Quantifying the impact of molecular defects on polymer network elasticity
Abstract
Elasticity, one of the most important properties of a soft material, is difficult to quantify in polymer networks because of the presence of topological molecular defects in these materials. Furthermore, the impact of these defects on bulk elasticity is unknown. We used rheology, disassembly spectrometry, and simulations to measure the shear elastic modulus and count the numbers of topological “loop” defects of various order in a series of polymer hydrogels, and then used these data to evaluate the classical phantom and affine network theories of elasticity. The results led to a real elastic network theory (RENT) that describes how loop defects affect bulk elasticity. Given knowledge of the loop fractions, RENT provides predictions of the shear elastic modulus that are consistent with experimental observations.
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?
Topological defects including intra-chain cycles, dangling chains, and free chains affect macroscopic mechanical and thermomechanical properties of real polymer networks in a non-constructive way but are statistically unavoidable.
“These defects affect the macroscopic mechanical and thermomechanical properties in a non-constructive way, but are statistically unavoidable30,31.”
From On demand shape memory polymer via light regulated topological defects in a dynamic covalent network (2020) · cites this paper as [30]
Cites
Rubinstein, M., & Colby, R. H. (2003) · doi:10.1093/oso/9780198520597.001.0001 · Cited by 5,686 · see citing works
A Theory of Large Elastic Deformation
Mooney, M. (1940) · Journal of Applied Physics · doi:10.1063/1.1712836 · Cited by 3,617 · 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
Theory of elasticity of polymer networks. The effect of local constraints on junctions
Flory, P. J. (1977) · The Journal of Chemical Physics · doi:10.1063/1.433846 · Cited by 467 · see citing works
Elastic modulus and equilibrium swelling of poly(dimethylsiloxane) networks
Patel, S. K., Malone, S., Cohen, C., Gillmor, J. R., & Colby, R. H. (1992) · Macromolecules · doi:10.1021/ma00046a021 · Cited by 297 · see citing works
Nonaffine deformation and elasticity of polymer networks
Rubinstein, M., & Panyukov, S. (1997) · Macromolecules · doi:10.1021/ma970364k · Cited by 248 · see citing works
Model networks based on `endlinking' processes: synthesis, structure and properties
Hild, G. (1998) · Progress in Polymer Science · doi:10.1016/s0079-6700(97)00055-5 · Cited by 239 · 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 236 · see citing works
Self-citationSynthesis of Degradable Model Networks via ATRP and Click Chemistry
Johnson, J. A., Lewis, D. R., Díaz, D. D., Finn, M. G., Koberstein, J. T., & Turro, N. J. (2006) · Journal of the American Chemical Society · doi:10.1021/ja0612910 · Cited by 219 · see citing works
Self-citationAkagi, Y., Gong, J. P., Chung, U., & Sakai, T. (2013) · Macromolecules · doi:10.1021/ma302270a · Cited by 219 · see citing works
Examination of the Theories of Rubber Elasticity Using an Ideal Polymer Network
Akagi, Y., Katashima, T., Katsumoto, Y., Fujii, K., Matsunaga, T., Chung, U., Shibayama, M., & Sakai, T. (2011) · Macromolecules · doi:10.1021/ma201088r · Cited by 143 · see citing works
Universal Cyclic Topology in Polymer Networks
Wang, R., Alexander‐Katz, A., Johnson, J. A., & Olsen, B. D. (2016) · Physical Review Letters · doi:10.1103/physrevlett.116.188302 · Cited by 129 · see citing works
Self-citationLoops versus Branch Functionality in Model Click Hydrogels
Kawamoto, K., Zhong, M., Wang, R., Olsen, B. D., & Johnson, J. A. (2015) · Macromolecules · doi:10.1021/acs.macromol.5b02243 · Cited by 104 · see citing works
Self-citationZhou, H., Schön, E., Wang, M., Glassman, M., Liu, J., Zhong, M., Díaz, D. D., Olsen, B. D., & Johnson, J. A. (2014) · Journal of the American Chemical Society · doi:10.1021/ja5042385 · Cited by 96 · see citing works
Self-citationStress–strain relation of entangled polymer networks
Grest, G. S., Pütz, M., Everaers, R., & Kremer, K. (2000) · Journal of Non-Crystalline Solids · doi:10.1016/s0022-3093(00)00224-6 · Cited by 76 · see citing works
Kinetics of End Crosslinking in Dense Polymer Melts
Grest, G. S., Kremer, K., & Duering, E. R. (1992) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/19/3/008 · Cited by 58 · see citing works
Molecular defects in organic materials
Müllen, K. (2016) · Nature Reviews Materials · doi:10.1038/natrevmats.2015.13 · Cited by 40 · see citing works
Theoretical and experimental studies of network formation and properties
