Federico Casanova Juan Perlo Bernhard Blümich. Editors. Single-Sided NMR

Transkript

1 Single-Sided NMR

2

3 Federico Casanova Juan Perlo Bernhard Blümich Editors Single-Sided NMR 123

4 Editors Dr. Federico Casanova RWTH Aachen Inst. Technische und Makromolekulare Chemie Worringerweg Aachen Sammelbau Chemie Germany fcasanova@mc.rwth-aachen.de Juan Perlo RWTH Aachen Inst. Technische und Makromolekulare Chemie Worringerweg Aachen Sammelbau Chemie Germany jperlo@mc.rwth-aachen.de Prof. Dr. Bernhard Blümich RWTH Aachen Inst. Technische und Makromolekulare Chemie Worringerweg Aachen Sammelbau Chemie Germany bluemich@mc.rwth-aachen.de ISBN e-isbn DOI / Springer Heidelberg Dordrecht London New York c Springer-Verlag Berlin Heidelberg 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: WMX Design GmbH, Heidelberg Printed on acid-free paper Springer is part of Springer Science+Business Media (

5 Preface The study of complex molecules requires high sensitivity and resolution for chemical analysis. This is why the NMR community pushes the development of ever more powerful superconducting magnets that generate stronger and more homogeneous magnetic fields every year. Today s NMR magnets are heavy giants installed in special NMR laboratories built to shield electromagnetic interference, control the temperature, and reduce magnetic field distortions in order to provide ideal experimental conditions in a small volume located inside the magnet. Besides the fact that samples must be taken to the magnet to be analyzed, they must fit in the limited space available in the magnet center. Large samples cannot be investigated in this way without cutting. This problem was already noted in the early days of NMR when the technique was identified as a potential tool to characterize rock formations in situ. Measuring properties of the pore structure as well as characterizing the saturating fluids downhole by NMR triggered the development of what today is called inside-out NMR. Here, instead of placing the sample inside the magnet, the apparatus is placed inside or at one side of the object. The implementation of this concept requires the construction of sensors projecting considerable magnetic and radiofrequency (rf) fields outside the magnet and inside the sample under study. For more than 30 years well-logging tools used the earth s magnetic field as polarization field, but the low sensitivity and poor spatial selectivity limited their commercial success. Potential application of open NMR sensors to measure, for example, moisture in building materials or soil motivated engineers to use electromagnets to increase the magnetic field strength. However, these instruments were large, weighing up to 300 kg and operated at low frequencies like 3 MHz. Perhaps the most important step toward reducing the size of the magnets was the use of permanent magnets to generate the static magnetic field. This eliminated most of the power consumption of these NMR devices. During the late 1980s and early 1990s various magnet geometries have been proposed by different well-logging companies, and a number of research groups proposed small singlesided magnets generating magnetic fields of about 0.5 T external to the sensor. An example is the known U-shaped magnet geometry used by the NMR-MOUSE, which is obtained by opening the C-shaped geometry used in conventional closed magnets. v

6 vi Preface The big challenge faced when working outside the magnet is posed by the large inhomogeneities in both the magnetic and the radiofrequency fields. Under such experimental conditions even hard rf pulses act as selective pulses and off-resonance effects are considerable. Therefore, during the 1990s, several groups set their attention on understanding the response of the spin system to pulse sequences known from conventional NMR, like the Carr-Purcell-Meiboom-Gill (CPMG) sequence extensively used to measure the transverse relaxation time T 2, when they are applied in the presence of a strongly inhomogeneous magnetic field. Chapter 2 provides the tools needed to evaluate the evolution of the magnetization to such pulse sequences implemented in the magnetic field generated by open NMR sensors. Besides providing the timing of some well-known pulse sequences and the phase cycle for the rf pulses required to eliminate unwanted signals generated by resonance offsets, typical features that must be considered at the time of implementing them are discussed. Moreover, a general expression is derived for the sensitivity of NMR experiments in inhomogeneous fields. The conclusions drawn from this analysis set the rules for optimizing magnet and rf coils to maximize the signal-to-noise ratio of single-sided sensors. In the presence of inhomogeneous magnetic fields, relaxation times and diffusion coefficients are the key NMR parameters to assess sample composition and dynamics. To extract maximum information from relaxation and diffusion measurements, a number of numerical tools have been proposed. One of the most powerful ones is based on calculating the inverse Laplace transform of the signal decay to obtain the relaxation time distribution from a relaxation measurement. Although initially this transformation has been applied to 1D data sets, recently the possibility to extend it to 2D experiments in reasonable computation times has been reported. It opened the door to measure powerful multi-dimensional diffusion relaxation and relaxation relaxation correlation spectra useful to disentangle overlapping signals in a way similar to conventional multi-dimensional Fourier NMR spectroscopy. This methodology is described in detail in Chap. 3. Although initially magnets were optimized to maximize sensitivity by maximizing magnetic field strength (at the expense of a strong static gradient) or the excited volume (at the expense of field strength), later, harder constrains have been imposed to the magnet design in order to generate convenient magnetic field profiles. Several of these magnets, including suitable rf coils, are presented in Chap. 4. A particularly useful field profile is the one that defines a uniform gradient along the depth direction. In the presence of such a field profile a slice parallel to the sensor surface can be exited at variable positions inside the object. Achieving depth resolution is useful to elucidate the depth structure of large samples. Moreover, furnishing these magnets with a set of coils that generate pulsed gradient fields along the two lateral directions, 3D spatial localization has been achieved. An important step toward a functioning open tomograph required the adaptation of single-point imaging sequences to work in inhomogeneous fields where multi-echo acquisition is mandatory to achieve maximum sensitivity. The different methods available to encode position during CPMG-like sequences are described in Chap. 5, where also

