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.

Comparative Evaluation of Boron Sorption Dynamics on Zeolites in Irrigation Waters: An Isothermal Modeling Approach

“…However, more complex models like Sips, which combines features of both Langmuir and Freundlich models to describe systems with sorption heterogeneity, showed an excellent fit with an R 2 of 0.985. This indicates that the Sips model may be particularly representative for this system, with the parameters reflecting a sorption capacity of 0.676 mg/g, a Sips constant of 4.392 L/mg, and an exponent of 1.512, indicating a strong affinity of boron for the zeolite, with behavior transitioning between monolayer and multilayer sorption depending on the boron concentration [ 28 ].…”

“…For the interpretation of equilibrium data, eight theoretical sorption models were applied, including Langmuir, Freundlich, Sips, Toth, Jovanovic, Temkin, Dubinin–Radushkevich (D-R), and Redlich–Peterson [ 22 , 28 , 31 , 32 , 33 , 34 , 35 , 36 ]. The specific equations for each of the studied models are presented in Table 5 .…”

“…On the other hand, the Sips model combines the properties of the Langmuir and Freundlich models, offering a more accurate description over the entire range of adsorbate concentrations. It reduces to the Langmuir model at low concentrations and to the Freundlich model at high concentrations [ 28 ]. Meanwhile, the Toth model introduces modifications to account for the adsorbent surface’s heterogeneity.…”