DEM-Based Approach for the Modeling of Gelation and Its Application to Alginate

The gelation of biopolymers is of great interest in the material science community and has gained increasing relevance in the past few decades, especially in the context of aerogels─lightweight open nanoporous materials. Understanding the underlying gel structure and influence of process parameters is of great importance to predict material properties such as mechanical strength. In order to improve understanding of the gelation mechanism in aqueous solution, this work presents a novel approach based on the discrete element method for the mesoscale for modeling gelation of hydrogels, similarly to an extremely coarse-grained molecular dynamics (MD) approach. For this, polymer chains are abstracted as dimer units connected by flexible bonds and interactions between units and with the environment, that is, diffusion in implicit water, are described. The model is based on Langevin dynamics and includes an implicit probabilistic ion model to capture the effects of ion availability during ion-mediated gelation. The model components are fully derived and parameterized using literature data and theoretical considerations based on a simplified representation of atomistic processes. The presented model enables investigations of the higher-scale network formation during gelation on the micrometer and millisecond scale, which are beyond classical modeling approaches such as MD. As a model system, calcium-mediated alginate gelation is investigated including the influence of ion concentration, polymer composition, polymer concentration, and molecular weight. The model is verified against numerous literature data as well as own experimental results for the corresponding Ca-alginate hydrogels using nitrogen porosimetry, NMR cryoporometry, and small-angle neutron scattering. The model reproduces both bundle size and pore size distribution in a reasonable agreement with the experiments. Overall, the modeling approach paves the way to physically motivated design of alginate gels.