Isotherms Based on the Langmuir Model

If mixtures of solutes are injected into a chromatographic system, not only interferences between the amount of each component and the adsorbent but also interferences between the molecules of different solutes occur. The resulting competition 

A prerequisite for Equation 2.57 is the equality of the maximum loadability (jsat of all n solutes. In case of different loadabilities for the different solutes qss.t.i satj). Equation 2.57 no longer fulfils the Gibbs-Duhem equation and is thus thermodynamically inconsistent (Broughton, 1948). This is, for example, the case if solutes with substantially different molecular masses are separated on sorbents where the pore accessibility is hindered for large molecules. 

The multicomponent Langmuir isotherm based on Equation 2.53 is shown in Equation 2.58 (Charton and Nicoud, 1995)  

The bi-Langmuir isotherm (Equation 2.54) can be extended in the same way to give the multicomponent bi-Langmuir isotherm (Equation 2.59) (Guiochon et al. 2006)  

Modified multicomponent Langmuir and multicomponent bi-Langmuir isotherms offer a large fiexibility for adjustment to measured data if all coefficients are chosen individually. To limit the number of free parameters that need to be specified it is sometimes possible to use in Equations 2.58 and 2.59 constant adjustment terms (Ij = 7.) or equal saturation capacities (qsat.i, i = sat,2,i = fet,i)  

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