Mesoscopic Modeling of Dynamic Tetra-PEG Hydrogel Networks

Abstract

We introduce a mesoscopic model of dynamic Tetra-PEG hydrogel networks based on a hybrid Dissipative Particle Dynamics/Monte Carlo (DPD/MC) approach. Polymer chains are described by Finite Extensible Nonlinear Elastic (FENE) potential, while reversible cross-links are modeled with Morse potential and Monte Carlo bond exchange governed by Bell's force-dependent kinetics. After systematic calibration against theory and experiments, the model reproduces the characteristic Maxwell-like viscoelastic response of these networks. In particular, the relaxation time follows the expected scaling, $τ_R \propto τ_b (p - p_{\text{gel}})$, and the simulated storage moduli agree with experimental rheology. The mesoscopic resolution allows for graph-based topological analysis, where Tetra-PEG molecules and cross-links are represented as nodes and edges, providing access to bond distributions, fraction of dangling chains, and size of percolating clusters that are challenging to measure experimentally. Comparison with permanent-network predictions further suggests that dynamic bond exchange can affect bond distributions and delay the formation of a system-spanning cluster. This model bridges macromolecular bond kinetics and macroscopic mechanical properties, providing a complementary tool for rational design of dynamic polymer networks.

Figures (12)

• Figure 1: Schematic representation of the dynamic polymer network model. The figure shows the overall network structure consisting of non-functional (grey) and functional (yellow and green) particles connected by covalent bonds (black) and dynamic cross-links (red). The inset detail illustrates the dynamic bonding mechanism between functional groups, where the association and dissociation rates are governed by forward ($k_f$) and backward ($k_b$) rate constants, with the probability of unbinding depending on the force exerted on the bond.
• Figure 2: Morse potential and force curves illustrating the natural dissociation criterion. Left: The Morse potential energy as a function of distance, showing the equilibrium position at $r_0$ (orange circle) where the potential reaches its minimum and the critical breaking distance (red square) at the inflection point. Right: The corresponding force curve, where the equilibrium position corresponds to zero force and $r_c^{\text{max-break}}$ marks the maximum attractive force. Beyond this point, the force decreases with increasing separation, indicating loss of binding character and providing a natural cutoff for bond dissociation in molecular dynamics simulations.
• Figure 3: Multi-scale structural characterization of the hydrogel network. The image shows the hierarchical organization from the macroscopic gel structure (left) to the mesoscopic network architecture (center) and microscopic polymer chain arrangement (right).
• Figure 4: Radius of gyration of Tetra-PEG arms from DPD simulations (orange line) compared with theoretical predictions from Flory's ideal chain model (green line).
• Figure 5: Comparison between analytical measurements obtained from experimental data and simulation results of active bonds in Tetra-PEG networks. Blue violin plots show the distribution of simulation results obtained using DPD with dynamic cross-linking.