Translational dynamics and magnetic resonance: principles of pulsed gradient spin echo NMR
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Oxford Univ. Press
2014
|
| Edition: | 1. publ. in paperback |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 547 S. graph. Darst. |
| ISBN: | 9780198700821 9780199556984 0198700822 |
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MARC
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| 100 | 1 | |a Callaghan, Paul T. |d 1947-2012 |e Verfasser |0 (DE-588)1043633162 |4 aut | |
| 245 | 1 | 0 | |a Translational dynamics and magnetic resonance |b principles of pulsed gradient spin echo NMR |c Paul T. Callaghan |
| 250 | |a 1. publ. in paperback | ||
| 264 | 1 | |a Oxford |b Oxford Univ. Press |c 2014 | |
| 300 | |a XVII, 547 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Record in the Search Index
| _version_ | 1804152203096621056 |
|---|---|
| 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
|
| any_adam_object | 1 |
| author | Callaghan, Paul T. 1947-2012 |
| author_GND | (DE-588)1043633162 |
| author_facet | Callaghan, Paul T. 1947-2012 |
| author_role | aut |
| author_sort | Callaghan, Paul T. 1947-2012 |
| author_variant | p t c pt ptc |
| building | Verbundindex |
| bvnumber | BV041854603 |
| classification_rvk | UM 3500 |
| classification_tum | PHY 517f |
| ctrlnum | (OCoLC)875734834 (DE-599)BVBBV041854603 |
| dewey-full | 538.362 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 538 - Magnetism |
| dewey-raw | 538.362 |
| dewey-search | 538.362 |
| dewey-sort | 3538.362 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | 1. publ. in paperback |
| format | Book |
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| id | DE-604.BV041854603 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:06:58Z |
| institution | BVB |
| isbn | 9780198700821 9780199556984 0198700822 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027298981 |
| oclc_num | 875734834 |
| open_access_boolean | |
| owner | DE-703 DE-M49 DE-BY-TUM DE-29T DE-20 |
| owner_facet | DE-703 DE-M49 DE-BY-TUM DE-29T DE-20 |
| physical | XVII, 547 S. graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| spelling | Callaghan, Paul T. 1947-2012 Verfasser (DE-588)1043633162 aut Translational dynamics and magnetic resonance principles of pulsed gradient spin echo NMR Paul T. Callaghan 1. publ. in paperback Oxford Oxford Univ. Press 2014 XVII, 547 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Spin-Echo-Verfahren (DE-588)4249411-4 gnd rswk-swf PFG-NMR-Spektroskopie (DE-588)4529007-6 gnd rswk-swf Magnetische Kernresonanz (DE-588)4037005-7 gnd rswk-swf PFG-NMR-Spektroskopie (DE-588)4529007-6 s Spin-Echo-Verfahren (DE-588)4249411-4 s DE-604 Magnetische Kernresonanz (DE-588)4037005-7 s 1\p DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf 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 Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| 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 |