Selectively observing the amplitude modulation under magic angle sample spinning

摘要

Magic angle sample spinning (MASS) averages the inhomogeneous magnetic field due to the susceptibility contrast in porous media by moduling the local magnetic field (frequency modulation). Molecular diffusion introduces a homogeneous broadening, which modulates the amplitude of the signal (amplitude modulation). The depth of amplitude modulation is determined by the interplay of molecular diffusion and MASS averaging and contains rich information on local magnetic fields, through which the spatial structure of the sample may be obtained. In this paper, we present two methods to quantify the amplitude modulation: a phase suppressed method and a more conventional two-dimensional (2D)-exchange method. The phase suppressed method directly observes the ampitude modulation in the time domain. The approximate equations are derived to extract the physical information from the time domain data. The conventional 2D-exchange spectrum contains both the frequency modulation and the amplitude modulation terms. The amplitude modulation introduces cross peaks in the 2D spectrum. The integration of the 2D spectrum along lines parallel to the main diagonal line will give a one-dimensional spectrum, that is the Fourier transform of the amplitude modulation.