Verfügbarkeit: Translational dynamics and magnetic resonance

Translational dynamics and magnetic resonance: principles of pulsed gradient spin echo NMR

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Bibliographische Detailangaben
Beteilige Person:	Callaghan, Paul T. 1947-2012 (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Oxford Oxford Univ. Press 2014
Ausgabe:	1. publ. in paperback
Schlagwörter:	Spin-Echo-Verfahren PFG-NMR-Spektroskopie Magnetische Kernresonanz
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027298981&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XVII, 547 S. graph. Darst.
ISBN:	9780198700821 9780199556984 0198700822

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Datensatz im Suchindex

DE-BY-TUM_call_number	1002 PHY 517f 2014 A 4956
DE-BY-TUM_katkey	2026348
DE-BY-TUM_location	10
DE-BY-TUM_media_number	040008230513
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adam_text	Contents я 1 Thermal processes and diffusion 1 1.1 Boltzmarm, Einstein, and molecules 1 1.2 Statistical physics and ensembles 2 1.2.1 Temperature and entropy 2 1.2.2 The Boltzmann distribution and partition function 7 1.2.3 Partition function, free energy, and entropy of an ideal monatomic gas 8 1.2.4 Ensembles and averages 10 1.2.5 Fluctuations, ergodicity, and the autocorrelation function 11 1.3 Thermal energy and self-diffusion 13 1.3.1 Fick s law 13 1.3.2 Brownian motion: the Einstein derivation 14 1.3.3 The probabilistic description 15 1.3.4 Relationship of diffusion to velocity autocorrelation function 20 1.3.5 The diffusion tensor 21 1.3.6 The Smoluchowski equation 22 1.3.7 The Langevin equation 22 1.3.8 Correlation and the fluctuating force 24 1.3.9 Ornstein-Uhlenbeck process 26 1.3.10 Diffusion in a harmonic potential 26 References 27 2 Flow and dispersion 29 2.1 Flow 30 2.1.1 Eulerian and Lagrangian descriptions 30 2.1.2 Substantive derivative and fluid dynamics 32 2.1.3 Navier-Stokes, inertia, and the Reynolds number 33 2.1.4 Stress and strain tensors 34 2.1.5 Navier-Stokes solutions and lattice Boltzmann 36 2.1.6 Conditional probability and average propagators for flow 39 2.2 Non-Newtonian fluids and viscoelasticity 41 2.2.1 Strain fields used in rheology 42 2.2.2 Linear viscoelasticity 44 2.2.3 Non-linear viscoelasticity 47 2.3 Dispersion 49 2.3.1 Stationary random flow and pseudo-diffusion 49 χ Contents 2.3.2 Porous medium characteristics 50 2.3.3 The dispersion tensor 53 2.3.4 Taylor dispersion in pipe flow 58 2.3.5 The velocity autocorrelation function and dispersion spectrum 60 2.3.6 Non-local dispersion 61 References 63 3 Quantum description of nuclear ensembles 65 3.1 Quantum mechanics and nuclear spin 66 3.1.1 Four key ideas in quantum mechanics 67 3.1.2 Representation of angular momentum 71 3.2 Spin ensembles and the density matrix 77 3.2.1 Spin-1 ensembles 79 3.2.2 Density matrix properties 81 3.2.3 Evolution and the quantum Liouville equation 82 3.2.4 Pure states, mixed states and quantum coherence 82 3.3 Tensor bases for the density matrix 83 3.3.1 Liouville space for spin-^ 83 3.3.2 Liouville space for I > 85 3.3.3 Product operator Liouville space for two coupled spin-^ nuclei 87 3.3.4 Spherical tensors 89 3.4 The spin Hamiltonian 94 3.4.1 The ¿-spin Hamiltonian 95 3.4.2 The Hamiltonian in terms of tensor products 96 3.4.3 Precession diagrams for I = 1/2 and 1 = 1 98 3.4.4 Spherical tensor precession for coupled spin-! 100 3.5 The thermal equilibrium density matrix 100 3.5.1 The Boltzmann form of the density matrix 100 3.5.2 Nuclear spins in thermal equilibrium — the high temperature approximation 101 3.5.3 Higher terms in the expansion—breakdown of the high temperature approximation 103 3.5.4 A closer look at thermal equilibrium 103 References 104 4 Introductory magnetic resonance 107 4.1 Introductory remarks 108 4.1.1 The NMR orchestra 108 4.1.2 Coherence and the spin echo 108 4.2 Resonant excitation 109 4.2.1 The rotating frame transformation 110 4.2.2 The resonant radiofrequency field 111 Contents χι 4.2.3 Quantum view of nutation 115 4.2.4 Classical descriptions of resonant reorientation 118 4.2.5 Semi-classical description 120 4.2.6 