Polydisperse polymer networks with irregular topologies I: Mechanics of cross-link distributions
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918388480081920 |
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| author | Mulderrig, Jason Buche, Michael Grasinger, Matthew |
| author_facet | Mulderrig, Jason Buche, Michael Grasinger, Matthew |
| contents | The structure of polymer networks, defined by chain lengths and connectivity patterns, fundamentally influences their bulk properties. While existing polymer network models connect chain properties to emergent network behavior, they are often limited to monodisperse networks with regular connectivities. In this work, we introduce a novel modeling framework that shifts the focus from individual polymer chains to cross-links and their connected chains as the fundamental unit of analysis. The key features of this framework are the relaxation of the cross-link junction position to satisfy local force balance, and physically intuitive means for satisfying material frame indifference. We explore two distinct limiting behaviors for the orientation of the frame of a cross-link: (1) the free rotation limit, which assumes the cross-link rotates to minimize free energy, and (2) the frame averaging limit, which incorporates structural heterogeneity by averaging over all possible cross-link orientations. It is found that an increase in variance in monomer numbers generally leads to network softening, while in bimodal networks, the onset of strain stiffening is controlled by shorter chains and the stiffening response is modulated by the ratio of short to long chains. By deriving closed-form approximations for both limits valid in the regimes of small deformation or small polydispersity, we offer an efficient computational approach to modeling the mechanics of complex, polydisperse networks. An aim of this framework is to take a step toward the rational modeling and design of heterogeneous polymer networks with structures tailored for specific properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17239 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Polydisperse polymer networks with irregular topologies I: Mechanics of cross-link distributions Mulderrig, Jason Buche, Michael Grasinger, Matthew Soft Condensed Matter The structure of polymer networks, defined by chain lengths and connectivity patterns, fundamentally influences their bulk properties. While existing polymer network models connect chain properties to emergent network behavior, they are often limited to monodisperse networks with regular connectivities. In this work, we introduce a novel modeling framework that shifts the focus from individual polymer chains to cross-links and their connected chains as the fundamental unit of analysis. The key features of this framework are the relaxation of the cross-link junction position to satisfy local force balance, and physically intuitive means for satisfying material frame indifference. We explore two distinct limiting behaviors for the orientation of the frame of a cross-link: (1) the free rotation limit, which assumes the cross-link rotates to minimize free energy, and (2) the frame averaging limit, which incorporates structural heterogeneity by averaging over all possible cross-link orientations. It is found that an increase in variance in monomer numbers generally leads to network softening, while in bimodal networks, the onset of strain stiffening is controlled by shorter chains and the stiffening response is modulated by the ratio of short to long chains. By deriving closed-form approximations for both limits valid in the regimes of small deformation or small polydispersity, we offer an efficient computational approach to modeling the mechanics of complex, polydisperse networks. An aim of this framework is to take a step toward the rational modeling and design of heterogeneous polymer networks with structures tailored for specific properties. |
| title | Polydisperse polymer networks with irregular topologies I: Mechanics of cross-link distributions |
| topic | Soft Condensed Matter |
| url | https://arxiv.org/abs/2504.17239 |