600 likes | 756 Views
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
E N D
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).
Soft glassy materials Eric Weeks
Soft glassy materials Eric Weeks
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
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
Simulations (LJ) L. Berthier, PRE 2002
Dynamical length scale in 2D granular media Lechenault et al., EPL 2008 Keys et al., Nat. Phys. 2007
Confocal microscopy on colloidal HS Weeks et al. Science 00 Weeks et al., J. Phys. Cond. Mat 07 « »
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)
Temporally heterogeneous dynamics homogeneous
Temporally heterogeneous dynamics heterogeneous homogeneous
Temporally heterogeneous dynamics heterogeneous homogeneous
Dynamical susceptibility in glassy systems Supercooled liquid (Lennard-Jones) <Q(t)> Lacevic et al., PRE 2002 c4=N var[Q(t)]
c4 (t) ~ Dynamical susceptibility in glassy systems Nblob regions c4=N var[Q(t)] ~ N (1/Nblob) = N/Nblob
How can we measure c4? Time-resolved light scattering experiments (TRC)
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
lag t time tw Time Resolved Correlation 2-time correlation function Cipelletti et. Al JPCM 03, Duri et al. PRE 2005
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
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
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
A « model system »: shaving cream 3D foam (DWS) Mayer et al. PRL 2004
age dependence of c tw c (tw,t) 4 t Coarsening of the foam tw
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!
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
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
« Diluted » samples Brownian behavior
« Diluted » samples R/100 !! DWS probes dynamics on a length scale ll*/L ~ 10 – 35 nm << R L
Concentrated samples: slow dynamics Fast dynamics (phototube) Slow dynamics (CCD)
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
Average dynamics Relaxation timet0 ~ jc = 0.752
Average dynamics Stretching exponent b
Fluctuations of the dynamics: c j = 0.738
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
c* Fluctuations of the dynamics: c* vs j
Measurement time issue? Merolle et al., PNAS 2005
tseg tseg tseg tseg tseg tseg Measurement time issue? g2(t,t)-1 Does c*(tseg,j) depend on tseg ?
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
DWS and intermittent dynamics Inspired by Durian, Weitz & Pine (Science, 1991)
DWS and intermittent dynamics Inspired by Durian, Weitz & Pine (Science, 1991) Light is decorrelated x
DWS and intermittent dynamics Inspired by Durian, Weitz & Pine (Science, 1991) Light is decorrelated x
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
DWS and intermittent dynamics Inspired by Durian, Weitz & Pine (Science, 1991) Light is decorrelated x p = 1 « brownian » rearrangements p = 2 « ballistic » rearrangements
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 )
Simulations vs. experiments experiments simulations
Simulation parameters p = 1.65 supradiffusive motion x3 - grows continuously with j -very large!! Cell thickness!
Conclusions Dynamics heterogeneous Non-monotonic behavior of c*
Conclusions Dynamics heterogeneous Non-monotonic behavior of c* Competition between - increasing size of dynamically correlated regions
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
Thanks to… V. Trappe D. Weitz L. Berthier G. Biroli M. Cloître CNES Softcomp ACI IUF