Understanding Adsorption Isotherms: Models and Applications
Adsorption Isotherm
An adsorption isotherm is the graphical representation of the relationship between the amount of adsorbate adsorbed on the surface of an adsorbent and the equilibrium pressure or concentration at a constant temperature. It is used to study the adsorption process and the adsorption capacity of materials.
Basic Assumptions
- Adsorption occurs only on the surface.
- The surface contains limited adsorption sites.
- Adsorption reaches equilibrium.
- Adsorption depends on pressure and temperature.
- At saturation, adsorption stops.
Importance of Adsorption Isotherm
- Explains the adsorption mechanism.
- Determines adsorption capacity.
- Helps in surface characterization.
- Used in industrial separation processes.
Types of Adsorption Isotherm
1. Langmuir Isotherm
- Explains monolayer adsorption.
- Assumes a homogeneous surface.
2. Freundlich Isotherm
- Explains adsorption on heterogeneous surfaces.
- Uses an empirical equation.
3. BET Isotherm
- Explains multilayer adsorption.
- Used for surface area measurement.
Applications
- Water purification
- Gas separation
- Catalysis
- Pollution control
- Pharmaceutical industries
Langmuir Adsorption Isotherm
The Langmuir adsorption isotherm was proposed by Irving Langmuir. It explains monolayer adsorption on a homogeneous surface. According to this model, adsorption occurs only on specific sites of the adsorbent surface. After all sites are occupied, no further adsorption takes place.
Basic Assumptions of the Langmuir Model
- The surface of the adsorbent is homogeneous.
- All adsorption sites are identical.
- Adsorption occurs in a single layer only.
- One site holds one molecule.
- No interaction occurs between adsorbed molecules.
- The heat of adsorption remains constant.
Langmuir Adsorption Equation
qe = (qmax × b × Ce) / (1 + b × Ce)
Where:
- qe = amount adsorbed at equilibrium
- qmax = maximum adsorption capacity
- Ce = equilibrium concentration
- b = Langmuir constant
Linear Form of Langmuir Isotherm
1/qe = 1/qmax + 1/(b × qmax × Ce)
Another linear form:
Ce/qe = 1/(b × qmax) + Ce/qmax
From the graph of Ce/qe versus Ce, the values of qmax and b are determined.
Limitations of Langmuir Isotherm
- Valid only for monolayer adsorption.
- Assumes a homogeneous surface.
- Ignores interaction between adsorbed molecules.
- Cannot explain multilayer adsorption.
Applications of Langmuir Isotherm
- Used to study the adsorption capacity of adsorbents.
- Used in gas adsorption studies.
- Applied in water purification processes.
- Useful in catalysis and surface chemistry.
- Helps in designing adsorption systems.
Freundlich Isotherm
The Freundlich adsorption isotherm was proposed by Herbert Freundlich in 1909. It explains adsorption on heterogeneous surfaces and is mainly used for multilayer adsorption. According to this model, the amount of adsorbate adsorbed increases continuously with an increase in pressure or concentration. It is an empirical equation used to describe the adsorption of gases and liquids on solid surfaces.
Basic Assumptions of Freundlich Isotherm
- The surface of the adsorbent is heterogeneous.
- Adsorption sites are not identical.
- The heat of adsorption decreases with an increase in adsorption.
- Adsorption occurs in multilayers.
- Different sites have different adsorption energies.
Freundlich Isotherm Equation
qe = Kf × Ce^(1/n)
Where:
- qe = amount of adsorbate adsorbed at equilibrium
- Ce = equilibrium concentration of adsorbate
- Kf = Freundlich constant related to adsorption capacity
- n = adsorption intensity constant
Linear Form of Freundlich Isotherm
log qe = log Kf + (1/n) log Ce
From the graph of log qe versus log Ce, the values of Kf and n can be determined.
Characteristics of Freundlich Isotherm
- Suitable for heterogeneous surfaces.
- Explains multilayer adsorption.
- Adsorption capacity increases with concentration.
- Widely used for gas and liquid adsorption studies.
Limitations of Freundlich Isotherm
- It is an empirical equation and not theoretically derived.
- It fails at very high pressure or concentration.
- It cannot predict the saturation of the adsorbent surface.
- Constants change with temperature.
Applications of Freundlich Isotherm
- Used in adsorption studies of gases and liquids.
- Applied in water purification.
- Used in environmental engineering.
- Useful for studying heterogeneous surfaces.
- Applied in wastewater treatment processes.
Difference Between Langmuir and Freundlich Isotherm
Langmuir Isotherm
- Proposed by Irving Langmuir.
- Explains monolayer adsorption.
- Surface of adsorbent is homogeneous.
- All adsorption sites are identical.
- Heat of adsorption remains constant.
- It is a theoretical model.
- Predicts saturation of the adsorbent surface.
- Suitable mainly for low pressure.
- No interaction between adsorbed molecules.
- Equation:
qe = (qmax × b × Ce)/(1 + b × Ce)
Freundlich Isotherm
- Proposed by Herbert Freundlich.
- Explains multilayer adsorption.
- Surface of adsorbent is heterogeneous.
- Adsorption sites are different.
- Heat of adsorption varies.
- It is an empirical model.
