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Dynamical heterogeneity at the jamming transition of concentrated colloids

LCVN. Dynamical heterogeneity at the jamming transition of concentrated colloids. P. Ballesta 1 , A. Duri 1 , Luca Cipelletti 1,2 1 LCVN UMR 5587 Université Montpellier 2 and CNRS, France 2 Institut Universitaire de France. lucacip@lcvn.univ-montp2.fr. Heterogeneous dynamics. homogeneous.

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Dynamical heterogeneity at the jamming transition of concentrated colloids

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  1. LCVN Dynamical heterogeneity at the jamming transition of concentrated colloids P. Ballesta1, A. Duri1, Luca Cipelletti1,2 1LCVN UMR 5587 Université Montpellier 2 and CNRS, France 2Institut Universitaire de France lucacip@lcvn.univ-montp2.fr

  2. Heterogeneous dynamics homogeneous

  3. Heterogeneous dynamics heterogeneous homogeneous

  4. Heterogeneous dynamics heterogeneous homogeneous

  5. Dynamical susceptibility in glassy systems Supercooled liquid (Lennard-Jones) Lacevic et al., PRE 2002 c4~ var[Q(t)]

  6. Dynamical susceptibility in glassy systems N regions c4~ var[Q(t)] c4 dynamics spatially correlated

  7. Decreasing T Glotzer et al. c4 increases when decreasing T

  8. Outline • Measuring average dynamics and c4 in colloidal suspensions • c4 at very high j : surprising results! • A simple model of heterogeneous dynamics

  9. Experimental system & setup PVC xenospheres in DOP radius ~ 10 mm, polydisperse j = 64% – 75% Excluded volume interactions

  10. Experimental system & setup CCD-based (multispeckle) Diffusing Wave Spectroscopy CCD Camera Laser beam Change in speckle field mirrors change in sample configuration Probe d << Rparticle

  11. lag t time tw fixed tw, vs.t 2-time intensity correlation function g2(tw,t) - 1 Time Resolved Correlation degree of correlationcI(tw,t) = - 1 < Ip(tw) Ip(tw+t)>p < Ip(tw)>p<Ip(tw+t)>p

  12. 2-time intensity correlation function f = 66.4% Fit: g2(tw,t) ~ exp[-(t /ts (tw))p(tw)] • Initial regime: « simple aging » (ts ~ tw1.1 ± 0.1) • Crossover to stationary dynamics, large fluctuations of ts

  13. 2-time intensity correlation function f = 66.4% Fit: g2(tw,t) ~ exp[-(t/ts(tw))p(tw)] Average dynamics : < ts >tw , < p >tw

  14. Average dynamics vs j Average relaxation time

  15. Average dynamics vs j Average relaxation time Average stretching exponent

  16. lag t time tw fixed t, vs.tw fluctuations of the dynamics var(cI)(t) c (t ) Fluctuations from TRC data degree of correlationcI(tw,t) = - 1 < Ip(tw) Ip(tw+t)>p < Ip(tw)>p<Ip(tw+t)>p

  17. Fluctuations of the dynamics vs j j = 0.74 var(cI) c4 (dynamical susceptibility)

  18. Fluctuations of the dynamics vs j j = 0.74 var(cI) c4 (dynamical susceptibility) Max of var (cI)

  19. A simple model of intermittent dynamics…

  20. A simple model of intermittent dynamics… fully decorrelated r Durian, Weitz & Pine (Science, 1991)

  21. Fluctuations in the DWP model Random number of rearrangements g2(t,t) – 1 fluctuates r

  22. Fluctuations in the DWP model Random number of rearrangements g2(t,t) – 1 fluctuates r r increases fluctuations increase

  23. Fluctuations in the DWP model increasing r,j r r increases fluctuations increase

  24. Approaching jamming… partially decorrelated r partially decorrelated

  25. Approaching jamming… Correlation after n events r Probability of n events during t

  26. Approaching jamming… r Poisson distribution:

  27. Approaching jamming… r Poisson distribution: Random change of phase Correlated change of phase

  28. Approaching jamming… r Poisson distribution: Random change of phase Correlated change of phase

  29. Approaching jamming… r Poisson distribution: b»1.5

  30. Average dynamics increasing j decreasing sf2 increasing j

  31. Fluctuations r Moderate j : large sf2 few events large flucutations Near jamming : small sf2 many events small flucutations

  32. Fluctuations increasing j decreasing sf2

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

  34. Conclusions Dynamics heterogeneous Non-monotonic behavior of c* Competition between increasing size of dynamically correlated regions and decreasing effectiveness of rearrangements

  35. Conclusions Dynamics heterogeneous Non-monotonic behavior of c* Competition between increasing size of dynamically correlated regions and decreasing effectiveness of rearrangements Dynamical heterogeneity dictated by the number of rearrangements needed to decorrelate

  36. A further test… Single scattering, colloidal fractal gel (Agnès Duri)

  37. sf2 ~q2d 2look at different q! A further test…

  38. sf2 ~q2d 2look at different q! A further test…

  39. sf2 ~q2d 2look at different q! A further test…

  40. Fluctuations of the dynamics vs j (1/2) St. dev. of stretching exponent St. dev. of relaxation time

  41. Average dynamics vs j Average relaxation time

  42. Dynamical hetereogeneity in glassy systems Supercooled liquid (Lennard-Jones) Glotzer et al., J. Chem. Phys. 2000 c4 increases when approaching Tg

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

  44. Conclusions Dynamics heterogeneous Non-monotonic behavior of c* Many localized, highly effective rearrangements

  45. Conclusions Dynamics heterogeneous Non-monotonic behavior of c* Many localized, highly effective rearrangements Many extended, poorly effective rearrangements

  46. Conclusions Dynamics heterogeneous Non-monotonic behavior of c* Many localized, highly effective rearrangements Many extended, poorly effective rearrangements Few extended, quite effective rearrangements General behavior

  47. lag t time tw Time Resolved Correlation degree of correlationcI(tw,t) = - 1 < Ip(tw) Ip(tw+t)>p < Ip(tw)>p<Ip(tw+t)>p

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