1. 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

2. Heterogeneous dynamics homogeneous

3. Heterogeneous dynamics homogeneous heterogeneous

4. Heterogeneous dynamics homogeneous heterogeneous

5. Dynamical susceptibility in glassy systems Supercooled liquid (Lennard-Jones) Lacevic et al., PRE 2002  4  var[Q(t)]

6. Dynamical susceptibility in glassy systems  4  var[Q(t)]  4 dynamics spatially correlated N regions

7.  4 increases when decreasing T Glotzer et al. Decreasing T

8. Outline Measuring average dynamics and  4 in colloidal suspensions  4 at very high  : surprising results! A simple model of heterogeneous dynamics

9. Experimental system & setup PVC xenospheres in DOP radius ~ 10  m, polydisperse  = 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  << R particle

11. Time Resolved Correlation time t w lag  degree of correlation c I (t w,  ) = - 1 p p p 2-time intensity correlation function g 2 (t w,  1 fixed t w, vs. 

12. 2-time intensity correlation function Initial regime: « simple aging » (  s ~ t w 1.1  0.1 ) Crossover to stationary dynamics, large fluctuations of  s  = 66.4% Fit: g 2 (t w,  exp[-(  /  s (t w )) p(tw) ]

13. 2-time intensity correlation function  = 66.4% Fit: g 2 (t w,  exp[-(  /  s (t w )) p(tw) ] Average dynamics : tw, tw

14. Average dynamics vs  Average relaxation time

15. Average dynamics vs  Average relaxation timeAverage stretching exponent

16. fixed , vs. t w fluctuations of the dynamics var(c I )(  )  Fluctuations from TRC data time t w lag  degree of correlation c I (t w,  ) = - 1 p p p

17. Fluctuations of the dynamics vs  var(c I )  4 (dynamical susceptibility)  = 0.74

18. Fluctuations of the dynamics vs  var(c I )  4 (dynamical susceptibility) Max of var (c I )  = 0.74

19. A simple model of intermittent dynamics…

20. r Durian, Weitz & Pine (Science, 1991) fully decorrelated

21. Fluctuations in the DWP model r Random number of rearrangements g 2 (t,  ) – 1 fluctuates

22. Fluctuations in the DWP model r Random number of rearrangements g 2 (t,  ) – 1 fluctuates r increases fluctuations increase

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

24. Approaching jamming… r partially decorrelated

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

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:   1.5

30. Average dynamics increasing  decreasing   2 increasing 

31. Fluctuations r Near jamming : small   2 many events small flucutations Moderate  : large   2 few events large flucutations

32. Fluctuations increasing  decreasing   2

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

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

35. Conclusions Dynamics heterogeneous Non-monotonic behavior of  * 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. A further test…   2  q 2  2  look at different q!

38. A further test…   2  q 2  2  look at different q!

39. A further test…   2  q 2  2  look at different q!

40. Fluctuations of the dynamics vs   St. dev. of relaxation time St. dev. of stretching exponent

41. Average dynamics vs  Average relaxation time

42. Dynamical hetereogeneity in glassy systems Supercooled liquid (Lennard-Jones) Glotzer et al., J. Chem. Phys. 2000  4 increases when approaching T g

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

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

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

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

47. Time Resolved Correlation time t w lag  degree of correlation c I (t w,  ) = - 1 p p p