Adsorption and ion-exchange isotherms in preparative chromatography

A systematic characterization of ion-exchange and adsorption isotherms is presented. This treatment serves to emphasize the singular nature of monovalent ion-exchange and classical Langmuir isotherms, and describes the more general homovalent and heterovalent isotherms that are applicable to both ion-exchange and adsorption. Such formalisms are applied to adsorptive systems for the first time, and could prove to be useful additions to the canon of available isotherms. The shielding effect of macromolecular adsorbates on the binding of other macromolecules is discussed, and its parallel to the characteristic charge of a macromolecule is brought out. The application of the general adsorptive formalism to reversed-phase chromatography yields a relationship between the retention factor and the modifier concentration that, in two limiting cases, reduces to two well-known results. The first, which is characteristic of small molecules, gives a linear relationship between the logarithmic retention factor and a linear or quadratic term in the modifier. The second, which is characteristic of large molecules, gives a linear relationship between the logarithmic retention factor and the logarithm of the modifier concentration. The use of appropriate concentration units is shown to resolve certain apparently non-standard (non-Tiselian) displacement patterns. The measurement of characteristic charges by displacement described above could be an interesting complement to the more common elution method, and could provide further insight into the underlying physico-chemical phenomena.