Molecular Relaxation in Liquids

ISBN : 9780199863327

Biman Bagchi
336 ページ
161 x 237 mm

This book brings together many different relaxation phenomena in liquids under a common umbrella and provides a unified view of apparently diverse phenomena. It aligns recent experimental results obtained with modern techniques with recent theoretical developments. Such close interaction between experiment and theory in this area goes back to the works of Einstein, Smoluchowski, Kramers' and de Gennes. Development of ultrafast laser spectroscopy recently allowed study of various relaxation processes directly in the time domain, with time scales going down to picosecond (ps) and femtosecond (fs) time scales. This was a remarkable advance because many of the fundamental chemical processes occur precisely in this range and was inaccessible before the 1980s. Since then, an enormous wealth of information has been generated by many groups around the world, who have discovered many interesting phenomena that has fueled further growth in this field. As emphasized throughout the book, the seemingly different phenomena studied in this area are often closely related at a fundamental level. Biman Bagchi explains why relatively small although fairly sophisticated theoretical tools have been successful in explaining a wealth of experimental data at a semi-phenomenological level.


Chapter 1. Basic Concepts
1.1 Introduction
1.2 Response Functions and Fluctuations
1.3 Time Correlation Functions
1.4 Linear Response Theory
1.5 Fluctuation-Dissipation Theorem
1.6 Diffusion, Friction and Viscosity
Chapter 2. Phenomenological Description of Relaxation in Liquids
2.1 Introduction
2.2 Langevin Equation
2.3 Fokker-Planck Equation
2.4 Smoluchowski Equation
2.5 Master Equations
2.6 The Special Case of Harmonic Potential
Chapter 3. Density and Momentum Relaxation in Liquids
3.1 Introduction
3.2 Hydrodynamics at Large Length Scales
3.2.1 Rayleigh-Brillouin Spectrum
3.3 Hydrodynamic Relation Self-diffusion Coefficient and Viscosity
3.4 Slow Dynamics at Large Wavenumbers: de Gennes Narrowing
3.5 Extended Hydrodynamics: Dynamics at Intermediate Length Scale
3.6 Mode Coupling Theory
Chapter 4. Relationship between Theory and Experiment
4.1 Introduction
4.2 Dynamic Light Scattering: Probe of Density Fluctuation at Long Length Scales
4.3 Magnetic Resonance Experiments: Probe of Single Particle Dynamics
4.4 Kerr Relaxation
4.5 Dielectric Relaxation
4.6 Fluorescence Depolarization
4.7 Solvation Dynamics (Time Dependent Fluorescence Stokes Shift)
4.8 Neutron Scattering: Coherent and Incoherent
4.9 Raman Lineshape Measurements
4.10 Coherent Anti-Stokes Raman Scattering (CARS)
4.11 Echo Techniques
4.12 Ultrafast Chemical Reactions
4.13 Fluorescence Quenching
4.14 Two-dimensional Infrared (2D IR) Spectroscopy
4.15 Single Molecule Spectroscopy
Chapter 5. Orientational and Dielectric Relaxation
5.1 Introduction
5.2 Equilibrium and Time-Dependent Orientational Correlation Functions
5.3 Relationship with Experimental Observables
5.4 Molecular Hydrodynamic Description of Orientational Motion
5.4.1 The Equations of Motion
5.4.2 Limiting Situations
5.5 Markovian Theory of Collective Orientational Relaxation: Berne Treatment
5.5.1 Generalized Smoluchowski Equation Description
5.5.2 Solution by Spherical Harmonic Expansion
5.5.3 Relaxation of Longitudinal and Transverse Components
5.5.4 Molecular Theory of Dielectric Relaxation
5.5.5 Hidden Role of Translational Motion in Orientational Relaxation
5.5.6 Orientational de Gennes Narrowing at Intermediate Wave Numbers
5.5.7 Reduction to the Continuum Limit
