Description of sigmoid adsorption isotherms of water pollutants by the Aranovich-Donohue equation

Abstract

In the field of adsorptive water remediation, the Brunauer-Emmett-Teller (BET) equation is often used to describe sigmoid type II isotherm data. A standard type II isotherm is a composite curve that comprises a type I and a type III curve at low and high concentrations, respectively. The BET equation uses a Langmuir-like function to describe the type I curve and a unique function to represent the type III curve. However, the ability of this mathematical combination to fit atypical type II isotherms is somewhat limited. The BET equation has been modified in various ways to improve its data fitting ability. The Aranovich-Donohue equation is an interesting modification in that it has a flexible equation structure that allows users to choose an isotherm model to describe the type I curve at low concentrations. It is shown here that the Aranovich-Donohue equation featuring the Sips equation is capable of accurately correlating anomalous acid red and acid black dye isotherm data, outperforming the original BET equation. Furthermore, the Aranovich-Donohue-Sips equation can accurately track a phenol isotherm characterized by a type V curve at low concentrations, demonstrating its versatility in fitting nonstandard type II isotherm data.