Comparative study of alginate/Ca²⁺ and alginate/Fe³⁺ beads: density functional calculations and bergamot oil release

This study comparatively investigates the structural organization, interaction energy and essential oil release behavior of sodium alginate (SA) beads crosslinked with calcium (Ca²⁺) or iron III (Fe³⁺). A Density Functional Theory (DFT)-based method was used to characterize cation-alginate interactions, revealing the mechanisms associated with their thermodynamic stabilization and structural order-disorder features correlated with electronic density of states contributions to the highest occupied molecular orbital (HOMO). The results indicate that the more compact structure of Fe-alginate, due to its stronger covalent character linked to the presence of d-orbitals, leads to a slower release of bergamot essential oil (BEO) compared to Ca-alginate beads. This difference is especially pronounced at neutral pH (∼7), where a higher number of COO^- groups are deprotonated, in contrast to acidic conditions where fewer groups are deprotonated. To confirm these findings, BEO was encapsulated in SA beads, which were characterized in terms of surface morphology and cation distribution both before and after the release process. ICP-OES analyses showed that Ca²⁺ loss reached 8 % at pH 7.4 and 19 % at pH 2, whereas Fe³⁺ loss was lower at neutral pH (5 %) but higher under acidic conditions (26 %), consistent with protonation-driven ion exchange. The encapsulation yield varied, with Ca²⁺ beads exhibiting higher encapsulation yield than Fe³⁺ beads (80.9 ± 4.5 wt% vs 54.3 ± 2.6 wt%). BEO release was faster at pH 2 than at pH 7.4 for both systems, with the release kinetics best described by the Korsmeyer-Peppas model, indicating a diffusion-controlled mechanism.