Relaxation and the Bloch equations 121 4.3 Signal detection 123 4.3.1 Free precession and Faraday detection 123 4.3.2 Fourier transformation and the spectrum 126 4.3.3 Digital Fourier transformation 128 4.4 Intrinsic spin interactions 129 4.4.1 Resolution in NMR 129 4.4.2 Chemical shift 131 4.4.3 Scalar coupling 131 4.4.4 Quadrupole coupling 134 4.4.5 Internile lear dipolar interactions 136 4.5 Fluctuations, spin relaxation, and motional averaging 138 4.5.1 Spin-lattice relaxation 139 4.5.2 Spin-spin relaxation 140 4.5.3 Motional averaging 142 4.6 Pulse sequences 144 4.6.1 Basic spin manipulation 144 4.6.2 Echoes 149 4.6.3 Multiple pulse line-narrowing 160 4.6.4 Multiquantum pathways 163 4.6.5 Multidimensional NMR 169 References 173 Magnetic field gradients and spin translation 177 5.1 Gradient fields and Maxwell s equations 178 5.2 Phase evolution of spin isochromats 180 5.2.1 Magnetisation phase 180 5.2.2 Spin isochromats in an inhomogeneous field 181 5.2.3 Phase evolution in the presence of a field gradient 181 5.3 Magnetic resonance imaging 184 5.3.1 Spatial Fourier relations 184 5.3.2 Trajectories in k-space 185 5.3.3 Selective excitation 188 5.4 Translational motion encoding 191 5.4.1 Time-varying gradients and phase factors 193 5.4.2 Coherent spin motion: velocity, acceleration, and jerk 196 5.4.3 The Carr-Purcell analysis of diffusion effects 197 5.4.4 The Bloch-Torrey equation for diffusion and flow 202 5.5 Pulsed gradient spin-echo NMR: diffusion and flow 204 5.5.1 The Stejskal-Tanner experiment 204 5.5.2 The role of background gradients 211 xii Contents 5.5.3 Echo schemes to reduce the effect of background gradients 212 5.5.4 More efficient encoding schemes 215 5.5.5 Using pulsed gradients to measure the diffusion tensor 220 5.6 Pulsed gradient spin-echo NMR: general motion 221 5.6.1 Narrow gradient pulse approximation and g-space 222 5.6.2 Low q limit 226 5.6.3 The meaning of k-space and q-space for time-varying gradients 227 5.7 Finite gradient pulses and generalised motion 228 5.7.1 Multiple propagator approach 228 5.7.2 Generalised gradients and the frequency domain 234 5.8 Phase effects of RF pulses and homospoiling 242 5.8.1 Rules for RF pulses 242 5.8.2 The spin echo and stimulated echo 244 5.9 Diffusion in the radiofrequency field 245 5.9.1 How RF field gradients work 245 5.9.2 Measurement of diffusion and flow 247 5.9.3 Advantages and disadvantages of RF gradients 248 References 248 6 Restricted diffusion 252 6.1 Apparent and effective diffusion coefficients 253 6.2 Time-dependent mean-squared displacement 254 6.2.1 Tortuosity and the long-time limit 254 6.2.2 The short-time limit for restricted diffusion 256 6.2.3 Interpolation of short- and long-time limits for restricted diffusion 259 6.2.4 Deff(t) and calculation of the apparent diffusion coefficient for any gradient waveform 259 6.2.5 The definition of the asymptotic limit 260 6.3 Spin relaxation in microscopically inhomogeneous media 261 6.3.1 Exchange between sites 262 6.3.2 Relaxation sinks and normal modes: wall relaxation and the Brownstein-Tarr relations 266 6.4 Diffusion in local inhomogeneous fields 269 6.4.1 Calculating the local field 270 6.4.2 Effect of molecular diffusion and the Anderson-Weiss treatment 270 6.4.3 Measuring relaxation in porous media. 273 6.4.4 Decay due to diffusion in the internal field 274 6.4.5 q-space analysis of internal field correlations 276 6.5 Restricted diffusion for spin echoes with steady gradients 278 6.5.1 Characteristic length scales 279 Contents xiii 6.5.2 Regimes of interest 280 6.5.3 Alternative non-dimensional parameters 282 6.6 Pulsed gradient spin-echo NMR for bounded molecules 283 6.6.1 Diffusion in a harmonic potential 284 6.6.2 Diffusion and exchange between two sites 285 6.6.3 Dimensional restriction: randomly distributed pipes and sheets 286 6.6.4 Curvilinear diffusion 289 6.6.5 Anisotropie diffusion in oriented liquid crystals 292 6.6.6 Diffusion in fractal geometries 294 6.7 Frequency-domain measurements and restricted motion 295 6.7.1 Spectral densities for free and restricted diffusion 297 6.7.2 Spectral analysis of flow 301 References 303 7 Restricted