NMR: Tomography, Diffusometry, Relaxometry

ISBN-13: 9783642644658 / Angielski / Miękka / 2011 / 526 str.

Rainer Kimmich

Opis

When I planned this book seven years ago I had my graduate students at the University of Ulm in mind, diploma as well as doctoral students, who often asked me what literature they should work with. I used to suggest a list of ten to twenty (for my taste: excellent) treatises on NMR. Apparently this did not make them entirely happy. The difficulty which newcomers to the field face is to practise and to apply theoretical formalisms from different sources while still learning the principles of NMR and being actively engaged in NMR research. Although the text presented here is largely based on my lecture notes, the result is a "working book" rather than an introduction. It is intended to provide direct access to the basic information one needs for NMR diffusometry, relaxometry, and tomography applications. A "working book" is certainly not suitable to be read starting on page one and then carrying on until the last page. Boldly extrapolating my own reading habits to those of the typical scientist I am sure that this is not the way in which monographs of this kind are read nowadays. So my aim was to produce a treatise that offers easy and quick access for the reader to relevant matters of interest. I tried hard to ease the comprehension of NMR principles by extensive cross-referencing among the sections and chapters. Tomography, diffusometry and relaxometry are fields based on common phys ical principles."

Spis treści

I: Spin Coherences and Echoes.- 1 Introductory Remarks.- 2 Isolated Spins in Inhomogeneous Fields.- 2.1 Two-Pulse Hahn Echo.- 2.2 Three-Pulse Hahn Echoes.- 2.3 Gradient-Recalled Echo.- 2.4 Multiple Echoes.- 3 Rotary Echoes.- 3.1 Signal at ?? = ?1.- 3.2 Signal at ?=?0.- 4 Solid Echoes of Dipolar-Coupled Spins.- 4.1 Two-Pulse Dipolar Solid Echoes.- 4.1.1 Systems of Two Equivalent Spins 1/2.- 4.1.2 Approximate Treatment of Multi-Spin 1/2 Systems.- 4.2 Three-Pulse Dipolar Solid Echoes.- 5 Solid Echoes of I =1 Quadrupole Nuclei.- 5.1 Two-Pulse Quadrupolar Solid Echo.- 5.2 Three-Pulse Quadrupolar Solid Echoes.- 6 Dipolar and Quadrupolar Magic Echoes.- 6.1 Principle.- 6.2 The “Magic Sandwich” Pulse Sequence.- 6.3 Dipolar-Coupled Two-Spin 1/2 Systems.- 6.4 Mixed Echoes.- 7 Coherence Transfer of J-Coupled Spins.- 7.1 Two RF Pulses.- 7.1.1 Correlated Two-Dimensional Spectroscopy.- 7.1.2 Echo Formation.- 7.1.3 Spin-Echo Correlated 2D Spectroscopy.- 7.1.4 Homonuclear J Resolved 2D Spectroscopy.- 7.2 Three RF Pulses.- 7.2.1 Longitudinal-Magnetization Transfer Echo.- 7.2.2 Scalar-Order Transfer Echo.- 7.2.3 Zero-Quantum Coherence-Transfer Echo.- 7.2.4 Single-Quantum Coherence-Transfer Echoes.- 7.2.5 Double-Quantum Coherence-Transfer Echo.- 7.3 Multiple-Quantum Coherence Based Spectroscopy.- 7.3.1 Double-Quantum Filtered Correlated Spectroscopy (DQF-COSY).- 7.3.2 Double-Quantum/Single-Quantum Correlated Spectroscopy.- 7.4 Discrimination of Coherence-Transfer Echoes.- II: Molecular Motion.- 8 Survey.