Attenuation of homo- and heteronuclear multiple spin echoes by diffusion

Abstract

Multiple spin echoes arise after “nonlinear” evolution of coherences in the presence of modulated demagnetizing fields. Such modulations can be prepared, for example, with the aid of a sequence of two 90° radio-frequency pulses in the presence of pulsed or steady field gradients. The echo amplitudes are sensitively attenuated by translational diffusion so that diffusivities can be determined on this basis. Homo- and heteronuclear variants of multiple-echo pulse sequences are considered here. A formalism based on the Bloch/Torrey equations is presented that describes the features displayed by the experimental data. The resulting attenuation formula for the homonuclear case generally accounts for all radio-frequency and field gradient pulse intervals occurring in the frame of this “pulsed gradient nonlinear spin echo” technique. Furthermore, an analogous formalism is reported for the heteronuclear case where the two nuclear species may populate different molecules with different diffusivities. It is shown that, apart from the conventional attenuation mechanism due to incomplete refocusing of the coherences, there are three additional processes contributing to homo- and heteronuclear multiple-echo attenuation by diffusion: Leveling of the magnetization helix and hence of the z magnetization grid formed by the second radiofrequency pulse, further leveling of that z magnetization grid by displacements of the dipoles producing the grid, and molecular displacements relative to the spatially modulated demagnetizing field.