Session B32: Polymer Networks, Gels, and Elastomers: Mechanics

Multiaxial Stretching of Nearly Critical Gels with Extremely Low Modulus

Linear dynamic viscoelasticity of the gelation systems near the critical point has been investigated intensively, but the large deformation behavior of nearly critical gels, which are obtained slightly beyond the gelation point, remains to be characterized. In contrast to matured gels, nearly critical gels have very low modulus due to the extremely sparse network structures. In this study, we have characterized the large deformation of the nearly critical gels by using a custom-made biaxial tensile tester optimized for very soft gels. Biaxial tensile dada varying the strains in two directions independently provide a definite basis to discuss the whole aspects of the large deformation behavior. The biaxial tensile data have revealed that the nearly critical gels exhibit minimal cross-effect of strains which results only from volume conservation in contrast to the matured gels with finite cross-effect. The feature of the nearly critical gels is attributed to their extremely sparse network structures.
  

Rate-dependent fracture mechanics of transient networks

Soft viscoelastic polymers and gels are commonly used as biomaterials and soft actuators owing to their ability to accommodate large deformations. Their applicability is however often limited by their tendency to abruptly fracture in ways that cannot be predicted by conventional elastic fracture mechanics. Our understanding of the fracturing process in these networks has particularly been hindered by the complex interplay between the viscous dissipation in the bulk and the accumulated damage around the crack tip.

To tackle this question, we explore the condition for a crack to initiate and propagate in transient polymer networks. We used a recently developed Transient Network Theory (TNT) that provides a statistical evolution of a transient network whose topology change as a result of macroscopic deformation and chain reconfiguration via transient crosslinks. This approach is particularly amenable to determine macroscopic measures characterizing the crack driving force. Based on the crack geometry and external loading, we determine the conditions that lead to crack blunting and crack propagation. By determining the interplay of these two mechanisms, we are able to predict fracture process of transient polymer networks with comparison to experiments.   

High-Rate Dynamics and Fracture Behavior of Model Swollen Polymer Network Characterized by Seeded Laser-Induced Cavitation

Mechanical characterization of soft materials at high strain rates is challenging due to their high compliance, slow wave speeds, and rate-dependent viscoelasticity. Swollen polymer networks are attractive model materials as they can be tuned to simulate the high-rate dynamics and damage mechanisms of soft tissues, such as the brain, under extreme mechanical stimuli. In this study, seeded laser induced cavitation (SLIC) is performed within polydimethylsiloxane gels containing a significant amount of solvent (50 - 80 wt.%), levels similar to those of soft tissues. Ultrafast stroboscopic observation of a laser-induced microscale cavity is exploited to characterize the viscoelastic response of the gels at strain rates of 10⁶ s^-1. By varying the molecular weight between crosslinks from 1.2 to 12 kg/mol, fracture initiation and post-cavitation characteristics of the gels are systematically controlled. The demonstrated SLIC framework can guide the development of tailored synthetic systems that precisely mimic the high-rate plastic behavior of soft tissues.
  

Chemical tools for investigating the topology of polymer networks

All polymer networks have topological heterogeneities that span various length scales and dictate their bulk properties. Nevertheless, these features have traditionally been difficult to quantify and control. Informed by classical crossover experiments in physical organic chemistry, we have developed experimental methods for the precise counting of cyclic topologies (loops) in polymer networks. These studies have enabled new theoretical advances pertaining to elasticity and the gel point, and have inspired new stimuli-responsive materials that leverage topology as a design principle.
  

Cavitation and Fracture of Soft Materials

Rapid expansion of soft solids subjected to a negative hydrostatic stress can occur through an elastic cavitation mechanism or an inelastic fracture mechanism. Balancing how these two mechanisms relate is important to applications in materials characterization, adhesive design, and tissue damage. Significant research effort has focused on understanding how these two mechanisms relate; however, the available experimental data in this area has been limited by both the techniques employed and materials considered. Experimental investigation into the transition between cavitation and fracture requires 1) knowledge of the initial cavity geometry and 2) a material system where both the elastic and fracture properties are independently characterized. In this work, recent improvements in needle-induced cavitation and independent characterization of elasticity and fracture in a set of model end-linked tetra-PEG gels are exploited to experimentally probe the relationship between the elasto-fracture length and cavitation and fracture. The results indicate that three distinct regimes exist where expansion occurs through either cavitation, cavitation-initiated fracture, or fracture.   