- 9 Categorization of Relaxation Phenomena.- 9.1 General Remarks.- 9.1.1 Observables Subject to Relaxation.- 9.1.2 Spin Interactions Subject to Fluctuations.- 9.1.3 The Autocorrelation and the Intensity Functions.- 9.2 Limits and Definitions for Spin-Lattice Relaxation.- 9.3 Limits and Definitions for Transverse Relaxation.- 9.3.1 Irreversibility and Spin-System Size.- 9.3.2 Irreversibility and Molecular Motion.- 9.3.3 Classification of Transverse Relaxation.- 10 Spin-Relaxation Functions.- 10.1 The Homonuclear Bloch Equations.- 10.2 Solutions for Laboratory-Frame Experiments.- 10.3 Solutions for Rotating-Frame Experiments.- 11 Perturbation Theory of Spin Relaxation.- 11.1 Iterative Approximation.- 11.2 The Master Equation.- 12 Spin-Lattice Relaxation.- 12.1 Laboratory-Frame Spin-Lattice Relaxation by Dipolar Coupling.- 12.1.1 Reduced Dipolar Correlation and Intensity Functions.- 12.1.2 S-Spin-Equilibrium Limit.- 12.1.3 Like-Spin limit.- 12.2 Laboratory-Frame Spin-Lattice Relaxation by Other Interactions.- 12.2.1 Scalar Coupling.- 12.2.2 Quadrupolar Coupling (I=1).- 12.2.3 Chemical-Shift Anisotropy.- 12.3 Rotating-Frame Spin-Lattice Relaxation by Dipolar Coupling.- 13 Transverse Relaxation.- 13.1 Motional-Averaging Limit.- 13.1.1 Single-Quantum Coherences of Dipolar-Coupled Spin Pairs.- 13.1.2 Single-Quantum Coherences of (I =1) Quadrupole Nuclei.- 13.1.3 Multiple-Quantum Coherences.- 13.2 Local-Field Theory.- 13.2.1 The Anderson/Weiss Ansatz.- 13.2.2 The Second Moment ??2?.- 13.2.3 Partial Motional Averaging.- 14 Examples of Autocorrelation Functions.- 14.1 Isotropic Continuous Rotational Diffusion.- 14.2 Discrete-Coupling Jump Models.- 14.2.1 Two-State Jump Model.- 14.3 Reorientation Mediated by Translational Displacements.- 14.3.1 Diffusion on Rugged Surfaces.- 14.3.2 Lévy-Walk Surface Diffusion.- 15 Field-Cycling NMR Relaxometry.- 15.1 Laboratory-Frame Experiments.- 15.1.1 Field-Cycling Magnets.- 15.1.2 The Switching Intervals.- 15.2 Spin-Lock Adiabatic Field-Cycling Imaging Relaxometry.- 15.2.1 Adiabatic Variation of the Effective Field.- 15.2.2 Spin-Lock Field-Cycling Laboratory-Frame Imaging Relaxometry.- 15.2.3 Spin-Lock Field-Cycling Rotating-Frame Imaging.- 16 Field-Cycling Relaxometry in Biosystems.- 16.1 Fluctuations in Proteins.- 16.2 Fluctuations in Lipid Bilayers.- 16.3 Deuteron T1 Frequency Dispersion of Protein Solutions.- 16.4 Critical Water Contents.- 16.5 Proton Relaxation in Tissue.- 17 The Dipolar-Correlation Effect.- 17.1 Outline of Attenuation Mechanisms and Time Scales.- 17.1.1 The Motional-Averaging Contribution to Echo Attenuation.- 17.1.2 The Residual-Coupling Contribution to Echo Modulation.- 17.2 Density-Operator Formalism for Equivalent Two-Spin 1/2 Systems.- 17.2.1 The Modified Primary Echo.- 17.2.2 The Modified Stimulated Echo.- 17.3 The Dipolar-Correlation Quotient.- 17.3.1 Exponential Correlation Function.- 17.3.2 Correlation Function for Liquid-Crystal Director Fluctuations.- 17.4 Applications of the Dipolar-Correlation Effect.- 17.4.1 Macroscopic Order.- 17.4.2 Short-Range Order and Polymers.- 18 Survey of NMR Diffusometry.