Field-dependent C-13 chemical shifts in solids: A second-order dipolar perturbation
- 1 February 1986
- journal article
- research article
- Published by AIP Publishing in The Journal of Chemical Physics
- Vol. 84 (3) , 1196-1205
- https://doi.org/10.1063/1.450511
Abstract
The observation of field‐dependent C‐13 chemical shifts in the presence of high‐power proton decoupling and magic angle sample spinning (MAS) is documented. While the principal data were taken at fields of 1.4 and 4.7 T, the difference in chemical shift, in ppm, between the crystalline resonance of polyethylene and a reference resonance of solid adamantane varied as (a+b B −2 0) in measurements taken at six different fields in as many laboratories. At a given field there is no dependence of this shift difference on proton resonance offset, proton rf field strength, or sample spinning speed. In rigid solids, the ‘‘b’’ term in the foregoing relationship is twice as large for a methylene as for a methine carbon. Results of chemical shiftmeasurements at two fields are reported for polyethylene, polypropylene, and three molecular solids including the normal alkane, nonadecane, which exhibits fast well‐defined molecular rotation in the solid rotator phase. The observed shift differences for several kinds of carbons at 1.4 and 4.7 T agree very well with the explanation that the b term in the above expression results from a second‐order energy perturbation involving the nonsecular ‘‘C’’ and ‘‘D’’ terms of the dipolar Hamiltonian. A simple theory is presented for a C‐13‐proton spin pair, and the role of MAS is examined. A line broadening equal to about one‐half of the mean shift is also associated with this phenomenon. The behavior of this second‐order shift is also considered for cases where fast molecular motion is present or where multiple protons are bonded to a carbon. Even at 1.4 T the shifts are rather small, i.e., 0.72 and 0.36 ppm, respectively, for a methylene and a methine carbon. Corrections which will account for this second‐order shift are easily made in powder samples of rigid molecules; thus, true chemical shifts can be recovered. Above an operating field of, say, 3 T, the degradation of linewidth due to the spread of these second‐order shifts is negligible (<3 Hz) even for a methylene group. Finally, a challenge is offered to consider whether similar second‐order shifts operate in homonuclear coupled systems in the presence of homonuclear decoupling and MAS.Keywords
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