Nuclear Spin Relaxation in Liquids

Theory, Experiments, and Applications, Second Edition

Jozef Kowalewski, Lena Maler

• Publisher: CRC Press
• Year: 2017
• Print ISBN:
  9781498782142
• eBook ISBN:
  9781351264587
• Topic: Physical Sciences
• Subtopic: Condensed Matter

Nuclear magnetic resonance (NMR) is widely used across many fields of science because of the rich data it produces, and some of the most valuable data come from studies of nuclear spin relaxation in solution. The first edition of this book, published more than a decade ago, provided an accessible and cohesive treatment of the field. The present second edition is a significant update, covering important new developments in recent years.

Collecting relaxation theory, experimental techniques, and illustrative applications into a single volume, this book clarifies the nature of the phenomenon, shows how to study it and explains why such studies are worthwhile. Coverage ranges from basic to rigorous theory and from simple to sophisticated experimental methods. Topics include cross-relaxation, multispin phenomena, relaxation studies of molecular dynamics and structure and special topics such as relaxation in systems with quadrupolar nuclei, in paramagnetic systems and in long-living spin states.

Avoiding overly demanding mathematics, the authors explain spin relaxation in a manner that anyone with a familiarity with NMR can follow. The focus is on illustrating and explaining the physical nature of relaxation phenomena. Nuclear Spin Relaxation in Liquids: Theory, Experiments and Applications, 2nd edition, provides useful supplementary reading for graduate students and is a valuable reference for NMR spectroscopists, whether in chemistry, physics or biochemistry.

1

Equilibrium and Non-
Equilibrium States in NMR

The concepts of equilibrium and deviation from equilibrium have a central role in physical ­chemistry. Once a system is in a non-equilibrium state, it will tend to return to equilibrium in a process that does not occur instantaneously. This general phenomenon of development towards equilibrium is called relaxation. In the specific context of nuclear magnetic resonance, the equilibrium state is that of a macroscopic sample of nuclear spins in a magnetic field. In order to talk about a development towards equilibrium, we need to define and be able to create an initial state, which is different from the equilibrium state. Using experimental techniques of present-day nuclear magnetic resonance (NMR) spectroscopy, in the first place radiofrequency pulses, it is possible to create a large variety of non-equilibrium states. Starting from a given non-equilibrium situation, the spin systems evolve in a complicated way, in which the “return to equilibrium” processes compete with related phenomena, converting one type of non-equilibrium into another. In NMR, the processes by which the return to equilibrium is achieved are denoted spin relaxation. Relaxation experiments were among the earliest NMR applications of modern Fourier transform NMR, and the development of applications and experimental procedures has been enormous. Consequently, there is a vast literature on NMR relaxation, regarding both theoretical considerations and advances in methodology. Relaxation is important, since it has effects on how NMR experiments are carried out, but perhaps even more valuable is the information content derived from relaxation parameters. Information about the physical processes governing relaxation can be obtained from experimental NMR parameters.

In order to set the stage for theoretical descriptions of spin relaxation, we need to define the spin system and the means of manipulating the spin systems to obtain non-equilibrium states. In this chapter, we provide elementary tools for the description of spin systems and their equilibrium and ­non-equilibrium states.

1.1Individual Spins: Elements of Quantum Mechanics

In order to arrive at a description of a large number of spins, we need to start with a single spin. The properties of spin are obtained using quantum mechanics. A brief account of the necessary quantum mechanical background is given in this section, and the reader is directed to Further reading (in particular the books by Atkins and Friedman, Keeler, Levitt and Slichter) for a more complete presentation. The basis of quantum mechanics can be formulated as a series of postulates, fundamental st...

Table of contents

• Cover
• Half-Title
• Title
• Copyright
• Contents
• Preface
• Further Reading List
• 1 Equilibrium and Non-Equilibrium States in NMR
• 2 Simple Relaxation Theory
• 3 Relaxation through Dipolar Interactions
• 4 The Redfield Relaxation Theory
• 5 Applications of Redfield Theory to Systems of Spin 1/2 Nuclei
• 6 Spectral Densities and Molecular Dynamics
• 7 NMR: The Toolbox
• 8 Measuring T 1 and T 2 Relaxation Rates
• 9 Cross-Relaxation Measurements
• 10 Cross-Correlation and Multiple-Quantum Relaxation Measurements
• 11 Relaxation and Molecular Dynamics
• 12 Applications of Relaxation-Related Measurements to Structure Determination
• 13 Relaxation and Chemical Exchange
• 14 Effects of Quadrupolar Nuclei
• 15 Nuclear Spin Relaxation in Paramagnetic Systems in Solution
• 16 Long-Lived Nuclear Spin States and Related Topics
• 17 Nuclear Spin-Relaxation in Other Aggregation States