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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Data availability
The data sets generated and/or analysed during the current study are available from the authors upon reasonable request.
Code availability
The computer code is available from the authors upon reasonable request.
Change history
19 May 2021
A Correction to this paper has been published: https://doi.org/10.1038/s41567-021-01252-w
References
Ruzicka, B. et al. Observation of empty liquids and equilibrium gels in a colloidal clay. Nat. Mater. 10, 56–60 (2011).
Dotera, T., Oshiro, T. & Ziherl, P. Mosaic two-lengthscale quasicrystals. Nature 506, 208–211 (2014).
Chen, Q., Bae, S. C. & Granick, S. Directed self-assembly of a colloidal kagome lattice. Nature 469, 381–384 (2011).
Hertlein, C., Helden, L., Gambassi, A., Dietrich, S. & Bechinger, C. Direct measurement of critical Casimir forces. Nature 451, 172–175 (2008).
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).
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).
Pham, K. N. et al. Multiple glassy states in a simple model system. Science 296, 104–106 (2002).
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).
Mattsson, J. et al. Soft colloids make strong glasses. Nature 462, 83–86 (2009).
Vlassopoulos, D. & Cloitre, M. Tunable rheology of dense soft deformable colloids. Curr. Opin. Colloid Interface Sci. 19, 561–574 (2014).
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).
Nigro, V. et al. Dynamical behavior of microgels of interpenetrated polymer networks. Soft Matter 13, 5185–5193 (2017).
Nigro, V. et al. Structural relaxation, softness and fragility of IPN microgels. Preprint at https://arxiv.org/abs/1807.01692 (2018).
Angell, C. A. Formation of glasses from liquids and biopolymers. Science 267, 1924–1935 (1995).
Debenedetti, P. G. & Stillinger, F. H. Supercooled liquids and the glass transition. Nature 410, 259–267 (2001).
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).
Philippe, A.-M. et al. Glass transition of soft colloids. Phys. Rev. E 97, 040601 (2018).
Landau, L. D. & Lifshitz, E. Theory of Elasticity 3rd edn, Vol. 7, 109 (Course of Theoretical Physics, Butterworth-Heinemann, 1986).
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).
Bergman, M. J. et al. A new look at effective interactions between microgel particles. Nat. Commun. 9, 5039 (2018).
Mohanty, P. S. et al. Interpenetration of polymeric microgels at ultrahigh densities. Sci. Rep. 7, 1487 (2017).
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).
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).
Urich, M. & Denton, A. R. Swelling, structure, and phase stability of compressible microgels. Soft Matter 12, 9086–9094 (2016).
De Aguiar, I. B. et al. Deswelling and deformation of microgels in concentrated packings. Sci. Rep. 7, 10223 (2017).
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).
Higler, R. & Sprakel, J. Apparent strength versus universality in glasses of soft compressible colloids. Sci. Rep. 8, 16817 (2018).
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).
Bachman, H. et al. Ultrasoft, highly deformable microgels. Soft Matter 11, 2018–2028 (2015).
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).
Berthier, L., Moreno, A. J. & Szamel, G. Increasing the density melts ultrasoft colloidal glasses. Phys. Rev. E 82, 060501 (2010).
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).
Kurzthaler, C., Leitmann, S. & Franosch, T. Intermediate scattering function of an anisotropic active Brownian particle. Sci. Rep. 6, 36702 (2016).
Schwarz-Linek, J. et al. Escherichia coli as a model active colloid: a practical introduction. Colloids Surf. B 137, 2–16 (2016).
Berne, B. J. & Pecora, R. Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics (Courier Corporation, 2000).
Cipelletti, L., Manley, S., Ball, R. & Weitz, D. Universal aging features in the restructuring of fractal colloidal gels. Phys. Rev. Lett. 84, 2275 (2000).
Angelini, R. et al. Dichotomic aging behaviour in a colloidal glass. Soft Matter 9, 10955–10959 (2013).
Ruta, B., Baldi, G., Monaco, G. & Chushkin, Y. Compressed correlation functions and fast aging dynamics in metallic glasses. J. Chem. Phys. 138, 054508 (2013).
Angelini, R. et al. Glass–glass transition during aging of a colloidal clay. Nat. Commun. 5, 4049 (2014).
Bouchaud, J.-P. & Pitard, E. Anomalous dynamical light scattering in soft glassy gels. Eur. Phys. J. E 9, 287–291 (2002).
Cipelletti, L. et al. Universal non-diffusive slow dynamics in aging soft matter. Faraday Discuss. 123, 237–251 (2003).
Duri, A. & Cipelletti, L. Length scale dependence of dynamical heterogeneity in a colloidal fractal gel. Europhys. Lett. 76, 972–978 (2006).
Bouzid, M., Colombo, J., Barbosa, L. V. & Del Gado, E. Elastically driven intermittent microscopic dynamics in soft solids. Nat. Commun. 8, 15846 (2017).
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).
Gao, J. & Frisken, B. Cross-linker-free n-isopropylacrylamide gel nanospheres. Langmuir 19, 5212–5216 (2003).
Scotti, A. et al. Hollow microgels squeezed in overcrowded environments. J. Chem. Phys. 148, 174903 (2018).
Grest, G. S. & Kremer, K. Molecular dynamics simulation for polymers in the presence of a heat bath. Phys. Rev. A 33, 3628 (1986).
Russo, J., Tartaglia, P. & Sciortino, F. Reversible gels of patchy particles: role of the valence. J. Chem. Phys. 131, 014504 (2009).
Rudnick, J. & Gaspari, G. The aspherity of random walks. J. Phys. A 19, L191–L193 (1986).
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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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 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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DOI: https://doi.org/10.1038/s41567-019-0480-1
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