Vitrimers Designed Both To Strongly Suppress Creep and To Recover Original Cross-Link Density after Reprocessing: Quantitative Theory and Experiments
Abstract
Vitrimers form a promising class of dynamic polymer networks, but they have an Achilles’ heel: elastomeric vitrimers exhibit significant creep under conditions where permanently cross-linked, elastomeric networks exhibit little or no creep. We demonstrate that vitrimers can be designed with strongly suppressed creep and excellent reprocessability by incorporating a substantial yet subcritical fraction of permanent cross-links. This critical fraction of permanent cross-links, which has little or no detrimental effect on reprocessability, is defined by the gelation point of only permanent cross-links leading to a percolated permanent network. Via a modification of classic Flory–Stockmayer theory, we have developed a simple theory that quantitatively predicts an approximate limiting fraction. To test our theory, we designed vitrimers with controlled fractions of permanent cross-links based on thiol–epoxy click chemistry. We characterized the rubbery plateau modulus before and after reprocessing as well as stress relaxation of our original vitrimers. Our experimental results strongly support our theoretical prediction: as long as the fraction of permanent cross-links is insufficient to form a percolated permanent network, the vitrimer can be reprocessed with full recovery of cross-link density. In particular, with a predicted limiting fraction of 50 mol %, a vitrimer system designed with 40 mol % permanent cross-links achieved full property recovery associated with cross-link density after reprocessing as well as 65–71% creep reduction (for both original and reprocessed samples) relative to a similar vitrimer without permanent cross-links. In contrast, a system with 60 mol % permanent cross-links could not be reprocessed into a well-consolidated sample, nor did it recover full cross-link density; it failed by breaking at early stages of creep tests. The ability to predict an approximate limiting fraction of permanent cross-links leading to enhanced creep resistance and full reprocessability represents an important advance in the science and design of vitrimers.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Existing strategies to create reprocessable thermosets have focused on dynamic covalent bond exchange, thermomechanical degradation, or wholesale replacement of network components with degradable versions.
“Existing strategies to create reprocessable thermosets have focused on dynamic covalent bond exchange, 3-8 thermomechanical degradation, 9 or wholesale replacement of network components with degradable versions. 10-13”
From Cleavable comonomers enable degradable, recyclable thermoset plastics (2020) · cites this paper as [8]
Cites
Viscoelastic Properties of Polymers
Jones, W. (1981) · Journal of Non-Newtonian Fluid Mechanics · doi:10.1016/0377-0257(81)80036-5 · Cited by 11,142 · see citing works
Non-symmetrical dielectric relaxation behaviour arising from a simple empirical decay function
Williams, G. J., & Watts, D. C. (1970) · Transactions of the Faraday Society · doi:10.1039/tf9706600080 · Cited by 4,466 · see citing works
Silica-Like Malleable Materials from Permanent Organic Networks
Montarnal, D., Capelot, M., Tournilhac, F., & Leibler, L. (2011) · Science · doi:10.1126/science.1212648 · Cited by 3,625 · see citing works
