Molecular Relaxation in Liquids

Hardcover | April 12, 2012

byBiman Bagchi

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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 interactionbetween 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 occurprecisely 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 asemi-phenomenological level.

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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 interactionbetween experiment and theory in this area goes b...

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

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Format:HardcoverDimensions:272 pages, 9.25 × 6.12 × 0.98 inPublished:April 12, 2012Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199863326

ISBN - 13:9780199863327

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Table of Contents

1. Basic Concepts1.1 Introduction1.2 Response Functions and Fluctuations1.3 Time Correlation Functions1.4 Linear Response Theory1.5 Fluctuation-Dissipation Theorem1.6 Diffusion, Friction and Viscosity2. Phenomenological Description of Relaxation in Liquids2.1 Introduction2.2 Langevin Equation2.3 Fokker-Planck Equation2.4 Smoluchowski Equation2.5 Master Equations2.6 The Special Case of Harmonic Potential3. Density and Momentum Relaxation in Liquids3.1 Introduction3.2 Hydrodynamics at Large Length Scales3.2.1 Rayleigh-Brillouin Spectrum3.3 Hydrodynamic Relation Self-diffusion Coefficient and Viscosity3.4 Slow Dynamics at Large Wavenumbers: de Gennes Narrowing3.5 Extended Hydrodynamics: Dynamics at Intermediate Length Scale3.6 Mode Coupling Theory4. Relationship between Theory and Experiment4.1 Introduction4.2 Dynamic Light Scattering: Probe of Density Fluctuation at Long Length Scales4.3 Magnetic Resonance Experiments: Probe of Single Particle Dynamics4.4 Kerr Relaxation4.5 Dielectric Relaxation4.6 Fluorescence Depolarization4.7 Solvation Dynamics (Time Dependent Fluorescence Stokes Shift)4.8 Neutron Scattering: Coherent and Incoherent4.9 Raman Lineshape Measurements4.10 Coherent Anti-Stokes Raman Scattering (CARS)4.11 Echo Techniques4.12 Ultrafast Chemical Reactions4.13 Fluorescence Quenching4.14 Two-dimensional Infrared (2D IR) Spectroscopy4.15 Single Molecule Spectroscopy5. Orientational and Dielectric Relaxation5.1 Introduction5.2 Equilibrium and Time-Dependent Orientational Correlation Functions5.3 Relationship with Experimental Observables5.4 Molecular Hydrodynamic Description of Orientational Motion5.4.1 The Equations of Motion5.4.2 Limiting Situations5.5 Markovian Theory of Collective Orientational Relaxation: Berne Treatment5.5.1 Generalized Smoluchowski Equation Description5.5.2 Solution by Spherical Harmonic Expansion5.5.3 Relaxation of Longitudinal and Transverse Components5.5.4 Molecular Theory of Dielectric Relaxation5.5.5 Hidden Role of Translational Motion in Orientational Relaxation5.5.6 Orientational de Gennes Narrowing at Intermediate Wave Numbers5.5.7 Reduction to the Continuum Limit5.6 Memory Effects in Orientational Relaxation5.7 Relationship between Macroscopic and Microscopic Orientational Relaxations5.8 The Special Case of Orientational Relaxation of Water6. Solvation Dynamics in Dipolar Liquids6.1 Introduction6.2 Physical Concepts and Measurement6.2.1 Measuring Ultrafast, Sub-100 fs Decay6.3 Phenomenological Theories: Continuum Model Descriptions6.3.1 Homogeneous Dielectric Models6.3.2 Inhomogeneous Dielectric Models6.3.3 Dynamic Exchange Model6.4 Experimental Results: A Chronological Overview6.4.1 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 Theories6.5.1 Molecular Hydrodynamics Description6.5.2 Polarization and Dielectric Relaxation of Pure Liquid6.5.2.1 Effects of Translational Diffusion in Solvation Dynamics6.6 Simple Idealized Models6.6.1 Overdamped Solvation: Brownian Dipolar Lattice6.6.2 Underdamped Solvation: Stockmayer Liquid6.7 Solvation Dynamics in Water, Acetonitrile and Methanol Revisited6.7.1 The Sub 100 fs Ultrafast Component: Microscopic Origin6.8 Effects of Solvation on Chemical Processes in the Solution Phase6.8.1 Limiting Ionic Conductivity of Electrolyte Solutions: Control of a Slow Phenomenon by Ultrafast Dynamics6.8.2 Effects of Ultrafast Solvation in Electron Transfer Reactions6.8.3 Non-equilibrium Solvation Effects in Chemical Reaction6.8.3.1 Strong Solvent Forces6.8.3.2 Weak Solvent Forces6.9 Solvation Dynamics in Several Related Systems6.9.1 Solvation in Aqueous Electrolyte Solutions6.9.2 Dynamics of Electron Solvation6.9.3 Solvation Dynamics in Super-Critical Fluids6.9.4 Nonpolar Solvation Dynamics6.10 Computer Simulation Studies: Simple and Complex Systems7. Activated Barrier Crossing Dynamics in Liquids7.1 Introduction7.2 Microscopic Aspects7.2.1 Stochastic Models: Understanding from Eigenvalue Analysis7.2.2 Validity of a Rate Law Description: Role of Macroscopic Fluctuations7.2.3 Time Correlation Function