Interpretation of Competitive Adsorption Isotherms in Terms of Affinity Distributions

In the present study we evaluate affinity distributions for competitive adsorption isotherms which involve several components. In such a multicomponent situation, the affinity distribution becomes a function of several affinity constants, and already in the case of two components, little is known about their features. In the two-component situation, we have calculated the affinity distributions from the adsorption isotherms with a numerical inversion technique. This technique is based on a constrained least-squares algorithm and uses a regularization function which biases the resulting affinity distribution toward a smooth function. The applicability of the procedure was tested with a newly derived isotherm, which is based on a fully uncorrelated affinity distribution, and with the generalized Langmuir-Freundlich (LF) isotherm, which is known to have a perfectly correlated distribution. The present study demonstrates that the extended Henderson-Hasselbalch (HH) isotherm has an underlying affinity distribution, which displays a partial correlation, while the non-ideal competitive adsorption (NICA) isotherm has an affinity distribution with a varying degree of correlation. In the competitive situation, the affinity distribution thus provides an interesting means to characterize the corresponding isotherms. As an illustration of the present techniques, experimental data of metal ion binding for a humic acid are analyzed in the same context.