Time-suspension multiple-pulse sequences: applications to solid-state imaging

Abstract

In this Communication, we introduce a 48-pulse homonuclear dipolar decoupling cycle which also refocuses chemical shifts and other resonance offsets. When applied by itself to a system of spins then it appears that the spin system does not evolve in the absence of irreversible effects. By carefully combining this multiple-pulse sequence with a time-dependent magnetic field gradient, the gradient-induced evolution can be preserved without destroying the line-narrowing benefits of the cycle. With this method we hope to obtain liquid-like images of solid samples. One approach to solid-state imaging, then, is to combine a multiple-pulse cycle which averages time-independent linear and bilinear Z, Hamiltonians with a temporally and spatially dependent linear Z, Hamiltonian in such a manner that this spatially dependent Hamiltonian does not interfere (I ) with the multiple-pulse averaging of the time-independent Hamiltonians. This approach allows high-resolution solid-state images to be obtained with modest magnetic field gradient strengths thereby avoiding the sensitivity cost associated with large detection bandwidths (2,3). In addition, the resulting images have nearly uniform spatial resolution unlike solid-state images that are acquired with multiple-pulse sequences in a time-independent magnetic field gradient. These “time-suspension” cycles average both linear and bilinear Z, Hamiltonians by toggling Z, and Z,Z: operators through a variety of states the temporal average of which is zero. We use time suspension here to connote setting to zero the time evolution of a propagator rather than the equivalent picture in which the spin-dependent part of the Hamiltonian is set to zero: this phrase is chosen in analogy to “time-reversal” sequences which change the sign of the spin Hamiltonian. Such discussions are only useful when one remembers that irreversible effects are excluded, and spin-lattice relaxation and molecular motions place a limit on the interval over which manipulations of the Hamiltonian may be equated to manipulations of time. Naturally, timesuspension only refers to the sampling point for the cycle, and spin evolution during the cycle is much more complicated. Time-suspension sequences are well known in solid-state imaging: an eight-pulse version was the basis of an early imaging scheme suggested by Mansfield and Grannel (4); Weitekamp et al. have used this approach for radio frequency gradient solid-state imaging (5, 6), and we have employed this approach for solid-state imaging with