Approach: Separation of Transient Behavior from Rate Law7.3 Transition State Theory7.4 Frictional Effects on Barrier Crossing Rate in Solution: Kramers' Theory7.4.1 Low Friction Limit7.4.2 Limitations of Kramers' Theory7.4.3 Comparison of Kramers' Theory with Experiments7.4.4 Comparison of Kramers' Theory with Computer Simulations7.5 Memory Effects in Chemical Reactions: Grote-Hynes Generalization of Kramers' Theory7.5.1 Frequency Dependence of Friction: General Aspects7.5.1.1 Frequency Dependent Friction from Hydrodynamics7.5.1.2 Frequency Dependent Friction from Mode Coupling Theory7.5.2 Comparison of Grote-Hynes Theory with Experiments and Computer Simulations7.6 Variational Transition State Theory7.7 Multidimensional Reaction Surface7.7.1 Multidimensional Kramers' Theory7.8 Transition Path Sampling7.9 Quantum Transition State TheoryAppendix8. Barrierless Reactions in Solutions8.1 Introduction8.2 Standard Models of Barrierless Reactions8.2.1 Exactly Solvable Models for Photochemical Reactions8.2.1.1 Oster-Nishijima Model8.2.1.2 Staircase Model8.2.1.3 Pinhole Sink Model8.2.2 Approximate Solutions for Realistic Models8.2.2.1 Delta Function Sink8.2.2.2 Gaussian Sink8.3 Inertial Effects in Barrierless Reactions: Viscosity Turnover of Rate8.4 Memory Effects in Barrierless Reactions8.5 Main Features of Barrierless Chemical Reactions8.5.1 Excitation Wavelength Dependence8.5.2 Negative Activation Energy8.6 Multidimensional Potential Energy Surface8.7 Analysis of Experimental Results8.7.1 Photoisomerization and Ground State Potential Energy Surface8.7.2 Decay Dynamics of Rhodopsin and Isorhodopsin8.7.3 Conflicting Crystal Violet Isomerization Mechanism9. Dynamical disorder, Geometric Bottlenecks and Diffusion Controlled Bimolecular Reactions9.1 Introduction9.2 Passage through Geometric Bottlenecks9.2.1 Diffusion in a Two Dimensional Periodic Channel9.2.2 Diffusion in a Random Lorentz Gas9.3 Dynamical Disorder9.4 Diffusion over a Rugged Energy Landscape9.5 Diffusion Controlled Bimolecular Reactions10. Electron Transfer Reactions10.1 Introduction10.2 Classification of Electron Transfer Reactions10.2.1 Classification of Electron Transfer Reactions Based on Ligand Participation10.2.2 Classification Based on Interactions between Reactant and Product Potential Energy Surfaces10.3 Marcus Theory10.3.1 Reaction Coordinate10.3.2 Free Energy Surfaces: Force Constant of Polarization Fluctuation10.3.3 Derivation of The Electron Transfer Reaction Rate10.3.4 Experimental Verification Of Marcus Theory10.4 Dynamical Solvent Effects on Electron Transfer Reactions (One Dimensional Descriptions)10.5 Role of Vibrational Modes in Weakening Solvent Dependence10.5.1 Role of Classical Intramolecular Vibrational Modes: Sumi-Marcus Theory10.5.2 Role of High-Frequency Vibration Modes10.5.3 Hybrid Model of Electron Transfer Reactions: Crossover from Solvent to Vibrational Control10.6 Theoretical Formulation of Multi-Dimensional Electron Transfer10.7 Effects of Ultrafast Solvation on Electron Transfer Reactions10.7.1 Absence of Significant Dynamic Solvent Effects on ETR in Water, Acetonitrile and MethanolAppendix11. FUrster Resonance Energy Transfer11.1 Introduction11.2 A Brief Historical Perspective11.3 Derivation of Frster Expression11.3.1 Emission (or, Fluorescence) Spectrum11.3.2 Absorption Spectrum11.3.3 The Final Expression of Forster11.4 Applications of Frster Theory in Chemistry, Biology and Material Science11.4.1 FRET Based Glucose Sensor11.4.2 FRET and Macromolecular Dynamics11.4.3 FRET and Single Molecule Spectroscopy11.4.4 FRET and Conjugated Polymers11.5 Beyond F"rster Formalism11.5.1 Orientation Factor11.5.2 Point Dipole Approximation11.5.3 Optically Dark States12. Vibrational Energy Relaxation12.1 Introduction12.2 Isolated Binary Collision (IBC) Model12.3 Landau-Teller Expression: The Classical Limit12.4 Weak Coupling Model: Time Correlation Function Representation of Transition Probability12.5 Vibrational Relaxation at High Frequency: Quantum Effects12.6 Experimental Studies of Vibrational Energy Relaxation12.7 Computer Simulation Studies of Vibrational Energy Relaxation12.7.1 Vibrational Energy Relaxation of Water12.7.2 Vibrational Energy Relaxation in Liquid Oxygen and Nitrogen12.8 Interference Effects on Vibrational Energy Relaxation on a Three Level Systems: Breakdown of the Rate Equation Description12.9 Vibrational Life Time Dynamics in Supercritical Fluids13. Vibrational Phase Relaxation13.1 Introduction13.2 Kubo-Oxtoby Theory of Vibrational Lineshapes13.3 Homogeneous vs. Inhomogeneous Linewidths13.4 Relative Role of Attractive and Repulsive Forces13.5 Vibration-Rotation Coupling13.6 Experimental Results of Vibrational Phase Relaxation13.6.1 Semi-Quantitative Aspects of Dephasing Rates in Solution13.6.2 Sub-Quadratic Quantum Number Dependence13.7 Vibrational Dephasing Near Gas-Liquid Critical Point13.8 Multidimensional IR Spectroscopy14. Epilogue