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The microscopic role of deformation in the dynamics of soft colloids

An Author Correction to this article was published on 19 May 2021

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Abstract

Soft colloids enable the exploration of states with densities exceeding that of random close packing, but it remains unclear whether softness controls the dynamics under these dense conditions. Experimental studies have reported conflicting results, and numerical studies have so far focused primarily on simple models that allow particles to overlap, but neglect particle deformations. This makes the concept of softness in simulations and experiments difficult to compare. Here, we propose a model system consisting of polymer rings with internal elasticity. At high packing fractions, the system displays compressed exponential decay of the intermediate scattering functions and super-diffusive behaviour of the mean-squared displacements. These features are explained in terms of the complex interplay between particle deformations and dynamic heterogeneities, which gives rise to persistent motion of ballistic particles. We also observe a striking variation of the relaxation times with increasing particle softness, clearly demonstrating the crucial role of deformation in the dynamics of realistic soft colloids.

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Fig. 1: Model system and dynamic properties as a function of packing fraction.
Fig. 2: Mean-squared displacements and ballistic particles.
Fig. 3: Analysis of deformation of rings.
Fig. 4: Softness-dependent fragility.

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The data sets generated and/or analysed during the current study are available from the authors upon reasonable request.

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The computer code is available from the authors upon reasonable request.

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References

  1. Ruzicka, B. et al. Observation of empty liquids and equilibrium gels in a colloidal clay. Nat. Mater. 10, 56–60 (2011).

    ADS  Google Scholar 

  2. Dotera, T., Oshiro, T. & Ziherl, P. Mosaic two-lengthscale quasicrystals. Nature 506, 208–211 (2014).

    ADS  Google Scholar 

  3. Chen, Q., Bae, S. C. & Granick, S. Directed self-assembly of a colloidal kagome lattice. Nature 469, 381–384 (2011).

    ADS  Google Scholar 

  4. Hertlein, C., Helden, L., Gambassi, A., Dietrich, S. & Bechinger, C. Direct measurement of critical Casimir forces. Nature 451, 172–175 (2008).

    ADS  Google Scholar 

  5. Sacanna, S., Irvine, W. T., Rossi, L. & Pine, D. J. Lock and key colloids through polymerization-induced buckling of monodisperse silicon oil droplets. Soft Matter 7, 1631–1634 (2011).

    ADS  Google Scholar 

  6. van Anders, G., Ahmed, N. K., Smith, R., Engel, M. & Glotzer, S. C. Entropically patchy particles: engineering valence through shape entropy. ACS Nano 8, 931–940 (2013).

    Google Scholar 

  7. Pham, K. N. et al. Multiple glassy states in a simple model system. Science 296, 104–106 (2002).

    ADS  Google Scholar 

  8. Royall, C. P., Williams, S. R., Ohtsuka, T. & Tanaka, H. Direct observation of a local structural mechanism for dynamic arrest. Nat. Mater. 7, 556–561 (2008).

    ADS  Google Scholar 

  9. Mattsson, J. et al. Soft colloids make strong glasses. Nature 462, 83–86 (2009).

    ADS  Google Scholar 

  10. Vlassopoulos, D. & Cloitre, M. Tunable rheology of dense soft deformable colloids. Curr. Opin. Colloid Interface Sci. 19, 561–574 (2014).

    Google Scholar 

  11. Seekell, R. P. III, Sarangapani, P. S., Zhang, Z. & Zhu, Y. Relationship between particle elasticity, glass fragility, and structural relaxation in dense microgel suspensions. Soft Matter 11, 5485–5491 (2015).

    ADS  Google Scholar 

  12. Nigro, V. et al. Dynamical behavior of microgels of interpenetrated polymer networks. Soft Matter 13, 5185–5193 (2017).

    ADS  Google Scholar 

  13. Nigro, V. et al. Structural relaxation, softness and fragility of IPN microgels. Preprint at https://arxiv.org/abs/1807.01692 (2018).

