A model free method for estimation of complicated adsorption isotherms in liquid chromatography

Here we show that even extremely small variations in the adsorption isotherm can have a tremendous effect on the shape of the overloaded elution profiles and that the earlier in the adsorption isotherms the variation take place, the larger its impact on the shape of the elution profile. These variations are so small that they can be "hidden" by the discretization and in the general experimental noise when using traditional experimental methods, such as frontal analysis, to measure adsorption isotherms. But as the effects of these variations are more clearly visible in the elution profiles, the Inverse Method (IM) of adsorption isotherm estimation is an option. However, IM usually requires that one selects an adsorption isotherm model prior to the estimation process. Here we show that even complicated models might not be able to estimate the adsorption isotherms with multiple inflection points that small variations might give rise to. We therefore developed a modified IM that, instead of fixed adsorption isotherm models, uses monotone piecewise interpolation. We first validated the method with synthetic data and showed that it can be used to estimate an adsorption isotherm, which accurately predicts an extremely "strange" elution profile. For this case it was impossible to estimate the adsorption isotherm using IM with a fixed adsorption model. Finally, we will give an example of a real chromatographic system where adsorption isotherm with inflection points is estimated by the modified IM.