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Adsorption isotherm
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Here we will briefly discuss the concept of adsorption isotherms and its role in chromatography.

 

An adsorption isotherm is a plot of the concentration or amount of a specie on a surface as a function of its concentration in the bulk phase. In liquid chromatography, the bulk phase is, of course, the mobile phase.

 

In the simplest form of chromatographic theory, it is assumed that the adsorption isotherm for the solute is linear, i.e.

 

Cs = K * Cm

 

where

Cs = the concentration of the solute on the surface

 

Cm = the concentration of the solute in the mobile phase.

 

K = adsorption constant of the  solute to the stationary phase surface.

 

The assumption of linear adsorption isotherm leads to the simple relation between retention factor, k, and the adsorption constant:

 

k = F*K

 

where F is the column phase ratio. ( Note that a unequivocal definition of the phase ratio needs to be made for the relation to hold rigorously. A discussion about this is made under the heading, Surface Excess.)

 

The linearity of the adsorption isotherm is, however, limited to a certain low concentration range. At higher concentrations the adsorption isotherm becomes non-linear and often have a convex ( downward ) shape. It is customary to describe this non-linearity with a Langmuir adsorption isotherm. The mathematical expression for this adsorption isotherm is:

 

Cs = qs*K*Cm / ( 1+K*Cm )

 

where qs is representing the saturation concentration of the solute on the stationary phase surface. There are, however, a large number of expressions for a non-linear adsorption isotherm and the best is if they can represent a physical picture of the adsorption process.

 

In chromatography, when the concentration of the solute is such that the adsorption isotherm is non-linear, the column is said to be over-loaded.

 

For a more comprehensive discussion about the role of non-linear adsorption isotherms in chromatography click here.

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