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[资源] Principles of Soft-Matter Dynamics

Principles of Soft-Matter Dynamics-----Basic Theories, Non-invasive Methods,Mesoscopic Aspects
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Practical applications of soft-matter dynamics are of vital importance in material science, chemical engineering, biophysics and biotechnology, food processing, plastic industry, micro- and nano-system technology, and other technologies based on non-crystalline and non-glassy materials. Principles of Soft-Matter Dynamics. Basic Theories, Non-invasive Methods, Mesoscopic Aspects covers fundamental dynamic phenomena such as diffusion, relaxation, fluid dynamics, normal modes, order fluctuations, adsorption and wetting processes. It also elucidates the applications of the principles and of the methods referring to polymers, liquid crystals and other mesophases, membranes, amphiphilic systems, networks, and porous media including multiphase and multi-component materials, colloids, fine-particles, and emulsions. The book presents all formalisms, examines the basic concepts needed for applications of soft-matter science, and reviews non-invasive experimental techniques such as the multi-faceted realm of NMR methods, neutron and light quasi-elastic scattering, mechanical relaxation and dielectric broadband spectroscopy which are treated and compared on a common and consistent foundation. The standard concepts of dynamics in fluids, polymers, liquid crystals, colloids and adsorbates are comprehensively derived in a step-by-step manner. Principles and analogies common to diverse application fields are elucidated and theoretical and experimental aspects are supplemented by computational-physics considerations. Principles of Soft-Matter Dynamics. Basic Theories, Non-invasive Methods, Mesoscopic Aspects appeals to graduate and PhD students, post-docs, researchers, and industrial scientists alike.
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1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Correlation Functions as a Link Between Different
Experimental Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.1 Orientation Correlation Functions . . . . . . . . . . . . . . . . . . . 4
1.1.2 Dynamic Structure Factors . . . . . . . . . . . . . . . . . . . . . . . . 6
1.1.3 Exponential Correlation Functions . . . . . . . . . . . . . . . . . . 8
1.1.4 The Long-Tail Detectability Problem . . . . . . . . . . . . . . . . 9
1.2 Linear-Response and the Fluctuation-Dissipation Theorem . . . . . . 10
1.3 A Word on Classical and Quantum-Mechanical Treatments . . . . . 12
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2 Basic Phenomena and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1 Molecular and Particle Interactions on Length Scales
from A ° to mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.1 Coulomb Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.1.2 Van der Waals Attractions . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1.3 Repulsive Interaction and Total Potential . . . . . . . . . . . . . 27
2.1.4 Hydrogen Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.1.5 Hydrophobic Interaction as an Entropic Force . . . . . . . . . . 29
2.1.6 From Molecular to Interfacial (“Casimir”) Interactions . . . 30
2.1.7 Depletion Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.1.8 Charged Surfaces and the Electric Double Layer . . . . . . . . 39
2.2 Remarks on Conservative Forces and Microreversibility . . . . . . . . 44
2.3 Stress, Strain, and Shear Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.3.1 Stress and the Stress Tensor . . . . . . . . . . . . . . . . . . . . . . . 46
2.3.2 Strain and the Strain Tensor . . . . . . . . . . . . . . . . . . . . . . . 52
2.3.3 Elastic Moduli (Hookean Limit) . . . . . . . . . . . . . . . . . . . . 55
2.3.4 Viscosity and Shear Stress Tensor . . . . . . . . . . . . . . . . . . 60
2.4 From Newton’s Equation of Motion to the Langevin Equation . . . 65
2.4.1 Strategy for a Better Tractability . . . . . . . . . . . . . . . . . . . 67
2.4.2 Fluctuations of Intermolecular Forces . . . . . . . . . . . . . . . . 68
xi
2.4.3 Langevin Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
2.4.4 Velocity Correlation Function . . . . . . . . . . . . . . . . . . . . . 72
2.5 Brownian Motion, Self-Diffusion, Interdiffusion,
and Rotational Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