  14. Angell, C. A. Formation of glasses from liquids and biopolymers. Science 267, 1924–1935 (1995).

    ADS  Google Scholar 

  15. Debenedetti, P. G. & Stillinger, F. H. Supercooled liquids and the glass transition. Nature 410, 259–267 (2001).

    ADS  Google Scholar 

  16. van der Scheer, P., van de Laar, T., van der Gucht, J., Vlassopoulos, D. & Sprakel, J. Fragility and strength in nanoparticle glasses. ACS Nano 11, 6755–6763 (2017).

    Google Scholar 

  17. Philippe, A.-M. et al. Glass transition of soft colloids. Phys. Rev. E 97, 040601 (2018).

    ADS  Google Scholar 

  18. Landau, L. D. & Lifshitz, E. Theory of Elasticity 3rd edn, Vol. 7, 109 (Course of Theoretical Physics, Butterworth-Heinemann, 1986).

  19. Mohanty, P. S., Paloli, D., Crassous, J. J., Zaccarelli, E. & Schurtenberger, P. Effective interactions between soft-repulsive colloids: experiments, theory, and simulations. J. Chem. Phys. 140, 094901 (2014).

    ADS  Google Scholar 

  20. Bergman, M. J. et al. A new look at effective interactions between microgel particles. Nat. Commun. 9, 5039 (2018).

    ADS  Google Scholar 

  21. Mohanty, P. S. et al. Interpenetration of polymeric microgels at ultrahigh densities. Sci. Rep. 7, 1487 (2017).

    ADS  Google Scholar 

  22. Sengupta, S., Vasconcelos, F., Affouard, F. & Sastry, S. Dependence of the fragility of a glass former on the softness of interparticle interactions. J. Chem. Phys 135, 194503 (2011).

    ADS  Google Scholar 

  23. De Michele, C., Sciortino, F. & Coniglio, A. Scaling in soft spheres: fragility invariance on the repulsive potential softness. J. Phys. Condens. Matter 16, L489–L494 (2004).

    Google Scholar 

  24. Urich, M. & Denton, A. R. Swelling, structure, and phase stability of compressible microgels. Soft Matter 12, 9086–9094 (2016).

    ADS  Google Scholar 

  25. De Aguiar, I. B. et al. Deswelling and deformation of microgels in concentrated packings. Sci. Rep. 7, 10223 (2017).

    Google Scholar 

  26. Weyer, T. J. & Denton, A. R. Concentration-dependent swelling and structure of ionic microgels: simulation and theory of a coarse-grained model. Soft Matter 14, 4530–4540 (2018).

    ADS  Google Scholar 

  27. Higler, R. & Sprakel, J. Apparent strength versus universality in glasses of soft compressible colloids. Sci. Rep. 8, 16817 (2018).

    ADS  Google Scholar 

  28. Conley, G. M., Aebischer, P., Nöjd, S., Schurtenberger, P. & Scheffold, F. Jamming and overpacking fuzzy microgels: deformation, interpenetration, and compression. Sci. Adv. 3, e1700969 (2017).

    ADS  Google Scholar 

  29. Bachman, H. et al. Ultrasoft, highly deformable microgels. Soft Matter 11, 2018–2028 (2015).

    ADS  Google Scholar 

  30. Virtanen, O. L. J., Mourran, A., Pinard, P. T. & Richtering, W. Persulfate initiated ultra-low cross-linked poly(n-isopropylacrylamide) microgels possess an unusual inverted cross-linking structure. Soft Matter 12, 3919–3928 (2016).

    ADS  Google Scholar 

  31. Berthier, L., Moreno, A. J. & Szamel, G. Increasing the density melts ultrasoft colloidal glasses. Phys. Rev. E 82, 060501 (2010).

    ADS  Google Scholar 

  32. Verso, F. L., Pomposo, J. A., Colmenero, J. & Moreno, A. J. Tunable slow dynamics in a new class of soft colloids. Soft Matter 12, 9039–9046 (2016).

    ADS  Google Scholar 

  33. Kurzthaler, C., Leitmann, S. & Franosch, T. Intermediate scattering function of an anisotropic active Brownian particle. Sci. Rep. 6, 36702 (2016).

    ADS  Google Scholar 

  34. Schwarz-Linek, J. et al. Escherichia coli as a model active colloid: a practical introduction. Colloids Surf. B 137, 2–16 (2016).

