Toxic dyes adsorption using sheep horn activated carbon: Mechanism, DFT study, artificial neural network, Box–Behnken modeling, and cost estimation

Abstract

Sheep horn activated carbon with KOH (SHAC) proved to be an effective adsorbent for removing Crystal Violet (CV) and Congo Red (CR). Fourier Transform Infrared (FTIR) analyses confirmed the presence of –OH, –SH, CC, CN, NH, and COO functional groups derived from keratin, while Thermogravimetric Analysis coupled with Differential Thermal Analysis (TGA/DTA) revealed the decomposition of oxidized proteins and the crystallization of KOH-bound water. For CV, the optimal adsorption equilibrium efficiency reached 98.62% at [CV] = 40 mg L⁻¹, dose = 1.25 g L⁻¹, pH = 10, contact time = 50 min; adsorption followed the Langmuir and pseudo-first-order models, indicating physisorption with increasing disorder. For CR, the maximum equilibrium adsorption is 73.89% at [CR] = 40 mg L⁻¹, adsorbent dose = 1.25 g L⁻¹, pH = 2, contact time = 50 min following Temkin, Freundlich, and pseudo-first-order kinetics, reflecting endothermic physisorption. The Artificial Neural Network (ANN) models perform excellently (R² = 0.965, MSE = 2.9374 for CV, and R² = 0.9718, MSE = 4.963 for CR), and Box Behnken Design (BBD) confirms their validity (ANOVA p-value = 0.0038 for CV, 0 for CR, Cook's distance <0.2). Density Functional Theory (DFT) calculations show that CV (ΔE = 1.735 eV, S = 0.567 eV, ω = 9.175 eV) is more reactive than CR (ΔE = 2.833 eV, η = 1.416 eV). Electrostatic potential (ESP) maps and Fukui indices identify nitrogen atoms, aromatic carbon atoms, and –SO₃⁻ and –N=N– groups as active sites. After 5 thermal regeneration cycles, SHAC retains 69% of its capacity for CV and 23% for CR. The adsorption cost is estimated at $0.32 L⁻¹, confirming the efficiency, durability, and cost-effectiveness of SHAC.