2.5.1 Diffusion Equations and Propagators . . . . . . . . . . . . . . . . 74
2.5.2 Classification of Normal and Anomalous Diffusion . . . . . . 78
2.5.3 Rotational Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
2.5.4 The Stokes/Einstein Relations . . . . . . . . . . . . . . . . . . . . . 84
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3 Non-invasive methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.1 Spin relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.1.1 General remarks and definitions . . . . . . . . . . . . . . . . . . . 91
3.1.2 Bloch equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.1.3 RF pulses, flip angle, and free-induction decay . . . . . . . . 100
3.1.4 Experiments for measuring spin relaxation times . . . . . . . 102
3.1.5 Bloch/Wangsness/Redfield theory of spin relaxation . . . . 117
3.1.6 Anderson/Weiss theory for transverse relaxation in the
presence of residual spin couplings . . . . . . . . . . . . . . . . . 155
3.1.7 A first example of correlation functions: The isotropic
rotational-diffusion model . . . . . . . . . . . . . . . . . . . . . . . 161
3.1.8 Quadrupole dips or peaks by cross-relaxation
from dipole to quadrupole nuclei . . . . . . . . . . . . . . . . . . 174
3.1.9 Translational diffusion as dipolar or scalar spin
relaxation mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . 175
3.2 Field-gradient NMR diffusometry . . . . . . . . . . . . . . . . . . . . . . . 177
3.2.1 The principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
3.2.2 Field-gradient diffusometry with Hahn echo
and stimulated-echo pulse sequences . . . . . . . . . . . . . . . 181
3.2.3 Spin echo attenuation by hydrodynamic dispersion . . . . . 190
3.3 NMR microscopy-based mapping techniques . . . . . . . . . . . . . . . 194
3.3.1 Spin-density diffusometry . . . . . . . . . . . . . . . . . . . . . . . 195
3.3.2 Mapping of self-diffusion coefficients . . . . . . . . . . . . . . . 202
3.3.3 Flow-velocity NMR mapping . . . . . . . . . . . . . . . . . . . . . 203
3.3.4 Flow-acceleration NMR mapping . . . . . . . . . . . . . . . . . . 205
3.3.5 Mapping of electric transport phenomena
in electrolyte solutions . . . . . . . . . . . . . . . . . . . . . . . . . . 206
3.3.6 Magnetization grid rotating-frame imaging
(MAGROFI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
3.4 Exchange NMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
3.4.1 Equation of motion for discrete spin environments . . . . . 215
3.4.2 HMM solutions in terms of eigenvalues . . . . . . . . . . . . . 218
3.4.3 Two-site exchange model . . . . . . . . . . . . . . . . . . . . . . . . 220
3.4.4 Two-dimensional exchange spectroscopy . . . . . . . . . . . . 222
3.4.5 Two-dimensional spin relaxation and diffusion
correlation maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
xii Contents
3.5 The dipolar-correlation effect . . . . . . . . . . . . . . . . . . . . . . . . . . 228
3.5.1 The residual dipolar coupling constant . . . . . . . . . . . . . . 230
3.5.2 Echo attenuation functions due to residual
dipolar couplings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
3.5.3 The dipolar-correlation quotient . . . . . . . . . . . . . . . . . . . 238
3.5.4 The phase-shift correlation functions . . . . . . . . . . . . . . . 239
3.6 Quasi-elastic neutron scattering . . . . . . . . . . . . . . . . . . . . . . . . . 242
3.6.1 Overview and terminology . . . . . . . . . . . . . . . . . . . . . . . 243
3.6.2 The experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
3.6.3 Theory of the double-differential cross-section . . . . . . . . 248
3.6.4 Coherent and incoherent scattering . . . . . . . . . . . . . . . . . 257
3.6.5 Probing translational diffusion of molecules
by incoherent scattering . . . . . . . . . . . . . . . . . . . . . . . . . 260
3.7 Dynamic light and X-ray scattering . . . . . . . . . . . . . . . . . . . . . . 262
3.7.1 The experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
3.7.2 Theory for dilute particle dispersions . . . . . . . . . . . . . . . 265
3.7.3 Derivation of the Siegert relation . . . . . . . . . . . . . . . . . . 269
3.8 Mechanical relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
3.8.1 Viscoelasticity and classification of experiments
probing it . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
3.8.2 Fundamental response functions for linear
viscoelasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
3.8.3 Step relaxation experiments . . . . . . . . . . . . . . . . . . . . . . 275
3.8.4 Periodic relaxation experiments . . . . . . . . . . . . . . . . . . . 277
3.9 Dielectric relaxation spectroscopy . . . . . . . . . . . . . . . . . . . . . . . 282
3.9.1 Some basic relations and definitions for stationary
electric fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
3.9.2 Time-varying electric fields . . . . . . . . . . . . . . . . . . . . . . 286
3.9.3 Isotropic rotational diffusion of uncorrelated
fluctuating dipoles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
3.9.4 Defect diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
3.10 Comparison and discussion of dynamic ranges . . . . . . . . . . . . . . 295
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
4 Fluid Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
4.1 Compressible and Incompressible Fluids . . . . . . . . . . . . . . . . . . 307
4.2 Lagrangian and Eulerian Description of Coherent Flow . . . . . . . 308
4.3 Total, Local, and Convective Acceleration . . . . . . . . . . . . . . . . . 309
4.4 Equations of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
4.4.1 Navier/Stokes Equation . . . . . . . . . . . . . . . . . . . . . . . . . 311
4.4.2 Euler Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
4.4.3 Bernoulli Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
4.4.4 Laplace Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316
4.5 Reynolds Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
4.6 Equation of Creeping Motion . . . . . . . . . . . . . . . . . . . . . . . . . . 318
4.7 Stokes’ Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
Contents xiii
4.8 Computational Fluid Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . 323
4.8.1 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 324
4.8.2 Principles of Numerical CFD Methods . . . . . . . . . . . . . . 330
4.9 Transport Through Pipes, Pores, and Percolation Clusters:
Theory, Simulations, and Experiments . . . . . . . . . . . . . . . . . . . . 334
4.9.1 Some Parameters Characterizing Porous Media . . . . . . . . 336
4.9.2 Laminar Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338
4.9.3 Hydrodynamic Dispersion in Porous Media . . . . . . . . . . . 344
4.9.4 Heat Conduction and Thermal Convection . . . . . . . . . . . 349
4.9.5 Electroosmotic Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 358
4.9.6 Ionic Currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370
5 Molecular Dynamics in Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
5.1 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
5.2 Microstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376
5.2.1 Chain End-to-End Distance . . . . . . . . . . . . . . . . . . . . . . . 378
5.2.2 From the Valence-Angle Chain to the Freely
Jointed Segment Chain . . . . . . . . . . . . . . . . . . . . . . . . . . 382
5.2.3 Random-Coil Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . 385
5.2.4 Worm-Like Chain Model and Persistence Length . . . . . . . 392
5.2.5 The Real-World Polymer, Excluded-Volume Effect,
and Y-Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395
5.3 Elastic Modules of Permanent Polymer Networks . . . . . . . . . . . . 401
5.4 Dynamic Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
5.4.1 Classification and Terminology . . . . . . . . . . . . . . . . . . . . 405
5.4.2 The Bead-and-Spring Model Chain . . . . . . . . . . . . . . . . . 411
5.4.3 Rouse Model (Freely Draining Polymer Chains) . . . . . . . . 416
5.4.4 The Renormalized Rouse Formalism (Entangled
Polymer Chains) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448
5.4.5 Harmonic Radial Tube Potential (Confined
Polymer Chains) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450
5.4.6 The Tube/Reptation Model . . . . . . . . . . . . . . . . . . . . . . . 468
5.4.7 Local Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488
5.4.8 Mesoscopic Confinement Effects on Polymer
Chain Dynamics (“Corset Effect”) . . . . . . . . . . . . . . . . . . 490
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495
6 Molecular and Collective Dynamics in Liquid Crystals
and Other Mesophases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499
6.1 Introductory Remarks: Collective Dynamics in Polymers
and Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499
