Larmor frequency molecular reorientation

The dynamic window of a given NMR technique is in many cases rather narrow, but combining several techniques allows one to almost completely cover the glass transition time scale. Figure 6 shows time windows of the major NMR techniques, as applied to the study of molecular reorientation dynamics, in the most often utilized case of the 2H nucleus. Two important reference frequencies exist The Larmor frequency determines the sensitivity of spin-lattice relaxation experiments, while the coupling constant 8q determines the time window of line-shape experiments. 2H NMR, as well as 31P and 13C NMR, in most cases determines single-particle reorientational dynamics. This is an important difference from DS and LS, which access collective molecular properties. 

Various 2H, 13C and 31P NMR techniques were used to follow the slowing down of molecular dynamics during the glass transition.3 In particular, 2H NMR proved very powerful since solely molecular reorientation is probed and isotopic labeling is easily achieved. Fig. 7 shows the correlation time windows of the major 2H NMR techniques. Two reference frequencies exist The Larmor frequency col determining the sensitivity of the spin-lattice relaxation and the coupling constant 8q fixing the time window of line-shape experiments. 

A number of mechanisms are known to contribute to spin-lattice relaxation in a molecule dipole-di-pole, spin-rotation, quadrupolar, scalar, and CSA, each associated with a corresponding relaxation rate. Analytical interest focuses only on the intemu-clear C-H dipole-dipole relaxation with a rate I IDD = 1/Tidd = (f//1.988)(l/Ti), which is proportional to the inverse sixth power of the carbon-proton distance rca, and depends on the rotational and internal molecular motion. For medium-sized molecules of nearly spherical shape (isotropic molecular reorientation) in solvents of low viscosity the condition of extreme narrowing holds, i.e. ct)cTc l for all Larmor frequencies ft)c, and therefore Ri=ANtc. The correlation time %c is a measure of the velocity of the molecule s rotational diffusion jumps. For N nearest protons within a distance rca the quantity A takes the form A = jrca... 

Variable frequency proton Ti studies were first used to detect the characteristic dependence of Ti due to director fluctuations [6.20] in liquid crystals. It was recognized soon after that besides the director fluctuations, relaxation mechanisms, which are effective in normal liquids such as translational self-diffusion and molecular reorientation [6.24], also contribute to the proton spin relaxation in liquid crystals. Though the frequency dependences of these latter mechanisms are different from the relaxation, the precise nature of proton Ti frequency dispersion studied over a limited frequency range using commercial NMR spectrometers often may not be unambiguously identified. Furthermore, because of a large number of particles involved in collective motions, the motional spectrum has much of its intensities in the low-frequency domain far from the conventional Larmor frequencies. The suppression of director fluctuations in the MHz region due... 

In the nematic phase the spin-lattice relaxation rate at high Larmor frequencies is determined by local reorientations of the molecule and internal molecular motions. The spin-spin relaxation rate, I/T2, on the other hand, is determined by nematic order director fluctuations and rotations induced by translational diffusion [216]. 

Figure 2 Spectral density J(co) for three values of correlation time, plotted as a function of frequency co. The spectral density has a cutoff frequency coc = l/tc, where tc is the correlation time of molecular reorientations. As molecular reorientations become faster, decreases and the spectral density dispersion becomes flatter. The terms T, T2 and NOE depend on the value of the spectral densities at 0, coq and 2coo, where coq is the Larmor frequency. (A) Spectral density for slowly reorienting molecules which have long correlation times (tc Vcoq). In such cases the spectral density has a negligible value at coq and 2coo, but large values at low frequencies. (B) Spectral density for intermediate values of correlation times, for which Tc Vcoq. (C) Spectral density for small molecules undergoing fast reorientation, which have short correlation times (tc Vcoq) and the spectral density has nearly equal values from 0 to 2(Oq. Since the area under the curves is constant, the spectral density has different magnitudes at each frequency in the above three cases.

The Ti relaxation time is the time constant for magnetisation to recover on the z axis (Figure 7.3b), restoring the equilibrium Boltzmann distribution of spins. This relaxation process occurs by energy loss to the surrounding lattice (any nearby molecules) and the efficiency of the process is determined by molecular reorientations occurring near the Larmor frequency (e.g. molecular rotations and internal motions). T, is measured with the inversion-recovery (IR) or saturation-recovery (SR) pulse sequence (see Section 7.7.2). 

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