5.6 Memory Effects in Orientational Relaxation
5.7 Relationship between Macroscopic and Microscopic Orientational Relaxations
5.8 The Special Case of Orientational Relaxation of Water
Chapter 6. Solvation Dynamics in Dipolar Liquids
6.1 Introduction
6.2 Physical Concepts and Measurement
6.2.1 Measuring Ultrafast, Sub-100 fs Decay
6.3 Phenomenological Theories: Continuum Model Descriptions
6.3.1 Homogeneous Dielectric Models
6.3.2 Inhomogeneous Dielectric Models
6.3.3 Dynamic Exchange Model
6.4 Experimental Results: A Chronological Overview
6.4.1 Discovery of Multi-exponential Solvation Dynamics: Phase-I (1980-1990)
6.4.2 Discovery of Sub-ps Ultrafast Solvation Dynamics: Phase-II (1990-2000)
6.4.3 Solvation Dynamics in Complex Systems: Phase III (2000 - )
6.5 Microscopic Theories
6.5.1 Molecular Hydrodynamics Description
6.5.2 Polarization and Dielectric Relaxation of Pure Liquid Effects of Translational Diffusion in Solvation Dynamics
6.6 Simple Idealized Models
6.6.1 Overdamped Solvation: Brownian Dipolar Lattice
6.6.2 Underdamped Solvation: Stockmayer Liquid
6.7 Solvation Dynamics in Water, Acetonitrile and Methanol Revisited
6.7.1 The Sub 100 fs Ultrafast Component: Microscopic Origin
6.8 Effects of Solvation on Chemical Processes in the Solution Phase
6.8.1 Limiting Ionic Conductivity of Electrolyte Solutions: Control of a Slow Phenomenon by Ultrafast Dynamics
6.8.2 Effects of Ultrafast Solvation in Electron Transfer Reactions
6.8.3 Non-equilibrium Solvation Effects in Chemical Reaction Strong Solvent Forces Weak Solvent Forces
6.9 Solvation Dynamics in Several Related Systems
6.9.1 Solvation in Aqueous Electrolyte Solutions
6.9.2 Dynamics of Electron Solvation
6.9.3 Solvation Dynamics in Super-Critical Fluids
6.9.4 Nonpolar Solvation Dynamics
6.10 Computer Simulation Studies: Simple and Complex Systems
Chapter 7. Activated Barrier Crossing Dynamics in Liquids
7.1 Introduction
7.2 Microscopic Aspects
7.2.1 Stochastic Models: Understanding from Eigenvalue Analysis
7.2.2 Validity of a Rate Law Description: Role of Macroscopic Fluctuations
7.2.3 Time Correlation Function Approach: Separation of Transient Behavior from Rate Law
7.3 Transition State Theory
7.4 Frictional Effects on Barrier Crossing Rate in Solution: Kramers' Theory
7.4.1 Low Friction Limit
7.4.2 Limitations of Kramers' Theory
7.4.3 Comparison of Kramers' Theory with Experiments
7.4.4 Comparison of Kramers' Theory with Computer Simulations
7.5 Memory Effects in Chemical Reactions: Grote-Hynes Generalization of Kramers' Theory
7.5.1 Frequency Dependence of Friction: General Aspects Frequency Dependent Friction from Hydrodynamics Frequency Dependent Friction from Mode Coupling Theory
7.5.2 Comparison of Grote-Hynes Theory with Experiments and Computer Simulations
7.6 Variational Transition State Theory
7.7 Multidimensional Reaction Surface
7.7.1 Multidimensional Kramers' Theory
7.8 Transition Path Sampling
7.9 Quantum Transition State Theory
Chapter 8. Barrierless Reactions in Solutions
8.1 Introduction
8.2 Standard Models of Barrierless Reactions
8.2.1 Exactly Solvable Models for Photochemical Reactions Oster-Nishijima Model Staircase Model Pinhole Sink Model
8.2.2 Approximate Solutions for Realistic Models Delta Function Sink Gaussian Sink
8.3 Inertial Effects in Barrierless Reactions: Viscosity Turnover of Rate
8.4 Memory Effects in Barrierless Reactions
8.5 Main Features of Barrierless Chemical Reactions
8.5.1 Excitation Wavelength Dependence
8.5.2 Negative Activation Energy
8.6 Multidimensional Potential Energy Surface
8.7 Analysis of Experimental Results
