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Book Details
Abstract
With the increasing role of porous solids in conventional and newly emerging technologies, there is an urgent need for a deeper understanding of fluid behaviour confined to pore spaces of these materials especially with regard to their transport properties. From its early years, NMR has been recognized as a powerful experimental technique enabling direct access to this information. In the last two decades, the methodological development of different NMR techniques to assess dynamic properties of adsorbed ensembles has been progressed. This book will report on these recent advances and look at new broader applications in engineering and medicine.
Having both academic and industrial relevance, this unique reference will be for specialists working in the research areas and for advanced graduate and postgraduate studies who want information on the versatility of diffusion NMR.
Table of Contents
| Section Title | Page | Action | Price |
|---|---|---|---|
| Cover | Cover | ||
| Contents | vii | ||
| Preface | v | ||
| Chapter 1 NMR under Confinement: Roots in Retrospect | 1 | ||
| References | 12 | ||
| Chapter 2 Fundamentals of Diffusion Measurements using NMR | 16 | ||
| 2.1 What is Diffusion? | 16 | ||
| 2.1.1 Self-diffusion, Mutual Diffusion, Flow and Dispersion | 16 | ||
| 2.1.2 Free and Restricted Diffusion | 18 | ||
| 2.1.3 Diffusion in General Porous Media | 28 | ||
| 2.2 How to Measure Diffusion using Magnetic Resonance | 30 | ||
| 2.2.1 Radiofrequency Pulses and Gradients | 30 | ||
| 2.2.2 Pulsed Gradient Diffusion Sequences | 32 | ||
| 2.2.3 The Torrey-Bloch Equations and Application to the PGSE Sequence | 33 | ||
| 2.2.4 Anisotropic Systems with Uniform Orientation | 35 | ||
| 2.2.5 Anisotropic Systems with Powder Distributions | 38 | ||
| 2.3 Experimental Measurements | 40 | ||
| 2.3.1 An ‘Ideal PGSE' Experiment and Analysis | 40 | ||
| 2.3.2 Optimising PGSE Experiments | 41 | ||
| 2.3.3 Real Experiments, Complications and Solutions | 44 | ||
| References | 46 | ||
| Chapter 3 From the Microstructure to Diffusion NMR, and Back | 52 | ||
| 3.1 Introduction | 52 | ||
| 3.2 Mathematical Background | 53 | ||
| 3.2.1 Bloch-Torrey Equation | 53 | ||
| 3.3 Boundary Conditions | 55 | ||
| 3.4 Diffusion-weighting Magnetic Field | 58 | ||
| 3.5 Characteristic Scales | 62 | ||
| 3.6 Solutions of the Bloch-Torrey Equation | 64 | ||
| 3.7 Theoretical Approaches | 66 | ||
| 3.7.1 Narrow-pulse Approximation | 66 | ||
| 3.7.2 Gaussian Phase Approximation | 70 | ||
| 3.8 Diffusion in Multi-compartmental Tissue | 79 | ||
| 3.8.1 Multi-exponential and Distributed Signals | 80 | ||
| 3.8.2 Bi-exponential Model | 81 | ||
| 3.8.3 Kärger Model\r | 84 | ||
| 3.8.4 Anomalous Diffusion Models | 86 | ||
| 3.8.5 Effective Medium Theory | 87 | ||
| 3.9 Towards Microscopic Geometric Models | 88 | ||
| 3.10 Towards High Gradients | 89 | ||
| 3.11 Conclusions and Perspectives | 94 | ||
| References | 96 | ||
| Chapter 4 Two-dimensional NMR of Diffusion and Relaxation | 111 | ||
| 4.1 Introduction | 111 | ||
| 4.2 Basic Pulse Sequence Building Blocks and Experiments | 112 | ||
| 4.2.1 Relaxation Correlation Experiments | 114 | ||
| 4.2.2 Diffusion-Relaxation Correlation Experiments | 115 | ||