Rheology: Principles, Measurements, and Applications
Macosko, C. W. (1994) · Cited by 3,494 · see citing works
A Thermally Re-mendable Cross-Linked Polymeric Material
Chen, X., Dam, M. A., Ono, K., Mal, A., Shen, H., Nutt, S., Sheran, K., & Wudl, F. (2002) · Science · doi:10.1126/science.1065879 · Cited by 2,649 · see citing works
Self-citationPrinciples of polymer chemistry
Oster, G. D. (1954) · Journal of Chemical Education · doi:10.1021/ed031p669.2 · Cited by 2,529 · see citing works
Molecular Size Distribution in Three Dimensional Polymers. I. Gelation 1
Flory, P. J. (1941) · Journal of the American Chemical Society · doi:10.1021/ja01856a061 · Cited by 1,924 · see citing works
Theory of Molecular Size Distribution and Gel Formation in Branched-Chain Polymers
STOCKMAYER, W. H. (1943) · The Journal of Chemical Physics · doi:10.1063/1.1723803 · Cited by 1,919 · see citing works
Vitrimers: permanent organic networks with glass-like fluidity
Denissen, W., Winne, J. M., & Prez, F. D. (2015) · Chemical Science · doi:10.1039/c5sc02223a · Cited by 1,810 · see citing works
Thiol-click chemistry: a multifaceted toolbox for small molecule and polymer synthesis
Hoyle, C. E., Lowe, A. B., & Bowman, C. N. (2010) · Chemical Society Reviews · doi:10.1039/b901979k · Cited by 1,639 · see citing works
High-performance vitrimers from commodity thermoplastics through dioxaborolane metathesis
Röttger, M., Domenech, T., van der Weegen, R., Breuillac, A., Nicolaÿ, R., & Leibler, L. (2017) · Science · doi:10.1126/science.aah5281 · Cited by 1,394 · see citing works
Catalytic Control of the Vitrimer Glass Transition
Capelot, M., Unterlass, M. M., Tournilhac, F., & Ludwik Leibler, B. (2012) · ACS Macro Letters · doi:10.1021/mz300239f · Cited by 1,217 · see citing works
Covalent Adaptable Networks (CANs): A Unique Paradigm in Cross-Linked Polymers
Kloxin, C. J., Scott, T. F., Adzima, B. J., & Bowman, C. N. (2010) · Macromolecules · doi:10.1021/ma902596s · Cited by 1,175 · see citing works
Denissen, W., Rivero, G., Nicolaÿ, R., Ludwik Leibler, B., Winne, J. M., & Prez, F. D. (2015) · Advanced Functional Materials · doi:10.1002/adfm.201404553 · Cited by 1,130 · see citing works
Dynamic Covalent Polymer Networks: from Old Chemistry to Modern Day Innovations
Zou, W., Dong, J., Luo, Y., Zhao, Q., & Xie, T. (2017) · Advanced Materials · doi:10.1002/adma.201606100 · Cited by 1,014 · see citing works
50th Anniversary Perspective : There Is a Great Future in Sustainable Polymers
Schneiderman, D. K., & Hillmyer, M. A. (2017) · Macromolecules · doi:10.1021/acs.macromol.7b00293 · Cited by 1,005 · see citing works
Hiemenz, P. C., & Lodge, T. P. (2007) · CRC Press eBooks · doi:10.1201/9781420018271 · Cited by 951 · see citing works
Heat‐ or Water‐Driven Malleability in a Highly Recyclable Covalent Network Polymer
Taynton, P., Yu, K., Shoemaker, R. K., Jin, Y., Qi, H. J., & Zhang, W. (2014) · Advanced Materials · doi:10.1002/adma.201400317 · Cited by 890 · see citing works
Mechanically Activated, Catalyst-Free Polyhydroxyurethane Vitrimers
Fortman, D. J., Brutman, J. P., Cramer, C. J., Hillmyer, M. A., & Dichtel, W. R. (2015) · Journal of the American Chemical Society · doi:10.1021/jacs.5b08084 · Cited by 811 · see citing works
Zheng, P., & McCarthy, T. J. (2012) · Journal of the American Chemical Society · doi:10.1021/ja2113257 · Cited by 624 · see citing works
A New Derivation of Post Gel Properties of Network Polymers
