Attenuation of homo- and heteronuclear multiple spin echoes by diffusion

Multiple spin echoes arise after "nonlinear" evolution of coherences in the presence of modulated demagnetizing fields. Such modulations can be prepar ed, for example, with the aid of a sequence of two 90 degrees radio-frequen cy pulses in the presence of pulsed or steady field gradients. The echo amp litudes are sensitively attenuated by translational diffusion so that diffu sivities 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 display ed by the experimental data. The resulting attenuation formula for the homo nuclear case generally accounts for all radio-frequency and field gradient pulse intervals occurring in the frame of this "pulsed gradient nonlinear s pin echo" technique. Furthermore, an analogous formalism is reported for th e heteronuclear case where the two nuclear species may populate different m olecules with different diffusivities. It is shown that, apart from the con ventional attenuation mechanism due to incomplete refocusing of the coheren ces, there are three additional processes contributing to homo- and heteron uclear multiple-echo attenuation by diffusion: Leveling of the magnetizatio n helix and hence of the z magnetization grid formed by the second radiofre quency pulse, further leveling of that z magnetization grid by displacement s of the dipoles producing the grid, and molecular displacements relative t o the spatially modulated demagnetizing field. (C) 2001 American Institute of Physics.