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Unexpected drop of dynamical heterogeneities in colloidal suspensions approaching the jamming transition

Unexpected drop of dynamical heterogeneities in colloidal suspensions approaching the jamming transition. Luca Cipelletti 1,2 , Pierre Ballesta 1,3 , Agnès Duri 1,4 1 LCVN Université Montpellier 2 and CNRS, France 2 Institut Universitaire de France 3 SUPA, University of Edinburgh

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Unexpected drop of dynamical heterogeneities in colloidal suspensions approaching the jamming transition

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  1. Unexpected drop of dynamical heterogeneities in colloidal suspensions approaching the jamming transition Luca Cipelletti1,2, Pierre Ballesta1,3, Agnès Duri1,4 1LCVN Université Montpellier 2 and CNRS, France 2Institut Universitaire de France 3SUPA, University of Edinburgh 4Desy, Hamburg P. Ballesta, A. Duri, and L. Cipelletti, Nature Physics 4, 550 (2008).

  2. Soft glassy materials Eric Weeks

  3. Soft glassy materials Eric Weeks

  4. Outline • What are dynamical heterogeneities ? • Why should we care about DH ? • How can we measure DH ? • Shaving cream: a model system for DH • Colloids: DH(very) close to jamming

  5. What quantities should we measure? Space and time-resolved correlation functions f(t,t+t,r) or particle displacement • Simulations (« far »  from Tg!) • Granular systems (2D, athermal, see Dauchot’s talk) • (Confocal) microscopy on colloidal systems

  6. Simulations (LJ) L. Berthier, PRE 2002

  7. Dynamical length scale in 2D granular media Lechenault et al., EPL 2008 Keys et al., Nat. Phys. 2007

  8. Confocal microscopy on colloidal HS Weeks et al. Science 00 Weeks et al., J. Phys. Cond. Mat 07 «  »

  9. What quantities should we measure? Space- and time-resolved correlation functions f(t,t+t,r) or particle displacement • Simulations (far  from Tg!) • Granular systems (2D, athermal) • (Confocal) microscopy on colloidal systems • ( stringent requirements on particles (size, optical mismatch…), difficult close to jamming) Time-resolved correlation functions f(t,t+t) (no space resolution)

  10. Temporally heterogeneous dynamics homogeneous

  11. Temporally heterogeneous dynamics heterogeneous homogeneous

  12. Temporally heterogeneous dynamics heterogeneous homogeneous

  13. Dynamical susceptibility in glassy systems Supercooled liquid (Lennard-Jones) <Q(t)> Lacevic et al., PRE 2002 c4=N var[Q(t)]

  14. c4 (t) ~ Dynamical susceptibility in glassy systems Nblob regions c4=N var[Q(t)] ~ N (1/Nblob) = N/Nblob

  15. How can we measure c4? Time-resolved light scattering experiments (TRC)

  16. Experimental setup CCD-based (multispeckle) Diffusing Wave Spectroscopy CCD Camera Laser beam Random walk w/ step l* Change in speckle field mirrors change in sample configuration

  17. lag t time tw Time Resolved Correlation 2-time correlation function Cipelletti et. Al JPCM 03, Duri et al. PRE 2005

  18. Average over tw ‘dynamical susceptibility’ c4(t ) intensity correlation function g2(t) - 1 fixed t, vs.tw fluctuations of the dynamics g2(tw,t) tw (sec) Average dynamics var(g2)(t) g2(t) - 1

  19. Outline • What are dynamical heterogeneities ? • Why should we care about DH ? • How can we measure DH ? • Shaving cream: a model system for DH • Colloids: DH (very) close to jamming

  20. A « model system »: shaving cream D.J. Durian, D.A. Weitz, D.J. Pine (1991) Science 252, 686 g2-1 = fraction of pathsnot rearranged x

  21. A « model system »: shaving cream 3D foam (DWS) Mayer et al. PRL 2004

  22. age dependence of c tw c (tw,t) 4 t Coarsening of the foam tw

  23. Scaling of c during coarsening 4 c (tw,t)/l*3(cm-3) Mayer et al. PRL 2004 4 cNblob 2<G>(tw)t Less bubbles more fluctuations!