Miller, D. R., & Macosko, C. W. (1976) · Macromolecules · doi:10.1021/ma60050a004 · Cited by 570 · see citing works
Chemical control of the viscoelastic properties of vinylogous urethane vitrimers
Denissen, W., Droesbeke, M. A., Nicolaÿ, R., Ludwik Leibler, B., Winne, J. M., & Prez, F. D. (2017) · Nature Communications · doi:10.1038/ncomms14857 · Cited by 559 · see citing works
Lü, Y.-X., & Guan, Z. (2012) · Journal of the American Chemical Society · doi:10.1021/ja306287s · Cited by 550 · see citing works
Brutman, J. P., Delgado, P. A., & Hillmyer, M. A. (2014) · ACS Macro Letters · doi:10.1021/mz500269w · Cited by 516 · see citing works
Imato, K., Nishihara, M., Kanehara, T., Amamoto, Y., Takahara, A., & Otsuka, H. (2011) · Angewandte Chemie International Edition · doi:10.1002/anie.201104069 · Cited by 497 · see citing works
Malleable and Recyclable Poly(urea‐urethane) Thermosets bearing Hindered Urea Bonds
Zhang, Y., Ying, H., Hart, K. R., Wu, Y., Hsu, A. J., Coppola, A. M., Kim, T. A., Yang, K., Sottos, N. R., White, S. R., et al. (2016) · Advanced Materials · doi:10.1002/adma.201601242 · Cited by 424 · see citing works
Chao, A., Negulescu, I. I., & Zhang, D. (2016) · Macromolecules · doi:10.1021/acs.macromol.6b01443 · Cited by 419 · see citing works
Reprocessable Acid-Degradable Polycarbonate Vitrimers
Snyder, R. L., Fortman, D. J., Hoe, G. X. D., Hillmyer, M. A., & Dichtel, W. R. (2018) · Macromolecules · doi:10.1021/acs.macromol.7b02299 · Cited by 391 · see citing works
Billiet, S., Bruycker, K. D., Driessen, F., et al. (2014) · Nature Chemistry · doi:10.1038/nchem.2023 · Cited by 356 · see citing works
Polgar, L. M., van Duin, M., Broekhuis, A. A., & Picchioni, F. (2015) · Macromolecules · doi:10.1021/acs.macromol.5b01422 · Cited by 291 · see citing works
Poly(thioether) Vitrimers via Transalkylation of Trialkylsulfonium Salts
Hendriks, B., Waelkens, J., Winne, J. M., & Prez, F. E. D. (2017) · ACS Macro Letters · doi:10.1021/acsmacrolett.7b00494 · Cited by 290 · see citing works
Dual-Triggered and Thermally Reconfigurable Shape Memory Graphene-Vitrimer Composites
Yang, Z., Wang, Q., & Wang, T. (2016) · ACS Applied Materials & Interfaces · doi:10.1021/acsami.6b07403 · Cited by 272 · see citing works
Acylhydrazones as Reversible Covalent Crosslinkers for Self‐Healing Polymers
Kuhl, N., Bode, S., Bose, R. K., Vitz, J., Seifert, A., Hoeppener, S., García, S. J., Spange, S., van der Zwaag, S., Hager, M. D., et al. (2015) · Advanced Functional Materials · doi:10.1002/adfm.201501117 · Cited by 262 · see citing works
Essentials of Chemical Reaction Engineering
(2017) · Focus on Catalysts · doi:10.1016/j.focat.2017.06.042 · Cited by 255 · see citing works
Bio‐based epoxy vitrimers: Reprocessibility, controllable shape memory, and degradability
Ma, Z., Wang, Y., Zhu, J., Yu, J., & Hu, Z. (2017) · Journal of Polymer Science Part A Polymer Chemistry · doi:10.1002/pola.28544 · Cited by 251 · see citing works
Responsive Gels Based on a Dynamic Covalent Trithiocarbonate Cross-Linker
Nicolaÿ, R., Kamada, J., Wassen, A. R. V., & Matyjaszewski, K. A. (2010) · Macromolecules · doi:10.1021/ma100378r · Cited by 242 · see citing works
Silica–Epoxy Vitrimer Nanocomposites
Legrand, A., & Soulié‐Ziakovic, C. (2016) · Macromolecules · doi:10.1021/acs.macromol.6b00826 · Cited by 241 · see citing works
Counting primary loops in polymer gels
