Thermodynamics of the glassy state / Luca Leuzzi, Theo M. Nieuwenhuizen.

Format:

Book

Author/Creator:

Leuzzi, Luca, 1972-

Contributor:

Nieuwenhuizen, Theo M.

Series:

Series in condensed matter physics

Language:

English

Subjects (All):

Spin glasses.

Glass.

Physical Description:

xix, 344 pages : illustrations ; 25 cm.

Place of Publication:

New York : Taylor & Francis, [2008]

Summary:

Thermodynamics of the Glassy State presents a comprehensive account of the modern theory of glasses, starting from basic principles (thermodynamics) to the experimental analysis of one of the most important consequences of thermodynamics- Maxwell relations. After a brief introduction to general theoretical concepts and historical developments, the book thoroughly describes glassy phenomenology and the established theory. The core of the book surveys the crucial technique of two-temperature thermodynamics, explains the success of this method in resolving previously paradoxical problems in glasses, and presents exactly solvable models, a physically realistic approach to dynamics with advantages over more established mean field methods. The authors also tackle the potential energy landscape approach and discuss more detailed theories of glassy states, including mode coupling, avoided critical point, replica, and random first-order transition theories.

This reference lucidly explores recent theoretical advances in the thermodynamics of slowing-aging (glassy) systems. It details the general properties of glassy states while also demonstrating how these properties are present in specific models, enabling readers to thoroughly understand this fundamental yet challenging area of study. Features: Introduces the technique of two-temperature thermodynamics for the first time in book form, Presents the physically realistic approach of exactly solvable models, Devotes an entire chapter to the potential energy landscape approach, widely used in numerical simulations of computer glass models, Reviews recent developments in the theory of the glassy state, many of which are not found in existing books.

Contents:

1 Theory and phenomenology of glasses 15

1.1 Processes, timescales and transitions 15

1.1.1 Dynamical glass transition 17

1.1.2 Thermal glass transition 19

1.2 Strong and fragile glass formers 23

1.3 Aging 26

1.3.1 Time sector separation 28

1.4 Configurational entropy 29

1.4.1 Kauzmann paradox 30

1.4.2 Static phase transition and Kauzmann temperature 31

1.4.3 "Classic" versus "modern" configurational entropy 31

1.4.4 An intrinsically dynamic "state" function 33

1.5 Adam-Gibbs entropic theory 34

1.5.1 Absence of flow in cathedral glasses 37

1.6 Fragility index 38

1.7 Kovacs effect 39

2 Two temperature thermodynamics 43

2.1 Elements of thermodynamics 46

2.1.1 First law and second law 46

2.1.2 Clausius-Clapeyron relation 47

2.1.3 Maxwell relation 48

2.1.4 Keesom-Ehrenfest relations and Prigogine-Defay ratio 48

2.2 Fictive temperature 50

2.3 Two temperature thermodynamics 53

2.3.1 Two temperature thermodynamics for glassy systems 55

2.4 Laws of thermodynamics for off-equilibrium systems 56

2.4.1 Maxwell relation for aging systems 58

2.4.2 Generalized Clausius-Clapeyron relation 59

2.4.3 Keesom-Ehrenfest relations and Prigogine-Defay ratio out of equilibrium 60

2.5 Laws of thermodynamics for glassy magnets 64

2.6 Effective temperature in thermal cycles 65

2.7 Fluctuation formula and effective temperatures 70

2.8 Fluctuation and dissipation out of equilibrium 72

2.8.1 Fluctuation-dissipation ratio 74

2.8.2 Limits to the role of FDR as a temperature 81

2.9 Direct measurement of the effective temperature 83

2.A Asymptotic solution in nonlinear cooling 87

3 Exactly solvable models for the glassy state 89

3.1 Harmonic oscillator model 91

3.1.1 Analytically solvable Monte Carlo dynamics 92

3.1.2 Parallel Monte Carlo versus Langevin dynamics 96

3.2 Kinetic models with separation of timescales 99

3.2.1 Statics and phase space constraint 101

3.2.2 Parallel Monte Carlo dynamics of the HOSS model: equations of motion 104

3.2.3 Dynamics of the strong glass model 106

3.2.4 Dynamics of the fragile glass model 109

3.2.5 Adam-Gibbs relation in the HOSS model 115

3.3 Out-of-equilibrium thermodynamics 116

3.3.1 Quasi-static approach 116

3.3.2 Effective temperature from generalized laws 118

3.3.3 Dynamic transition rate and effective temperature 120

3.3.4 FDR and effective temperature 123

3.3.5 Heat flow of [alpha] processes 131

3.3.6 Effective temperature from a fluctuation formula 131

3.4 Below the Kauzmann transition 132

3.4.1 Instantaneous relaxation time 134

3.5 Kovacs effect: limits of two temperature thermodynamics 135

3.5.1 Analytical solution in the long-time regime 138

3.5.2 Effective temperature and effective field 140

3.6 Measuring effective temperature in HO models 142

3.6.1 Heat flux between off-equilibrium systems 144

3.7 Mode-dependent effective temperature 146

3.7.1 Quasi-static effective temperature 148

3.7.2 Mode-dependent fluctuation-dissipation ratio 149

3.7.3 Transition rate effective temperature 150

3.A HOSS equations of motion for one-time variables 152

3.A.1 Strong glass 152

3.A.2 Fragile glass 152

3.A.3 Analytic expressions for the Kovacs effect 157

3.B Monte Carlo integrals in one- and two-time dynamics 158

3.B.1 Coefficients of the two-time variables equations 160

4 Aging urn models 163

4.1 The backgammon model 166

4.1.1 Equilibrium thermodynamics 167

4.1.2 Dynamics 170

4.1.3 Adiabatic approximation and effective temperature 174

4.1.4 Entropic barriers and a microcanonic derivation of the equation of motion 178

4.1.5 Backgammon random walker 179

4.2 Two-time dynamics and FDR effective temperature 181

4.2.1 Effective temperature(s) in the backgammon model 184

4.3 A model for collective modes 185

4.3.1 Observables and equilibrium 187

4.3.2 Dynamics of the disordered backgammon model 190

4.3.3 Relaxational spectrum in equilibrium 196

4.3.4 Specific examples of continuous energy distribution 197

4.3.5 A method to determine the threshold energy scale 201

4.A Occupation probability density equations 203

4.B Ansatz for the adiabatic approximation 205

4.C Approach to equilibrium of occupation densities 207

4.D Probability distribution of proposed energy updates 208

5 Glassiness in a directed polymer model 211

5.1 The directed polymer model 212

5.1.1 Disordered situation and Lifshitz-Griffiths singularities 213

5.1.2 Static phase diagram 216

5.1.3 Dual view in temperature 218

5.2 Directed polymer dynamics 219

5.3 Cooling and heating setups 223

5.3.1 Poincare recurrence time 223

6 Potential energy landscape approach 225

6.1 Potential energy landscape 228

6.1.1 Steepest descent 229

6.1.2 Features of the PEL description borrowed from vitreous properties 231

6.1.3 Inter- and intra-basins transitions: scales separation 232

6.1.4 Inherent structures distribution: formal treatment 233

6.1.5 Harmonic approximation 236

6.2 Thermodynamics in supercooled liquids 237

6.2.1 Inherent structure pressure 237

6.2.2 Random energy model and Gaussian approximation 239

6.2.3 Equation of state 241

6.2.4 IS equation of State 243

6.3 The solid amorphous phase 244

6.3.1 PEL effective temperature from direct comparison to the aging dynamics 245

6.3.2 PEL effective temperature and pressure in the two temperature thermodynamic framework 246

6.3.3 The pressure in glasses 249

6.4 Fragility in the PEL 251

6.5 PEL approach to the random orthogonal model 253

6.5.1 Effective temperature in the ROM 254

6.6 PEL approach to the harmonic oscillator models 256

6.6.1 PEL effective temperature in the HOSS model 259

6.6.2 Quasi-static definition of IS effective temperature 261

6.A Many-body glassy models 264

6.A.1 Soft spheres 265

6.A.2 Lennard-Jones many-body interaction potential 266

6.A.3 Lewis-Wahnstrom model for orthoterphenyl 267

6.A.4 Simple point charge extended model for water 268

7 Theories of the glassy state 269

7.1 Mode-coupling theory 269

7.2 Replica theory for glasses with quenched disorder 274

7.2.1 The random energy model 275

7.2.2 The p-spin model 276

7.2.3 Complexity 279

7.2.4 Mean-field scenario 281

7.3 Glass models without quenched disorder: clone theory 283

7.3.1 Equilibrium thermodynamics of the cloned m-liquid 283

7.3.2 Analytic tools and specific behaviors in cloned glasses 285

7.3.3 Effective temperature for the cloned molecular liquid 287

7.4 Frustration limited domain theory 289

7.4.1 Geometric frustration 289

7.4.2 Avoided critical point 291

7.4.3 Critical assessment of the approach 294

7.4.4 Heuristic scaling arguments 297

7.5 Random first order transition theory 298

7.5.1 Adam-Gibbs theory, revisited 300

7.5.2 Entropic driven "nucleation" and mosaic state 301

7.5.3 Density functional for the RFOT theory 305

7.5.4 Beyond entropic driving I: droplet partition function 311

7.5.5 Beyond entropic driving II: library of local states 315.

Notes:

Includes bibliographical references (pages 319-338) and index.

ISBN:

9780750309974

0750309970

OCLC:

145732932