6.2 Classification of Mesophase Order . . . . . . . . . . . . . . . . . . . . . . . 500
6.2.1 Ordering Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . 502
6.2.2 Structural Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503
6.2.3 Order Director and Order Parameter . . . . . . . . . . . . . . . . 504
6.2.4 Alignment in External Fields . . . . . . . . . . . . . . . . . . . . . 505
xiv Contents
6.3 Elasticity of Uniaxial Nematic Liquid Crystals . . . . . . . . . . . . . . 508
6.4 Order-Director Fluctuations in Nematic Liquid Crystals . . . . . . . 512
6.5 Spin–Lattice Relaxation Dispersion in Nematic
Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517
6.6 The Dipolar-Correlation Effect for Nematic Order-Director
Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523
6.7 Dynamic Light Scattering in Nematic Liquid Crystals . . . . . . . . 528
6.7.1 The Scattering Mechanism Dominating
in Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 528
6.7.2 Eigenmodes of Order-Director Fluctuations
for Different Frank Elastic Constants . . . . . . . . . . . . . . . 530
6.7.3 First- and Second-Order Correlation Functions . . . . . . . . 532
6.8 Spin Relaxation in Smectic Liquid Crystals and Lamellar
Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534
6.8.1 Collective Fluctuations in Smectic Liquid Crystals . . . . . 534
6.8.2 Distinction of Local and Collective Molecular
Motions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535
6.8.3 Local Motions in the Alkane Chain Phase
of Lipid Bilayers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537
6.8.4 Shape Fluctuations of Vesicles . . . . . . . . . . . . . . . . . . . . 539
6.9 Type D Mesophases of Poly(Dialkylsiloxanes) . . . . . . . . . . . . . . 545
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547
7 Dynamics at Fluid Solid Interfaces: Porous Media and Colloidal
Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549
7.1 Survey and Some Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . 549
7.1.1 Characterization of Pore Spaces . . . . . . . . . . . . . . . . . . . . 550
7.1.2 Adsorption Versus Restricted-Geometry Effects . . . . . . . . 552
7.1.3 Categories of Restricted-Geometry Effects
on Translational Diffusion . . . . . . . . . . . . . . . . . . . . . . . . 552
7.1.4 Rotational Versus Translational Diffusion . . . . . . . . . . . . . 553
7.1.5 Fluid Phases and the Intricacy of the Term “Exchange” . . . 554
7.2 Exchange Limits for Two-Phase Systems . . . . . . . . . . . . . . . . . . 555
7.2.1 Exchange Limits Relative to Measuring Time Scales . . . . . 556
7.2.2 Exchange Limits Relative to the Time Scale
of Orientation Correlation Functions . . . . . . . . . . . . . . . . . 557
7.2.3 Combined Limits for Spin Relaxation
in “Two-Phase/Fast-Exchange Systems” . . . . . . . . . . . . . . 560
7.3 Adsorption Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562
7.4 Translational Diffusion of Low-Molecular Fluids
Under Confinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565
7.4.1 Fluids in Saturated Mesoscopic Pore Spaces . . . . . . . . . . . 565
7.4.2 Translational Diffusion in the Adsorbed Phase . . . . . . . . . 570
7.4.3 Single-File Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576
7.4.4 Diffusion Enhanced by a Coexisting Vapor Phase . . . . . . . 577
Contents xv
7.5 Reorientational Dynamics in Surface-Dominated Systems . . . . . . 589
7.5.1 From Translational to Rotational Diffusion . . . . . . . . . . . . 589
7.5.2 Spin–Lattice Relaxation in Low-Molecular Solvents
Confined in Inorganic Porous Media . . . . . . . . . . . . . . . . . 590
7.5.3 Surface-Diffusion Formalism for Spin Relaxation
in Fluids in the Strong-Adsorption Case . . . . . . . . . . . . . . 593
7.5.4 A First Test Experiment for the Surface-Diffusion
Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 599
7.5.5 Spin Relaxation in Aqueous Protein Solutions
and Tissue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 600
7.5.6 Special Surface Topologies . . . . . . . . . . . . . . . . . . . . . . . 615
7.5.7 The NMR Flow-Relaxation Effect . . . . . . . . . . . . . . . . . . 627
7.5.8 Electron-Paramagnetic Surface Relaxation Sinks . . . . . . . . 633
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635
Glossary of Frequent Symbols, Units, Constants and Abbreviations . . . 639
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645

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