Chapter 2: Essentials of the Theory of Spin Relaxation as Needed for Field-cycling NMR

To profit fully from the potential of field-cycling NMR relaxometry, accompanying theoretical development is greatly needed. Theoretical models appropriate for a thorough analysis of field-cycling relaxation data should take into account complex, quantum mechanical scenarios of relaxation processes, including different types of spin interactions in diamagnetic, paramagnetic and superparamagnetic systems, remain valid for arbitrary motional conditions (from slow dynamics expected in solids and biomolecules to the fast motion regime) and link the relaxation features with specific dynamic and structural properties of molecular and ionic systems in different phases. Formulating such comprehensive theoretical models has proven to be a great challenge. This chapter provides an overview of theoretical approaches needed to address the demanding theoretical tasks – from the perturbation relaxation theory for simple (model) systems, via systems of increasing complexity in terms of spin interactions, to the application of the stochastic Liouville equation, combined with different models of the underlying dynamic processes.