Topological linking determines elasticity in limited valence networks
Source abstract
Abstract
Abstract Understanding the relationship between the microscopic structure and topology of a material and its macroscopic properties is a fundamental challenge across a wide range of systems. Here we investigate the viscoelasticity of DNA nanostar hydrogels—a model system for physical networks with limited valence—by coupling rheology measurements, confocal imaging and molecular dynamics simulations. We discover that these networks display a large degree of interpenetration and that loops within the network are topologically linked, forming a percolating network-within-network structure. Below the overlapping concentration, the fraction of branching points and the pore size determine the high-frequency elasticity of these physical gels. At higher concentrations, we discover that this elastic response is dictated by the abundance of topological links between looped motifs in the gel. Our findings highlight the emergence of ‘topological elasticity’ as a previously overlooked mechanism in generic network-forming liquids and gels and inform the design of topologically controllable material behaviours.
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Research context
OpenAlex topics: Pickering emulsions and particle stabilization · Supramolecular Self-Assembly in Materials · Surface Chemistry and Catalysis
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References (55)
Show source-provided references
1. de Gennes, P. Scaling Concepts in Polymer Physics (Cornell Univ. Press, 1979).
2. Neophytou, A., Chakrabarti, D. & Sciortino, F. Topological nature of the liquid–liquid phase transition in tetrahedral liquids. Nat. Phys. 18, 1248–1253 (2022).10.1038/s41567-022-01698-6 ↗
3. Gutiérrez Fosado, Y. A., Michieletto, D. & Martelli, F. Link to densify: topological transitions and origin of hysteresis during the compression and decompression of amorphous ices. Phys. Rev. Lett. (in the press).
4. Everaers, R. et al. Rheology and microscopic topology of entangled polymeric liquids. Science 303, 823–826 (2004).10.1126/science.1091215 ↗
5. Tubiana, L. et al. Topology in soft and biological matter. Phys. Rep. 1075, 1–137 (2024).10.1016/j.physrep.2024.04.002 ↗
6. Flory, P. J. Principles of Polymer Chemistry (Cornell Univ. Press, 1953).
7. Gu, Y., Schauenburg, D., Bode, J. W. & Johnson, J. A. Leaving groups as traceless topological modifiers for the synthesis of topologically isomeric polymer networks. J. Am. Chem. Soc. 140, 14033–14037 (2018).10.1021/jacs.8b07967 ↗
8. Gu, Y., Zhao, J. & Johnson, J. A. A (macro)molecular-level understanding of polymer network topology. Trends Chem. 1, 318–334 (2019).10.1016/j.trechm.2019.02.017 ↗
9. Lin, T.-S., Wang, R., Johnson, J. A. & Olsen, B. D. Topological structure of networks formed from symmetric four-arm precursors. Macromolecules 51, 1224–1231 (2018).10.1021/acs.macromol.7b01829 ↗
10. Michieletto, D. & Turner, M. S. A topologically driven glass in ring polymers. Proc. Natl Acad. Sci. USA 113, 5195–5200 (2016).10.1073/pnas.1520665113 ↗
11. Kapnistos, M. et al. Unexpected power-law stress relaxation of entangled ring polymers. Nat. Mater. 7, 997–1002 (2008).10.1038/nmat2292 ↗
12. Smrek, J., Garamella, J., Robertson-Anderson, R. & Michieletto, D. Topological tuning of DNA mobility in entangled solutions of supercoiled plasmids. Sci. Adv. 7, abf9260 (2021).10.1126/sciadv.abf9260 ↗
13. O’Connor, T. C., Ge, T., Rubinstein, M. & Grest, G. S. Topological linking drives anomalous thickening of ring polymers in weak extensional flows. Phys. Rev. Lett. 124, 27801 (2020).10.1103/PhysRevLett.124.027801 ↗
14. Krajina, B. A., Zhu, A., Heilshorn, S. C. & Spakowitz, A. J. Active DNA Olympic hydrogels driven by topoisomerase activity. Phys. Rev. Lett. 121, 148001 (2018).10.1103/PhysRevLett.121.148001 ↗
15. Lang, M., Fischer, J., Werner, M. & Sommer, J. U. Swelling of Olympic gels. Phys. Rev. Lett. 112, 238001 (2014).10.1103/PhysRevLett.112.238001 ↗
16. He, P., Katan, A. J., Tubiana, L., Dekker, C. & Michieletto, D. Single-molecule structure and topology of kinetoplast DNA networks. Phys. Rev. X 13, 21010 (2023).
