A gaussian model for substrates of entangled cross-linked poly(ethylene glycol) in biomedical applications

Cells usually spread on a synthetic substrate through bonds between receptors and chemical groups on the substrate (ligands). Therefore, it is valuable to study the effects of the average number density of these chemical groups and the average distance between them to model and predict the cell behavior. Poly(ethylene glycol) [PEG] modified with peptide groups has been used widely in biomedical applications as a substrate material. In this study, a coarse-grained model is proposed for PEG to predict the average number density of ligands and the average distance between them. Molecular information such as initial molecular weight distribution, average molecular weight between cross-links, and average molecular weight between entanglements is used as input parameters. Based on simulation results, it is concluded that both entanglement and cross-link densities are required to create a network structure. The results suggest that an average initial molecular weight 2-3 times the average molecular weight between entanglements and a moderate cross-link density are sufficient to create a closed network structure with a high ligand density and a small average distance between them.