Hi! I will hope help you with this, when sips exponent (nS) is:

nS > 2 the isotherm reaches equilibrium (qmaxS) at a smaller metal concentration. nS = 1 the Sips isotherm takes the form of the Langmuir isotherm

Regards

Hi, I hope this will help:

When Ce approaches a low value, the Sips isotherm effectively reduces to Freundlich, while at high Ce, it predicts the Langmuir monolayer sorption characteristic. The Sips isotherm equation is characterized by the dimensionless heterogeneity factor, n , which can also be employed to describe the system’s heterogeneity when n is between 0 and 1. When n=1 , the Sips equation reduces to the Langmuir equation and it implies a homogeneous adsorption process.

Journal of Chemistry (Hindawi) Volume 2014 (2014), Article ID 468975, 6 pages

Dear Ikemefuna Usifoh ,

are you talking about the exponential factor associated with equilibrium solution concentrations in the often-called Freundlich-Langmuir model? Sorbed concentration=maximal capacity*KC^n/(1+KC^n)? It is just to be sure that it is not the inverse value (which is also often defined). Anyway, when the exponent n associated with concentration is less than 1, it is rather related to a Gaussian distribution of sorption/binding sites by energy (in contrast to an exponential distribution leading to a regular Freundlich isotherm). These cases were specifically examined by Sips in his old original work (which is yet important!). When the exponent is more than 1, which is sometimes happening, it is another story. This is a kind of cooperative interactions when sorption of one (first) molecule/ion enhances sorption of more others, and the exponent may become in some cases to represent the formal number of molecules cooperaing in such a "collaborative" interaction. It "works" just as a chemical reaction describing complex formation with several ligands. Specific mechanisms may be very different, e.g., cooperative interactions of several ligands with a biological macromolecule (e.g., a protein) when forming a complex 1 to 1 immediately leads to a dominating portion of a 1 to n complex, a cooperative swelling, or just lateral interactions at the interface or surface. The latter case may be very common. Anyway, if this exponent was obtained, it is a good indication on interesting mechanisms. If we talk about the same exponent, the value 1.7 suggests that two molecules cooperate when adsorbing. It may well be a lateral interaction case. You might want to look at our paper in which this issue is briefly discussed, with references to the literature and in regarding to our systems (but you may find, surely, more studies in the literature).

Sorption Interactions of Organic Compounds with Soils Affected by Agricultural Olive Mill Wastewater, 2015, Chemosphere - Global Change Science 138:462-468, DOI 10.1016/j.chemosphere.2015.06.085

These answers has been so enlightening. Thanks for your responses. @Mikhail Borisover your paper has been most revealing. Thank you. and yes the formula is you stated. 'Sorbed concentration=maximal capacity*KC^n/(1+KC^n)'.

The adsorbent i used was carbonized groundnut shells at 400 degree Celsius while the adsorbate in aqueous solution was lead.

The Sips model is a hybrid model combining both Langmuir and Freundlich models. Sips model can describe the homogeneous or heterogeneous systems. when ns = 1 the Sips model becomes the Langmuir model, on the other hand, sips becomes the Freundlich model at low concentration.