A network model of transient polymers: exploring the micromechanics of nonlinear viscoelasticity

Filled Elastomers: Mechanistic and Physics-Driven Modeling and Applications as Smart Materials

Elastomers are made of chain-like molecules to form networks that can sustain large deformation. Rubbers are thermosetting elastomers that are obtained from irreversible curing reactions. Curing reactions create permanent bonds between the molecular chains. On the other hand, thermoplastic elastomers do not need curing reactions. Incorporation of appropriated filler particles, as has been practiced for decades, can significantly enhance mechanical properties of elastomers. However, there are fundamental questions about polymer matrix composites (PMCs) that still elude complete understanding. This is because the macroscopic properties of PMCs depend not only on the overall volume fraction (ϕ) of the filler particles, but also on their spatial distribution (i.e., primary, secondary, and tertiary structure). This work aims at reviewing how the mechanical properties of PMCs are related to the microstructure of filler particles and to the interaction between filler particles and polymer matrices. Overall, soft rubbery matrices dictate the elasticity/hyperelasticity of the PMCs while the reinforcement involves polymer-particle interactions that can significantly influence the mechanical properties of the polymer matrix interface. For ϕ values higher than a threshold, percolation of the filler particles can lead to significant reinforcement. While viscoelastic behavior may be attributed to the soft rubbery component, inelastic behaviors like the Mullins and Payne effects are highly correlated to the microstructures of the polymer matrix and the filler particles, as well as that of the polymer-particle interface. Additionally, the incorporation of specific filler particles within intelligently designed polymer systems has been shown to yield a variety of functional and responsive materials, commonly termed smart materials. We review three types of smart PMCs, i.e., magnetoelastic (M-), shape-memory (SM-), and self-healing (SH-) PMCs, and discuss the constitutive models for these smart materials.

Molecular Simulation of Covalent Adaptable Networks and Vitrimers: A Review

Covalent adaptable networks and vitrimers are novel polymers with dynamic reversible bond exchange reactions for crosslinks, enabling them to modulate their properties between those of thermoplastics and thermosets. They have been gathering interest as materials for their recycling and self-healing properties. In this review, we discuss different molecular simulation efforts that have been used over the last decade to investigate and understand the nanoscale and molecular behaviors of covalent adaptable networks and vitrimers. In particular, molecular dynamics, Monte Carlo, and a hybrid of molecular dynamics and Monte Carlo approaches have been used to model the dynamic bond exchange reaction, which is the main mechanism of interest since it controls both the mechanical and rheological behaviors. The molecular simulation techniques presented yield sufficient results to investigate the structure and dynamics as well as the mechanical and rheological responses of such dynamic networks. The benefits of each method have been highlighted. The use of other tools such as theoretical models and machine learning has been included. We noticed, amongst the most prominent results, that stress relaxes as the bond exchange reaction happens, and that at temperatures higher than the glass transition temperature, the self-healing properties are better since more bond BERs are observed. The lifetime of dynamic covalent crosslinks follows, at moderate to high temperatures, an Arrhenius-like temperature dependence. We note the modeling of certain properties like the melt viscosity with glass transition temperature and the topology freezing transition temperature according to a behavior ruled by either the Williams-Landel-Ferry equation or the Arrhenius equation. Discrepancies between the behavior in dissociative and associative covalent adaptable networks are discussed. We conclude by stating which material parameters and atomistic factors, at the nanoscale, have not yet been taken into account and are lacking in the current literature.

Catch bond kinetics are instrumental to cohesion of fire ant rafts under load

Dynamic networks composed of constituents that break and reform bonds reversibly are ubiquitous in nature owing to their modular architectures that enable functions like energy dissipation, self-healing, and even activity. While bond breaking depends only on the current configuration of attachment in these networks, reattachment depends also on the proximity of constituents. Therefore, dynamic networks composed of macroscale constituents (not benefited by the secondary interactions cohering analogous networks composed of molecular-scale constituents) must rely on primary bonds for cohesion and self-repair. Toward understanding how such macroscale networks might adaptively achieve this, we explore the uniaxial tensile response of 2D rafts composed of interlinked fire ants (S. invicta). Through experiments and discrete numerical modeling, we find that ant rafts adaptively stabilize their bonded ant-to-ant interactions in response to tensile strains, indicating catch bond dynamics. Consequently, low-strain rates that should theoretically induce creep mechanics of these rafts instead induce elastic-like response. Our results suggest that this force-stabilization delays dissolution of the rafts and improves toughness. Nevertheless, above 35[Formula: see text] strain low cohesion and stress localization cause nucleation and growth of voids whose coalescence patterns result from force-stabilization. These voids mitigate structural repair until initial raft densities are restored and ants can reconnect across defects. However mechanical recovery of ant rafts during cyclic loading suggests that-even upon reinstatement of initial densities-ants exhibit slower repair kinetics if they were recently loaded at faster strain rates. These results exemplify fire ants' status as active agents capable of memory-driven, stimuli-response for potential inspiration of adaptive structural materials.

