Classical and Fractal-like Sorption Kinetic Studies of Methylene Blue on Unmodified Plantain Peduncle Biomass and Activated Carbon

The kinetic behaviour of methylene blue (MB) dye solution in relation to unmodified biomass and activated carbon from plantain (Musa paradisiaca) peduncle was studied, considering both time-dependent and time-independent aspects. MB dye solutions were exposed to unmodified biomass and activated carbon from plantain peduncle at intervals ranging from 5 to 210 minutes, at fixed concentrations of 15 mg/L and 30 mg/L. Equilibrium times were recorded at 160 and 200 minutes. Classical and fractal-like pseudo-order kinetic models were applied to the adsorption data to determine the rate-controlling order and the surface complexity of MB molecule adsorption. The Hurst fractal exponent (h) was calculated to establish the fractal-like surface pattern of adsorption sites. For 15UM, the Hurst fractal exponent h was negative in both FL-PFO (-0.638) and FL-PSO (-1.2649). For 30UM, the exponents were 0.3031 and 0.2971 for FL-PFO and FL-PSO, respectively. For 15AC, the exponents were 0.7434 and 0.745 for FL-PFO and FL-PSO, respectively, while for 30AC, the exponents were 0.7245 and 0.7209 for FL-PFO and FL-PSO, respectively. The coefficient of determination (R²) and correlation coefficient (r) of the fractal fittings were both greater than 0.96, outperforming conventional pseudo-order kinetics. Time-dependent behaviour was observed in the samples with h > 0.5 (15AC and 30AC), suggesting a persistent and stable adsorption process. Time-independent behaviour was observed in samples with 0 < h < 0.5 (30UM) and h < 0 (15UM). The Weber-Morris diffusion model was also used to assess intraparticle diffusion, revealing significant but not prevalent intraparticle diffusion. The presence of prevalent fractal-like kinetics indicates surface complexity in both plantain peduncle samples.