displacements and diffraction phenomena 309 7.1 PGSE NMR diffraction in pores 310 7.1.1 A historical precursor: rectangular boundaries 311 7.1.2 Diffusive diffraction in an enclosed pore 312 7.1.3 The pore density assumption revisited 316 7.1.4 Diffusive diffraction in a matrix of enclosing pores 317 7.1.5 Long-narrow PGSE NMR: direct imaging of the structure factor by diffusive diffraction 318 7.2 Finite time diffraction in planar, cylindrical and spherical pores 322 7.2.1 Finite Δ: the exact treatment 322 7.2.2 Parallel plane pore 323 7.2.3 Cylindrical pore 325 7.2.4 Spherical pore 328 7.2.5 Finite width gradient pulses and relaxation effects 329 7.3 Interconnected pores 331 7.3.1 Eigenmodes of the interconnected pore space 332 7.3.2 Pore equilibration model 335 7.3.3 Long-narrow PGSE NMR and interconnected pores 342 7.4 Applications of g-space diffraction 343 7.4.1 Emulsions and capsules 343 7.4.2 Biology and medicine 344 7.4.3 Pulsed gradient spin-echo ESR 345 7.5 Flow diffraction 347 7.6 Related issues 348 7.6.1 Frequency-domain modulated gradient NMR and diffusive diffraction 348 7.6.2 Return to origin probability 349 References 350 xiv Contents 8 Double wavevector encoding 354 8.1 Double PGSE NMR 355 8.1.1 The double scattering process 355 8.1.2 Compensated and uncompensated sequences 356 8.2 Double PGSE NMR and dispersion 356 8.2.1 Propagator and ensemble descriptions 356 8.2.2 Dispersion measurement and the iow-q limit 358 8.2.3 Reversible and irreversible dispersion 362 8.3 Phase cycling for double PGSE NMR 363 8.3.1 Characterising the coherences 364 8.3.2 Coherence selection 365 8.4 Non-local dispersion tensor 367 8.4.1 The pulse sequence for velocity and displacement encoding 367 8.4.2 Non-local dispersion for porous media flow 372 8.4.3 Non-local dispersion for pipe flow 373 8.5 Restricted diffusion and double wavevector encoding with long mixing time 375 8.5.1 Correlated and uncorrelated phase encoding 375 8.5.2 The propagator description rm » a2/D 376 8.5.3 Local anisotropy, global isotropy 378 8.6 Restricted diffusion and double wavevector encoding with infinitesimal mixing 383 8.6.1 The Mitra paradox 384 8.6.2 Propagator description, rm <C a2/D 385 8.7 Restricted diffusion and double wavevector encoding with finite mixing time 389 8.7.1 First-order expression for restricted isotropie geometries with general pulse timings 389 8.7.2 Isotropie fluid with unrestricted diffusion and finite width gradient pulse effects 391 8.8 Diffusive diffraction with double PGSE NMR 391 8.8.1 Difrractograms with signed amplitude 392 8.8.2 Unravelling structure in polydisperse systems 394 References 395 9 Multidimensional PGSE NMR 397 9.1 Fourier or Laplace? 398 9.1.1 An example from PGSE NMR 398 9.1.2 Forward and inverse 398 9.2 Inverse Laplace transformations 400 9.2.1 Analytic and numerical inverse Laplace transformations 400 9.2.2 Regularised non-negative least squares in 1-D 402 Contents xv 9.2.3 Regularised non-negative least squares in 2-D 404 9.2.4 Testing using known distributions and pearling effects 406 9.3 Multi-dimensional Fourier-Fourier methods 407 9.3.1 VEXSY 407 9.3.2 SERPENT 411 9.3.3 POXSY 412 9.3.4 Two-dimensional propagators 413 9.3.5 Inhomogeneous field exchange 414 9.4 Fourier Laplace methods 416 9.4.1 Diffusion-resolved spectroscopy 417 9.4.2 Propagator-resolved T2 419 9.5 Multidimensional Laplace-Laplace correlation methods 421 9.5.1 Relaxation relaxation 421 9.5.2 Negative peaks and coupled eigenmodes 423 9.5.3 Diffusion-relaxation 425 9.5.4 Diffusion-local field and relaxation-local field 427 9.5.5 DDCOSY 430 9.6 Multidimensional Laplace-Laplace exchange methods 433 9.6.1 DEXSY 434 9.6.2 Relaxation exchange spectroscopy 437 9.6.3 Symmetry and peak amplitude sign in exchange and correlation spectroscopy 439 9.7 Diffusion tensor measurement 440 9.7.1 Frame transformation 440 9.7.2 Echo experiment for diffusion tensor 442 9.7.3 Choice of diffusion gradient directions 443 9.7.4 Diagonalisation and diffusion matrix parameters 444 9.7.5 Diffusion tensor imaging 445 9.7.6 Cancelling the effect of imaging gradients 446 9.7.7 Extracting and displaying the information content 