Role of Topological Defects on Fracture of Polymer Networks

Chemically crosslinked polymer networks often possess various types of topological defects such as loops and bridges, which are shown to have a noticeable effect on elastic properties of the material. In this work, we use theory and simulations to investigate the influence of such defects on the fracture of the material. A Monte Carlo algorithm is first used to generate a series of 3D periodic networks having varying concentration of defects. The respective networks are then subjected to tensile deformation with the bond breaking events modeled using a kinetic theory of fracture incorporating the experimentally-measured mechanochemical characteristics of covalent bonds. We discuss the effect of both the fraction of primary loops and their spatial distribution on the fracture toughness of the material. Additionally, we use the classical Lake-Thomas theory to estimate the ultimate strength of defects-containing networks, and compare the resulting predictions to simulation results. Using both theory and simulations, this work provides insight into the molecular origins of fracture in polymer networks.   

Indentation Rate Sensitive Relaxation of Soft Hydrogels

Mechanical behavior of hydrogels is strongly time-dependent, often characterized as a combination of viscoelastic and poroelastic relaxation. Load-relaxation of hydrogels largely depends on gel composition. Here, we further demonstrate that mechanical loading conditions also influence load relaxation of hydrogels. Spherical indentation experiments are performed for agar, gelatin and polyacrylamide gels with a range of indentation rates. As expected, faster indentation results in more pronounced relaxation in all three gels. The rate-sensitivity is also indentation depth-dependent, such that the degree of relaxation decreases with depth for a constant rate. We interpret the findings within both viscoelastic and poroelastic frameworks. The theoretical analysis demonstrates that viscoelastic relaxation is more rate sensitive compared to poroelastic relaxation. Hydrogels become more viscid at higher indentation rates, indicating significant network reorganization at short time-scales. On the contrary, intrinsic permeability is observed to be largely indentation rate-independent, meaning solvent migration is not affected significantly. Overall, the findings emphasize the importance of loading conditions during mechanical characterization of hydrogels and hydrated biological materials.

  

Influence of polymer concentration and midblock length on the mechanical behavior of [ABA] triblock copolymer gels in a B-selective solvent

We present the effect of polymer concentration and midblock length on the large deformation behavior of [ABA] triblock copolymer gels in a midblock selective solvent. In our case, “A” represents poly(styrene) [PS], “B” represents poly(isoprene) [PI], and the solvent is mineral oil. The micellar microstructure of these gels consists of collapsed PS endblock aggregates acting as crosslinks, which are bridged by PI midblocks. The polymer concentration and polymer midblock lengths were varied to introduce midblock entanglement in the gels. Small-angle x-ray experiments capture the micellar microstructure of these gels. Tensile testing reveals a rate dependent moduli for the samples with entangled midblocks. The sample stretchability is governed by stretch rate, midblock length, and polymer concentration. Fracture experiments with a predefined crack reveal a linear dependence of energy release rate with the crack-tip velocity. Fracture in these gels occurs due to endblock pullout from the aggregates and we have estimated the theoretical energy release rate by considering all entropic and enthalpic processes.
  

Fracture of Model End-Linked Networks

Advances in polymer chemistry over the last decade have enabled the synthesis of well-defined networks that exhibit homogeneous structure. These well-defined polymer gels create the opportunity to assess and verify novel and existing molecular models of network elasticity and fracture. A novel theory of network fracture that accounts for loop defects by drawing on recent advances in network elasticity is proposed. This loop modified Lake-Thomas Theory is tested against both MD simulations and experimental fracture measurements on model gels. Good agreement between the theory and measurement is obtained. These findings enable a priori estimation of fracture energy in swollen gels where chain scission becomes an important failure mechanism.   

