Experimental adsorption isotherms for four anionic dyes (Acid Blue 25, Acid Yellow 99, Reactive Yellow 23 and Acid Blue 74) on to cationized cotton have been analyzed using a multilayer adsorption model. For such purpose, the double-layer model showed the best fit with a high correlation coefficient R². The analytical expression of the model has been established from an application of the grand canonical ensemble of statistical physics. This method allowed an estimation of all the mathematical parameters in the model. Thus, the receptor site density and the half-saturation concentration have been related to physicochemical variables such as the chemical potential, the adsorption energy, the anchorage number, etc. A physical interpretation of the model parameters has been provided and some results relating to the adsorption process discussed.

In this study, two theoretical expressions for the Type VI isotherm in the IUPAC classification are presented. The formulation of these new expressions is based on a rigorous statistical mechanical description. The expressions allow for the estimation of physicochemical parameters within the theoretical model. The proposed models allow a good correlation to Type VI experimental isotherms taken from the literature such as adsorption isotherms for adsorption of methane onto MgO (100) and onto an exfoliated graphite surface. The parameters intervening in the adsorption process have been deduced directly from experimental adsorption isotherms by numerical simulation. The theoretical expressions provide an understanding and interpretation of the adsorption isotherms at the microscopic level.