Dynamical heterogeneity at the jamming transition of concentrated colloids

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