Stepto, R. F. T. (1979) · Polymer · doi:10.1016/0032-3861(79)90270-2 · Cited by 35 · see citing works
Monte‐carlo modelling of the formation, structure and properties of polymer networks
Dutton, S., Stepto, R. F. T., & Taylor, D. J. R. (1996) · Die Angewandte Makromolekulare Chemie · doi:10.1002/apmc.1996.052400104 · Cited by 32 · see citing works
Dušek, K., Dušková‐Smrc̆ková, M., Huybrechts, J., et al. (2013) · Macromolecules · doi:10.1021/ma302396u · Cited by 14 · see citing works
Intramolecular Reaction and Network Formation and Properties
Stepto, R. F. T. (1988) · Springer eBooks · doi:10.1007/978-94-009-1343-1_10 · Cited by 12 · see citing works
Formation, structure and properties of polymer networks: theory and modelling
Stepto, R. F. T., Cail, J. I., & Taylor, D. J. R. (2003) · Materials Research Innovations · doi:10.1080/14328917.2003.11784752 · Cited by 10 · see citing works
The Crystal Imperfection; Lattice Defects
Mittemeijer, E. J. (2010) · Springer eBooks · doi:10.1007/978-3-642-10500-5_5 · Cited by 7 · see citing works
Formation, structure and properties of polymer networks: theory and modelling
Stepto, R. F. T., Cail, J. I., & Taylor, D. J. R. (2003) · Materials Research Innovations · doi:10.1007/s10019-002-0216-0 · Cited by 5 · see citing works
Balazs, A. C. (2013) · Nature · doi:10.1038/493172a · Cited by 4 · see citing works
Synthesis and Characterization of Tetraazaparacyclophane Disulfone
Yang, Y., Yang, B., Li, M., et al. (2008) · Synthetic Communications · doi:10.1080/00397910701796733 · Cited by 1 · see citing works
Kolb (2001) · doi:10.1002/1521-3773(20010601)40:11
Flagged first, then by citations
Cited by
Sorted by citations
50th Anniversary Perspective: Networks and Gels: Soft but Dynamic and Tough
Creton, C. (2017) · Macromolecules · doi:10.1021/acs.macromol.7b01698 · Cited by 463 · see citing works
Polymer Networks: From Plastics and Gels to Porous Frameworks
Gu, Y., Zhao, J., & Johnson, J. A. (2020) · Angewandte Chemie International Edition · doi:10.1002/anie.201902900 · Cited by 388 · see citing works
Self-citationPhotoswitching topology in polymer networks with metal–organic cages as crosslinks
Gu, Y., Alt, E. A., Wang, H., Li, X., Willard, A. P., & Johnson, J. A. (2018) · Nature · doi:10.1038/s41586-018-0339-0 · Cited by 371 · see citing works
Self-citationOn demand shape memory polymer via light regulated topological defects in a dynamic covalent network
Miao, W., Zou, W., Jin, B., Ni, C., Zheng, N., Zhao, Q., & Xie, T. (2020) · Nature Communications · doi:10.1038/s41467-020-18116-1 · Cited by 152 · see citing works
Light-triggered topological programmability in a dynamic covalent polymer network
Zou, W., Jin, B., Wu, Y., Song, H., Luo, Y., Huang, F., Qian, J., Zhao, Q., & Xie, T. (2020) · Science Advances · doi:10.1126/sciadv.aaz2362 · Cited by 143 · see citing works
Counting loops in sidechain-crosslinked polymers from elastic solids to single-chain nanoparticles
Wang, J., Wang, R., Gu, Y., Sourakov, A., Olsen, B. D., & Johnson, J. A. (2019) · Chemical Science · doi:10.1039/c9sc01297d · Cited by 48 · see citing works
Self-citationTopology mediates transport of nanoparticles in macromolecular networks
Dai, X., Zhang, X., Gao, L., Xu, Z., & Yan, L.-T. (2022) · Nature Communications · doi:10.1038/s41467-022-31861-9 · Cited by 44 · see citing works
- Authors
- Zhong, M., Wang, R., Kawamoto, K., Olsen, B. D., & Johnson, J. A.
- Affiliations
- Massachusetts Institute of Technology (US)
- Corresponding author
- Zhong, Mingjiang
- Wang, Rui
- Kawamoto, Ken
- Olsen, Bradley D.
- Johnson, Jeremiah A.
- Venue
- Science
- Published
- 2016-09-16
- Volume
- 353
- Issue
- 6305
- Pages
- 1264-1268
- ISSN
- 0036-8075 (ISSN-L)
- 1095-9203
- OpenAlex
- W2520809832
- Cited by
- 528
- References
- 27
- Citations by year
- 2026: 56 · 2025: 66 · 2024: 55 · 2023: 68 · 2022: 61 · 2021: 53 · 2020: 54 · 2019: 44 · 2018: 39 · 2017: 28 · 2016: 4
- FWCI
- 18.34
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Science (publishedVersion)
- PubMed (publishedVersion)
- Funders
- NSF (CHE-1334703)
- U.S. Army Research Office (W911NF-07-D-0004)
- NSF Materials Research Science and Engineering Centers (DMR-14190807)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Medicine › Hydrogels: synthesis, properties, applications
- Physical Sciences › Chemical Engineering › Fluid Flow and Transfer Processes › Rheology and Fluid Dynamics Studies
- Physical Sciences › Engineering › Mechanical Engineering › Advanced Materials and Mechanics
- Keywords
- topological defects, polymer hydrogels, shear modulus, soft materials
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