Zhou, H., Woo, J., Cok, A. M., Wang, M., Olsen, B. D., & Johnson, J. A. (2012) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1213169109 · Cited by 237 · see citing works
Zheng, N., Hou, J., Xu, Y., Fang, Z., Zou, W., Zhao, Q., & Xie, T. (2017) · ACS Macro Letters · doi:10.1021/acsmacrolett.7b00037 · Cited by 237 · see citing works
Maximizing the symbiosis of static and dynamic bonds in self-healing boronic ester networks
Cash, J. J., Kubo, T., Dobbins, D. J., & Sumerlin, B. S. (2018) · Polymer Chemistry · doi:10.1039/c8py00123e · Cited by 231 · see citing works
Chen, X., Li, L., Jin, K., & Torkelson, J. M. (2017) · Polymer Chemistry · doi:10.1039/c7py01160a · Cited by 226 · see citing works
Self-citationFang, Z., Zheng, N., Zhao, Q., & Xie, T. (2017) · ACS Applied Materials & Interfaces · doi:10.1021/acsami.7b05713 · Cited by 224 · see citing works
Demongeot, A., Groote, R., Goossens, H., Hoeks, T. L., Tournilhac, F., & Ludwik Leibler, B. (2017) · Macromolecules · doi:10.1021/acs.macromol.7b01141 · Cited by 221 · see citing works
Vitrimeric Silicone Elastomers Enabled by Dynamic Meldrum’s Acid-Derived Cross-Links
Ishibashi, J. S. A., & Kalow, J. A. (2018) · ACS Macro Letters · doi:10.1021/acsmacrolett.8b00166 · Cited by 209 · see citing works
A mechanical model for creep, recovery and stress relaxation in polymeric materials
Fancey, K. S. (2005) · Journal of Materials Science · doi:10.1007/s10853-005-2020-x · Cited by 195 · see citing works
Recycling Tires? Reversible Crosslinking of Poly(butadiene)
Trovatti, E., Lacerda, T. M., Carvalho, A. J. F., et al. (2015) · Advanced Materials · doi:10.1002/adma.201405801 · Cited by 172 · see citing works
Amamoto, Y., Kamada, J., Otsuka, H., Takahara, A., & Matyjaszewski, K. A. (2011) · Angewandte Chemie · doi:10.1002/ange.201003888 · Cited by 165 · see citing works
Poly(butylene terephthalate)/Glycerol-based Vitrimers via Solid-State Polymerization
Zhou, Y., Goossens, H., Sijbesma, R. P., & Heuts, J. P. A. (2017) · Macromolecules · doi:10.1021/acs.macromol.7b01142 · Cited by 151 · see citing works
Catalyst Selection, Creep, and Stress Relaxation in High-Performance Epoxy Vitrimers
Liu, W., Schmidt, D. F., & Reynaud, E. (2017) · Industrial & Engineering Chemistry Research · doi:10.1021/acs.iecr.6b03829 · Cited by 137 · see citing works
Otsuka, H. (2013) · Polymer Journal · doi:10.1038/pj.2013.17 · Cited by 136 · see citing works
Average Property Relations for Nonlinear Polymerization with Unequal Reactivity
Miller, D. R., & Macosko, C. W. (1978) · Macromolecules · doi:10.1021/ma60064a008 · Cited by 132 · see citing works
Recyclable Crosslinked Polymer Networks via One‐Step Controlled Radical Polymerization
Jin, K., Li, L., & Torkelson, J. M. (2016) · Advanced Materials · doi:10.1002/adma.201600871 · Cited by 128 · see citing works
Self-citationHall, D. B., Dhinojwala, A., & Torkelson, J. M. (1997) · Physical Review Letters · doi:10.1103/physrevlett.79.103 · Cited by 121 · see citing works
Self-citationCuring and viscoelasticity of vitrimers
Snijkers, F., Pasquino, R., & Maffezzoli, A. (2016) · Soft Matter · doi:10.1039/c6sm00707d · Cited by 114 · see citing works
Trapping Dynamic Disulfide Bonds in the Hard Segments of Thermoplastic Polyurethane Elastomers
Zhang, L., Chen, L., & Rowan, S. J. (2016) · Macromolecular Chemistry and Physics · doi:10.1002/macp.201600320 · Cited by 108 · see citing works
