‘Colloids in space’: recent work and outlook for the Milano and Montpellier Groups G. Brambilla 1, L. Cipelletti 1, L. Berthier 1, S. Buzzaccaro 2, R. Piazza 2 1 L2C, Université Montpellier 2 and CNRS 2 Politecnico di Milano V. Trappe Fribourg University

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

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

CCD-based Dynamic Light Scattering diaphragm sample CCD

Time Resolved Correlation (TRC) time t lag  degree of correlation c I (t,  ) = - 1 p p p Cipelletti et al. J. Phys:Condens. Matter 2003, Duri et al. Phys. Rev. E 2006

intensity correlation function g 2 (  1 Average over t degree of correlation c I (t,  ) = - 1 p p p Average dynamics g 2 (  1 ~ f(  ) 2

intensity correlation function g 2 (  1 Average over t degree of correlation c I (t,  ) = - 1 p p p fixed , vs. t fluctuations of the dynamics Average dynamics g 2 (  1 ~ f(  ) 2 var[c I (  )] ~  (  )

10  m Homogeneous vs heterogeneous dynamics 100  m Gillette Comfort Glide Foam Brownian particles Intensity correlation function

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

Speckle Visibility Spectroscopy By the group of Doug Durian Speckel contrast c I (t,  ) = - 1 p p 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

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

2.3 mm Local, instantaneous dynamics: c I ( t, ,  r) p(r) p p(r) c I (t, , r) = - 1 Note: t > r = g 2 (  )-1 [g 2 (  )-1] ~ f(  ) 2

DAM movie: 2x real time, 6.15 x 4.69 mm 2, lag  = 40 msec Dynamical Activity Maps: foam cIcI Dynamical Activity Map c I (r, t w,  ) local rearrangement no motion

DAM movie: 2x real time, 6.15 x 4.69 mm 2, lag  = 40 msec cIcI Dynamical Activity Map c I (r, t w,  ) local rearrangement no motion Dynamical Activity Maps: foam

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

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

Dynamic Activity Maps: gels Colloidal gel g 2 (  )-1~ exp[-(  /  r ) 1.5 ]  r = 5000 s c I (t 0,  r /10, r) Movie accelerated 500x 2 mm

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

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 . - Slow dynamics -> long experiments, ISS

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

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

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

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

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

COMPRESSION MODULUS: A POWER LAW BEHAVIOR

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

D) Collapse and ageing of a gel: macroscopic dynamics Time evolution of the gel height (  P ≈ 0.12,U att ≈ 4.5 k B T ) Spinodal decomposition and cluster formation Settling of a cluster phase (linear in time) GELATION Poroelastic restructuring of an arrested gel

THE POROELASTIC REGIME PICTURE: A FLUID (COUNTER)FLOWING THROUGH AN ELASTIC POROUS MEDIUM ● FORCE BALANCE: PERMEABILITY GRAVITATIONAL STRESS ELASTIC RESPONSE ● INPUT FOR NUMERICAL SIMULATIONS: EFFECTIVE COMPRESSIONAL MODULUS IN RESPONSE TO AN APPLIED STRESS  FROM STEADY-STATE PROFILE  a   i)i) WITH  0 AND m CHOSEN TO FIT THE TIME-DEPENDENCE OF THE GEL HEIGHT ii)

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

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!)  1/e scales as  -1

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

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

EXPERIMENTAL RANGE 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 DEPLETANT C 12 E 8 - nonionic surfactant Hydrophilic head Hydrophobic tail C 12 E 8 concentration T ≈ 70°C ≈ 2% L-L coexistence LC r ≈3.4 nm Aggregation number N ≈ 100 Globular Micelles PHASE SEPARATION WITH WATER BY RAISING T

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

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

SEPARATION POINTS vs. 

BUT: ALMOST T-INDEPENDENT!

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!

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.