The microscopic role of deformation in the dynamics of soft colloids


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.

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.


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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).

Author information

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

Correspondence to Nicoletta Gnan or Emanuela Zaccarelli.

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The authors declare no competing interests.

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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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