| 4.2.3 Correlation Experiments in Static Field Gradients | 116 | ||
| 4.2.4 Correlation Experiments in RF Field Gradients | 116 | ||
| 4.2.5 Mixed Diffusion and Relaxation Experiment | 117 | ||
| 4.2.6 Diffusion Time Correlation Experiment | 117 | ||
| 4.2.7 Diffusion Anisotropy Correlation | 120 | ||
| 4.2.8 DDIF-CPMG | 120 | ||
| 4.2.9 Fast Acquisition of 2D NMR | 121 | ||
| 4.2.10 Summary | 122 | ||
| 4.3 Diffusion Dynamics in Porous Media | 122 | ||
| 4.3.1 Theory | 122 | ||
| 4.3.2 NMR Experiments | 123 | ||
| 4.4 Laplace Inversion | 125 | ||
| 4.4.1 General Theory | 126 | ||
| 4.4.2 Data Compression | 126 | ||
| 4.4.3 Mellin Transform | 128 | ||
| 4.4.4 Max Entropy Method | 130 | ||
| 4.4.5 Monte Carlo Inversion | 133 | ||
| 4.4.6 Time-domain Analysis | 135 | ||
| 4.4.7 Summary | 136 | ||
| 4.5 Applications | 136 | ||
| 4.5.1 Well-logging | 136 | ||
| 4.5.2 Water Saturation | 136 | ||
| 4.5.3 Drilling Fluid Invasion | 138 | ||
| 4.5.4 Oil Composition Measurement | 139 | ||
| 4.5.5 Surface Relaxivity | 139 | ||
| 4.5.6 Diffusion Correlation | 141 | ||
| 4.5.7 Pore Structure | 141 | ||
| 4.5.8 Nanoporous Shales | 143 | ||
| 4.5.9 Biological Materials | 145 | ||
| 4.5.10 Food Materials | 146 | ||
| 4.5.11 Cement and Other Materials | 146 | ||
| 4.5.12 Environmental Sciences | 147 | ||
| 4.6 Instrumentation | 147 | ||
| 4.7 Summary | 148 | ||
| References | 148 | ||
| Chapter 5 Transport in Structured Media: Multidimensional PFG-NMR Applied to Diffusion and Flow Processes | 156 | ||
| 5.1 Introduction: Diffusion vs. Transport | 156 | ||
| 5.2 Theoretical Background | 158 | ||
| 5.2.1 Encoding of Transport Properties | 158 | ||
| 5.2.2 Two- and Higher-dimensional Sequences | 161 | ||
| 5.3 Examples for Flow and Correlations in Displacements | 164 | ||
| 5.3.1 Velocity EXchange SpectroscopY (VEXSY) | 164 | ||
| 5.3.2 Diffusion EXchange SpectroscopY (DEXSY) | 167 | ||
| 5.3.3 Two- and Three-dimensional Propagators | 170 | ||
| 5.3.4 Local Anisotropy of Diffusion | 179 | ||
| 5.4 Velocity Encoding and Imaging: Recent Developments | 181 | ||
| 5.5 Summary | 190 | ||
| References | 190 | ||
| Chapter 6 Real Time PGSE NMR Through Direct Acquisition of Averaged Propagators in the Time Domain Using Pulsed Second Order Magnetic Fields | 194 | ||
| 6.1 Introduction | 194 | ||
| 6.1.1 General Background | 194 | ||
| 6.1.2 PGSE NMR for Diffusion and Flow | 196 | ||
| 6.2 Time Domain Signal as the Averaged Propagator | 197 | ||
| 6.2.1 The Conventional PGSE Experiment | 197 | ||
| 6.2.2 The PGSE Experiment using Second Order Magnetic Fields | 199 | ||
| 6.3 Applications | 208 | ||
| 6.3.1 Real Time Propagator Measurements | 208 | ||
| 6.3.2 Single-shot Surface-to-volume Ratios for Porous Materials | 215 | ||
| 6.4 Conclusions | 220 | ||
| References | 221 | ||
| Chapter 7 NMR Methods for Studying Microscopic Diffusion Anisotropy | 226 | ||
| 7.1 Introduction | 226 | ||
| 7.2 Tensors | 228 | ||
| 7.2.1 Tensor Size and Shape | 229 | ||
| 7.2.2 Tensors with Axial Symmetry | 231 | ||
| 7.2.3 Alternative Measures of Tensor Anisotropy | 232 | ||
| 7.3 Ensembles of Diffusion Tensors | 233 | ||
| 7.3.1 Diffusion Tensor Distributions | 233 | ||
| 7.3.2 Size and Shape Distributions | 234 | ||
| 7.3.3 Means and Variances | 234 | ||
| 7.3.4 Orientation Distributions and Order Tensors | 235 | ||
