The pulsed field gradient spin‐echo nuclear magnetic resonance method is used to measure the translational diffusion of solvents and solutes in homogeneous and heterogeneous systems. It is widely used in the characterization of molecules and materials in general, via phenomena such as ‘diffusion interference’. It is also the basis of tissue discrimination in magnetic resonance imaging, via diffusion tensor imaging. The mathematical equation used to analyze data from a simple noninteracting solute (using a pair of magnetic field gradient pulses that are applied in the experiment) was first derived by Stejskal and Tanner. However, in the article and in subsequent presentations the basic derivation, which we call the the “theoretical physics” of the theory, is not presented in extenso. Conversely, many papers in which the exploration of the effects of magnetic field gradient pulses of shapes other than simple rectangles generally begin with the time‐dependent integral that emerges from the original theoretical physics. To fill this “pedagogical gap” we use here a rigorous step‐by‐step approach to the theoretical physics of the Stejskal–Tanner equation and indicate how it was based on earlier theories. We also take the opportunity to indicate a contemporary approach to deriving new relationships between user‐defined magnetic field gradient pulse shapes and the diffusion coefficient; and we show how these can be rapidly and accurately derived using symbolic computation. © 2012 Wiley Periodicals, Inc. Concepts Magn Reson Part A 40A: 205–214, 2012.

No abstract

No abstract

Electron-electron double resonance pulsed electron paramagnetic resonance (EPR) at 95 GHz (3.3 T) is used to follow the dynamics of the electron spin polarization during the first stages of dynamic nuclear polarization in solids. The experiments were performed on a frozen solution of Gd(+3) (S=7/2) in water/glycerol. Focusing on the central vector -1/2 --> vector +1/2 transition we measured the polarization transfer from the Gd(3+) electron spin to the adjacent (1)H protons. The dependence of the echo detected EPR signal on the length of the microwave irradiation at the EPR "forbidden" transition corresponding to an electron and a proton spin flip is measured for different powers, showing dynamics on the microsecond to millisecond time scales. A theoretical model based on the spin density matrix formalism is suggested to account for this dynamics. The central transition of the Gd(3+) ion is considered as an effective S = 1/2 system and is coupled to (1)H (I = 1/2) nuclei. Simulations based on a single electron-single nucleus four level system are shown to deviate from the experimental results and an alternative approach taking into account the more realistic multinuclei picture is shown to agree qualitatively with the experiments.