- 18.1 The Diffusion Propagator.- 19 Main-Field Gradient NMR Diffusometry.- 19.1 The Principle.- 19.2 Pulsed-Gradient Spin-Echo (PGSE) Diffusometry.- 19.2.1 The Displacement-Correlation Function.- 19.2.2 The Mean Squared Phase Shift.- 19.2.3 The Echo-Attenuation Factor for Anomalous Diffusion.- 19.2.4 The Echo-Attenuation Factor for Ordinary Diffusion.- 19.2.5 Direct Evaluation of the Mean Squared Displacement.- 19.3 Steady-Gradient Spin-Echo (SGSE) Diffusometry.- 19.3.1 Echo-Attenuation Factors.- 19.3.2 Relaxation-Compensated Pulse Sequences.- 20 Reciprocal- vs Real-Space Representations.- 20.1 The Generalized Reciprocal-Space Formalism.- 20.2 The Real-Space Representation.- 20.2.1 The Longitudinal-Magnetization Grid.- 20.2.2 One-Dimensional Real-Space Evaluation.- 20.2.3 Two-Dimensional Real-Space Evaluation.- 20.2.4 Geometrical Confinements.- 21 RF-Field-Gradient NMR Diffusometry.- 21.1 Magnetization-Grid Rotating-Frame Imaging.- 21.1.1 Rapid MAGROFI Diffusometry.- 21.1.2 Experimental Aspects of MAGROFI Diffusometry.- 21.2 Comparison of B0 and B1 Gradient Methods.- 22 Examples for Anomalous Self-Diffusion.- 22.1 Anomalous Diffusion in Lacunar Systems.- 22.2 Reptation/Tube Model.- 22.2.1 The Doi/Edwards Limits.- 22.2.2 Evaluation Formula for PGSE/SGSE Experiments.- 23 Exchange.- 23.1 Equation of Motion for Discrete Spin Environments.- 23.1.1 Interpretation of the HMM Matrices.- 23.1.2 HMM Solutions in Terms of Eigenvalues.- 23.1.3 Two-Environment-Exchange Model.- 23.2 Two-Dimensional Exchange Spectroscopy.- 23.2.1 Matrix Formalism.- 23.2.2 Exchange Between Two Environments.- 23.2.3 Comparison with 2D Exchange NQR Spectroscopy.- III: Localization and Imaging.- 24 Survey.- 25 Fundamentals of NMR Imaging.- 25.1 Slice Selection by Soft Pulses.- 25.1.1 Approximation for Small Tip Angles.- 25.1.2 Frequently Used Pulseshapes.- 25.1.3 Refocusing of the Coherences.- 25.1.4 Variation of the Slice Width and Position.- 25.2 Phase Encoding.- 25.3 (Larmor) Frequency Encoding.- 25.4 Two- and Three-Dimensional Fourier Imaging.- 25.4.1 2DFT Imaging.- 25.4.2 3DFT Imaging.- 25.4.3 Gradient-Recalled Spin-Echo Imaging.- 25.4.4 Echo-Planar Imaging.- 26 Parameter-Weighted Contrasts.- 26.1 Contrast Parameters of Conventional Images.- 26.2 Contrasts in Gradient-Echo Tomography.- 26.3 Relaxation-Weighted Contrasts.- 26.4 Functional Tomography.- 26.5 Diffusive Attenuation and “Edge Enhancement”.- 27 Relaxation-Dispersion Maps.- 28 Frequency-Offset Maps.- 28.1 MRSI Pulse Sequences.- 28.2 Theory of MRSI.- 28.3 Post-Detection MRSI Data Processing.- 28.4 Post-Detection Correction of Frequency-Offset Artifacts.- 28.5 Spectroscopic Maps and Shift-Selective Images.- 29 Gradient-Pulse Moments and Motions.- 29.1 Bipolar Gradient Pulses.- 29.2 Velocity-Compensated Gradient Pulses.- 30 Velocimetry and Velocity Maps.- 30.1 Phase Encoding of the Velocity.- 30.2 Mapping of Velocity Fields.- 30.3 Typical Applications.- 31 Diffusivity Maps.- 32 Resolution.- 32.1 Field of View, Spectral Width, Velocity Range.- 32.2 Digital Resolution.- 32.3 Physical Resolution Limits.