This study presents an innovative approach using statistical physical modeling to analyze the effect of experimental conditions and adsorbent features on removing Allura Red dye by chitosan. Five models based on statistical physics were employed to understand the removal mechanism under different experimental conditions, including variations in pH, particle sizes, chitosan deacetylation degrees, and temperatures. The best models were determined through rigorous statistical analysis and a detailed evaluation of the estimated parameters, considering their physical meaning and standard deviations. The models demonstrated high predictive capacity (coefficients of determination greater than 0.9 and low mean squared error values < 110). Analysis of the effects of experimental conditions revealed that a pH of 6.6, particles smaller than 0.10 mm, a high degree of deacetylation (84 %), and temperatures of 298 K and 308 K present the greatest potential for dye removal by chitosan. Furthermore, it was observed that, in general, the dye removal mechanism involves the formation of a double layer with two adsorption energies under the best experimental conditions, and the process occurs predominantly by physical forces (adsorption energy below 35 kJ/mol). This work contributes significantly to understanding how experimental conditions influence the mechanism of dye adsorption by chitosan, offering valuable and new insights for future applications and optimizations in the treatment of effluent-containing dyes.
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