Cross-relaxation and Cross-correlation Parameters in NMR

Molecular Approaches

Daniel Canet, Daniel Canet

• Publisher: Royal Society of Chemistry
• Year: 2017
• ISBN:
  9781788012362
• Edition: 1
• Topic: Medicina
• Subtopic: Imágenes diagnósticas

Spin relaxation parameters, although difficult to interpret, are attracting interest in NMR as these parameters are capable of yielding both structural and dynamic information. Cross-relaxation and cross-correlation parameters afford a non-ambiguous approach to molecular structure and dynamics although they require some special skills for their experimental determination and for their exploitation. This work will start with an introduction to nuclear spin cross-relaxation and cross-correlation phenomena in liquids then look in more detail at molecules in soft matter and large biomolecules. Providing a detailed, timely account, the authors are filling a gap in the present NMR literature for the analytical scientist.

CHAPTER 1

Introduction to Nuclear Spin Cross-relaxation and Cross-correlation Phenomena in Liquids

DANIEL CANET

Université de Lorraine, France
Email: [email protected]

Nuclear magnetic resonance (NMR) cross-relaxation and cross-correlation phenomena are part of the general nuclear spin relaxation processes. What is meant by relaxation is very common in physics, chemistry, biochemistry, etc. and is related to the recovery of a system that has been subjected to different constraints. As far as NMR is concerned, the nuclear spin system tends to recover toward its equilibrium configuration, which consists of the so-called macroscopic magnetization, collinear with the polarizing static magnetic field B₀. This magnetization originates from the magnetic momentum associated with each spin momentum. A nuclear spin system can be moved from its equilibrium configuration by changing, non-adiabatically, the B₀ field value or, more commonly, by applying pulses of an oscillating magnetic field called also the radio-frequency field. The latter is generally denoted B₁ and, with a frequency close to the nuclear resonances, can induce the NMR signal. As a matter of fact, the consideration of nuclear spin relaxation was a key issue for the first NMR experiments.¹ Moreover, although the prime interest of NMR for chemists was its ability to reveal the molecular structure via chemical shifts and coupling constants, it was rapidly realized that the relaxation parameters could also provide not only dynamical but structural information.

Very early (in 1948, whereas the first NMR experiments were performed in 1946), Bloembergen, Purcell and Pound² were able to interpret the two major relaxation parameters: T₁, the spin–lattice relaxation time (longitudinal relaxation time), related to the nuclear magnetization component along the B₀ field; and T₂, the spin–spin relaxation time (transverse relaxation time), related to the nuclear magnetization components perpendicular to the B₀ field. These two relaxation times are involved in the famous Bloch equations³ that, in a phenomenological way, accounts for the evolution of the three components of the nuclear magnetization (or polarization, magnetization being the polarization times the gyromagnetic ratio). These equations are perfectly valid if the system encompasses a single spin species. However, as soon as one is dealing with a multi-spin system, it is mandatory to consider a polarization for each spin species and, possibly, further quantities describing different spin states. Although T₁ and T₂ remain active for each individual polarization (they will be referred to as auto-relaxation parameters), it turns out that all spin states, including the polarization for each species, may be coupled by various spin relaxation pathways. The corresponding parameters include the so-called cross-relaxation and cross-correlation relaxation rates, which are the subject of this book. They arise from different relaxation mechanisms (considered in Section 1.1) and are active through the so-called spectral densities, a concept also developed in Section 1.1. How these parameters may be involved in dedicated experimental procedures is not a simple matter. It requires some knowledge of spin quantum mechanics (Section 1.2), which will be used for a detailed approach of cross-relaxation (Section 1.3) and cross-correlation (Section 1.4). Finally, the type of molecular information that can be gained from cross...