Experimental and Computational Research on Cooperative Rearrangement in Glassy Systems Open Access

Du, Xin (2016)

Permanent URL: https://etd.library.emory.edu/concern/etds/xd07gs92m?locale=en
Published

Abstract

The study of the dynamics properties of the soft materials approaching jamming transition is very important for understanding the universal mechanism underlying the jamming transition. In this dissertation, we study the jamming transition from two aspects: the correlation between the cooperative dynamics of jamming system with the free energy landscape of the system and the correlation between the dynamic properties with the structural heterogeneity of the system.

In the simulation project, we study the free energy landscape of a simple model possessing some qualitative features of glass transition. The model consists of three soft Brownian disks confined in a circular confinement, in which there are two energy local minima and one transition state. The two energy local minima correspond to two inherent structures and the transition between the local minima involves cooperative rearrangement of the disks. If the circular region is large, the disks freely rearrange, but rearrangements are rarer for smaller system sizes. We directly measure a one-dimensional free energy landscape characterizing the dynamics. This landscape has two local minima, separated by a free energy barrier which governs the rearrangement rate. We study several different interaction potentials and demonstrate that the free energy barrier is composed of a potential energy barrier and an entropic barrier. The heights of both of these barriers depend on temperature and system size, demonstrating how non-Arrhenius behavior can arise close to the glass transition.

In experimental project, we study the jamming of a slowly evaporating quasi two-dimensional emulsion system. In this system, water slowly evaporates from an open edge of the chamber and, as a consequence, the packing fraction of oil droplets gradually increases. By means of microscopy, we track the dynamics of droplets and identify the droplet's outlines and geometric properties. By qualifying the structural heterogeneity based on the Voronoi Vector field [1], we find the correlation between the geometric response and mechanical response to the slow increase of packing fraction.

Table of Contents

Contents

Abstract Cover Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

Cover Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . .v

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x

Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii

1 Introduction 1

1.1 Soft Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Jamming Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 The Energy Landscapes of Glassy System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Energy barriers, entropy barriers, and non-Arrhenius behavior in a minimal glassy model 15

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2 The Model System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.3.1 Free energy landscapes . . . . . . . . . . . . . . . . . . . . . . 23

2.3.2 Dynamics and free energy barriers . . . . . . . . . . . . . . . . 25

2.3.3 Simple models for the transition state . . . . . . . . . . . . . . 32

2.3.4 Barriers: Energy and Entropy . . . . . . . . . . . . . . . . . . 36

2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3 Extensions of three-disk model 44

3.1 Mapping particles with soft interaction potentials onto hard particles

with an effective size . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.2 Entropic Barrier for Hard Disks . . . . . . . . . . . . . . . . . . . . . 48

3.3 Apply Forward Flux Sampling to Glassy Model System . . . . . . . . 51

3.3.1 Forward Flux Sampling . . . . . . . . . . . . . . . . . . . . . . 51

3.3.2 Optimized Interface Placement in Forward Flux Sampling . . . 54

3.3.3 Applying Forward Flux Sampling to Glassy Model System . . . 55

3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4 Rearrangements During Slow Compression of a Jammed 2-D Emulsion 62

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.3 Method of Voronoi Vector Field . . . . . . . . . . . . . . . . . . . . . 66

4.4 The Directionality of Droplets Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.5 The Magnitude of Droplet Displacement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 84

4.6 Evolution of Geometric and Dynamic Parameters in Jamming Systems . . . . . . . . . . . . . 87

4.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

4.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

5 Summary 94

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