  24. Outline • What are dynamical heterogeneities ? • Why should we care about DH ? • How can we measure DH ? • Shaving cream: a model system for DH • Colloids: DH(very) close to jamming

  25. Experimental system • PVC xenospheres in DOP • radius R ~ 5 mm • Polydisperse (~ 33%) • Brownian • Excluded volume interactions • j = 64% – 75% (close to jamming) • L = 2 mm • l* = 200 mm

  26. « Diluted » samples Brownian behavior

  27. « Diluted » samples R/100 !! DWS probes dynamics on a length scale ll*/L ~ 10 – 35 nm << R L

  28. Concentrated samples: slow dynamics Fast dynamics (phototube) Slow dynamics (CCD)

  29. 2-time intensity correlation function f = 66.4% t0 (sec) Fit: g2(tw,tw+t) - 1 = aexp[-(t/t0)b] • Initial regime: « simple aging » (t0 ~ tw1.1 ± 0.1) • Crossover to stationary dynamics, large fluctuations of ts

  30. Average dynamics Relaxation timet0 ~ jc = 0.752

  31. Average dynamics Stretching exponent b

  32. Fluctuations of the dynamics: c j = 0.738

  33. c vs c4: different normalization ~ correlation volume In our experiments: No N factor • N is not known precisely • Need model to extract correlation volume x3 from c

  34. c* Fluctuations of the dynamics: c* vs j

  35. Measurement time issue? Merolle et al., PNAS 2005

  36. tseg tseg tseg tseg tseg tseg Measurement time issue? g2(t,t)-1 Does c*(tseg,j) depend on tseg ?

  37. Not a measurement time issue !

  38. Proposed physical mechanism Competition between : Growth of x on approaching jc Smaller displacement associated with each rearrangement event (tigther packing) Nblobc* More events c* required to relax system

  39. DWS and intermittent dynamics Inspired by Durian, Weitz & Pine (Science, 1991)

  40. DWS and intermittent dynamics Inspired by Durian, Weitz & Pine (Science, 1991) Light is decorrelated x

  41. DWS and intermittent dynamics Inspired by Durian, Weitz & Pine (Science, 1991) Light is decorrelated x

  42. DWS and intermittent dynamics Inspired by Durian, Weitz & Pine (Science, 1991) Light is decorrelated x Number of events between t and t +t Mean squared change of phase for 1 event

  43. DWS and intermittent dynamics Inspired by Durian, Weitz & Pine (Science, 1991) Light is decorrelated x p = 1 « brownian » rearrangements p = 2 « ballistic » rearrangements

  44. Simulations • Photon paths as random walks on a 3D cubic lattice • Lattice parameter = l*, match cell dimensions • Random rearrangement events of size x3 • Calculate with x • Parameters : • p(use one single p for all j) • x3 • s2f (we expect s2f as j jc )

  45. Simulations vs. experiments experiments simulations

  46. Simulation parameters p = 1.65 supradiffusive motion x3 - grows continuously with j -very large!! Cell thickness!

  47. Conclusions Dynamics heterogeneous Non-monotonic behavior of c*

  48. Conclusions Dynamics heterogeneous Non-monotonic behavior of c* Competition between - increasing size of dynamically correlated regions

  49. Conclusions Dynamics heterogeneous Non-monotonic behavior of c* Competition between - increasing size of dynamically correlated regions - decreasing effectiveness of rearrangements Dynamical heterogeneity dictated by the number of rearrangements needed to relax the system on the probed length scale

  50. Thanks to… V. Trappe D. Weitz L. Berthier G. Biroli M. Cloître CNES Softcomp ACI IUF

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