Slow anomalous dynamics close to MCT higher order singularities. A numerical study of short-range attractive colloids. (and some additional comments) Francesco Sciortino Titolo ! UCGMG Capri, June 2003

In collaboration with ….. Giuseppe Foffi Piero Tartaglia Emanuela Zaccarelli Wolfgang Goetze, Thomas Voigtman, Mattias Sperl Kenneth Dawson collaboratori

riassunto Outline of the talk -The MCT predictions for SW (repetita juvant) -Experiments -Simulations A3, A4 ? Glass-Glass ? Hopping Phenomena ? Gels in SW ?

The MCT predictions for short-range attractive square well MCT predictions for short range attractive square-well hard-sphere glass (repulsive) Short-range attractive glass fluid Type B A3A3  Fluid-Glass on cooling and heating !! Controlled by  Fabbian et al PRE R1347 (1999) Bergenholtz and Fuchs, PRE (1999)

Depletion Interactions Cartoons Depletion Interaction: A Cartoon

Science Pham et al Fig 1 Glass samples Fluid samples MCT fluid- glass line Fluid-glass line from experiments Temperature

Berths PRL (no polymer-with molymer) Colloidal-Polymer Mixture with Re-entrant Glass Transition in a Depletion Interactions T. Eckert and E. Bartsch Phys.Rev. Lett (2002) HS (increasing  ) Adding short-range attraction T. Eckert and E. Bartsch

Barsh PRL (phi effect) Temperature

MCT IDEAL GLASS LINES (PY) - SQUARE WELL MODEL - CHANGING  PRE Role of the width  A3A3 A4A4 V(r)

Isodiffusivity Isodiffusivity curves (MD Binary Hard Spheres) Zaccarelli et al PRE 66, (2002).

Tracing the A4 point Tracing the A 4 point: Theory and Simulation   D   PY T MD  T PY PY PY + transformation FS et al, cond-mat/ PY-MCT overestimates ideal attractive glass T by a factor of 2

MSD logaritmico Slope 1

 q (t)=f q -h q [B (1) ln(t/  ) + B (2) q ln 2 (t/  )]. Phi(t) Same T and , different 

Phi hat  q (t  q (t)-f q )/h q ^

 X (t)=f X -h X [B (1) ln(t/  ) + B (2) X ln 2 (t/  )]. H(q)

Check List  Reentrance (glass-liquid-glass) (both experiments and simulations) √  A4 dynamics √ (simulation)  Glass-glass transition Check List

Glass glass theory low T high T t

Jumping into the glass aging Zaccarelli et al, cond-mat/

Glass glass The attractive glass is not stable ! low T high T Zaccarelli et al, cond-mat/

dfasdd Confronto tempi diversi

  Bond No-bond t

Phase diagram

Sq spinodal decomposition

A summary Nice model for theoretical and numerical simulation Very complex dynamics - benchmark for microscopic theories of super-cooled liquid and glasses (MCT does well!) Model for activated processes For the SW model, the gel line cannot be approached from equilibrium (what are the colloidal gels ? What is the interaction potential ?) A summary

Structural Arrest Transitions in Colloidal Systems with Short-Range Attractions Taormina, Italy, December A workshop organized by Sow-Hsin Chen (MIT) Francesco Mallamace (U of Messina) Francesco Sciortino (U of Rome La Sapienza) Purpose: To discuss, in depth, the recent progress on both the mode coupling theory predictions and their experimental tests on various aspects of structural arrest transitions in colloidal systems with short-range attractions. Pubblicita’ Advertisement

van Megen and S.M. Underwood Phys. Rev. Lett. 70, 2766 (1993) HS e MCT  (t) HS (slow) dynamics

MCT fq BMLJ SiO 2

HS Hard Spheres at  =0.58, the system freezes forming disordered aggregates. MCT transition  =51.6% 1.W. van Megen and P.N. Pusey Phys. Rev. A 43, 5429 (1991) 2.U. Bengtzelius et al. J. Phys. C 17, 5915 (1984) 3.W. van Megen and S.M. Underwood Phys. Rev. Lett. 70, 2766 (1993) Potential  V(r) r (No temperature, only density)

The mean square displacement (in the glass) The MSD in HS log(t) (0.1  ) 2 MSD

Non ergodicity parameters for the two glasses Wavevector dependence of the non ergodicity parameter (plateau) along the glass line Fabbian et al PRE R1347 (1999) Bergenholtz and Fuchs, PRE (1999)

Correlatori lungo la linea Density-density correlators along the iso-diffusivity locus

Non-ergodicity factor Non ergodicity parameter along the isodiffusivity curve from MD

Sub diffusive !  ~(0.1  ) 2 R2 lungo la linea

Volume Fraction Temperature Liquid Repulsive Glass Attractive Glass Gel ? Glass-glass transition Non-adsorbing -polymer concentration glass line Summary 2 (and open questions) ! Activated Processes ? Fig 2 of Natmat

Equations MCT ! Equazioni base della MCT

The cage effect (in HS) Explanation of the cage and analysis of correlation function Rattling in the cage Cage dynamics log(t)  (t) fqfq

Log(t) Mean squared displacement repulsive attractive (0.1  ) 2  Figure 1 di Natmat A model with two different localization length How does the system change from one (glass) to the other ?

What if …. Hard Spheres Potential Square-Well short range attractive Potential   Can the localization length be controlled in a different way ? What if we add a short-range attraction ? Attractive Glass   lowering T

Funzioni di correlazione MD simulation

Dati Thomas Giuseppe Comparing MD data and MCT predictions for binary HS See next talk by G. Foffi