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 Anatomy of cage formation in a two-dimensional glass-forming liquid


As a glass-forming liquid is cooled, the dynamics of its constituent particles changes from being liquid-like to more solid-like. The solidity of the resulting glassy material is believed to be due to a cage-formation process, whereby the motion of individual particles is increasingly constrained by neighbouring particles. This process begins at the temperature (or particle density) at which the glass-forming liquid first shows signs of glassy dynamics; however, the details of how the cages form remain unclear1,2,3,4. Here we study cage formation at the particle level in a two-dimensional colloidal suspension (a glass-forming liquid). We use focused lasers to perturb the suspension at the particle level and monitor the nonlinear dynamic response of the system using video microscopy. All observables that we consider respond non-monotonically as a function of the particle density, peaking at the density at which glassy dynamics is first observed. We identify this maximum response as being due to cage formation, quantified by the appearance of domains in which particles move in a cooperative manner. As the particle density increases further, these local domains become increasingly rigid and dominate the macroscale particle dynamics. This microscale rheological deformation approach demonstrates that cage formation in glass-forming liquids is directly related to the merging of such domains, and reveals the first step in the transformation of liquids to glassy materials1,5.

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Fig. 1: The experimental system and responses to local perturbations.
Fig. 2: Excitation properties are non-monotonic in packing density.
Fig. 3: Particle displacements for different packing fractions.

Data availability

The figures and videos that support the findings of this study are available at

Code availability

The code used is available from B.L.


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We thank L. Cipelletti and M. D. Ediger for discussions. This study was supported by the Korean Institute for Basic Science (project code IBS-R020-D1) and grant ANR-15-CE30-0003-02. W.K. is senior member of the Institut Universitaire de France.

Author information

Authors and Affiliations



B.L., W.K. and S.G. designed the research. B.L. and K.L. carried out the measurements. B.L. analysed the data. B.L., W.K. and S.G. wrote the paper.

Corresponding authors

Correspondence to Bo Li, Walter Kob or Steve Granick.

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Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature thanks George Petekidis, Eric Weeks and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Details of laser-beam setup.

a, Bright-field image of a sample under a four-point laser beam designed to allow parallel accumulation of large amounts of statistics in the same experiment. The illuminated spots are sufficiently distant that the excitations are independent. Scale bar, 12 μm. b, Displacement as a function of time for four typical particles with different distances to the centre of the laser beam (ϕ = 0.35). To show the direct effect of the laser, we chose particles that do not collide with others during the whole excitation event. Dashed lines are guides to the eye. c, d, Nmax (c) and Rg (d) as a function of distance between the beam centre and mass centre of the particle closest to the laser spot (ϕ = 0.60, A = 99 mW). e, Brightness intensity profile across the laser spot for two beam powers (see legend). The curve for A = 0 shows the noise of the signal in the absence of a beam. f, The half-width of the intensity profile as a function of A. The dashed line is a guide to the eye. g, Displacement of an isolated particle that has been hit by a laser pulse with intensity A and duration 0.5 s (ϕ = 0.32). The dashed line is a linear fit.

Extended Data Fig. 2 Static and dynamic properties of the quiescent system.

a, The radial distribution function g(r) for samples with different ϕ (0.45, 0.52, 0.57, 0.60, 0.65 and 0.73). Inset, height of the first peak of g(r) as a function of ϕ. b, Mean squared displacement Δ2 as a function of time t, for samples with different ϕ. c, The first (logarithmic) derivative of the mean square displacement as a function of t, for samples with different ϕ. d, The van Hove function for ϕ = 0.60 at different times (see also Supplementary Videos 24). e, Intermediate scattering function Fs for samples with different ϕ. The wavevector is q = 2.2 μm−1. f, The non-Gaussian parameter α2 as a function of t for samples with different ϕ.

Extended Data Fig. 3 Influence of laser-pulse duration on excitation pattern.

a, A change in τα (defined as the time at which Fs in Extended Data Fig. 2e decays to 1/e) by a factor of two (indicated by the horizontal blue dashed lines) corresponds to a substantial change in the corresponding packing fraction ϕ (indicated by the vertical red dashed lines). b, Size of an excitation as a function of ϕ, for two laser durations (A = 99 mW). c, Variance of the Nmax as a function of ϕ.

Extended Data Fig. 4 The non-monotonic response of the system is independent of the laser intensity.

a, The average excitation size as a function of A. Dotted lines are linear fits. b, The variance of the excitation size as a function of A. Dotted lines are guides to the eye. c, Three-dimensional plot of the excitation size as a function of ϕ and A. The colour represents the variance of the excitation size.

Extended Data Fig. 5 Excitation patterns for different laser intensities.

ac, Excitation patterns for A = 25 mW in a sample with ϕ = 0.58, 5 s after the laser has been turned off. The colour represents the displacement of the particles (see colour scale). The duration of the pulse was 0.5 s. The separation between two excitation events was around 20 s. Scale bars, 10 μm. df, Same as ac, but for A = 59 mW. The white crosses indicate the position of the laser spot.

Supplementary information

Supplementary Video 1

Femtosecond laser pulse. Video showing how a femtosecond laser pulse hits a particle in a colloidal sample and sets up an excitation.

Supplementary Video 2

Excitation below the onset packing fraction. Video showing the displacement field (left panel) after a laser pulse hits the sample (right panel). Packing fraction is 0.50.

Supplementary Video 3

Excitation at the onset packing fraction. Video showing the displacement field (left panel) after a laser pulse hits the sample (right panel). Packing fraction is 0.60.

Supplementary Video 4

Excitation above the onset packing fraction. Video showing the displacement field (left panel) after a laser pulse hits the sample (right panel). Packing fraction is 0.70.

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Li, B., Lou, K., Kob, W. et al.  Anatomy of cage formation in a two-dimensional glass-forming liquid. Nature 587, 225–229 (2020).

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