Understanding the equilibrium relationship between an adsorbent and an adsorbate is fundamental to designing effective water treatment systems. Isotherm models provide crucial insights into the adsorption mechanism, the distribution of adsorbate molecules on the adsorbent surface, and the maximum adsorption capacity. This article delves into the isotherm analysis of Direct Blue 86 (DB86) dye adsorption onto cellulose hydrogel (CAH), examining key models like Langmuir, Freundlich, Temkin, and Dubinin-Radushkevich.

The adsorption process involves dye molecules transferring from the aqueous solution to the surface of the cellulose hydrogel. Isotherm models help us quantify this process at equilibrium. Each model makes certain assumptions about the nature of the adsorption sites and the interactions between adsorbate molecules.

The Langmuir Isotherm (LIM) model posits that adsorption occurs on a finite number of homogeneous sites, forming a monolayer of adsorbate. It assumes uniform adsorption energy and no interaction between adsorbed molecules. From the Langmuir model, a maximum adsorption capacity (Qm) can be determined, representing the theoretical maximum amount of dye that can be adsorbed when the entire surface is covered by a single layer of dye molecules. In the study, the Qm for DB86 on CAH was calculated to be 53.76 mg/g, indicating a significant potential for dye binding.

The Freundlich Isotherm (FIM) model, on the other hand, describes adsorption on heterogeneous surfaces where adsorption capacity is related to the concentration of adsorbate, and it does not assume monolayer formation. The Freundlich model yielded a heterogeneity factor 'n' greater than 1, suggesting a favorable adsorption process with stronger interactions between the adsorbate and adsorbent as the surface becomes more occupied.

The Temkin Isotherm (TIM) model considers the effect of adsorbate-adsorbent interactions on the adsorption process. It assumes that the heat of adsorption decreases linearly with increasing coverage due to these interactions. The analysis using the Temkin model in this study indicated favorable adsorption conditions, with constants related to the heat of sorption being calculated.

The Dubinin-Radushkevich Isotherm (DRIM) model provides information about the porosity of the adsorbent and the mean free energy of adsorption. The calculated mean free energy values for DB86 adsorption on CAH were found to be below 8 kJ/mol, suggesting that the process is primarily governed by physical adsorption (physi-sorption), which involves weaker van der Waals forces.

To determine the best-fit model for the experimental data, a chi-square error analysis was employed. This statistical method helps to quantitatively assess how well each isotherm model describes the observed experimental results. Based on this analysis, the Temkin Isotherm (TIM) was identified as the best-fitting model for the adsorptive removal of DB86 dye by CAH. This suggests that the interactions between the dye molecules and the cellulose hydrogel surface play a dominant role in determining the adsorption equilibrium.

The insights gained from these isotherm studies are invaluable for optimizing wastewater treatment processes. By understanding the adsorption characteristics, engineers can predict how much dye can be removed under different conditions, select the most appropriate adsorbent dosage, and design efficient adsorption systems to effectively tackle dye pollution from industrial effluents.