Double-network beads of carboxymethyl cellulose/poly(tertiary amine)/FeCl3 as mechanically robust hybrids: Application of Hertzian elasticity to analyze composition-dependent mechanics

Double-network beads consisting of carboxymethyl cellulose/poly(2-(dimethylamino)ethyl methacrylate-co-N-(3-(dimethylamino)propyl)methacrylamide))/diethyleneglycol dimethacrylate/ferric chloride, CMC/P(DAEM-DAPMA)/FeCl₃, were designed by combination of chemical and ionic cross-linking. Various optimization factors, including single and double network formation, CMC-integration, alternating polymerization temperatures, and cylindrical vs bead-shaped geometries, were systematically evaluated. Elasticity assessment of single- and double-network CMC-integrated cylindrical gels was governed by Rubber elasticity theory, whereas force-displacement of CMC-integrated double-network beads was analyzed using Hertz theory. CMC-integration increased modulus of cylindrical single-network cryogels from 5.61 to 14.78 kPa, reaching 41.09 kPa in double-network cryogels. This mechanical approach, based on functionalized design, addresses formation-structure relationships of hybrid beads through Hertz scaling analysis. Bead size directly altered the stiffness, while formation of a double network structure through CMC-integration played a dominant role in determining hybrid properties. Hybrid cryobeads, featuring a core-shell structure induced by cryopolymerization, swelled less than corresponding hydrobeads due to more inhomogeneous crosslinking. Their compact network effectively resisted the swelling, whereas larger bead sizes enhanced water retention. Reflecting these structural variations, scaling parameter was determined as 1.79 (±0.12) for hybrid hydrobeads and a higher value of 1.86 (±0.29) for cryobeads. The effectiveness of these tertiary amine-containing structures in azorubine removal was comparatively analyzed by considering effects of time, concentration, and pH. For hybrid cryobeads, q_max at pH 3.0 ranged from 99.3 to 495.9 (mg/g), and experimental data showed a good fit to Freundlich and Tóth models indicating multilayer adsorption. Based on their natural polysaccharide component and aqueous processing, CMC-integrated hybrid systems offer distinct advantages for future large-scale applications.