Coupled bond dynamics alters relaxation in polymers with multiple intrinsic dissociation rates

Dynamic networks containing multiple bond types within a continuous network grant engineers another design parameter - relative bond fraction - by which to tune storage and dissipation of mechanical energy. However, the mechanisms governing emergent properties are difficult to deduce experimentally. Therefore, we here employ a network model with prescribed fractions of dynamic and stable bonds to predict relaxation characteristics of hybrid networks. We find that during stress relaxation, predominantly dynamic networks can exhibit long-term moduli through conformationally inhibited relaxation of stable bonds due to exclusion interactions with neighboring chains. Meanwhile, predominantly stable networks exhibit minor relaxation through non-affine reconfiguration of dynamic bonds. Given this, we introduce a single fitting parameter, ξ, to Transient Network Theory via a coupled rule of mixture, that characterizes the extent of stable bond relaxation. Treating ξ as a fitting parameter, the coupled rule of mixture's predicted stress response not only agrees with the network model's, but also unveils likely micromechanical traits of gels hosting multiple bond dissociation timescales.

Micromechanics and damage in slide-ring networks

We explore the mechanics and damage of slide-ring gels by developing a discrete model for the mechanics of chain-ring polymer systems that accounts for both crosslink motion and internal chain sliding. The proposed framework utilizes an extendable Langevin chain model to describe the constitutive behavior of polymer chains undergoing large deformation and includes a rupture criterion to innately capture damage. Similarly, crosslinked rings are described as large molecules that also store enthalpic energy during deformation and thus have their own rupture criterion. Using this formalism, we show that the realized mode of damage in a slide-ring unit is a function of the loading rate, distribution of segments, and inclusion ratio (number of rings per chain). After analyzing an ensemble of representative units under different loading conditions, we find that failure is driven by damage to crosslinked rings at slow loading rates, but polymer chain scission at fast loading rates. Our results indicate that increasing the strength of the crosslinked rings may improve the toughness of the material.

Thermosensitive P(AAc-co-NIPAm) hydrogels display enhanced toughness and self-healing via ion-ligand interactions

Hydrogels containing thermosensitive polymers such as poly(N-isopropylacrylamide) (P(NIPAm)) may contract during heating and show great promise in fields ranging from soft robotics to thermosensitive biosensors. However, these gels often exhibit low stiffness, tensile strength, and mechanical toughness, limiting their applicability. Through copolymerization of P(NIPAm) with poly(Acrylic acid) (P(AAc)) and introduction of ferric ions (Fe³⁺ ) that coordinate with functional groups along the P(AAc) chains, we here introduce a thermoresponsive hydrogel with significantly enhanced mechanical extensibility, strength, and toughness. Using both experimentation and constitutive modeling, we find that increasing the ratio of m(AAc):m(NIPAm) in the prepolymer decreases strength and toughness but improves extensibility. In contrast, increasing Fe³⁺ concentration generally improves strength and toughness with little decrease in extensibility. Due to reversible coordination of the Fe³⁺ bonds, these gels display excellent recovery of mechanical strength during cyclic loading and self-healing ability. While thermosensitive contraction imbued by the underlying P(NIPAm) is reduced slightly with increased Fe³⁺ concentration, the temperature transition range is widened and shifted upwards towards that of human body temperature (between 30 and 40°C), perhaps rendering these gels suitable as in vivo biosensors. Finally, these gels display excellent adsorptive properties with a variety of materials, rendering them possible candidates in adhesive applications. This article is protected by copyright. All rights reserved.

Constitutive Theory for Direct Coupling of Molecular Frictions and the Viscoelasticity of Soft Materials

How to directly relate frictions at the level of a single molecular chain to the viscoelasticity of soft materials is intriguing. Here, we choose to investigate classical elastomers, where molecular frictions are known to be generated when dangling chains move relatively to the surrounding polymer chain network. With explicit forms employed for the relationship between friction and velocity at the molecular scale, a constitutive theory is then developed for the coupling of molecular frictions and the macroscopic viscoelasticity of elastomers. With the utilization of this theory, viscoelastic behaviors of varied elastomeric materials are predicted, which agree well with existing experiments at both low and high strain rates under different loading conditions. The theory also reproduces the time-temperature equivalent principle of elastomers. We suggest that this work might have provided a modeling framework that directly couples frictions at the level of a single molecular chain to the viscoelasticity of soft materials.