Analyzing phenol adsorption behavior on natural sorbents using kinetics and probabilistic physics: clay, pomegranate and Vicia faba

Abstract

In this current research, we investigate the phenol adhesion to three natural sorbents (Clay, Pomegranate Peel, and Vicia faba) employing two numerical schemes (Probabilistic formalism and Kinetics) to describe the recorded isotherms corresponding to the selected adsorbents. For Vicia faba, the Hill model exhibited the best fit, while for Pomegranate Peel, the multilayer saturation model performed best. For Clay, the single-layer model with two energy levels achieved the highest agreement. Several key statistical physics parameters were extracted to probe accumulation kinetics. At very low concentrations, adsorption half-times (τ_1/2) were moderate for Vicia faba and Pomegranate Peel (~ 90 to 120 s), whereas Clay exhibited larger fluctuations exceeding 300 s. Our achieved calculation has pointed to van der Waals interactions dominative in adhesion energy values (ΔE ~ 32 kJ mol⁻¹). From a structural viewpoint, the filling rate for Vicia faba (δ = 0.7687) suggests fewer than one phenol molecule per site. In contrast, Clay exhibits dual-layer adhesion (δ₁ = 3.5004, δ₂ = 1.6703), indicating multiple entities per cavity. Pomegranate Peel also supports multi-molecular retention, with a single-layer δ = 1.9166.