Fitting a little-known isotherm equation to S-shaped adsorption equilibrium data

A research topic of current interest concerns the measurement and modeling of adsorption isotherms of water contaminants. The bulk of measured equilibrium isotherms exhibit the convex-upward or favorable curve shape, which can be described by the two-parameter Hill-Langmuir and Freundlich isotherms. An increasing number of recent studies have however reported S-shaped or sigmoidal equilibrium isotherms. Modeling such equilibrium data requires the use of isotherm equations with a highly flexible functional form. This work introduces a littleknown isotherm useful for tracking the trajectory of S-shaped equilibrium data. This relatively simple three-parameter isotherm, first proposed by Krishnamurti in 1951, has theoretical merit because it is based on a cooperative adsorption mechanism. It is shown that previously reported S-shaped equilibrium data of water contaminants can be represented by the Krishnamurti isotherm. Specific examples discussed are (1) ammonium ion adsorption by the clay mineral sepiolite, (2) uptake of the antibiotic ciprofloxacin by a magnetic nanosorbent, and (3) fluoride ion removal by a layered double hydroxide adsorbent. Additionally, it is found that a modified form of the Krishnamurti isotherm is superior to its original counterpart. The original and modified Krishnamurti isotherms can be practically very useful to describe S-shaped equilibrium data and for adsorptive process modeling.

Automated summary

Current research interest lies in the measurement and modeling of adsorption isotherms of water contaminants, with recent studies revealing S-shaped or sigmoidal equilibrium isotherms. The Krishnamurti isotherm is proposed as a useful tool to track the trajectory of S-shaped equilibrium data, offering theoretical merit based on a cooperative adsorption mechanism. Examples including ammonium ion adsorption, antibiotic uptake, and fluoride ion removal demonstrate the utility of the original and modified Krishnamurti isotherms for describing S-shaped equilibrium data.