neous material. In the simplest case of a single component, In the present study we evaluate affinity distributions for comthe affinity distribution is defined as an integral transform petitive adsorption isotherms which involve several components. of the adsorption isotherm u(c), where u represents the frac-In such a multicomponent situation, the affinity distribution betional amount adsorbed and c the bulk concentration (or comes a function of several affinity constants, and already in the solution activity) of the component of interest. Taking a case of two components, little is known about their features. In simple Langmuir isotherm as the so-called local isotherm, the two-component situation, we have calculated the affinity distrithe adsorption isotherm can be written as (1, 2) butions 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 appli-
cability 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 where K is the affinity constant and P(K) the normalized is known to have a perfectly correlated distribution. The present affinity distribution. The forward problem is straightforstudy demonstrates that the extended Henderson-Hasselbalch ward-given the affinity distribution, the corresponding iso-(HH) isotherm has an underlying affinity distribution, which distherm can be evaluated either analytically or numerically.
plays a partial correlation, while the non-ideal competitive adsorp-
The inverse problem was elegantly solved by Sips (2, 3).
tion (NICA) isotherm has an affinity distribution with a varying
By making some tacit, but generally proper assumptions (4), degree of correlation. In the competitive situation, the affinity Sips was able to derive a general expression for P(K) by distribution thus provides an interesting means to characterize the corresponding isotherms. As an illustration of the present tech-means of analytical continuation of u(c) into the complex niques, experimental data of metal ion binding for a humic acid plane. By applying his inversion relation to the classical are analyzed in the same context.