Unveiling the effects of molecular topology on the viscoelasticity of entangled polymers under gelation

When polymer molecules are constantly crosslinked during the curing process, the presence of intramolecular loops and tree-like hyperbranched structure make the prediction of viscoelastic properties rather complex due to the change of molecular topology. Based on the effective potential in primitive path fluctuations for the relaxation of star polymers [Milner & McLeish, Macromolecules 1997], we propose a novel strategy, i.e., by defining effective relaxation potentials at the “termini” of each polymer strand in a hierarchical manner, to determine the timely movement of the relaxation “front” [Read et al. Science 2011] between the fully relaxed outer layer and the unrelaxed inner core in an arbitrary molecular architecture. For monodisperse polymer systems with specified molecular structure, this model is shown to capture the stress relaxation quite well when compared to those from analytical theories and experimental data. By implementing a kinetic Monte Carlo method [Rui et al. PRL 2016] to access the topological information of crosslinked polymers, this model allows for the prediction of a change in the exponent of power law relationships for rheological moduli at intermediate frequencies with different conversions, which is consistent with the experimental measurements.   

Constitutive modelling of responsive and non-responsive polymer gels with limited compressibility

Design of futuristic synthetic materials to replicate biological mechanisms has been a challenge for science and engineering. Polymer gels that are intrinsically powered by self-oscillating Belousov Zhabotinsky (BZ) reaction are systems that utilize chemo-mechanical transduction to produce mechanical work from chemical energy. Here, we develop the chemo-mechanical theory for modelling these systems under isothermal conditions. Our approach harnesses the finite element framework to combine the reaction-diffusion phenomena with large elastic deformations of the non-gaussian compressible polymeric networks. In particular, we use Oregonator model to capture BZ kinetics while the modified Flory-Huggins theory is used to capture interactions between BZ-catalyst and polymer gel. Using our model we simulated the dynamics of BZ and non-responsive gels under equilibrium and transient conditions; we validated our results with the existing models and experimental results. In essence, we develop and establish a framework to design and study responsive materials with complex geometries. Moreover, we believe that by extending our methodology it is possible to capture large deformations akin to volume phase transitions in polymer gels under non-isothermal conditions.   

New Insights into the Chain Dynamics and Microstructure of Highly Crosslinked Polymer Networks as a Function of Network Heterogeneity

Key physicochemical phenomena in polymer networks are critically impacted by the spatial distribution of crosslinks, i.e., network heterogeneity. Despite this fact, the chain dynamics and microstructure of heterogeneous networks, particularly bulk thermosets, have not been well characterized. To this end, we present a detailed investigation of novel photopolymerized thiol-ene networks. High glass transition temperatures and continuously tunable network heterogeneity were achieved by varying the stoichiometry between aromatic thiol and acrylate monomers. The chain dynamics and microstructure of these materials were characterized using a combination of dynamic mechanical analysis, solid-state nuclear magnetic resonance spectroscopy, and small angle x-ray scattering. We found that heterogeneous networks exhibited enhanced mobility deep in the glassy state, in contrast to their homogeneous counterparts. In addition, the heterogeneous and homogeneous networks were distinguished by their fractal structures. These new insights may help guide the future design of new crosslinked polymers with carefully controlled network heterogeneity.   

Deformation of Inhomogeneous End-linked Polymer Networks

Polymer networks represent an important class of soft materials with a broad range of applications in adhesives, coatings, membranes and natural materials. In particular, synthetic end-linked polymer gels, where the network is swollen in solvent, has received growing attention in the biomedical field due to their structural and mechanical similarities to tissues. Failure of these materials during mechanical deformations is intimately tied to their elastic and fracture properties. Synthetic and natural gels have highly complex environments that contain defects and phase boundaries, and the interplay between these molecular structures and the elastic and fracture responses remains an open question. In this study, we use molecular dynamics simulations to prepare and characterize two-phase polymer networks with one glassy and one rubbery domain. We characterize their mechanical properties and how the strain localizes in the glassy and rubbery domains as a function of the polymer chain length. Our simulations reveal that structural features on multiple length-scales serve to localize the site of failure.