    Google Scholar 

  35. Berne, B. J. & Pecora, R. Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics (Courier Corporation, 2000).

  36. Cipelletti, L., Manley, S., Ball, R. & Weitz, D. Universal aging features in the restructuring of fractal colloidal gels. Phys. Rev. Lett. 84, 2275 (2000).

    ADS  Google Scholar 

  37. Angelini, R. et al. Dichotomic aging behaviour in a colloidal glass. Soft Matter 9, 10955–10959 (2013).

    ADS  Google Scholar 

  38. Ruta, B., Baldi, G., Monaco, G. & Chushkin, Y. Compressed correlation functions and fast aging dynamics in metallic glasses. J. Chem. Phys. 138, 054508 (2013).

    ADS  Google Scholar 

  39. Angelini, R. et al. Glass–glass transition during aging of a colloidal clay. Nat. Commun. 5, 4049 (2014).

    ADS  Google Scholar 

  40. Bouchaud, J.-P. & Pitard, E. Anomalous dynamical light scattering in soft glassy gels. Eur. Phys. J. E 9, 287–291 (2002).

    ADS  Google Scholar 

  41. Cipelletti, L. et al. Universal non-diffusive slow dynamics in aging soft matter. Faraday Discuss. 123, 237–251 (2003).

    ADS  Google Scholar 

  42. Duri, A. & Cipelletti, L. Length scale dependence of dynamical heterogeneity in a colloidal fractal gel. Europhys. Lett. 76, 972–978 (2006).

    ADS  Google Scholar 

  43. Bouzid, M., Colombo, J., Barbosa, L. V. & Del Gado, E. Elastically driven intermittent microscopic dynamics in soft solids. Nat. Commun. 8, 15846 (2017).

    ADS  Google Scholar 

  44. Pelaez-Fernandez, M., Souslov, A., Lyon, L., Goldbart, P. M. & Fernandez-Nieves, A. Impact of single-particle compressibility on the fluid-solid phase transition for ionic microgel suspensions. Phys. Rev. Lett. 114, 098303 (2015).

    ADS  Google Scholar 

  45. Gao, J. & Frisken, B. Cross-linker-free n-isopropylacrylamide gel nanospheres. Langmuir 19, 5212–5216 (2003).

    Google Scholar 

  46. Scotti, A. et al. Hollow microgels squeezed in overcrowded environments. J. Chem. Phys. 148, 174903 (2018).

    ADS  Google Scholar 

  47. Grest, G. S. & Kremer, K. Molecular dynamics simulation for polymers in the presence of a heat bath. Phys. Rev. A 33, 3628 (1986).

    ADS  Google Scholar 

  48. Russo, J., Tartaglia, P. & Sciortino, F. Reversible gels of patchy particles: role of the valence. J. Chem. Phys. 131, 014504 (2009).

    ADS  Google Scholar 

  49. Rudnick, J. & Gaspari, G. The aspherity of random walks. J. Phys. A 19, L191–L193 (1986).

    ADS  MATH  Google Scholar 

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Acknowledgements

We thank F. Camerin, L. Cipelletti, C. Maggi, A. Ninarello and D. Truzzolillo for useful discussions and comments. We acknowledge support from the European Research Council (ERC Consolidator Grant 681597, MIMIC) and from ETN-COLLDENSE (H2020-MCSA-ITN-2014, grant 642774).

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N.G. and E.Z. designed and performed the research, and wrote the paper.

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Correspondence to Nicoletta Gnan or Emanuela Zaccarelli.

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Journal peer review information: Nature Physics thanks Grzegorz Szamel and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Video 1

The dynamics of elastic polymer rings with elastic hertzian strength U = 1,000 at three different packing fractions ζ = 0.463, 0.812 and 1.264. Rings change colour in time according to their asphericity following the colour code in Supplementary Fig. 1 (from blue for spherical rings to red for strongly aspherical ones). Each movie is composed of frames separated by a time of ~40 (in reduced units) for up to a total time of 800.

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Gnan, N., Zaccarelli, E. The microscopic role of deformation in the dynamics of soft colloids. Nat. Phys. 15, 683–688 (2019). https://doi.org/10.1038/s41567-019-0480-1

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