The Sips isotherm equation: Often used and sometimes misused

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.