This book covers some fundamental aspects and frontiers in non-equilibrium physics and soft matter research. Apart from the basic knowledge on nonlinear statistic physics, dynamics, computer simulations, and main approaches and emerging systems in soft matter research, particular attention is devoted to new conceptual flexible functional materials and the enriching areas, such as silk meso-molecular materials, molecular gels, liquid crystals, flexible electronics and new types of catalysis, etc. One of the main characteristics of this book is to start with the structure formation dynamics and the correlation between the structures and macroscopic performance. This lays down the foundation for the mesoscopic materials design and functionalization. The book is intended for upper undergraduate students, graduate students, and researchers who are interested in soft matter researches. As one of main references, the basic principles and technologies of computer simulations and experimental methods adopted in soft matter research are also explained. Illustrations and tables are included in this book to improve the readability, and examples and exercises are added to help understanding.
Author(s): Xiang-Yang Liu
Series: Soft and Biological Matter
Publisher: Springer
Year: 2021
Language: English
Pages: 352
City: Cham
Preface
Contents
1 Introduction to Nonequilibrium Statistical Physics and Its Foundations
1.1 Prologue: The Realm of Theories and Measurements
1.2 Continuum Description
1.3 Brownian Motion: Fluctuations Reveal Atoms
1.3.1 Langevin Treatment
1.3.2 Exercise
1.3.3 Exercise
1.4 Fluctuation-Dissipation Theorem
1.4.1 Exercise: Derivation of Eq.(1.98)
1.4.2 Application: Johnson-Nyquist Noise
1.4.3 Recent Variations of Brownian Motion: Active Matter
1.4.4 Recent Variations of Brownian Motion: Detection of Gravitational Waves
1.5 Fluctuations Dissipation Relations
1.6 Particle Systems in Phase Space
1.6.1 Boltzmann Equation and H-Theorem
1.7 Local Thermodynamic Equilibrium
1.8 Linear Response
1.8.1 Modern Developments of Linear Response
1.8.2 Linear Response in Magnetic Field
1.9 Beyond Linearity: Anomalies and Fluctuation Relations
1.9.1 Transient and Steady State Fluctuation Relations
1.9.2 t-Mixing and a General Theory of Response
1.10 From Ergodic Theory to Big Data
1.11 Concluding Remarks
References
2 On the Foundational Principles of Statistical Mechanics
2.1 Statistical Laws
2.2 Canonical Ensemble
2.3 Microcanonical Ensemble
2.4 Phase Transition and Breaking of Ergodicity
2.5 Thermodynamic Limit and Supporting Set of Distribution
2.6 Analogue to Thermodynamics: Heat and Free Energy
2.7 Arrow of Time: Irreversibility
2.8 Time Evolution of the Distribution Function
References
3 Generalized Onsager Principle and It Applications
3.1 Introduction
3.2 Onsager Principle for Dissipative Systems
3.2.1 Constructive Onsager Principle
3.2.2 Onsager Principle Accounting for Inertia
3.2.3 Variational Onsager Principle
3.2.4 Onsager Principle in an Open System
3.2.5 Effect of External Forces
3.2.6 Extension of Onsager Principle to Spatially Inhomogeneous Systems
3.2.7 Lagrange Mechanics-A Complementary Formulation
3.3 Generalized Onsager Principle
3.4 Applications of the Generalized Onsager Principle
3.4.1 Dissipative Thermodynamical Models for Nonequilibrium Systems
3.4.2 Gross-Pitaevskii Equations
3.4.3 Generalized Hydrodynamic Theories
3.4.4 Kinetic Theory for Liquid Crystalline Polymer Solutions
3.5 Conclusion
References
4 An Introduction to Emergence Dynamics in Complex Systems
4.1 Introduction
4.2 Emergence: Research Paradigms
4.2.1 Entropy Analysis and Dissipative Structure
4.2.2 Slaving Principles and the Emergence of Order Parameters
4.2.3 Networks: Topology and Dynamics
4.3 Emergence of Rhythms
4.3.1 Biological Rhythms: An Introduction
4.3.2 The Dominant Phase-Advanced Driving (DPAD) Method
