Phantom-Chain Simulations for the Effect of Node Functionality on the Fracture of Star-Polymer Networks
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arXiv
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| Natura: | Preprint |
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2023
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| author | Masubuchi, Yuichi Doi, Yuya Ishida, Takato Sakumichi, Naoyuki Sakai, Takamasa Mayumi, Koichi Sato, Kotaro Uneyama, Takashi |
| author_facet | Masubuchi, Yuichi Doi, Yuya Ishida, Takato Sakumichi, Naoyuki Sakai, Takamasa Mayumi, Koichi Sato, Kotaro Uneyama, Takashi |
| contents | The influence of node functionality (f) on the fracture of polymer networks remains unclear. While many studies have focused on multi-functional nodes with f>4, recent research suggests that networks with f=3 exhibit superior fracture properties compared to those with f=4. To clarify this discrepancy, we conducted phantom chain simulations for star-polymer networks varying f between 3 and 8. Our simulations utilized equimolar binary mixtures of star branch prepolymers with a uniform arm length. We employed a Brownian dynamics scheme to equilibrate sols and induce gelation through end-linking reactions. We prevented the formation of odd-order loops owing to the binary reaction and second-order loops algorithmically. We stored network structures at various conversion ratios (ϕ_c) and minimized energy to reduce computation costs induced by structural relaxation. We subjected the networks to stretching until fracture to determine stress and strain at break and work for fracture, ε_b, σ_b, and W_b. These fracture characteristics are highly dependent on ϕ_c for networks with small f but relatively insensitive for those with large f. Thus, the networks with small f exhibit greater fracture properties than those with large f at high ϕ_c, whereas the opposite relationship occurs at low ϕ_c. We analyzed ε_b, σ_b, and W_b concerning the cycle rank ξ and the broken strand fraction ϕ_bb. We found ε_b, σ_b/ϕ_bb, and W_b/ϕ_bb monotonically decrease with increasing ξ, and the data for various f and ϕ_c superpose with each other to draw master curves. These results imply that the mechanical superiority of the networks with small f comes from their smaller ξ that gives higher ε_b, σ_b/ϕ_bb, and W_b/ϕ_bb than the networks with large f. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2307_09832 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Phantom-Chain Simulations for the Effect of Node Functionality on the Fracture of Star-Polymer Networks Masubuchi, Yuichi Doi, Yuya Ishida, Takato Sakumichi, Naoyuki Sakai, Takamasa Mayumi, Koichi Sato, Kotaro Uneyama, Takashi Soft Condensed Matter The influence of node functionality (f) on the fracture of polymer networks remains unclear. While many studies have focused on multi-functional nodes with f>4, recent research suggests that networks with f=3 exhibit superior fracture properties compared to those with f=4. To clarify this discrepancy, we conducted phantom chain simulations for star-polymer networks varying f between 3 and 8. Our simulations utilized equimolar binary mixtures of star branch prepolymers with a uniform arm length. We employed a Brownian dynamics scheme to equilibrate sols and induce gelation through end-linking reactions. We prevented the formation of odd-order loops owing to the binary reaction and second-order loops algorithmically. We stored network structures at various conversion ratios (ϕ_c) and minimized energy to reduce computation costs induced by structural relaxation. We subjected the networks to stretching until fracture to determine stress and strain at break and work for fracture, ε_b, σ_b, and W_b. These fracture characteristics are highly dependent on ϕ_c for networks with small f but relatively insensitive for those with large f. Thus, the networks with small f exhibit greater fracture properties than those with large f at high ϕ_c, whereas the opposite relationship occurs at low ϕ_c. We analyzed ε_b, σ_b, and W_b concerning the cycle rank ξ and the broken strand fraction ϕ_bb. We found ε_b, σ_b/ϕ_bb, and W_b/ϕ_bb monotonically decrease with increasing ξ, and the data for various f and ϕ_c superpose with each other to draw master curves. These results imply that the mechanical superiority of the networks with small f comes from their smaller ξ that gives higher ε_b, σ_b/ϕ_bb, and W_b/ϕ_bb than the networks with large f. |
| title | Phantom-Chain Simulations for the Effect of Node Functionality on the Fracture of Star-Polymer Networks |
| topic | Soft Condensed Matter |
| url | https://arxiv.org/abs/2307.09832 |