- 32.3.1 Spatial In-Plane Resolution.- 32.3.2 The Sensitivity Limit.- 33 Multi-Stripe/Plane Tagging.- 33.1 DANTE Pulse Combs.- 33.2 Imaging Pulse Scheme and Applications.- 34 Rotating-Frame Imaging.- 34.1 Nutation Frequency Encoding.- 34.2 Multi-Dimensional Representations.- 34.3 Rapid Rotating-Frame Imaging.- 35 Imaging of Solid Samples.- 35.1 Experimental Strategies of Materials Imaging.- 35.1.1 The Reservoir of Contrast Parameters.- 35.1.2 The Spatial-Resolution Problem.- 35.2 Magic- and Mixed-Echo Phase-Encoding Imaging.- 35.3 Magnetic Resonance Force Microscopy.- 36 Slice-Selective Homonuclear Spin-Locking.- 36.1 Review of Slice-Selection Principles.- 36.2 Theory of Slice Selection by Spin-Locking.- 36.2.1 Liquid-State Limit.- 36.2.2 Solid-State Limit.- 36.3 Variation of the Slice Width and Position.- 37 Homonuclear Localized NMR.- 37.1 The Homonuclear VOSY/VOSING Family.- 37.1.1 Double-Quantum Volume-Selective Spectral Editing.- 37.1.2 Cyclic Polarization Transfer Volume-Selective Spectral Editing.- 37.1.3 Volume-Selective Relaxometry, Diffusometry, and Velocimetry.- 37.2 The Homonuclear LOSY Pulse Sequence.- 38 Cross-Polarization Principles.- 38.1 Categorization of Cross-Polarization Techniques.- 38.2 Spatially Selective HH-Matching.- 38.3 Adiabatic J Cross-Polarization.- 38.3.1 Adiabatic Level-Crossing Condition.- 38.3.2 The Principle of Adiabatic J Cross-Polarization.- 39 Single-Transition Operator Theory of Cross-Polarization.- 39.1 Weakly Coupled AX Spin Systems.- 39.1.1 Laboratory-Frame Hamiltonian.- 39.1.2 Transformation to the Tilted Doubly-Rotating Frame.- 39.1.3 Single-Transition Operator Representation.- 39.1.4 Solution of the Liouville/von Neumann Equation.- 39.1.5 The Cross-Polarized Magnetizations.- 39.1.6 HH-Matched Resonant Cross-Polarization.- 39.1.7 HH-Mismatch Losses of Resonant Cross-Polarization (VJCP).- 39.1.8 Off-Resonance Losses of HH Cross-Polarization (JCP-LOSY).- 39.1.9 Resonant Adiabatic J Cross-Polarization (AJCP).- 39.1.10 Adiabatic J Cross Polarization Localized Spectroscopy (AJCP-LOSY).- 39.2 From Two-Spin to Multi-Spin Systems and Solids.- 40 Proton-Detected Localized 13C NMR.- 40.1 Heteronuclear MQF-VOSING Spectroscopy.- 40.2 Cyclic Cross-Polarization Localized Spectroscopy (CYCLCROP-LOSY).- 41 Heteronuclear Imaging.- 41.1 Proton-Detected 13C Imaging.- 41.1.1 Multiple-Quantum Edited Hydrocarbon Maps.- 41.1.2 Cross-Polarization Edited Hydrocarbon Maps.- IV: Analytical NMR Toolbox.- 42 Miscellaneous Formulae and Rules.- 42.1 Some Algebraic Symbols.- 42.2 The Delta Function.- 42.3 Fourier Transforms.- 42.4 Spherical Harmonics.- 42.5 Classification of Operators.- 42.6 Spin-Operator Relations.- 42.6.1 Spin-Operator Representations.- 42.6.2 Ladder Operators.- 42.6.3 Spherical Spin Operators.- 42.6.4 Relations for Spin-1/2 Operators.- 42.6.5 Relations for Spin-1 Operators.- 42.6.6 Two-Spin Systems.- 42.6.7 Single-Transition Operators.- 42.6.8 An Instructive Exarhple.- 43 Rules for Traces.- 44 Commutator Algebra.- 44.1 General Operators.- 44.2 Spin Operators.- 45 Exponential and Trigonometric Operators.