Sorption isotherm

Sorption isotherms describe the equilibrium state of sorption of a substance at constant temperature. When the adsorption isotherms, the equilibrium between adsorption and desorption is at a surface ( generally at an interface ). They represent the amount of substance bound to the surface ( the sorbate ) as a function of the amount present in the gas phase or in solution dar. adsorption isotherms are determined by adsorption, i.e., an unloaded sorbent is contacted with a solution containing the substance under consideration. In contrast, a loaded sorbent with an unladen solution is brought into contact in the determination of desorption isotherms. Adsorption and desorption isotherms are due to hysteresis usually not identical.

Sorption isotherms are often used as empirical models that do not make statements about underlying mechanisms and influences, and often not explicitly distinguish between adsorption and absorption processes. They are obtained from measured data by means of regression analyzes. Since sorption isotherms sometimes be the sum of several, often not mathematically separable effects, its application is often only theoretical. However, most models are derived kinetically or thermodynamically, and can provide state variables in appropriate circumstances.

Below, the most commonly used isotherms are listed. There are many other models that are often modifications of the models mentioned.

Linear isotherm

• Q - loading of the sorbents ( sorbate mass relative to the mass Sorbent )
• Kd - linear coefficient, Kd
• Ceq - concentration of the sorbate in solution

Linear isotherms are very popular because they simplify calculations considerably. Therefore, they are often also used when actually more complicated models should be used. Applicable they are usually only for the low concentrations.

Linear isotherms are particularly suitable for the sorption of gases in liquids also called Henry isotherms. See also: Henry's law.

Freundlich isotherm

• Q - loading of the sorbents ( sorbate mass relative to the mass Sorbent )
• K - Freundlich coefficient
• Ceq - concentration of the sorbate in solution
• N - Freundlich exponent ( to be able to specify to numbers greater than 1 that is replaced n in the equation often by 1 / n. )

Freundlich isotherms reflect the fact that at a higher load of Sorptionsoberflächen of sorbents less sorbate can be added. Due to the power - growth, however, a complete loading of the surface can not be mapped. This is convenient for the isothermal case where the saturation pressure of the adsorbent is relatively high, or can not be reached ( superfluid media). The Freundlich isotherm is a special form of Zeldowitsch isotherm.

Langmuir isotherm

• Q - loading of the sorbents ( sorbate mass relative to the mass Sorbent )
• KL - Langmuir sorption coefficient
• Qmax - maximum absorbable concentration of sorbate ( sorbate mass relative to the mass Sorbent )
• Ceq - concentration of the sorbate in solution

The Langmuir isotherm [ læŋmjʊə -; after the amer. Physicist I. Langmuir ] is the simplest sorption model, which has physical basics. There are the assumptions that

• Adsorption in a single molecular layer takes place,
• All sorption are equivalent, and the surface is uniform,
• There are no interactions between adjacent sorption and the adsorbed particles.

The Langmuir isotherm can represent a maximum loading of Sorptionsoberflächen and is therefore the basis for further Adsorptionsmodelle.

BET model

• Q - loading of the sorbents ( sorbate mass relative to the mass Sorbent )
• K - sorption coefficient
• Qmax - maximum concentration of the sorbate (by weight of the sorbate to the weight of sorbent ) in a layer on the surface of the sorbent
• Ceq - concentration of the sorbate in solution
• Csat - solubility of the sorbate

The BET model extends the Langmuir isotherm to the behavior at high concentration of the sorbate near the solubility or saturation concentration. The model is based on the sorption in several molecular layers at the surface of the sorbent. The loading can therefore rise to infinity. The model is applied to the surface measurement.