research article

A mesoscale model for the micromechanical study of gels

Anonymous — Sat, 11 Mar 2023 20:55:51 +0000

A mesoscale model for the micromechanical study of gels Anonymous (not verified) Sat, 03/11/2023 - 13:55

Robert Wagner

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. https://doi.org/10.1016/j.jmps.2022.104982.

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Rate-Dependent Damage Mechanics of Polymer Networks with Reversible Bonds

Anonymous — Sat, 11 Mar 2023 20:35:25 +0000

Rate-Dependent Damage Mechanics of Polymer Networks with Reversible Bonds Anonymous (not verified) Sat, 03/11/2023 - 13:35

Samuel Lamont

Brief Description

In this work, we develop a statistical theory of damage for transient networks that can directly bridge the molecular mechanisms and macroscopic response. The final model being able to capture the evolution of rate-dependent and anisotropic damage in transient networks.

Abstract

Dynamic polymer networks utilize weak bonding interactions to dissipate the stored energy and provide a source of self-healing for the material. Due to this, tracking the progression of damage in these networks is poorly understood as it becomes necessary to distinguish between reversible and irreversible bond detachment (by kinetic bond exchange or chain rupture, respectively). In this work, we present a statistical formulation based on the transient network theory to track the chain conformation space of a dynamic polymer network whose chains rupture after being pulled past a critical stretch. We explain the predictions of this model by the observable material timescales of relaxation and self-healing, which are related to the kinetic rates of attachment and detachment. We demonstrate our model to match experimental data of cyclic loading and self-healing experiments, providing physical interpretation for these complex behaviors in dynamic polymer networks.

Figures

Top: Distinction between chain rupture and chain detachment in a transient network. In this network, a chain can be found in three distinct states: attached, detached, and ruptured. The ruptured chains are unable to create new network connections and are at the origin of irreversible damage.

Bottom: Cyclic loading experiment performed at a constant strain rate λ̇. (a) High Weissenberg loading. Energy dissipation is primarily a result of chain rupture. (b) Low Weissenberg loading. Energy dissipation is primarily due to reversible bond kinetics. Contour plots indicate the distribution ϕ at the respective stage of loading.

Citation

Lamont, S. C.; Mulderrig, J.; Bouklas, N.; Vernerey, F. J. Rate-Dependent Damage Mechanics of Polymer Networks with Reversible Bonds. Macromolecules 2021, 54 (23), 10801–10813. https://doi.org/10.1021/acs.macromol.1c01943.

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Computational exploration of treadmilling and protrusion growth observed in fire ant rafts

Anonymous — Sat, 11 Mar 2023 19:53:19 +0000

Computational exploration of treadmilling and protrusion growth observed in fire ant rafts Anonymous (not verified) Sat, 03/11/2023 - 12:53

Robert Wagner

Brief Description

Cooperative behavior in organisms often permits groups to achieve collective tasks that are unattainable to individuals. Such is the case of fire ant workers that aggregate together to create buoyant rafts that unify their colonies and ensure survival during floods. Under certain conditions, these rafts undergo a process called treadmilling that allows them to morph perpetually over the span of several hours. This morphogenesis includes the growth of tether-like protrusions that colonies can use as land-bridges to escape water. Employing a discrete, agent-based model, we here demonstrate how the local interactions between ants in these systems may be sufficient to cause stochastic and spontaneous protrusion emergence in the absence of external gradients, long-range interactions, or targeted stimuli.

Abstract

Collective living systems regularly achieve cooperative emergent functions that individual organisms could not accomplish alone. The rafts of fire ants (Solenopsis invicta) are often studied in this context for their ability to create aggregated structures comprised entirely of their own bodies, including tether-like protrusions that facilitate exploration of and escape from flooded environments. While similar protrusions are observed in cytoskeletons and cellular aggregates, they are generally dependent on morphogens or external gradients leaving the isolated role of local interactions poorly understood. Here we demonstrate through an ant-inspired, agent-based numerical model how protrusions in ant rafts may emerge spontaneously due to local interactions. The model is comprised of a condensed structural network of agents that represents the monolayer of interconnected worker ants, which floats on the water and gives ant rafts their form. Experimentally, this layer perpetually contracts, which we capture through the pairwise contraction of all neighboring structural agents at a strain rate of d. On top of the structural layer, we model a dispersed, on-lattice layer of motile agents that represents free ants, which walk on top of the floating network. Experimentally, these self-propelled free ants walk with some mean persistence length and speed that we capture through an ant-inspired phenomenological model. Local interactions occur between neighboring free ants within some radius of detection, R, and the persistence length of freely active agents is tuned through a noise parameter, [eta] as introduced by the Vicsek model. Both R and [eta] where fixed to match the experimental trajectories of free ants. Treadmilling of the raft occurs as agents transition between the structural and free layers in accordance with experimental observations. Ultimately, we demonstrate how phases of exploratory protrusion growth may be induced by increased ant activity as characterized by a dimensionless parameter, A. These results provide an example in which functional morphogenesis of a living system may emerge purely from local interactions at the constituent length scale, thereby providing a source of inspiration for the development of decentralized, autonomous active matter and swarm robotics.

Figures

Top: Ant Raft Treadmilling.

Bottom: (A-G) Agent Based Model Schematic.

Citation

Wagner, R. J.; Vernerey, F. J. Computational Exploration of Treadmilling and Protrusion Growth Observed in Fire Ant Rafts. PLoS Comput Biol 2022, 18 (2), e1009869. https://doi.org/10.1371/journal.pcbi.1009869.

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