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Phantom chain simulations for fracture of polymer networks created from star polymer mixtures of different functionalities

Polymer Journal volume 56, pages 163–171 (2024)Cite this article

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Abstract

Fujiyabu et al. [1] experimentally reported that mixing of 3-arm star prepolymers into 4-arm analogs improves the toughness of the resultant polymer networks compared to that of the base network composed of only 4-arm star polymers. The present study investigated the mechanism of this phenomenon based on phantom chain simulations for polymer networks consisting of mixtures of star branch prepolymers with equal arm length and different arm numbers, \(\left({f}_{1},{f}_{2}\right)=\left({{{{\mathrm{3,4}}}}}\right)\), \(\left({{{{\mathrm{3,6}}}}}\right)\) and \(\left({{{{\mathrm{3,8}}}}}\right)\), for various \({f}_{1}=3\) prepolymer fractions \({\varphi }_{3}\). These networks were created via end-linking reactions between prepolymers traced by a Brownian dynamics scheme, and the network structure was stored at different conversion ratios \({\varphi }_{c}\), ranging from 0.6 to 0.9. The cycle rank of the gelated networks \(\xi\) is entirely consistent with that given by mean-field theory, demonstrating that the examined network structure is statistically valid. The networks were stretched with energy minimization until the break, and fracture characteristics including strain at break \({\varepsilon }_{b}\), stress at break \({\sigma }_{b}\), work for fracture \({W}_{b}\), and the ratio of broken strands \({\varphi }_{{bb}}\), were obtained. Plots of \({\varepsilon }_{b}\), \({\sigma }_{b}/{\varphi }_{{bb}}\), and \({W}_{b}/{\varphi }_{{bb}}\) versus \(\xi\) roughly follow the master curves reported for the base networks without mixing, implying that the change of fracture properties by the mixing of \({f}_{1}=3\) mainly corresponds to a decrease in \(\xi\). The mixing slightly suppresses \({\sigma }_{b}/{\varphi }_{{bb}}\) and \({W}_{b}/{\varphi }_{{bb}}\) for large \({f}_{2}\) cases compared to the base networks because of a biased breakage at the network strands without extenders, which are prepolymers with only two reacted arms. The analysis also revealed a new master curve for the \(\xi\)-dependence of the molecular weight of broken strands.

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Acknowledgements

This study is partly supported by JST-CREST (JPMJCR1992) and JSPS KAKENHI (22H01189).

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  1. Department of Materials Physics, Nagoya University, Nagoya, 4648603, Japan

    Yuichi Masubuchi

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Correspondence to Yuichi Masubuchi.

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Masubuchi, Y. Phantom chain simulations for fracture of polymer networks created from star polymer mixtures of different functionalities. Polym J 56, 163–171 (2024). https://doi.org/10.1038/s41428-023-00862-w

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