Statistical Physics Quantification of Steric, Energetic and Thermodynamic Adsorption Attributes of Methylene Blue onto Super-Adsorbent Hydrogel (NaSS-DMA monomers) for water detoxification

Abstract

<title>Abstract</title> 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 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 (𝜀₁ = 15.73 kJ/mol and 𝜀₂ = 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 anchored in the same receptor site. The docking 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.