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Abstract

Gels are comprised of polymer networks swelled by some interstitial solvent. They are under wide investigation by material scientists and engineers for their broad applicability in fields ranging from adhesives to tissue engineering. Gels’ mechanical properties greatly influence their efficacy in such applications and are largely dictated by their underlying microstructures and constituentscale properties. Yet predictively mapping the local-to-global property functions of gels remains difficult due - in part - to the complexity introduced by solute-solvent interactions. We here introduce a novel, discrete mesoscale modeling method that preserves local solute concentrationdependent gradients in osmotic pressure through the Flory-Huggins mixing parameter, χ. The iteration of the model used here replicates gels fabricated from telechelically crosslinked starshaped polymers and intakes χ, macromer molecular weight (Mw), crosslink functionality (f ), and as-prepared solute concentration (ϕ∗) as its inputs, all of which are analogues to the control parameters of experimentalists. Here we demonstrate how this method captures solventdependent homogenization (χ ≤ 0.5) or phase separation (χ > 0.5) of polymer suspensions in the absence of phenomenological pairwise potentials. We then demonstrate its accurate, ab initio prediction of gel topology, isotropic swelling mechanics, and uniaxial tensile stress for a 10k tetra-PEG gel. Finally, we use the model to predict trends in the mechanical response and failure of multi-functional PEG-based gels over a range of Mw and f , while investigating said trends’ micromechanical origins. The model predicts that increased crosslink functionality results in higher initial chain stretch (as measured at the equilibrated swollen state) for gels of the same underlying chain length, which improves modulus and failure stress but decreases failure strain and toughness.

Figures

Top: Hierarchical length scales of gels. A gel at (A) the macroscale (>∼ 10^-4 m) is depicted with schematic illustrations of its topological structure at (B–E) diminishing length scales. (A) At the macroscale, smoothing assumptions permit application of continuum approaches, but these methods prohibit detailed study of damage or the influence of defects. (B,C) The discrete methods introduced here represent gel structures at intermediate length scales or the “mesoscale” by coarse-graining polymer chains as nonlinear mechanical springs. In modeling individual polymer chains, mesoscale approaches are equipped to capture the mechanical effects of topological defects and damaged regions, with reduced computational expense. (D-E) The most detailed models track constituents (either atoms, molecules, or Kuhn segments) utilizing discrete MD approaches. However, capturing defects on the order of 10^1 nm to 10^-1 μm, or conducting large ensembles of repeated in silico experiments becomes computationally untenable using these fine-grained approaches. The gel topology shown is meant to loosely represent a tetra-PEG hydrogel whose mesh size is on the order of 10^-8 m and which has 4 functional arms per macromer.

Bottom: Fracture of gels with L= 44nm and different functionalities. (A) A schematic of a tetra-functional macromer is depicted, alongside snapshots of a simulated 10k tetra-PEG gel as it undergoes uniaxial extension. (B) A schematic of an octa-functional macromer is depicted, alongside snapshots of a simulated 20k octa-PEG gel as it undergoes uniaxial extension. The macromer schematics are depicted at the same scale, whereas the sizes of the gel snapshots are indicated by their respective scale bars, each representing L. Red crosses in the gel snapshots demark which chains rupture before the next displayed snapshot. The rightmost snapshots depict the osmotic pressure landscapes of the domains at initial fracture.

Citation

Wagner, R. J.; Dai, J.; Su, X.; Vernerey, F. J. A Mesoscale Model for the Micromechanical Study of Gels. Journal of the Mechanics and Physics of Solids 2022, 167, 104982. .