The Sips isotherm equation: Often used and sometimes misused

ABSTRACT

The Sips isotherm equation, proposed in 1948, is popularly used to describe the adsorption of a diverse array of water contaminants by engineered and natural adsorbents. However, that apparent popularity conceals problematic application issues. Our critique of its use in water contaminant adsorption research is threefold. First, we show that a linear version of the Sips equation promoted by several reviews is bogus. We also highlight application problems associated with two other linear versions. Second, we show that it is inappropriate to compare the Sips and Langmuir–Freundlich equations in data correlation. Because the two equations are mathematically equivalent, they must provide exactly the same fit to a given set of isotherm data. Third, we argue that there is little to be gained by applying the Sips equation to type I isotherms, which are hyperbolic curves. Such isotherm shapes can be adequately interpreted by simple two-parameter isotherm models such as the Langmuir and Freundlich equations. The modeling power of the Sips equation can be more profitably exploited by applying it to type V isotherms, which are sigmoid curves.

KEYWORDS:

• Adsorption isotherm
• misuse
• misapplication
• linearization
• S-shaped
• sigmoid

Disclosure statement

The authors declare that they have no known competing financial interests.

Statement of novelty

The Sips isotherm equation is widely used to correlate water contaminant adsorption data. However, that apparent popularity conceals problematic application issues. For the first time, this paper addresses three application issues found in the literature of adsorptive water remediation. They are: (1) the dubious practice of using linear versions of the Sips equation to fit adsorption data; (2) the questionable practice of comparing the Sips and Langmuir–Freundlich equations; and (3) the trivial practice of fitting the Sips equation to hyperbolic type I isotherm data. It is hoped that the material presented in this work will lead to a better comprehension of the Sips equation.

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.