| 7.3.5 Ensemble-averaged Diffusion Tensor | 237 | ||
| 7.4 NMR Methods and Application Examples | 238 | ||
| 7.4.1 Diffusion Encoding with Magnetic Field Gradients | 238 | ||
| 7.4.2 Method Classification Based on the Shape of the b-Tensor | 239 | ||
| 7.4.3 General Principles for Designing Measurement Protocols | 242 | ||
| 7.4.4 Signal from Powders | 242 | ||
| 7.4.5 Powder-averaging of the Signal | 245 | ||
| 7.4.6 Detecting Microscopic Diffusion Anisotropy | 246 | ||
| 7.4.7 Cumulant Expansion of the Signal | 247 | ||
| 7.4.8 Variance of Isotropic Diffusivities and Mean-square Anisotropy from the 2nd Moment | 248 | ||
| 7.4.9 Model-free Estimation of the 2nd Moment | 249 | ||
| 7.4.10 Mapping the Variance of Isotropic Diffusivities and Mean-square Anisotropy | 250 | ||
| 7.4.11 Mapping Microscopic Diffusion Tensors and Orientational Order Tensors | 251 | ||
| 7.4.12 Microscopic Anisotropy Parameters for Clinical MRI | 251 | ||
| 7.4.13 Removing the Need for Powder Averaging: The Covariance Tensor | 253 | ||
| 7.4.14 2D Size-shape Diffusion Tensor Distribution | 253 | ||
| 7.5 Conclusions | 255 | ||
| Acknowledgments | 255 | ||
| References | 255 | ||
| Chapter 8 Beyond the Limits of Conventional Pulsed Gradient Spin Echo (PGSE) Diffusometry: Generalization of the Magnetization-grating Principle | 260 | ||
| 8.1 Introduction | 260 | ||
| 8.2 Diffusometry using the B0 Gradients of the Fringe Field of Magnets | 262 | ||
| 8.2.1 Formalism for the Fringe-field SGSE Technique | 264 | ||
| 8.2.2 Determination of the Size of Polymeric Capsules with the Aid of the Fringe-field SGSE Technique | 269 | ||
| 8.3 Diffusometry using B1 Gradients | 271 | ||
| 8.3.1 Stimulated Rotary Spin Echo | 271 | ||
| 8.3.2 Nutation Spin Echo | 275 | ||
| 8.3.3 MAGROFI | 277 | ||
| 8.3.4 Applications of Rotating-frame Techniques for Diffusion Studies | 280 | ||
| 8.4 Laboratory-frame Diffusometry Based on Non-linear (or ‘‘multiple\") Stimulated Echoes | 283 | ||
| 8.4.1 The Demagnetizing Field | 284 | ||
| 8.4.2 Formation of Non-linear Stimulated Echoes and Evaluation of Diffusion Coefficients | 285 | ||
| 8.5 Conclusions | 289 | ||
| Acknowledgments | 291 | ||
| References | 292 | ||
| Chapter 9 Probing Exchange and Diffusion in Confined Systems by 129Xe NMR Spectroscopy | 294 | ||
| 9.1 Introduction to the Use of 129Xe NMR to Investigate the Structure and Transport Phenomena in Confined Systems | 294 | ||
| 9.2 Theoretical Background and Hardware | 296 | ||
| 9.2.1 Factors Influencing the Chemical Shift of 129Xe | 296 | ||
| 9.2.2 The Spin Exchange Optical Pumping Method | 299 | ||
| 9.2.3 Hardware Aspects | 301 | ||
| 9.3 NMR Experiments and their Application | 305 | ||
| 9.3.1 EXSY-experiments | 306 | ||
| 9.3.2 The Hyperpolarized Tracer Exchange Experiment | 311 | ||
| 9.3.3 The HyperCEST Approach | 313 | ||
| 9.4 Summary | 314 | ||
| References | 314 | ||
| Chapter 10 Diffusive Dynamics in Porous Materials as Probed by NMR Relaxation-based Techniques | 318 | ||
| 10.1 Introduction | 318 | ||
| 10.2 Limiting Nuclear Magnetic Relaxation Processes of a Liquid in Pores | 320 | ||
| 10.3 Nuclear Magnetic Relaxation Dispersion of Longitudinal Relaxation Rate in Calibrated Micropores | 323 | ||
| 10.3.1 Theory | 323 | ||
| 10.3.2 Application to Aprotic Liquids | 327 | ||
| 10.3.3 Application to Protic (Water) Liquid | 328 | ||