Gordon, M. B., French, J. M., Wagner, N. J., & Kloxin, C. J. (2015) · Advanced Materials · doi:10.1002/adma.201503870 · Cited by 93 · see citing works
Kennedy, J. P., & Castner, K. F. (1979) · Journal of Polymer Science Polymer Chemistry Edition · doi:10.1002/pol.1979.170170715 · Cited by 81 · see citing works
Dhinojwala, A., Hooker, J. C., & Torkelson, J. M. (1994) · Journal of Non-Crystalline Solids · doi:10.1016/0022-3093(94)90447-2 · Cited by 80 · see citing works
Self-citationKinetic Monte Carlo Simulation for Quantification of the Gel Point of Polymer Networks
Wang, R., Lin, T., Johnson, J. A., & Olsen, B. D. (2017) · ACS Macro Letters · doi:10.1021/acsmacrolett.7b00586 · Cited by 74 · see citing works
Jin, K., Wilmot, N., Heath, W. H., & Torkelson, J. M. (2016) · Macromolecules · doi:10.1021/acs.macromol.6b00141 · Cited by 67 · see citing works
Self-citationSelf-Dynamics and Collective Swap-Driven Dynamics in a Particle Model for Vitrimers
Rovigatti, L., Nava, G., Bellini, T., & Sciortino, F. (2018) · Macromolecules · doi:10.1021/acs.macromol.7b02186 · Cited by 63 · see citing works
Kennedy, J. P., & Castner, K. F. (1979) · Journal of Polymer Science Polymer Chemistry Edition · doi:10.1002/pol.1979.170170714 · Cited by 62 · see citing works
Recyclable Thermosets Based on Dynamic Amidation and Aza-Michael Addition Chemistry
Baruah, R., Kumar, A., Ujjwal, R. R., Kedia, S., Ranjan, A., & Ojha, U. (2016) · Macromolecules · doi:10.1021/acs.macromol.6b01807 · Cited by 61 · see citing works
Tran, T. N., Rawstron, E., Bourgeat‐Lami, É., & Montarnal, D. (2018) · ACS Macro Letters · doi:10.1021/acsmacrolett.8b00173 · Cited by 51 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Scheutz, G. M., Lessard, J. J., Sims, M. B., & Sumerlin, B. S. (2019) · Journal of the American Chemical Society · doi:10.1021/jacs.9b07922 · Cited by 934 · see citing works
Cleavable comonomers enable degradable, recyclable thermoset plastics
Shieh, P., Zhang, W., Husted, K. E. L., Kristufek, S. L., Xiong, B., Lundberg, D. J., Lem, J., Veysset, D., Sun, Y., Nelson, K. A., et al. (2020) · Nature · doi:10.1038/s41586-020-2495-2 · Cited by 498 · see citing works
Li, L., Chen, X., & Torkelson, J. M. (2019) · Macromolecules · doi:10.1021/acs.macromol.9b01359 · Cited by 224 · see citing works
Self-citation
- Authors
- Li, L., Chen, X., Jin, K., & Torkelson, J. M.
- Affiliations
- Northwestern University (US)
- Corresponding author
- Torkelson, John M.
- Venue
- Macromolecules
- Publisher
- American Chemical Society (ACS)
- Published
- 2018-07-17
- Volume
- 51
- Issue
- 15
- Pages
- 5537-5546
- ISSN
- 0024-9297 (ISSN-L)
- 1520-5835
- OpenAlex
- W2884182729
- Cited by
- 424
- References
- 64
- Citations by year
- 2026: 55 · 2025: 89 · 2024: 69 · 2023: 65 · 2022: 57 · 2021: 38 · 2020: 30 · 2019: 20 · 2018: 1
- FWCI
- 11.10
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Macromolecules (publishedVersion)
- Funders
- Northwestern University
- Topics
- Physical Sciences › Materials Science › Polymers and Plastics › Polymer composites and self-healing
- Physical Sciences › Materials Science › Materials Chemistry › Material Dynamics and Properties
- Physical Sciences › Engineering › Mechanical Engineering › Epoxy Resin Curing Processes
- Keywords
- vitrimers, reprocessability, dynamic polymer networks, percolation network, Flory-Stockmayer theory, stress relaxation, rubbery plateau modulus, gel point
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
