‘Colloids in space’: recent work and outlook for the Milano and Montpellier Groups

1. ‘Colloids in space’: recent work and outlook for the Milano and Montpellier Groups G. Brambilla1, L. Cipelletti1, L. Berthier1, S. Buzzaccaro2, R. Piazza2 1L2C, Université Montpellier 2 and CNRS 2Politecnico di Milano V. Trappe Fribourg University

2. Outlook 1) Research in Montpellier/Milano : Slow dynamics and dynamical heterogeneity in soft glasses / jammed materials. 2) Space Proposal: Solidification of colloids in space 3) Foam - C

3. Dynamical heterogeneity is ubiquitous! Repulsive disks Granular matter Colloidal Hard Spheres Keys et al. Nat. Phys. 2007 Weeks et al. Science 2000 A. Widmer-Cooper Nat. Phys. 2008

4. CCD-based Dynamic Light Scattering sample diaphragm CCD

5. lag t time t Time Resolved Correlation (TRC) degree of correlationcI(t,t) = - 1 < Ip(t) Ip(t+t)>p < Ip(t)>p<Ip(t+t)>p Cipelletti et al. J. Phys:Condens. Matter 2003, Duri et al. Phys. Rev. E 2006

6. Average over t intensity correlation function g2(t) - 1 degree of correlationcI(t,t) = - 1 < Ip(t) Ip(t+t)>p < Ip(t)>p<Ip(t+t)>p Average dynamics g2(t) - 1 ~ f(t)2

7. Average over t intensity correlation function g2(t) - 1 degree of correlationcI(t,t) = - 1 < Ip(t) Ip(t+t)>p < Ip(t)>p<Ip(t+t)>p fixed t, vs.t fluctuations of the dynamics Average dynamics g2(t) - 1 ~ f(t)2 var[cI(t)] ~ c(t)

8. Homogeneous vs heterogeneous dynamics 10mm Brownian particles Intensity correlation function 100mm Gillette Comfort Glide Foam

9. Dynamical susceptibility Colloids close to rcp Supercooled liquid (Lennard-Jones) Lacevic et al., Phys. Rev. E 2002 Ballesta et al., Nature Physics 2008 • PVC in DOP • a ~ 5 µm • polidispertsity ~33% • jclose to rcp

10. Speckle Visibility Spectroscopy By the group of Doug Durian Speckel contrast cI(t,t = 0) = - 1 < Ip(t) Ip(t)>p < Ip(t)>p<Ip(t)>p • Dynamics on the time scale of the CCD exposure time • Pros: • “Light” algorithm (can be calculated on the fly) • Fast time scales (µsec – msec) • Cons: • Time delays larger than the exposure time are not accessible • Need to adjust laser power to probe different time scales • Different time scales require separated runs

11. sample object plane Dq Dq lens focal plane diaphragm image plane CCD Space-resolved DLS: Photon Correlation Imaging 2.3 mm Duri et al., Phys. Rev. Lett. 2009 q = 90° 1/q ~ 45 nm

12. Local, instantaneous dynamics: cI( t, t,r) < Ip(t) Ip(t+t)>p(r) cI(t, t , r) = - 1 < Ip(t)>p<Ip(t+t)>p(r) Note: <<cI(t, t , r)>t>r = g2(t)-1 [g2(t)-1] ~ f(t)2 2.3 mm

13. Dynamical Activity Maps: foam 1.0 cI 0.0 DAM movie: 2x real time, 6.15 x 4.69 mm2 , lag t = 40 msec Dynamical Activity Map no motion cI (r, tw,t) local rearrangement

14. 1.0 cI 0.0 DAM movie: 2x real time, 6.15 x 4.69 mm2 , lag t = 40 msec Dynamical Activity Maps: foam Dynamical Activity Map no motion cI (r, tw,t) local rearrangement

15. Random in time, correlated in space Sessoms et al., Soft Matter 2010

16. Strain field and µ-scopic dynamics Dynamics of actin/fascin networks strain field @ late stages of network formation J. Kaiser, O. Lielig,, G. Brambilla, LC, A. Bausch, Nature Materials 2011 age average strain field microcopic dynamics

17. Dynamic Activity Maps: gels Colloidal gel g2(t)-1~ exp[-(t/tr)1.5] tr = 5000 s cI (t0,tr/10 , r) Movie accelerated 500x 2 mm

18. Spatial correlation of the dynamics: x ~ system size in jammed soft matter! Maccarrone et al., Soft Matter 2010

19. Space experiments • ESA Proposal (2004): Solidification of Colloids in space: structure and dynamics of crystal, gel, and glassy phases • Piazza (Milano), Van Blaaderen, Kegel (Utrecht), Cipelletti (Montpellier) • Motivation for µ-g: • - Solid like structures -> gravitational stress transmitted over large distances. • Mixture of particles with different r. • Slow dynamics -> long experiments, ISS

20. Space experiments Original plan : investigate slow dynamics and DH in glassy colloidal systems (repulsive, attractive) Difficulty: only a limited set of samples will (hopefully) be flown Proposal: depletion force: a system with tunable (thermosensitive) attractive interactions

21.      DEPLETION EFFECTS IN COLLOIDS ADDING TO A SUSPENSION OF LARGE SPHERES SMALLER SPHERES (POLYMERS, SURFACTANT MICELLES)… FORCE VIEW SMALL SPHERES CANNOT ENTER HERE! Osmotic pressure unbalance yields an ATTRACTIVE force between colloids IF the depletant can be regarded as an IDEAL GAS AO POTENTIAL U = PVexc ENTROPY VIEW Large particles subtract free volume to the small ones (which DOMINATE ENTROPY) Small spheres gain entropy by PHASE SEGREGATION of the large colloids

