## 3 Results and Discussions
### Crystal Growth Mechanisms of CaCO\({}_{3}\) Nanoparticles in Chitosan Hydrogels
Natural mineralized tissues are typically subject to a variety of stringent regulatory processes in the organism, ensuring that the desired minerals are mineralized and precipitated in a specific manner, resulting in functional biological tissues [32; 33]. Before discussing the growth mechanism of CaCO\({}_{3}\) crystals in a chitosan hydrogel medium, it is essential to understand the mineralization process in nature and the crystal growth process in solution. According to the literature, the pearl layer structure of mollusk shells, teeth, bones, and similar tissues are ceramic/polymer composite structures [34; 35; 36; 37]. A common feature of these structures is that the organic matrix regulates and directs the growth and orientation of mineral crystals in the organism. Organisms obtain ions from food or the environment and transport them through the bloodstream to areas requiring mineralization. The organic matrix forms a reticular network that provides support for mineral generation. The mineralization process is divided into two stages: nucleation and growth. The formation of nucleation sites on the organic matrix reduces the system's  
Figure 5: SEM images of chitosan/CaCO\({}_{3}\) composite hydrogel after 3 and 6 h mineralization. (**a–c**) depict the cross-sections after 3 h of mineralization, where (**b**) is near the surface and (**c**) is near the center. (**d–f**) present the cross-sections after 6 h of mineralization, with (**e**) representing the area near the surface and (**f**) representing the area near the center. free energy, causing minerals to precipitate from the solution. Organisms can selectively promote or inhibit crystal growth to control the shape and distribution of crystals. This selective promotion or inhibition, regulated by cells and other complex mechanisms, allows organisms to control the morphology and precise arrangement of minerals. The growth of crystals in the solution is governed by crystal kinetics and thermodynamics, requiring the use of supersaturation as a driving force to control crystal nucleation and growth [38]. Both biomineralization and the process of crystal growth in the solution involve ion diffusion, which not only affects the rate of crystal growth but also determines the morphology and properties of the crystals. The surface and cross-section of the chitosan/CaCO\({}_{3}\) composite hydrogel observed by SEM reveal that nanoscale CaCO\({}_{3}\) grew internally, differing from the larger micrometer-sized particles present on the surface. [PERSON] et al. [24] have previously utilized polymer networks to control the orientation and morphology of CaCO\({}_{3}\), producing single-crystal composites with anisotropic structures. This finding suggests that the three-dimensional network within polymers can influence crystal growth. In this study, the 3D network of chitosan hydrogel, used as the crystallization substrate, potentially regulates the crystal nucleation and growth process mechanically. By comparing SEM images of CaCO\({}_{3}\) nanoparticles and the chitosan network in the samples at different mineralization times, a mechanistic understanding of the in situ growth of CaCO\({}_{3}\) in the hydrogel using this method can be derived (Figure 7). The crystalline microenvironment of the chitosan hydrogel is almost entirely determined by the porous structure of the hydrogel network. The dense and complex interlaced network structure within the chitosan hydrogel eliminates the space and conditions necessary for convection and laminar flow, causing the diffusion of the primary mode of transfer in this medium. This process can be analyzed according to [PERSON]'s second law of diffusion as follows [39; 40; 41]:  
Figure 6: TEM images of chitosan/CaCO\({}_{3}\) composite hydrogel. (**a**,**b**) TEM image of nanoparticles formed via in situ growth. (**c**–**f**) TEM images and diffraction patterns of chitosan/CaCO\({}_{3}\) composite hydrogel. Nanoparticles show single crystal-like diffraction pattern.