From Glass to Lorentz Gas

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From Glass to Lorentz Gas
Crossover of Slow Dynamics in Random Media
Kunimasa Miyazaki
Collaborators
Kang Kim and Shinji Saito (IMS)
(Japan-France 11/20/2008)
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OVERVIEW

• Introduction

1. Spatially /dynamically heterogeneous systems
2. Krakoviacks replica MCT

• Slow dynamics of fluids in random matrices

1. Type A to Type B transition
2. Dynamic heterogeneities
3. Re-entrant transition?

• Summary

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INTRODUCTION

• Slow dynamics in spatially/dynamically
  heterogeneous systems

Glasses

• Slow dynamics with kinetic arrest
• Spatially homogeneous but dynamically
• inhomogeneous

(Weeks, 2000)
Colloidal Gels

• Slow dynamics with kinetic arrest
• Spatially and/or dynamically inhomogeneous

(Lu, 2008)
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INTRODUCTION
Slow dynamics in spatially/dynamically
heterogeneous systems
Density
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INTRODUCTION
Slow dynamics in spatially/dynamically
heterogeneous systems
Type B Sudden appearance of 2 step relaxation
Type A Continuous and 1 step relaxation
Density
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INTRODUCTION
Slow dynamics in spatially/dynamically
heterogeneous systems
Type B Broad and high NEP escorted by
microscopic length scale
Type A Low NEP escorted by large length scale
Density
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INTRODUCTION
Slow dynamics in spatially/dynamically
heterogeneous systems
Dynamic Heterogeneities
Glass Dynamic origin
Gel Static origin
Density
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INTRODUCTION
Slow dynamics in spatially/dynamically
heterogeneous systems
Glasses

• Slow dynamics with kinetic arrest
• Spatially homogeneous but dynamically
• inhomogeneous

(Weeks, 2000)
Colloidal Gels

• Slow dynamics with kinetic arrest
• Spatially and/or dynamically inhomogeneous

(Lu, 2008)
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INTRODUCTION
Slow dynamics in spatially/dynamically
heterogeneous systems
Glasses

• Slow dynamics with kinetic arrest
• Spatially homogeneous but dynamically
• inhomogeneous

(Weeks, 2000)
Diffusing particles in random media

• Slow dynamics with kinetic arrest
• Spatially and/or dynamically inhomogeneous

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INTRODUCTION
Slow dynamics in spatially/dynamically
heterogeneous systems
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INTRODUCTION
Replica Mode Coupling Theory (Krakoviack, 2005,
2007)
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INTRODUCTION
Replica Mode Coupling Theory (Krakoviack, 2005,
2007)
Glass phase
Fluid phase
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INTRODUCTION
Replica Mode Coupling Theory (Krakoviack, 2005,
2007)
Correlation functions
Glass phase
Type B transition
Fluid phase
Type A transition
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INTRODUCTION
Replica Mode Coupling Theory (Krakoviack, 2005,
2007)
Non-Ergodic Parameters
Glass phase
Type B transition
Fluid phase
Type A transition
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INTRODUCTION
Replica Mode Coupling Theory (Krakoviack, 2005,
2007)
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INTRODUCTION
1. Type A-Type B transition exists?
2. Dynamic heterogeneities?
3. Re-entrant transition really exists?
Is this a good minimal model for more complex
heterogeneous systems such as gels?
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Slow Dynamics of Fluids in Random Matrices
MD simulation of soft binary and hard spheres
systems
3 dimension hard sphere system
Fluid particle density
Matrix particle density
Random matrix is made by quenching equilibrium
configurations
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Slow Dynamics of Fluids in Random Matrices
1.Type A to Type B transition
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Slow Dynamics of Fluids in Random Matrices
1. Type A to Type B transition Non-Ergodic
Parameters
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Slow Dynamics of Fluids in Random Matrices
2. Dynamic heterogeneities
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Slow Dynamics of Fluids in Random Matrices
2. Dynamic heterogeneities MCT analysis
Krakoviacks Replica MCT
F12 Schematic Model
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Slow Dynamics of Fluids in Random Matrices
2. Dynamic heterogeneities MCT analysis
for a schematic model
(Franz and Parisi (2000) and Biroli, Bouchaud,
KM, Reichman (2006))
System under perturbation given by 2 point
correlation
Linear response for 2-point correlation
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Slow Dynamics of Fluids in Random Matrices
2. Dynamic heterogeneities MCT analysis
Type A
Type B
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Slow Dynamics of Fluids in Random Matrices
3. Re-entrant behavior
Other particles kick out the caged particle?
(Krakoviack)
?
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Slow Dynamics of Fluids in Random Matrices
3. Re-entrant behavior
Other particles kick out the caged particle?
(Krakoviack)
?
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Summary
More Questions than Answers
1. How dymamic length scales cross over to static
ones?
( should be analyzed using
and MCT)
2. Re-entrant transition really exist??
3. This model is a good model for gelation?
(MCT description for gelation?)
4. At least, the model is a good test bench for
the study of An singularities
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