22. DEPLETANT: Triton X100 Hydrophilic head ● A nonionic surfactant forming globular micelles in a wide conc. range Hydrophobic tail r ≈3.4 nm Aggregation number N ≈ 100 ● When added to a MFA suspension, first adsorbs on the particles, leading to colloid stabilization even in the presence of salt ● At higher surfactant concentration: MICELLAR DEPLETION

23. TO THE ROOTS OF GELATION GEL GELATION AS ARRESTED SPINODAL DECOMPOSITION Miller & Frenkel coex. line for AHS FLUID SOLID

24. BIRTH OF A GEL Quenching into the L-L gap: FAST SEDIMENTATION (hours vs. months!) A MUCH MORE EXPANDED PHASE

25. COMPRESSION MODULUS: A POWER LAW BEHAVIOR

26. A) COLLAPSE OF DEPLETION GELSG. Brambilla, S. Buzzaccaro, R. P., L. Berthier, and L. Cipelletti (to appear in PRL)

27. D) Collapse and ageing of a gel: macroscopic dynamics Timeevolutionof the gel height (FP ≈ 0.12,Uatt ≈ 4.5 kBT ) Spinodal decomposition and cluster formation Settling of a cluster phase (linear in time) Poroelastic restructuring of an arrested gel GELATION

28. THE POROELASTIC REGIME PICTURE: A FLUID (COUNTER)FLOWING THROUGH AN ELASTIC POROUS MEDIUM ● FORCE BALANCE: ELASTIC RESPONSE GRAVITATIONAL STRESS PERMEABILITY s = aF30.3 ● INPUT FOR NUMERICAL SIMULATIONS: EFFECTIVE COMPRESSIONAL MODULUS IN RESPONSE TO AN APPLIED STRESS s FROM STEADY-STATE PROFILE i) WITH k0 AND m CHOSEN TO FIT THE TIME-DEPENDENCE OF THE GEL HEIGHT ii)

29. VELOCIMETRY LOCAL SETTLING VELOCITY v(t) (AT VARIOUS SETTLING TIMES) ● THE VELOCITY PROFILE IS ALMOST LINEAR FOR ANY SETTLING TIME, EXCEPT IN THE UPPERMOST LAYER OF THE GEL. t =30 h ● A z-INDEPENDENT (BUT t-DEPENDENT) STRAIN RATE: t =80 h

30. Collapse and ageing of a gel: microscopic dynamics Local TRC correlation functions in the gel SAME decay time at all values of z (like for strain rate!) t1/e scales as e-1

31. B) CRITICAL DEPLETANTS(depletion vs. critical Casimir effect)S. Buzzaccaro, J. Colombo, A. Parola, and R. P.Phys. Rev. Lett. 105, 198301 (2010)

32. COLLOID PHASE SEPARATION IN CRITICAL MIXTURES (Beysens & Estève, 1985) Beysens and Esteve, 1985 SURFACE TRANSITIONS (CRITICAL WETTING) NOT NECESSARILY LINKED TO BULK SEPARATION ! Critical wetting layer ? CRITICAL CASIMIR EFFECT C. Bechinger & coworkers (2008): Fisher - De Gennes 1978 Dietrich & coworkers (1998) Universal scaling of the force between a colloidal particle immersed in a critical binary mixture and the container walls Casimir forces pop up also when fluctuations are thermal instead of quantum, e. g. close to L-L demixing. A “depletion” of critical fluctuations! TIRM measurements of forces between a silica plate and a polystyrene sphere dispersed in a critical liquid mixture.

33. Hydrophilic head DEPLETANT C12E8 - nonionic surfactant • Forms globular micelles in a wide conc. range • Micellar radius r ≈ 3.4 nm → q = r/R ≈ 0.04 • Adsorbs on MFA, leading to steric stabilization • MICELLAR DEPLETION at larger surfactant concentration Hydrophobic tail • PHASE SEPARATION WITH WATER BY RAISING T Globular Micelles T L-L coexistence ≈ 70°C LC r ≈3.4 nm EXPERIMENTAL RANGE Aggregation number N ≈ 100 ≈ 2% C12E8 concentration

34. MINIMUM SURFACTANT AMOUNT TO INDUCE PHASE SEPARATION vs. T C12E8/WATER COEXISTENCE GAP PHASE SEPARATED q-temperature STABLE

35. SEPARATION vs. OSMOTIC PRESSURE T - Tc ≈ 4°C: P has decreased by a factor of 200. Two orders of magnitude increase in depletion “efficiency”!

36. SEPARATION POINTS vs. x

37. BUT: ALMOST T-INDEPENDENT!

38. What we would need to use Foam C Levels of confinement to be checked Stirring capability Temperature control would enable us to span a wide range of attractive forces with one single sample. T up to ~70°C, actual range/accuracy to be checked with R. Piazza Long runs: moderate frame rate (down to 10 Hz), tens of tau spanning several decades -> image storage and post processing. ~1 Gb / run, post processing time ~ 10'. Ground tests on the setup!

39. Thanks! Collaborators: V. Trappe (Fribourg) Students: P. Ballesta, G. Brambilla, A. Duri, D. El Masri Postdocs: S. Maccarrone, M. Pierno Funding: CNES, ESA, Région Languedoc Roussillon, ANR, MIUR.