Through a statistical physics modeling approach, a detailed theoretical scrutiny was conducted utilizing four distinct models based on the grand canonical ensemble to fit the Methylene Blue adsorption isotherms onto Sodium StyreneSulfonate-co-Dimethylacrylamide (NaSS-DMA) hydrogel surface. Steriographic along with energetic-thermodynamic metrics have been inspected in response to combined effects of temperature and concentration. The uptake process was best described by a bimodal-energy linking monolayer scenario involving two sites and energies ( \(\varepsilon_{1}\) = 15.73 kJ/mol and \(\varepsilon_{2}\) = 17.85 kJ/mol) characterized by a multi-molecule adsorption process (n1 = 8.383 and n2 = 2.5967) at T = 295 K. Steriographic discussion revealed that the position of the adsorbate is non-parallel but a larger number of entities can be linked in the same receptor site. The adhesion reaction is exothermic and when the concentration exceeds 95 mg/L, the adsorbed amount decreases significantly in response to incremented heat conditions. More importantly, the investigated linking process is primarily driven by weak van der Waals forces (energies below 45 kJ/mol) while the negative values of Gibbs free energy validated its spontaneity. These outcomes supported the development of a robust mathematical framework that accurately predicts removal efficiencies of Methylene Blue onto NaSS-DMA hydrogel surface providing a deeper understanding of the involved nanoscale surface linking. The findings can be effectively translated into real-world applications for water treatment and environmental detoxification through the use of super-adsorbent hydrogels. By leveraging their optimized steric, energetic and thermodynamic properties, these hydrogels exhibit exceptional adsorption efficiency, enabling the removal of hazardous contaminants like Methylene Blue from polluted water systems. Their high capacity for adsorption, combined with stability and reusability, makes them ideal for large-scale applications in wastewater treatment plants and industrial effluent management. Finally, their compatibility with existing water purification technologies allows seamless integration into current systems, offering a cost-effective, sustainable and scalable solution for addressing water pollution challenges.