17. Leigh, D. A. et al. Tying different knots in a molecular strand. Nature 584, 562–568 (2020).10.1038/s41586-020-2614-0 ↗
18. Imran, A. B. et al. Extremely stretchable thermosensitive hydrogels by introducing slide-ring polyrotaxane cross-linkers and ionic groups into the polymer network. Nat. Commun. 5, 5124 (2014).10.1038/ncomms6124 ↗
19. Smith, A. D., Donley, G. J., Del Gado, E. & Zavala, V. M. Topological data analysis for particulate gels. ACS Nano 18, 28622–28635 (2024).10.1021/acsnano.4c04969 ↗
20. Smallenburg, F. & Sciortino, F. Liquids more stable than crystals in particles with limited valence and flexible bonds. Nat. Phys. 9, 554–558 (2013).10.1038/nphys2693 ↗
21. Conrad, N., Kennedy, T., Fygenson, D. K. & Saleh, O. A. Increasing valence pushes DNA nanostar networks to the isostatic point. Proc. Natl Acad. Sci. USA 116, 7238–7243 (2019).10.1073/pnas.1819683116 ↗
22. Sharma, A. et al. Strain-controlled criticality governs the nonlinear mechanics of fibre networks. Nat. Phys. 12, 584–587 (2016).10.1038/nphys3628 ↗
23. Chen, Q., Bae, S. C. & Granick, S. Directed self-assembly of a colloidal kagome lattice. Nature 469, 381–384 (2011).10.1038/nature09713 ↗
24. Wang, Y. et al. Colloids with valence and specific directional bonding. Nature 491, 51–55 (2012).10.1038/nature11564 ↗
25. Biffi, S. et al. Phase behavior and critical activated dynamics of limited-valence DNA nanostars. Proc. Natl Acad. Sci. USA 110, 15633–15637 (2013).10.1073/pnas.1304632110 ↗
26. Biffi, S. et al. Equilibrium gels of low-valence DNA nanostars: a colloidal model for strong glass formers. Soft Matter 11, 3132–3138 (2015).10.1039/C4SM02144D ↗
27. Xing, Z. et al. Microrheology of DNA hydrogels. Proc. Natl Acad. Sci. USA 115, 8137–8142 (2018).10.1073/pnas.1722206115 ↗
28. Rovigatti, L., Smallenburg, F., Romano, F. & Sciortino, F. Gels of DNA nanostars never crystallize. ACS Nano 8, 3567–3574 (2014).10.1021/nn501138w ↗
29. Gutiérrez Fosado, Y. A. Nanostars planarity modulates the rheology of DNA hydrogels. Soft Matter 19, 4820–4828 (2023).10.1039/D2SM00221C ↗
30. Dudukovic, N. A. & Zukoski, C. F. Evidence for equilibrium gels of valence-limited particles. Soft Matter 10, 7849–7856 (2014).10.1039/C4SM01389A ↗
31. Schmidt, R. F., Kiefer, H., Dalgliesh, R., Gradzielski, M. & Netz, R. R. Nanoscopic interfacial hydrogel viscoelasticity revealed from comparison of macroscopic and microscopic rheology. Nano Lett. 24, 4758–4765 (2024).
