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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.
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A network model of transient polymers: exploring the micromechanics of nonlinear viscoelasticity
Dynamic networks contain crosslinks that re-associate after disconnecting, imparting them with viscoelastic properties. While continuum approaches have been developed to analyze their mechanical response, these approaches can only describe their evolution in an average sense, omitting local, stochastic mechanisms that are critical to damage initiation or strain localization. To address these limitations, we introduce a discrete numerical model that mesoscopically coarse-grains the individual constituents of a dynamic network to predict its mechanical and topological evolution. Each constituent consists of a set of flexible chains that are permanently cross-linked at one end and contain reversible binding sites at their free ends. We incorporate nonlinear force–extension of individual chains via a Langevin model, slip-bond dissociation through Eyring's model, and spatiotemporally-dependent bond attachment based on scaling theory. Applying incompressible, uniaxial tension to representative volume elements at a range of constant strain rates and network connectivities, we then compare the mechanical response of these networks to that predicted by the transient network theory. Ultimately, we find that the idealized continuum approach remains suitable for networks with high chain concentrations when deformed at low strain rates, yet the mesoscale model proves necessary for the exploration of localized stochastic events, such as variability of the bond kinetics, or the nucleation of micro-cavities that likely conceive damage and fracture.
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- Award ID(s):
- 1761918
- PAR ID:
- 10295769
- Date Published:
- Journal Name:
- Soft Matter
- ISSN:
- 1744-683X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1039/D1SM00753J