8.7.1 Photoisomerization and Ground State Potential Energy Surface
8.7.2 Decay Dynamics of Rhodopsin and Isorhodopsin
8.7.3 Conflicting Crystal Violet Isomerization Mechanism
Chapter 9. Dynamical disorder, Geometric Bottlenecks and Diffusion Controlled Bimolecular Reactions
9.1 Introduction
9.2 Passage through Geometric Bottlenecks
9.2.1 Diffusion in a Two Dimensional Periodic Channel
9.2.2 Diffusion in a Random Lorentz Gas
9.3 Dynamical Disorder
9.4 Diffusion over a Rugged Energy Landscape
9.5 Diffusion Controlled Bimolecular Reactions
Chapter 10. Electron Transfer Reactions
10.1 Introduction
10.2 Classification of Electron Transfer Reactions
10.2.1 Classification of Electron Transfer Reactions Based on Ligand Participation
10.2.2 Classification Based on Interactions between Reactant and Product Potential Energy Surfaces
10.3 Marcus Theory
10.3.1 Reaction Coordinate
10.3.2 Free Energy Surfaces: Force Constant of Polarization Fluctuation
10.3.3 Derivation of The Electron Transfer Reaction Rate
10.3.4 Experimental Verification Of Marcus Theory
10.4 Dynamical Solvent Effects on Electron Transfer Reactions (One Dimensional Descriptions)
10.5 Role of Vibrational Modes in Weakening Solvent Dependence
10.5.1 Role of Classical Intramolecular Vibrational Modes: Sumi-Marcus Theory
10.5.2 Role of High-Frequency Vibration Modes
10.5.3 Hybrid Model of Electron Transfer Reactions: Crossover from Solvent to Vibrational Control
10.6 Theoretical Formulation of Multi-Dimensional Electron Transfer
10.7 Effects of Ultrafast Solvation on Electron Transfer Reactions
10.7.1 Absence of Significant Dynamic Solvent Effects on ETR in Water, Acetonitrile & Methanol
Chapter 11. Forster Resonance Energy Transfer
11.1 Introduction
11.2 A Brief Historical Perspective
11.3 Derivation of Forster Expression
11.3.1 Emission (or, Fluorescence) Spectrum
11.3.2 Absorption Spectrum
11.3.3 The Final Expression of Forster
11.4 Applications of Forster Theory in Chemistry, Biology and Material Science
11.4.1 FRET Based Glucose Sensor
11.4.2 FRET and Macromolecular Dynamics
11.4.3 FRET and Single Molecule Spectroscopy
11.4.4 FRET and Conjugated Polymers
11.5 Beyond Forster Formalism
11.5.1 Orientation Factor
11.5.2 Point Dipole Approximation
11.5.3 Optically Dark States
Chapter 12. Vibrational Energy Relaxation
12.1 Introduction
12.2 Isolated Binary Collision (IBC) Model
12.3 Landau-Teller Expression: The Classical Limit
12.4 Weak Coupling Model: Time Correlation Function Representation of Transition Probability
12.5 Vibrational Relaxation at High Frequency: Quantum Effects
12.6 Experimental Studies of Vibrational Energy Relaxation
12.7 Computer Simulation Studies of Vibrational Energy Relaxation
12.7.1 Vibrational Energy Relaxation of Water
12.7.2 Vibrational Energy Relaxation in Liquid Oxygen and Nitrogen
12.8 Interference Effects on Vibrational Energy Relaxation on a Three Level Systems: Breakdown of the Rate Equation Description
12.9 Vibrational Life Time Dynamics in Supercritical Fluids
Chapter 13. Vibrational Phase Relaxation
13.1 Introduction
13.2 Kubo-Oxtoby Theory of Vibrational Lineshapes
13.3 Homogeneous vs. Inhomogeneous Linewidths
13.4 Relative Role of Attractive and Repulsive Forces
13.5 Vibration-Rotation Coupling
13.6 Experimental Results of Vibrational Phase Relaxation
13.6.1 Semi-Quantitative Aspects of Dephasing Rates in Solution
13.6.2 Sub-Quadratic Quantum Number Dependence
13.7 Vibrational Dephasing Near Gas-Liquid Critical Point
13.8 Multidimensional IR Spectroscopy
Chapter 14. Epilogue


Biman Bagchi is Professor at the Indian Institute of Science in Bangalore, India.