Due to their unique properties such as high water content and soft gel-like consistency hydrogels have proven useful in a variety of fields including biomedicine, drug delivery, tissue engineering, and sensor development. The rheological properties of hydrogels which refer to their flow and deformation behavior under external force application play a key role in determining their suitability for specific applications. Understanding their rheological properties allows us to predict their response to applied mechanical stress either in the human body or in a specific device. In my master's thesis I studied alginate hydrogels. I prepared hydrogels samples by physical crosslinking of alginate solutions using Ca$^{2+}$, Sr$^{2+}$, Ba$^{2+}$, Mg$^{2+}$, Cu$^{2+}$ , Al$^{3+}$ and Fe$^{3+}$ cations of various concentrations. I then measured their shear modulus. A model equation was previously developed for calcium ions, which states that the crosslinking density increases exponentially with the concentration of crosslinking cations. As a part of my master's thesis I managed to confirm the assumption that analogous equation also applies to a certain set of other divalent cations. The thesis that the parameter in the model equation, called ionic affinity, is related to the size of the cross-linker ion i.e. its value should decrease with increasing ionic radius of the cross-linker, also proved to be true. Furthermore, I managed to extend the assumptions of the previous theory and the aforementioned model equation to trivalent aluminum and iron cations, whose ability to form hydrogels with alginate was previously known . However, it turned out that the value of the affinity parameter is even more strongly influenced by the charge of the crosslinking cations than its size (ionic radius). The cross-linking density and corresponding shear modulus are thus higher for trivalent ions and the ionic affinity parameter is correspondingly lower than in the case of using divalent ions of the same molar concentration. As a part of my master's thesis, I also developed a mathematical model which predicts the crosslinking density of alginate hydrogels and their corresponding shear modulus at various concentrations of cross-linking agent. The basis of the model is a simplified simulation of the ionic cross-linking process of alginate solution. Based on this, we were able to clarify the connection between the concentration of cross-linking agent and the obtained crosslinking density and shear modulus of the resulting hydrogel. In its final form the model also accounts for the binding affinities and specific coordination abilities of individual metals and represents a potential predictive tool for adapting the rheological properties of alginate hydrogels to specific applications. My master's work results thus contribute to a deeper understanding of the fundamental interactions which regulate the ionic cross-linking process in biopolymer systems.
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