is super useful for things like making catalysts work better or cleaning up pollutants from water and air.

Adsorption in Surface Chemistry

Concept and Significance

• Adsorption accumulates atoms, ions, or molecules from a gas, liquid, or dissolved solid onto a surface, forming a thin film
• Occurs at the interface between two phases (solid-gas or solid-liquid)
• Modifies surface properties such as reactivity, catalytic activity, and wettability
• Applied in gas separation, purification, catalysis, and environmental remediation
• Extent of adsorption depends on temperature, pressure, surface area, and the nature of the adsorbent and adsorbate

Factors Affecting Adsorption

• Temperature influences the extent of adsorption, with lower temperatures generally favoring adsorption
• Pressure affects the amount of adsorbate that can be adsorbed, with higher pressures leading to increased adsorption
• Surface area of the adsorbent determines the available sites for adsorption, with larger surface areas allowing for more adsorption
• Nature of the adsorbent (surface chemistry, pore size, and structure) and adsorbate (size, polarity, and chemical properties) govern the specific interactions and selectivity of adsorption

Physisorption vs Chemisorption

Physisorption Characteristics

• Weak, reversible interaction between the adsorbate and the surface
• Involves van der Waals forces, dipole-dipole interactions, or hydrogen bonding
• Lower enthalpy of adsorption (20-40 kJ/mol)
• Can occur in multilayers
• Less specific and can occur for a wide range of adsorbates
• More sensitive to temperature changes

Chemisorption Characteristics

• Strong, often irreversible interaction between the adsorbate and the surface
• Involves the formation of chemical bonds
• Higher enthalpy of adsorption (40-400 kJ/mol)
• Limited to a monolayer
• More selective and depends on the chemical compatibility between the adsorbate and the surface
• Less affected by temperature fluctuations

Examples and Applications

• Physisorption examples: adsorption of gases (nitrogen, carbon dioxide) on activated carbon, adsorption of organic pollutants on clay minerals
• Chemisorption examples: adsorption of hydrogen on metal surfaces (palladium, platinum), adsorption of oxygen on metal oxides (titanium dioxide, zinc oxide)
• Physisorption applications: gas storage, gas separation, purification, and environmental remediation
• Chemisorption applications: heterogeneous catalysis, chemical sensors, and surface functionalization

Adsorption Isotherm Analysis

Types of Adsorption Isotherms

• Represent the relationship between the amount of adsorbate adsorbed on a surface and the equilibrium pressure or concentration at a constant temperature
• Langmuir adsorption isotherm assumes monolayer adsorption, a homogeneous surface, and no interaction between adsorbed molecules, characterized by a plateau at high pressures
• Freundlich adsorption isotherm is an empirical model accounting for heterogeneous surfaces and multilayer adsorption, following a power law relationship
• Brunauer-Emmett-Teller (BET) adsorption isotherm extends the Langmuir model to multilayer adsorption, assuming each adsorbed layer acts as a substrate for the next layer, used to determine the specific surface area of solids

Isotherm Shape Interpretation

• Shape of the adsorption isotherm provides information about the adsorption mechanism, surface heterogeneity, and interactions between adsorbed molecules
• Type I isotherm (Langmuir) indicates monolayer adsorption on a homogeneous surface with a plateau at high pressures
• Type II isotherm (BET) suggests multilayer adsorption on a non-porous or macroporous surface
• Type III isotherm indicates weak adsorbate-adsorbent interactions and the formation of multilayers at higher pressures
• Type IV and V isotherms exhibit hysteresis loops, indicating the presence of mesopores and capillary condensation

Adsorption Isotherm Modeling

Langmuir Adsorption Isotherm

• Relates the surface coverage ($\theta$) to the equilibrium pressure ($P$) and the adsorption equilibrium constant ($K$): $\theta = KP / (1 + KP)$
• Can be linearized to determine the adsorption equilibrium constant and the maximum adsorption capacity from experimental data
• Assumptions: monolayer adsorption, homogeneous surface, no interaction between adsorbed molecules

Freundlich Adsorption Isotherm

• Relates the amount adsorbed ($q$) to the equilibrium pressure ($P$) and the Freundlich constants ($K$ and $n$): $q = KP^{(1/n)}$
• Freundlich constants can be determined by plotting $log(q)$ versus $log(P)$ and fitting a straight line to the data
• Accounts for heterogeneous surfaces and multilayer adsorption

BET Adsorption Isotherm

• Relates the amount adsorbed to the equilibrium pressure, the saturation pressure, and the BET constant ($C$)
• Used to determine the specific surface area of solids by measuring the amount of gas adsorbed at different pressures
• Extends the Langmuir model to multilayer adsorption, assuming each adsorbed layer acts as a substrate for the next layer

Applications of Adsorption Isotherm Models

• Optimize adsorption processes by selecting appropriate adsorbents and operating conditions
• Predict the performance of adsorption-based systems for gas storage, separation, and purification
• Characterize the surface properties of materials, such as specific surface area, pore size distribution, and surface heterogeneity
• Design and develop new adsorbents with tailored properties for specific applications (carbon capture, water treatment, catalysis)