- Does not predict saturation of the surface.
- Applicable over a moderate concentration range.
- Interaction between adsorbed molecules may occur.
- Equation:
qe = Kf × Ce^(1/n)
Difference Between BET and Langmuir Isotherm
Langmuir Isotherm
- Explains monolayer adsorption only.
- Adsorption occurs on a homogeneous surface.
- Only one layer of adsorbate molecules is formed.
- Assumes all adsorption sites are identical.
- No interaction occurs between adsorbed molecules.
- Mainly applicable at low pressure.
- Proposed by Irving Langmuir.
- Used mainly for simple gas adsorption studies.
BET Isotherm
- Explains multilayer adsorption.
- Adsorption occurs in many layers.
- Mainly used for porous and heterogeneous materials.
- Assumes multilayer formation on the surface.
- Interaction between layers is considered indirectly.
- Applicable over a wider pressure range.
- Proposed by Brunauer, Emmett, and Teller.
- Mainly used for surface area determination of solids and porous materials.
BET Isotherm
The BET isotherm was proposed by Brunauer, Emmett, and Teller in 1938. This theory explains multilayer adsorption on solid surfaces. The BET theory is an extension of the Langmuir adsorption isotherm and is mainly used for determining the surface area of porous materials. It assumes that adsorption occurs in multiple layers instead of a single layer.
Basic Assumptions of BET Isotherm
- Adsorption occurs in multilayers.
- The surface of the adsorbent is homogeneous.
- Adsorption sites are identical.
- There is no interaction between adjacent adsorbed layers.
- Langmuir theory is applicable to each layer.
- An infinite number of adsorption layers can be formed.
- The heat of adsorption for the first layer is different from the remaining layers.
BET Isotherm Equation
1 / [v((P0/P) − 1)] = 1/(vm × C) + [(C − 1)/(vm × C)] × (P/P0)
Where:
- v = volume of gas adsorbed
- vm = monolayer adsorbed gas volume
- P = equilibrium pressure
- P0 = saturation pressure
- C = BET constant related to adsorption energy
Drawbacks of BET Adsorption Theory
- Assumes a homogeneous surface.
- Ignores interaction between adsorbed molecules.
- Assumes infinite multilayer adsorption.
- Accurate only in a limited pressure range.
- Cannot explain chemical adsorption properly.
- Less suitable for microporous materials.
Applications of BET Isotherm
- Determination of the surface area of solids.
- Study of porous materials.
- Catalyst characterization.
- Adsorption studies in industries.
- Analysis of powders and nanoparticles.
Types of BET Isotherm
BET adsorption isotherms are classified into six types based on the nature of adsorption and the pore structure of adsorbents.
Type I Isotherm
- Observed in microporous materials.
- Adsorption occurs rapidly at low pressure.
- Monolayer adsorption takes place.
- After saturation, adsorption becomes constant.
- Seen in activated carbon and zeolites.
Type II Isotherm
- Observed in non-porous or macroporous solids.
- Monolayer adsorption occurs first.
- Multilayer adsorption occurs at higher pressure.
- No clear saturation point is present.
- Seen in silica gel and metal surfaces.
Type III Isotherm
- Adsorbate–adsorbent interaction is weak.
- Adsorption is low at low pressure.
- Adsorption increases at high pressure.
- Monolayer formation does not occur.
- Curve is convex in shape.
Type IV Isotherm
- Observed in mesoporous materials.
- Monolayer and multilayer adsorption occur.
- Capillary condensation takes place.
- A hysteresis loop is present.
- Seen in porous catalysts and silica materials.
Type V Isotherm
- Similar to Type III isotherm.
- Weak adsorbate–adsorbent interaction occurs.
- Multilayer adsorption occurs at higher pressure.
- A hysteresis loop may appear.
- Seen in water adsorption on hydrophobic surfaces.
Type VI Isotherm
- Stepwise multilayer adsorption occurs.
- Adsorption takes place layer by layer.
- Observed on highly uniform surfaces.
- Rarely seen in practical systems.
- Seen in graphite-like surfaces.
Dubinin–Radushkevich (D-R) Adsorption Isotherm Model
The Dubinin–Radushkevich (D-R) adsorption isotherm model is used to study the adsorption mechanism and the nature of adsorption. It helps to distinguish between physical adsorption and chemical adsorption. Unlike the Langmuir isotherm, the D-R isotherm does not assume a homogeneous surface or constant adsorption energy.
Basic Assumptions of D-R Isotherm
- Adsorption occurs on heterogeneous surfaces.
- Adsorption follows a pore-filling mechanism.
- Adsorption energy varies on the surface.
- Suitable mainly for physical adsorption.
D-R Isotherm Equation
ln qe = ln qm − βε²
Where:
- qe = amount adsorbed at equilibrium
- qm = maximum adsorption capacity
- β = constant related to adsorption energy
- ε = Polanyi potential
Importance of D-R Isotherm
- Helps identify the adsorption type.
- Used for porous materials.
- Useful in adsorption studies and water treatment.
- Distinguishes physical and chemical adsorption.
Limitations of D-R Isotherm
- Calculations are complex.
- Not suitable for all adsorption systems.
- Less accurate at high concentration.