7 Preface vii suitable pulsed field gradient sequences are discussed to measure molecular velocity in the presence of a strong background gradient. Accepting the field inhomogeneities as unavoidable for open sensors, pulse sequences specially designed to minimize off-resonance effects have been proposed. A particularly challenging problem that attracted considerable attention over the years was the possibility to recover spectroscopic information from experiments performed in inhomogeneous fields. For a long time this was thought to be impossible because the static magnetic field inhomogeneities are usually orders of magnitude larger than those created by the microscopic structure of the molecules to be detected. In addition, terms in the spin Hamiltonian arising from chemical shifts or field inhomogeneities are formally identical. As a natural consequence, no radiofrequency pulse sequence was deemed capable of differentiating both types of interactions. A breakthrough was achieved in 2001 when an innovative alternative to recover a chemical-shift resolved spectrum in an inhomogeneous magnetic field was presented. The technique is based on matching the spatial dependence of the static and the rf magnetic fields, to generate nutation echoes whose phase is only sensitive to chemical-shift differences. This methodology and its implementation in a single-sided magnet are discussed in Chap. 6. Although for decades magnetic field inhomogeneity was assumed to be a handicap inherent to these sensors, during the last years an important step ahead toward recovering spectroscopic resolution has been reported. In particular, it has recently been proven that highly homogeneous fields can be generated even outside a magnet by furnishing the main magnet with a shim unit built from small and adjustable permanent magnet blocks. Moreover, a way has been suggested to combine magnetic materials with different temperature coefficients to build a magnet with a temperature-compensated magnetic field. The strategy followed to homogenize the stray field of a single-sided magnet is discussed in Chap. 7. Over the years, single-sided sensors have found applications in diverse fields such as the non-destructive testing of rubber and polymer products, food and life stock analysis, as well as the state assessment of objects of cultural heritage. Applications in the area of biological tissue are discussed in Chap. 8, while those in the area of material science and quality control are presented in Chap. 9. Finally, Chap. 10 intends to familiarize the reader with the particular hardware requirements of singlesided NMR. Aachen, Germany December 2010 Federico Casanova Juan Perlo Bernhard Blümich

8

9 Contents 1 Single-Sided NMR... 1 Federico Casanova, Juan Perlo, and Bernhard Blümich 1.1 Development of Open NMR Sensors Well-Logging Tools Mobile Single-Sided Sensors The NMR-MOUSE Methods for Mobile NMR... 6 References NMR in Inhomogeneous Fields Federico Casanova and Juan Perlo 2.1 Introduction Evolution of the Magnetization During a Pulse Sequence Separation of the Magnetization into Coherence Pathways Numerical Calculation of the NMR Signal Pulse Sequence Analysis Single rf Pulse The Generation of Hahn Echoes The CPMG Sequence Inversion and Saturation Recovery Diffusion Measurements The SNR in Inhomogeneous Fields The Reciprocity Principle Numerical Calculations of the SNR An Analytical Solution for the SNR References Ex Situ Measurement of One- and Two-Dimensional Distribution Functions Martin D. Hürlimann 3.1 Introduction Relaxation ix