- 46 Spin Hamiltonians.- 46.1 Zeeman Interaction.- 46.2 RF Irradiation.- 46.3 Internal Spin Interactions.- 46.3.1 Chemical-Shift Interaction.- 46.3.2 Dipolar, Scalar, and Indirect Couplings.- 46.3.3 Quadrupolar and Spin-Rotation Couplings.- 47 The Density Operator.- 47.1 Definition of the Density Operator.- 47.2 Thermal Equilibrium.- 47.3 Evolution of the Density Operator.- 47.3.1 Segmented Treatments.- 47.3.2 Average Hamiltonians.- 48 Unitary Transformations in NMR.- 48.1 Diagonalization of a Matrix.- 48.1.1 The Eigenvalue Problem.- 48.1.2 Transformation Matrices.- 48.1.3 The Inverse Matrix.- 48.2 Coordinate Systems.- 48.3 Euler Angles.- 48.4 Transformation of the Chemical-Shift Tensor.- 48.5 Transformations by Single-Spin Operators.- 48.5.1 Transformation to the Rotating Frame.- 48.5.2 RF Pulses and Unitary Transformations.- 48.5.3 Precession.- 48.6 Transformations by Bilinear Spin-1/2 Operators.- 48.7 Equations of Motion in the Rotating Frame.- 48.7.1 Classical Precession Equation.- 48.7.2 Liouville/von Neumann Equation.- 48.7.3 Time Dependent Schrödinger Equation.- 48.7.4 Heisenberg Equation.- 48.8 Rotating-Frame Hamilton Operators.- 48.9 Dipolar Hamiltonian in the Tilted Rotating Frame.- 48.10 Quadrupolar Hamiltonian in the Tilted Rotating Frame.- 48.11 Spin-Spin Coupling in the Doubly-Rotating Frame.- 49 Irreducible Spherical Tensor Operators.- 49.1 Rotational Transformation of IST Operators.- 49.2 Commutation of IST and Spin Operators.- 49.3 Analytical Form of IST Operators.- 49.4 Wigner/Eckart Theorem.- 49.5 Selection Rules for Stationary Nuclear Moments.- 49.6 IST Representation of the Quadrupolar Hamiltonian.- 50 Derivation of Basic NMR Spectra.- 50.1 Pake Spectrum.- 50.1.1 Dipolar Coupling.- 50.1.2 Quadrupolar Coupling.- 50.2 Chemical-Shift Anisotropy Spectrum.- 50.3 A2, AB, and AX Spectra.- 51 Product Operators for Spins.- 51.1 Simple Example of a Product Operator Basis Set.- 51.2 Orthogonality.- 51.3 Matrix Interpretation.- 51.3.1 Example 1: In-phase Single-quantum Coherences.- 51.3.2 Example 2: Multiple-quantum Coherences.- 51.3.3 Example 3: Longitudinal Scalar Order.- 51.3.4 Summary of the Interpretations of Cartesian Product Operators.- 51.4 Hamiltonians and Applicability Limits.- 51.5 Evolution Rules for Cartesian Product Operators.- 51.6 Evolution Rules for Spherical Product Operators.- 52 Spin Operators for I = 1 Quadrupole Nuclei.- References.

Blurb

Tomography, diffusometry and relaxometry are fields based on common physical principles. The combined use of such techniques provides synergistic insight into physicochemical material properties of an object. The difficulty which newcomers to the field face is to practice and to apply theoretical formalisms from different sources while still learning the principles of NMR and while being already engaged in NMR research. So the author's ambition is a treatise that offers easy and quick access for the reader to any implied matter of interest. He has exerted himself to facilitate the comprehension of NMR principles by extensive cross-referencing among the sections and chapters.