The Kiselev isotherm for adsorption at the liquid-solid interface: Solving the mystery of negative equilibrium constants

Abstract

Equilibrium data for aqueous adsorption systems are often correlated using isotherm models originally developed for adsorption at the gas-solid interface. A prominent example is the Langmuir isotherm, which has been used in thousands of investigations to describe the adsorption of dissolved substances at the liquid-solid interface. Another example is the Kiselev isotherm, which was proposed to account for adsorption at the gas-solid interface when adsorbate-adsorbate interactions are significant. Researchers who have applied the Kiselev isotherm to adsorption data for liquid-solid systems were puzzled by the fact that data fittings in most cases returned negative values for the adsorbate-adsorbate association equilibrium constant. It is shown in the present study that the data fitting problem is a direct consequence of misusing the Kiselev isotherm. In all previous studies, the Kiselev isotherm was used to fit type I isotherm data. Because the concept of adsorbate-adsorbate interactions is incompatible with a type I isotherm, fitting the Kiselev isotherm to such data can lead to nonsensical parameter estimates. The Kiselev isotherm was devised to account for type V isotherms exhibiting a sigmoid or S-shaped data trend. Physically meaningful parameter estimates can be obtained if the Kiselev isotherm is applied to type V isotherm data.