Semiempirical equilibrium models of competitive, two-component binding
of simple ions to heterogeneous materials are based on a combination
of independent binding isotherms, such as two-component Langmuir isoth
erms or exchange isotherms. Such models are usually sufficiently flexi
ble to rationalize various experimental data sets quantitatively. Sinc
e such models are thermodynamically consistent, they have substantial
predictive capabilities. Furthermore, such models are rather simple, m
ay depend on a relatively small number of parameters, and provide an i
ntuitive framework for comparison of binding properties of different m
aterials. We solve the ill-posed data inversion problem with constrain
ed, regularized least-squares techniques. This approach to the interpr
etation of two-component competitive ion binding to heterogeneous mate
rials is illustrated with two data sets; the binding of Sr2+ and H+ to
ferrihydrite (amorphous FeOOH) and that of Cu2+ and H+ to a humic aci
d.