The role of multivalent cations in determining the cross-linking affinity of alginate hydrogels: A combined experimental and modeling study

• Systematic analysis of multivalent cations in alginate hydrogel cross-linking. • Developed model predicts cross-linking density at different ion concentrations. • Binding affinity is influenced by ionic radius, valence, and electron configuration. • Unique deviations in Mg²⁺ and Cu²⁺ binding due to distinct coordination chemistry. • The model accounts for interaction range influenced by cation properties. This study explores the development of a comprehensive mathematical model to predict the cross-link density of alginate hydrogels using varying concentrations of divalent and trivalent ions. By systematically investigating the effects of Ca²⁺, Ba²⁺, Cu²⁺, Sr²⁺, Mg²⁺, Fe 3⁺ and Al³⁺, the research describes the relationship between ion concentration and cross-link density. Experimental data reveals that the type and concentration of these ions critically influence the mechanical properties of the resulting hydrogels, with trivalent ions such as Fe³⁺ forming stronger, triple cross-links that significantly enhance the hydrogel's mechanical strength. Among the divalent ions, the trend in binding affinity is as follows: Ba²⁺ with the highest affinity followed by Sr²⁺, Ca²⁺ and Cu²⁺, while Mg²⁺ stands out with the lowest affinity, significantly differing from the others. The deviation of Cu²⁺ (transition metal ion) from the expected trend in ion interactions suggests that coordination chemistry, along with ionic radius, valence, and cation coordination abilities, plays a significant role in determining interaction strength with alginate. The proposed model, enhanced with fitting parameters k 1 and k 2 to account for ion-specific effects, leverages the unique binding affinities and coordination chemistry of each ion to tailor alginate hydrogels for specific applications. The parameter k 1 reflects the affinity of the ions for the alginate chains, while k 2 captures the coordination abilities and cross-linking efficiency. This work not only advances the understanding of ion-mediated cross-linking in alginate systems but also offers a valuable tool for the design and optimization of hydrogels with precise mechanical properties governed by various applications.