447 References 447 10 Velocimetry 451 10.1 Imaging the propagator 452 10.1.1 Pulse sequence 452 10.1.2 Data processing 453 10.1.3 Velocity resolution limit 455 10.1.4 Velocity null experiments 456 10.2 Single-step phase encoding for velocity 457 10.2.1 Reference phase processing 458 10.2.2 Fourier analysis 459 10.2.3 Choice of method 460 10.3 Fast encoding and real-time velocimetry 461 10.3.1 Flow tirnescale 461 xvi Contents 10.3.2 Velocimetry timescale 461 10.3.3 Echo planar imaging 463 10.3.4 Rapid acquisition relaxation enhanced imaging 466 10.3.5 FLASH 469 10.3.6 SPRITE 470 10.4 Velocimetry applications in materials science, biology, and medicine 474 10.4.1 Porous media flow 474 10.4.2 Inerţial flow and turbulence 475 10.4.3 Rheo-NMR 476 10.4.4 Electro-osmotic and electrophoretic flow 481 10.4.5 Biology 483 10.4.6 Granular flow 483 10.5 Potential artifacts 484 References 485 11 Translational dynamics and quantum coherence 491 11.1 Diffusion measurement using multiple-quantum coherences 492 11.1.1 Use of dipolar couplings 492 11.1.2 Use of the quadrupole interaction 496 11.1.3 Scalar couplings and heteronuclear states 499 11.2 Singlet states and time extension 504 11.2.1 Product states, singlet-triplet states, and symmetry 505 11.2.2 Sequence for translation measurement 507 11.2.3 Measurement of diffusion via the singlet state 509 11.3 Intermolecular quantum coherence 510 11.3.1 The quantum description 512 11.3.2 Multi-echo and CRAZED phenomena 515 11.3.3 Experimental verification of multiple echo effect 519 11.3.4 Probing structure via intermolecular coherences 520 References 521 12 Tricks of the trade 524 12.1 Instrumental limits 524 12.1.1 The diffusion baseline 524 12.1.2 Test samples 525 12.1.3 Non-Gaussian displacements 526 12.2 Conquering artifacts 526 12.2.1 Real-time monitoring 526 12.2.2 Sample movement 526 12.2.3 Eddy currents 528 12.2.4 Pulse mismatch 530 12.2.5 Small is beautiful 531 12.2.6 Fringe field diffusometry 532 Contents xvii 12.3 Pulse-sequence compensation 533 12.3.1 Eddy current fields 533 12.3.2 Convection compensation 534 12.3.3 Gradient pulse mismatch compensation 535 12.3.4 Varying q 538 12.4 Final thoughts 538 References 539 Index 541
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isbn	9780198700821 9780199556984 0198700822
language	English
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publisher	Oxford Univ. Press
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spellingShingle	Callaghan, Paul T. 1947-2012 Translational dynamics and magnetic resonance principles of pulsed gradient spin echo NMR Spin-Echo-Verfahren (DE-588)4249411-4 gnd PFG-NMR-Spektroskopie (DE-588)4529007-6 gnd Magnetische Kernresonanz (DE-588)4037005-7 gnd
subject_GND	(DE-588)4249411-4 (DE-588)4529007-6 (DE-588)4037005-7
title	Translational dynamics and magnetic resonance principles of pulsed gradient spin echo NMR
title_auth	Translational dynamics and magnetic resonance principles of pulsed gradient spin echo NMR
title_exact_search	Translational dynamics and magnetic resonance principles of pulsed gradient spin echo NMR
title_full	Translational dynamics and magnetic resonance principles of pulsed gradient spin echo NMR Paul T. Callaghan
title_fullStr	Translational dynamics and magnetic resonance principles of pulsed gradient spin echo NMR Paul T. Callaghan
title_full_unstemmed	Translational dynamics and magnetic resonance principles of pulsed gradient spin echo NMR Paul T. Callaghan
title_short	Translational dynamics and magnetic resonance
title_sort	translational dynamics and magnetic resonance principles of pulsed gradient spin echo nmr
title_sub	principles of pulsed gradient spin echo NMR
topic	Spin-Echo-Verfahren (DE-588)4249411-4 gnd PFG-NMR-Spektroskopie (DE-588)4529007-6 gnd Magnetische Kernresonanz (DE-588)4037005-7 gnd
topic_facet	Spin-Echo-Verfahren PFG-NMR-Spektroskopie Magnetische Kernresonanz
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027298981&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT callaghanpault translationaldynamicsandmagneticresonanceprinciplesofpulsedgradientspinechonmr

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