Answer
In Langmuir adsorption isotherm, it was assumed that the adsorption sites on the adsorbent surface have the same energy of adsorption, the adsorbate molecules do not interact with each other and that adsorption stops after the formation of a monolayer. This isotherm is ideal for microporous materials, showing type-I isotherm. There is a sharp rise at low-pressure regions due to the narrow pore width of the micropores resulting in a high adsorption potential. The flat region afterward is attributed to the complete filling of the micropores.
The BET theory is an extension of the Langmuir isotherm and says that there can be multilayer adsorption if the first adsorbed layer can act as a substrate. For a typical gas isotherm, high uptake at low pressure is because of the presence of micropores. If multilayer adsorption occurs, then there will be a rise in gas uptake at mid-pressure regions for mesopores and high-pressure regions for macropores (in contrast to the isotherm leveling off after high gas adsorption at low pressure for Langmuir isotherm). Therefore, the BET theory can be applied in case there are mesopores, macropores, or mixed pores present.
Temkin and Freuendlich isotherms are applicable in case of surface heterogeneity, meaning that the adsorption sites are not showing same behavior unlike Langmuir isotherm. In Langmuir isotherm, the heat of adsorption does not depend on surface coverage, whereas it is seen often that the energetically active sites are filled first and the enthalpy of adsorption gradually becomes less negative with increasing surface coverage. This occurs when the adsorption of gas molecules gradually decreases because it becomes difficult for the gas molecules to find specific adsorption sites as surface coverage increases. Temkin isotherm assumes that there is a linear change in enthalpy of adsorption with pressure whereas Freundlich isotherm postulates that the change is not linear but is exponential. This can be applied in case of adsorbate-adsorbate interactions.
Work Step by Step
In Langmuir adsorption isotherm, it was assumed that the adsorption sites on the adsorbent surface have the same energy of adsorption, the adsorbate molecules do not interact with each other and that adsorption stops after the formation of a monolayer. This isotherm is ideal for microporous materials, showing type-I isotherm. There is a sharp rise at low-pressure regions due to the narrow pore width of the micropores resulting in a high adsorption potential. The flat region afterward is attributed to the complete filling of the micropores.
The BET theory is an extension of the Langmuir isotherm and says that there can be multilayer adsorption if the first adsorbed layer can act as a substrate. For a typical gas isotherm, high uptake at low pressure is because of the presence of micropores. If multilayer adsorption occurs, then there will be a rise in gas uptake at mid-pressure regions for mesopores and high-pressure regions for macropores (in contrast to the isotherm leveling off after high gas adsorption at low pressure for Langmuir isotherm). Therefore, the BET theory can be applied in case there are mesopores, macropores, or mixed pores present.
Temkin and Freuendlich isotherms are applicable in case of surface heterogeneity, meaning that the adsorption sites are not showing same behavior unlike Langmuir isotherm. In Langmuir isotherm, the heat of adsorption does not depend on surface coverage, whereas it is seen often that the energetically active sites are filled first and the enthalpy of adsorption gradually becomes less negative with increasing surface coverage. This occurs when the adsorption of gas molecules gradually decreases because it becomes difficult for the gas molecules to find specific adsorption sites as surface coverage increases. Temkin isotherm assumes that there is a linear change in enthalpy of adsorption with pressure whereas Freundlich isotherm postulates that the change is not linear but is exponential. This can be applied in case of adsorbate-adsorbate interactions.
