Phenol Adsorption on Commercial Palm Shell Activated Carbon: A Framework for Resolving Multi‐Model Paradoxes Through Objective Selection and Mechanistic Reconciliation

ABSTRACT Conventional adsorption studies frequently encounter a methodological paradox where multiple kinetic and isotherm models provide statistically valid fits while suggesting contradictory physical mechanisms. This study presents a systematic framework to resolve such contradictions and derive a unified mechanistic understanding. Using phenol adsorption on palm shell activated carbon as a case study, we demonstrate a pathway that moves beyond routine model cataloging. The framework integrates: (1) Objective model discrimination using Akaike (AIC) and Bayesian (BIC) Information Criteria, which decisively identified the Pseudo‐Second Order model ( R 2 = 0.9992, AICc = −648.2) over the misleadingly high‐ R 2 Pseudo‐First Order model, establishing chemisorption as rate‐limiting; (2) Paradox resolution through the Sips isotherm model, which reconciles excellent Langmuir and Freundlich fits by quantifying surface heterogeneity (n s = 0.3215 at 25°C) while accounting for high‐affinity sites; and (3) Advanced diffusion diagnostics via fractal analysis, revealing concentration‐dependent sub‐diffusive transport (fractal exponent a decreasing from 0.916 to 0.726). Thermodynamics confirmed strong chemisorption (ΔH° = −68.1 to −104.5 kJ/mol). This work provides a criterial protocol for transforming conflicting adsorption model outputs into coherent, evidence‐based mechanisms applicable across diverse adsorbent systems.