| 10.4 Continuous Multi-scales NMR Relaxation Investigation of Microstructure Evolution of Cement-based Materials | 330 | ||
| 10.5 Direct Probing of the Nano-wettability of Plaster Pastes | 335 | ||
| 10.6 Dynamical Surface Affinity of Diphasic Liquids as a Probe of Wettability of Multimodal Macroporous Petroleum Rocks | 341 | ||
| 10.7 Dynamics and Wettability of Oil and Water in the Dual Organic and Mineral Porosity of Shales Oils | 345 | ||
| 10.7.1 Samples | 345 | ||
| 10.7.2 Methods | 345 | ||
| 10.7.3 Interpretation of the Nuclear Magnetic Relaxation Dispersion Data | 347 | ||
| 10.8 Conclusion | 350 | ||
| Acknowledgments | 350 | ||
| References | 350 | ||
| Chapter 11 Industrial Applications of Magnetic Resonance Diffusion and Relaxation Time Measurements | 353 | ||
| 11.1 Introduction | 353 | ||
| 11.2 NMR Petrophysics | 355 | ||
| 11.2.1 Magnetic Resonance Well Logging | 355 | ||
| 11.2.2 Laboratory Core Analysis | 357 | ||
| 11.2.3 Relaxation Time Distributions | 358 | ||
| 11.2.4 Diffusion as a Contrast Mechanism | 359 | ||
| 11.2.5 Internal Gradients | 362 | ||
| 11.3 Rock Lithology | 364 | ||
| 11.3.1 Sandstone | 364 | ||
| 11.3.2 Carbonates | 366 | ||
| 11.3.3 Unconventionals | 368 | ||
| 11.4 Advanced NMR Petrophysics | 371 | ||
| 11.4.1 Wettability | 371 | ||
| 11.4.2 Capillary Pressure | 373 | ||
| 11.4.3 Hydrodynamics | 374 | ||
| 11.4.4 Oil Recovery | 377 | ||
| 11.5 Applications in Other Industries | 381 | ||
| 11.6 Summary | 383 | ||
| Acknowledgments | 384 | ||
| References | 384 | ||
| Chapter 12 Confined Fluids: NMR Perspectives on Confinements and on Fluid Dynamics | 390 | ||
| 12.1 Introduction | 390 | ||
| 12.2 Basic Properties of Confined Fluids | 391 | ||
| 12.2.1 Phase State | 391 | ||
| 12.2.2 Diffusion Mechanisms | 393 | ||
| 12.2.3 Trajectory Analysis for Multi-phase Systems | 395 | ||
| 12.2.4 Restricted Diffusion | 398 | ||
| 12.2.5 Potentials of NMR for Delivering Complementary Information | 399 | ||
| 12.3 Structural Information Accessible by Diffusion NMR | 401 | ||
| 12.3.1 Tortuosity of the Pore Space | 401 | ||
| 12.3.2 Surface-to-volume Ratio | 404 | ||
| 12.3.3 Pore Size in Closed and Interconnected Pore Systems | 408 | ||
| 12.3.4 Pore Space Anisotropy | 412 | ||
| 12.3.5 Hierarchical Pore Spaces | 413 | ||
| 12.3.6 Pore Space Organization | 418 | ||
| 12.4 Fluid Behavior in Confined Spaces | 419 | ||
| 12.4.1 Surface Diffusion | 419 | ||
| 12.4.2 Global Equilibration Dynamics | 422 | ||
| 12.4.3 Memory Effects in Confined Fluids | 424 | ||
| 12.4.4 Ergodicity Theorem for Diffusion | 426 | ||
| 12.5 Conclusions and Perspectives | 428 | ||
| References | 428 | ||
| Chapter 13 NMR and Complementary Approaches to Establishing Structure-Transport Relationships in Disordered Porous Solids | 435 | ||
| 13.1 Introduction | 435 | ||
| 13.2 Surface Diffusion | 437 | ||
| 13.2.1 NMR Studies of Surface Diffusion | 437 | ||
| 13.2.2 Structure-Transport Model for Surface Diffusion Validated by NMR | 438 | ||
| 13.3 Pore Diffusion | 448 | ||
| 13.4 Structural Characterization and its Validation | 448 | ||
| 13.4.1 Gas Sorption | 448 | ||
| 13.4.2 Pore-Pore Co-operation Effects | 451 | ||
| 13.4.3 Cryoporometry | 452 | ||
| 13.4.4 Application of NMR Diffusometry to Improving Structural Characterization | 452 | ||
