Experimental and theoretical investigation of methylene blue adsorption onto cupules of scales: entropy, free enthalpy, and internal energy insights from statistical physics modeling and full factorial design

Abstract Dye-laden wastewater presents a critical global environmental issue, requiring sustainable and bio-based treatment strategies for the effective removal of hazardous pollutants. The adsorption of methylene blue (MB), a cationic dye, using raw cupule scale (CR) as a natural bioadsorbent was investigated in this study. Additionally, untreated cupule scales were selected for further evaluation of the cationic dye adsorption process. The physicochemical characterization of the adsorbents was carried out using Fourier transform infrared spectroscopy (FTIR), thermogravimetric analysis (TGA), and the determination of the point of zero charge (pH PZC ) (7.2). The influence of key operational parameters, including contact time, adsorbent dosage, solution pH, and initial dye concentration, was systematically investigated and optimized using the Box–Behnken Design (BBD). The equilibrium data showed an excellent fit to the Langmuir isotherm model with correlation coefficient R 2 = 0.99 at 20°C while kinetic analysis indicated that the pseudo-second-order model best described the adsorption behavior, suggesting a chemisorption-controlled mechanism with a maximum adsorption capacity of 102.315 mg/g. Among the advanced isotherm models evaluated, the double-energy monolayer model provided the most accurate description of MB adsorption on CRs (R 2 greater than 0.9981, MRSE little than 0.015), revealing a multimolecular adsorption mechanism with a primary receptor site density (Nm 1 ) reaching up to 318.2 mg/g. Thermodynamic analysis confirmed that the adsorption process is exothermic and spontaneous, with adsorption efficiency decreasing at higher temperatures. These findings underscore the potential of CR as an effective, natural, and cost-efficient adsorbent for mitigating MB contamination in aqueous systems.