Activated carbon for multicomponent heavy-metal removal: bridging macroscopic adsorption performance and microscopic statistical-physics modeling.

Banana peel-derived activated carbon (BPAC) was synthesized and evaluated for the ternary adsorption of Ni(ii), Cd(ii), and In(iii) from aqueous solutions at 30-50 °C. Experimental isotherms were interpreted using an extended statistical physics model that explicitly accounts for solution-phase interactions and excluded-volume effects, providing a physically consistent description of non-ideal multicomponent adsorption. Adsorption kinetics were best described by the pseudo-second-order model, and BPAC retained approximately 89% of its initial adsorption capacity after five adsorption-desorption cycles, demonstrating excellent reusability. Microscopic analysis revealed that BPAC possesses a high density of accessible receptor sites (R Mi ) together with low cohesion pressure (a i ) and covolume (b i ) parameters, thereby reducing lateral interactions and enhancing adsorption performance relative to commercial activated carbon (CAC). Adsorption energy distribution (AED) analysis revealed broader, higher-energy profiles for Ni(ii) and Cd(ii), indicating heterogeneous high-affinity sites and stronger adsorbate-surface interactions, whereas In(iii) exhibited lower-energy interactions consistent with predominantly physisorption. Thermodynamic analysis yielded negative Gibbs free energies for all ions (approximately -65.6 to -97.8 kJ mol-1 for Ni(ii), -54.6 to -83.6 kJ mol-1 for Cd(ii), and -42.3 to -21.4 kJ mol-1 for In(iii)), confirming the spontaneous nature of the adsorption process. Increasing temperature enhanced the adsorption of Ni(ii) and Cd(ii) but reduced that of In(iii). Overall, the explicit incorporation of lateral interaction parameters proved essential for accurately interpreting adsorption capacity, energetics, and selectivity, establishing BPAC as an efficient and sustainable adsorbent for multicomponent heavy-metal removal.