| 13.5 Conclusion | 462 | ||
| References | 462 | ||
| Chapter 14 NMR Diffusometry for the Study of Energy-related Soft Materials | 464 | ||
| 14.1 Introduction to Energy-related Soft Materials | 464 | ||
| 14.1.1 Soft Materials: Polymers, Ionic Liquids, Plastic Crystals, Liquid Crystals, Gels | 465 | ||
| 14.1.2 Morphology vs. Molecular Features that Influence Transport | 468 | ||
| 14.2 How Can NMR Diffusometry Help Us Understand Soft Materials? | 469 | ||
| 14.2.1 Overview: Chemical Selectivity and Tunable Translational Time/Length Scale | 469 | ||
| 14.2.2 Signal Analysis: SGP and GPD Approximations | 471 | ||
| 14.2.3 Restricted Diffusion in Polymer Membranes | 473 | ||
| 14.2.4 Activation Energy: A Window into Molecular Motion on ~1 nm Scales\r | 474 | ||
| 14.3 Key Challenges and Experimental Aspects in Nanostructured Soft Materials | 476 | ||
| 14.3.1 Lower Length-scale Limit, Short T2, and Signal Loss | 476 | ||
| 14.3.2 Artifacts When Using High Gradients to Observe Slow Diffusing Species | 477 | ||
| 14.3.3 Pre-averaging over Small Length Scale Heterogeneity | 480 | ||
| 14.3.4 Fruitful Combinations of NMR Techniques: Multimodal NMR | 481 | ||
| 14.4 Key Applications in Energy-related Soft Materials | 482 | ||
| 14.4.1 Nanostructured Ionic Polymer Membranes: Nanochannel Alignment and Diffusion Anisotropy | 482 | ||
| 14.4.2 Ionic Liquids Inside Nanostructured Polymers: Ion Associations | 486 | ||
| 14.4.3 Organic Ionic Plastic Crystals | 488 | ||
| 14.4.4 Ion Motions in Polymer-gel Battery Electrolytes | 490 | ||
| 14.5 Conclusion and Outlook | 493 | ||
| Acknowledgments | 494 | ||
| References | 494 | ||
| Chapter 15 Diffusion Magnetic Resonance Imaging in Brain Tissue | 497 | ||
| 15.1 Introduction | 497 | ||
| 15.1.1 Diffusion Basics | 498 | ||
| 15.1.2 How are dMRI Experiments Performed? | 500 | ||
| 15.2 Water Diffusion in Brain Tissue | 503 | ||
| 15.2.1 Complex Brain Microstructure and the Apparent Diffusion Coefficient | 503 | ||
| 15.2.2 Diffusion Tensor Imaging | 507 | ||
| 15.2.3 Non-Gaussian Diffusion | 510 | ||
| 15.3 Selected Applications of dMRI | 513 | ||
| 15.3.1 Diffusion Contrast in Ischemic Stroke | 513 | ||
| 15.3.2 Diffusion Changes in Development and Aging | 515 | ||
| 15.3.3 Fibre Tractography and Human Connectomics | 517 | ||
| 15.4 Conclusions | 519 | ||
| References | 520 | ||
| Chapter 16 Surface Effect Dominates Water Diffusion at Nanoscopic Length Scales | 529 | ||
| 16.1 Introduction | 529 | ||
| 16.2 1H ODNP Theory and Analysis of Local Water Diffusivity | 535 | ||
| 16.2.1 Moving from ξ to Dbulk/Dlocal\r | 535 | ||
| 16.2.2 Experimentally Determining ξ\r | 537 | ||
| 16.3 Results: ODNP Case Studies | 538 | ||
| 16.3.1 Translational Diffusivity of LUV Surface Water and Its Activation Energy | 538 | ||
| 16.3.2 Decoupling of Surface Water Dynamics on LUV from Bulk Solvent Viscosity | 542 | ||
| 16.3.3 LUV Bilayer-internal Water Diffusion and Its Activation Energy | 546 | ||
| 16.3.4 Lipid Membrane Integrity Relies on Stable Hydration Shell | 551 | ||
| 16.3.5 Effect of Confinement in a Biological GroEL/GroES Chaperone on Water | 554 | ||
| 16.3.6 Heterogeneous Water Dynamics within Nafion® Inner Membranes | 556 | ||
| 16.4 Conclusion | 563 | ||
| Acknowledgments | 563 | ||
| References | 563 | ||
| Subject Index | 568 |