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Deuterium NMR – a powerful tool in studying molecular order

The analysis of deuterium NMR (2H-NMR) spectra depends on the way the quadrupolar hamiltonian is averaged by molecular motions. In the presence of fast, anisotropic molecular motions the quadrupolar interaction is averaged to a non-zero value, which results in a doublet of Lorentzian lines characterized by a splitting Δν. In the general case of fast uniaxial motions around a local symmetry axis denoted by , the splitting is given by: Δν = 2νq|<P2(ϑ)> P2(Ω)|, (1) in which P2(ϑ) is the second order Legendre polynomial: P2(ϑ) = (3 cos2 ϑ – 1) / 2. (2) ϑ(t) is the instantaneous angle between the C−D bond and the local axisn, Ω is the angle between n and the static magnetic field B. The overbar denotes a time averaging over motions faster than the characteristic time νq-1. The factor <P2(ϑ)> is the local orientational order parameter which describes the degree of motional anisotropy of the C−D bond with respect to the symmetry axis. For C−D bonds in −CD2− or −CD3 groups, νq = 125 kHz. In the fast motion limit, the line width of each component of the doublet depends on the relaxation time T2 and is generally small or comparable to the value of the splitting. This leads to well resolved spectral lines. In a disordered system, the resulting spectrum is the superposition of such doublets, and the resulting line shape is thus directly related to the distribution of residual interactions in the system. In a macroscopically oriented system, the spectrum is a doublet, which gives a direct measurement of the macroscopic order parameter. Based on measured splitting values and the known value of macroscopic angle Ω, the mean degree of orientational order parameter (S) can be calculated as: S = Δν / [2νq / |P2(cos Ω)|]. (3) Some typical 2H-NMR spectra of various anisotropic systems will be presented and analyzed.

Deuterium NMR; orientational order; anisotropic motion

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