Interpretation of ion-exchange chromatographic retention based on an electrical double-layer model

An ion-exchange chromatographic model based on the Stern-Gouy-Chapman electrical double-layer theory is presented. We assume several equilibria occurring at the surface of an ion-exchange resin, such as the ion-pair formation of counterions with an ion-exchange site, the adsorption of ions, and the ion-pair formation of an adsorbed ions with their counterions. These equilibria are affected by the potential at the planes (the surface and the Stern layer potential) where the reactions occur. In addition, the nonselective accumulation of ions in the diffuse layer is also taken into account. Based on the developed model and derived equations, the nature of log k'-log X (X is the concentration of an eluent ion) plots is investigated for various sets of parameters and is compared with that of possible experimental results. Three extreme cases can be distinguished:  (1) ion-pair-controlled, (2) adsorption-controlled, and (3) accumulation in the diffuse layer-controlled retention. Though log k'-log X plots, when they are studied over wide eluent concentration ranges (more than 2 orders), do not necessarily show precise linearity especially in the presence of eluent adsorption and extremely high eluent ion-pair formation, the linear regression analyses give negative unit slopes (within 10% deviations) for monovalent solute-eluent combinations. Since the deviation from linearity relation is mostly found in very low k' ranges (e.g., k' < 1), it is possible only in very limited cases to confirm nonlinearity experimentally. This may have mistakenly led to the idea that selectivity coefficients can be regarded as constants and thus the log k'-log X plots should be linear with the slope equal to (charge ratios) × (-1) in ion-exchange chromatographic experiments. The efficiency of the developed model is verified by its ability to predict experimental results, e.g., nonlinear log k'-log X plots, changes in separation factors with varying ion-exchange affinity of an eluent ion, adsorption isotherms at different salt concentration, etc.