32. Henrich, O., Gutiérrez Fosado, Y. A., Curk, T. & Ouldridge, T. E. Coarse-grained simulation of DNA using LAMMPS: an implementation of the oxDNA model and its applications. Eur. Phys. J. E 41, 57 (2018).10.1140/epje/i2018-11669-8 ↗
33. Mason, T. G. Estimating the viscoelastic moduli of complex fluids using the generalized Stokes-Einstein equation. Rheol. Acta 39, 371–378 (2000).10.1007/s003970000094 ↗
34. Ramírez, J., Sukumaran, S. K., Vorselaars, B. & Likhtman, A. E. Efficient on the fly calculation of time correlation functions in computer simulations. J. Chem. Phys. 133, 154103 (2010).10.1063/1.3491098 ↗
35. Lee, W. B. & Kremer, K. Entangled polymer melts: relation between plateau modulus and stress autocorrelation function. Macromolecules 42, 6270–6276 (2009).10.1021/ma9008498 ↗
36. Flenner, E. & Szamel, G. Long-range spatial correlations of particle displacements and the emergence of elasticity. Phys. Rev. Lett. 114, 025501 (2015).10.1103/PhysRevLett.114.025501 ↗
37. Sorichetti, V., Hugouvieux, V. & Kob, W. Determining the mesh size of polymer solutions via the pore size distribution. Macromolecules 53, 2568–2581 (2020).10.1021/acs.macromol.9b02166 ↗
38. Zhong, M., Wang, R., Kawamoto, K., Olsen, B. D. & Johnson, J. A. Quantifying the impact of molecular defects on polymer network elasticity. Science 353, 1264–1268 (2016).10.1126/science.aag0184 ↗
39. Bantawa, M. et al. The hidden hierarchical nature of soft particulate gels. Nat. Phys. 19, 1178–1184 (2023).10.1038/s41567-023-01988-7 ↗
40. Jeon, B.-j, Nguyen, D. T. & Saleh, O. A. Sequence-controlled adhesion and microemulsification in a two-phase system of DNA liquid droplets. J. Phys. Chem. B 124, 8888–8895 (2020).10.1021/acs.jpcb.0c06911 ↗
41. Lattuada, E., Pietrangeli, T. & Sciortino, F. Interpenetrating gels in binary suspensions of DNA nanostars. J. Chem. Phys. 157, 135101 (2022).10.1063/5.0117047 ↗
42. Rubinstein, M. & Panyukov, S. Elasticity of polymer networks. Macromolecules 35, 6670–6686 (2002).10.1021/ma0203849 ↗
43. Svaneborg, C., Everaers, R., Grest, G. S. & Curro, J. G. Connectivity and entanglement stress contributions in strained polymer networks. Macromolecules 41, 4920–4928 (2008).10.1021/ma800018f ↗
44. James, H. M. Statistical properties of networks of flexible chains. J. Chem. Phys. 15, 651–668 (1947).10.1063/1.1746624 ↗
45. Sorichetti, V. et al. Effect of chain polydispersity on the elasticity of disordered polymer networks. Macromolecules 54, 3769–3779 (2021).10.1021/acs.macromol.1c00176 ↗
46. Sorichetti, V. et al. Structure and elasticity of model disordered, polydisperse, and defect-free polymer networks. J. Chem. Phys. 158, 074905 (2023).10.1063/5.0134271 ↗
47. Michieletto, D., Marenduzzo, D. & Orlandini, E. Is the kinetoplast DNA a percolating network of linked rings at its critical point? Phys. Biol. 12, 036001 (2015).10.1088/1478-3975/12/3/036001 ↗
48. Klotz, A. R., Soh, B. W. & Doyle, P. S. Equilibrium structure and deformation response of 2D kinetoplast sheets. Proc. Natl Acad. Sci. USA 117, 121–127 (2020).10.1073/pnas.1911088116 ↗
49. Sciortino, F. & Zaccarelli, E. Equilibrium gels of limited valence colloids. Curr. Opin. Colloid Interface Sci. 30, 90–96 (2017).10.1016/j.cocis.2017.06.001 ↗
50. Rauscher, P. M., Schweizer, K. S., Rowan, S. J. & DePablo, J. J. Thermodynamics and structure of poly[n]catenane melts. Macromolecules 53, 3390–3408 (2020).10.1021/acs.macromol.9b02706 ↗
51. Wood, T., Lintuvuori, J., Schofield, A., Marenduzzo, D. & Poon, W. A self-quenched defect glass in a colloid-nematic liquid crystal composite. Science 334, 79–83 (2011).10.1126/science.1209997 ↗
52. Conrad, N., Chang, G., Fygenson, D. K. & Saleh, O. A. Emulsion imaging of a DNA nanostar condensate phase diagram reveals valence and electrostatic effects. J. Chem. Phys. 157, 234203 (2022).10.1063/5.0130808 ↗
53. Zadeh, J. N. et al. NUPACK: analysis and design of nucleic acid systems. J. Comput. Chem. 32, 170–173 (2011).10.1002/jcc.21596 ↗
54. Mason, T. G. & Weitz, D. A. Optical measurements of frequency-dependent linear viscoelastic moduli of complex fluids. Phys. Rev. Lett. 74, 1250–1253 (1995).10.1103/PhysRevLett.74.1250 ↗
55. Gutiérrez Fosado, Y. A., Palombo, G., Weir, S. & Michieletto, D. Topological elasticity. Edinburgh DataShare https://doi.org/10.7488/ds/7839 (2024).10.7488/ds/7839 ↗