Susceptibility corrections in solid state NMR experiments with oriented membrane samples. Part II: theory.

In solid state NMR analysis of oriented biomembranes the samples typically have the shape of a rectangular block, formed by stacking a number of glass slides coated with the membranes under investigation. Reference material may be provided internally in the volume of the block or as an external layer on its surface, as described in the accompanying paper [J. Magn. Reson. 164 (2003) 104-114]. The demagnetizing field resulting in such non-spheroidal samples is inhomogeneous. It shifts and broadens the NMR lines of both the sample and of the reference, as compared to the ideal of a spherical sample. The magnitude of these effects is typically of the order of a few ppm. To determine the necessary corrections, a general analysis is presented here for the demagnetizing field of a layered sample of rectangular block geometry, with the normal of the layers parallel to the main field or tilted about an axis of the block. The correction to the line position of the block sample is found to be approximately equal to that of the spheroid which can be inscribed into the block, and for which the correction is well known. For an external reference layer, placed on top of the block, the correction can be found by the same approximation, invoking a simple mirror concept. The layered structure of the block can be accounted for by using an average magnetic susceptibility. Sample and support materials contribute to that average according to their volume filling factors. If the sample material is anisotropic at the molecular level, as e.g. lipid bilayers are, the resulting anisotropy of the block is reduced by the filling factor of the sample material.