Response Surface Methodology Optimization of Electron-Beam-Irradiated Carboxymethyl Cellulose/Citric Acid-Based Hydrogels

Electron beam irradiation (EBI) is an environmentally friendly cross-linking technique that can form covalent bonds between natural polymers without the use of chemical cross-linkers. In this study, carboxymethyl cellulose (CMC; 3000 cPs) and citric acid (CA) were used to prepare hydrogels under low-dose EBI conditions (7 kGy). The effects of composition variables were statistically analyzed using response surface methodology based on central composite design. The concentrations of CMC (4–14 wt%) and CA (1–4 wt%) were selected as independent variables, while the gel fraction, water absorption, and elastic modulus were employed as responses. Analysis of variance confirmed that the quadratic models were statistically significant (p < 0.05) with a high predictive reliability (R² = 0.91–0.98). Statistical validation demonstrated that the residuals were normally distributed and that all data fell within the 95% prediction interval, verifying the robustness of the model. Multi-response optimization identified an optimal composition of 8.88 wt% CMC and 0.03 wt% CA, yielding a predicted gel fraction of 88.7%, water absorption of 256 g/g, and modulus of 2273 Pa. The extended condition (CMC 9.12 wt%, CA 2.17 × 10⁻⁷ wt%) achieved similar absorbency with a ~9% higher modulus. This study established a reliable predictive model correlating the composition and properties of EBI-induced CMC–CA hydrogels, providing a foundation for optimizing eco-friendly hydrogel processes and scaling them up in the future.