4.3.3 The Functional-Weight (FW) Approach
4.3.4 Self-sustained Oscillation in Excitable Networks
4.3.5 Sustained Oscillation in Gene Regulatory Networks
4.4 Synchronization: Cooperations of Rhythms
4.4.1 Synchrony: An Overview
4.4.2 Microdynamics of Synchronization
4.4.3 Kuramoto Model: Self-Consistency Approach
4.4.4 Order Parameter Dynamics: Equations of Motion
4.4.5 Emergence of Order Parameters
4.4.6 Synchronizations on Star Networks
4.5 Remarks
References
5 Basics of Molecular Modeling and Molecular Simulation
5.1 Molecular Simulation
5.1.1 Computational Physics: A Bridge Connecting Theories and Experiments
5.1.2 Molecular Simulations: Studying Physical Properties at the Molecular Level
5.2 First-Principles Calculations
5.2.1 Electronic Structure Methods
5.2.2 Density Functional Theory
5.3 Basic Concepts of Equilibrium Statistical Physics
5.3.1 Basic Concepts
5.3.2 Common Ensembles
5.3.3 Common Thermodynamic Variables
5.4 Molecular Modeling
5.4.1 Reduced Unit
5.4.2 Lennard-Jones Potential
5.4.3 Force Fields for Metals
5.4.4 Chemical and Biomolecular Force Fields
5.4.5 Coarse-Graining Methodology
5.5 Monte Carlo (MC) Simulation
5.5.1 Purpose
5.5.2 Importance Sampling
5.5.3 Metropolis Algorithm
5.6 Molecular Dynamics (MD) Simulation
5.6.1 Idea of Molecular Dynamics
5.6.2 MD Simulation and Sampling
5.7 Simple Data Analysis
5.7.1 Energy-Related Data
5.7.2 Correlation Coefficients
5.7.3 Structural Properties
5.7.4 Diffusion Coefficient
References
6 Cocoon Silk: From Mesoscopic Materials Design to Engineering Principles and Applications
6.1 Introduction
6.1.1 Silkworm Silk and Silk Fibroin (SF) Materials
6.1.2 Structural Factors Correlated to Macroscopic Properties
6.1.3 Scope of This Chapter
6.2 Silk Road: From Ancient Textiles to Smart Flexible Functional Materials
6.2.1 History and Life Cycle of Silkworms
6.2.2 Processing and Fabrication of Cocoon Silk and Various Forms of SF Materials
6.3 Hierarchical Mesoscopic Network Structure of SF Materials in Correlation with Macroscopic Performance
6.3.1 Primary (Level One) Structure of SF Materials
6.3.2 Secondary (Level Two) Structures of SF Materials
6.3.3 Tertiary (Level Three) Structures of SF Materials and Crystalline Binding Interaction
6.3.4 Level Four Structure of SF Materials: Fishnet-Like Crystallite Networks and Nanofibrils
6.3.5 Level Five Structure of SF Materials
6.3.6 Summary of Hierarchical Structure of SF Materials
6.4 Characterization Technologies
6.4.1 Structural Characterization Techniques
6.4.2 Imaging Techniques
6.5 Self-assembly Kinetic Pathways of Silk Materials
6.5.1 Key Mesoscopic Structural Elements: Crystallites, Crystal Networks, and Nanofibril Networks
6.5.2 Nucleation Mechanism
6.5.3 Experiments on SF Nucleation
6.5.4 Reconstruction and Meso-Functionalization of Silk Fibers
6.6 Conclusions and Perspectives
References
7 A Primer on Gels (with an Emphasis on Molecular Gels)
7.1 Introduction: General Classifications
7.2 A Short (Prejudiced) History of Gels
7.3 Molecular Gels and Approaches to Their Analyses
7.4 Making Molecular Gels
7.5 How Do Aggregation and Growth of Molecular Gelator Networks Occur?
7.6 Experimental Determination of What Is and Is Not a Gel
7.7 The Role of the Liquid Component
7.8 Organic Gelator Molecules and Their Assemblies. Starting from the Simplest Molecular Structures and Increasing the Complexity
7.8.1 n-Alkanes and Their Simple Derivatives
7.8.2 Some Tubule Assemblies of More Complex Alkane-Derived Surfactants
7.8.3 Some Tubule Assemblies of Steroidal Surfactants
7.9 Final Thoughts About the Scope and Intent of This Chapter
References
8 Fréedericksz-Like Positional Transition Triggered by An External Electric Field
8.1 Introduction
8.2 Fréedericksz Transition in NLC
8.3 Theoretical Modeling
8.4 Results and Discussions
8.4.1 Homeotropic Boundary Condition
8.4.2 Planar Boundary Condition
8.5 Conclusion
References
