Fractal dimension as a predictive morphological metric for dye removal in polyurethane foams

Abstract

This study presents fractal dimension (D_f) as a predictive metric to optimize polyurethane foams (PUFs) for the adsorption of methylene blue (MB) as a toxic dye. PUFs were prepared by varying the amount of amine catalyst mixture (trimethylamine and triethylenediamine) (0.2–1.2 g), while chemical formulation was kept constant, including polyol (saturated aliphatic polyester), isocyanate (methylene diphenyl diisocyanate), catalyst (ethylenediamine, dibutyltin dilaurate), chemical blowing agent (water), isocyanate-index: 100%, and water content: 1%. This approach resulted in different cellular morphologies but constant chemistry. The D_f, calculated via box-counting analysis of binarized optical microscopy images, ranged from 1.5415 to 1.8554. PUF properties including density (0.016–0.031 g/cm³), average cell size (49–133 μm), open-cell content (30–35%), and specific surface area (2.33–0.67 m²/g) were characterized. Adsorption evaluations were conducted at both high (100–900 mg/L) and low (10–90 mg/L) MB concentrations. Results demonstrated a strong correlation between D_f and dye removal efficiency. Increasing D_f from 1.5415 to 1.8554, at a consistent open-cell content (∼30%), significantly boosted removal efficiency by approximately 108%, regarding to a greater structural complexity and accessible surface area. Adsorption kinetics followed a pseudo-second-order model (R² > 0.99), and equilibrium isotherms best fit the Freundlich model, indicating multilayer adsorption. The optimal formulation (density: 0.03 g/cm³, open-cell content: 30 ± 2%, cell size: 49 ± 5 µm, D_f: 1.8554) achieved a removal efficiency of 44.5% at 900 mg/L MB concentration. The findings demonstrate that D_f can serve as a useful integrated morphological descriptor for assessing PUF adsorption performance. This approach offers a practical strategy for tailoring the PUF structures in wastewater treatment applications.