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.

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Experimental adsorption of synthetic dyes, FD&C red no. 40 and Tartrazine, onto Spirulina platensis has been analyzed using a statistical physics treatment at different temperatures (298, 308, 318, and 328 K) and at different values of pH (4, 6, and 8). The statistical physics formalism was used to develop the analytical expressions of models. The interpretation of the adsorption of these dyes on Spirulina platensis was achieved by choosing the adequate model and by presenting the evolution of the parameters involved in the analytical expression of this model such as the number of adsorbed dye molecules per site (n), the receptor sites density (D), the adsorbed quantity at saturation (q), and the molar adsorption energy (ΔE). Thus, several interpretations and results describing the adsorption of dyes on Spirulina platensis are extracted regarding the behaviors of these parameters at different temperatures and different values of pH. Thermodynamic functions such as the Gibbs free energy, the internal energy, and the entropy are studied at different values of pH.

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