10 x Contents Diffusion Diffusion Relaxation Distribution Functions Pulse Sequences and Spin Dynamics in Inhomogeneous Fields Relaxation Measurement: Carr-Purcell-Meiboom-Gill Sequence Diffusion Measurements with Static Gradients T 1 Measurements in Inhomogeneous Fields One-Dimensional Distribution Functions Data Inversion Regularization Systematic Errors Uncertainties Two-Dimensional Diffusion Relaxation Distribution Functions Two-Dimensional Diffusion-Relaxation Measurements Data Analysis Interpretation of Distribution Functions Applications of Two-Dimensional Distribution Functions Two-Component Systems Wettability Complex Miscible Fluid Structured Fluid Pore Geometry of Porous Media Conclusion References Magnets and Coils for Single-Sided NMR Juan Perlo 4.1 Magnets B 0 Perpendicular to the Sensor Surface, the Bar Magnet Geometry B 0 Parallel to the Sensor Surface, the U-Shaped Geometry Magnets for Depth Profiling Sweet-Spot Magnets RF Coils Coils for Depth Profiling Coils for Sweet-Spot Magnets Gradient Coils References Single-Sided Tomography Federico Casanova 5.1 Depth Resolution Using the Static Field Gradient Spatial Encoding by Fourier Imaging Multi-Echo Acquisition Schemes...117

11 Contents xi RARE-Like Imaging Sequence CPMG-CP for Quadrature Detection Performance of the Multi-Echo Detection Scheme Sensitivity Improvement Relaxation and Diffusion Contrast D Imaging Displacement Encoding PFG Methods in Inhomogeneous Fields Measurement of Velocity Distributions Spatially Resolved Velocity Distributions D Velocity Maps References High-Resolution NMR in Inhomogeneous Fields Vasiliki Demas, John M. Franck, Jeffrey A. Reimer, and Alexander Pines 6.1 Introduction Approaches Based on Spin Interactions Ex Situ NMR: Spatially Dependent z-rotations Ex Situ Matching: Compensating Static Field Inhomogeneities via Spatially Matched rf Shim Pulses: Corrections Based on Gradient Modulations During an Adiabatic Double Passage Adjusted Chirp Shim Pulses Summary References High-Resolution Spectroscopy in Highly Homogeneous Stray Fields. 165 Ernesto P. Danieli 7.1 Sensor Design Main Unit Shim Unit Shimming Magnetic Fields with Movable Permanent Magnets Generation of Linear Terms Along y Generation of Linear Terms Along x and z Generation of Quadratic Terms x 2 and z Experimental Results Shimming the Magnet to Higher Order Improving Resolution and Working Volume Size Temperature Compensation Conclusions References Applications in Biology and Medicine Bernhard Blümich 8.1 Skin Tendon...192

12 xii Contents 8.3 Mummies and Bones Unilateral Imaging of Biological Matter Conclusions References Applications in Material Science and Cultural Heritage Jürgen Kolz 9.1 Elastomers Crosslink Density Aging Imaging Hard Polymers Ingress of Solvents Cultural Heritage References Spectrometer Hardware Jörg Felder 10.1 Single-Sided vs. Conventional: Systematic Differences Frontend Design Matching and Balancing Transmit-Receive Switching Transmitter Design Conventional Power Amplifiers Alternative Amplifier Designs Receiver Design Low-Noise Amplifier Frequency Generation and Mixing Digital Hardware Frontend Signal Processor Selection Digital Phase Sensitive Detector References Index...241

13 Contributors Bernhard Blümich Institut für Technische Chemie und Makromolekulare Chemie, RWTH Aachen University, D-52074, Aachen, Germany, Federico Casanova Institut für Technische Chemie und Makromolekulare Chemie, RWTH Aachen University, D-52074, Aachen, Germany, Ernesto P. Danieli Institut für Technische Chemie und Makromolekulare Chemie, RWTH Aachen University, D-52074, Aachen, Germany, Vasiliki Demas University of California, Berkeley, CA 94720, USA; T2 Biosystems, Inc. Cambridge, MA 02141, USA, Jörg Felder Institut für Hochfrequenztechnik, RWTH-Aachen University, D Aachen, Germany; Institute of Neuroscience and Medicine 4, Medical Imaging Physics, Forschungszentrum Juelich GmbH, Juelich, Germany, John M. Franck University of California, Berkeley, CA 94720, USA, Martin D. Hürlimann Schlumberger-Doll Research, Cambridge, MA 02141, USA, Jürgen Kolz Institut für Technische Chemie und Makromolekulare Chemie, RWTH Aachen University, D-52074, Aachen, Germany; ACT GmbH, Aachen, Germany, Juan Perlo Institut für Technische Chemie und Makromolekulare Chemie, RWTH Aachen University, D-52074, Aachen, Germany, Alexander Pines University of California, Berkeley, CA 94720, USA, Jeffrey A. Reimer University of California, Berkeley, CA 94720, USA, xiii