Narrowing the Lines

An inherent difficulty in observing a narrow absorption line is that it does not absorb very much flux. The narrower the line, the less flux absorbed. In fact, the ideal -function line absorbs none at all. This statement may be verified by evaluating the integrated absorptance... 

Use solutions of low viscosity, and avoid solvents whose molecules have magnetic nuclei, especially protons. If broadening from protons of the medium is observed, replacement by deuterium will narrow the lines. 

An interesting example is available of inequivalent nuclei becoming equivalent on raising the temperature and going through a phase transition, reversibly. This occurs in squaric acid C4(0)2(0H)2, studied by single-crystal 13C NMR,29 and later (2004) also by 170 NMR. Here, MAS was used to narrow the lines sufficiently to observe the changes in the isotropic parts of the chemical-shift matrices. The phase transition occurs at 373 K. 

For such an experiment to work, we have to be able to distinguish the different domains during the evolution and the detection period of the two-dimensional experiment. Since proton spectral resolution in typical solids is very poor, we have to use homonuclear dipolar-decoupling methods to narrow the lines sufficiently to obtain spectral resolution. The 2D spin-diffusion CRAMPS spectrum was first recorded by Caravatti et al. [68] for blends of polystyrene (PS) and polyvinyl methyl-ether (PVME). There are other methods to generate an initial nonequilibrium polarization based on differences in linewidth or relaxation times. The reader is referred to the excellent book of Schmidt-Rohr and Spiess [67] for an overview. 

Hypercrosslinked resins have also been the subject of an NMR study [44] (see Section 3.4). CP/MAS NMR has been used to estimate the degree of crosslinking in a series of these species. The resins were examined in a solvent swollen and a nonswollen state to determine if with swelling in a deuterated solvent it was possible to narrow the line lines further. Determination of the level of crosslinking was carried out by deconvolution of the quaternary aromatic peak at ca. 146ppm (Figure 15.2.39). 

We noted in section 4.2 that the more rapidly the time domain signal decays the broader the lines become. A weighting function designed to improve the SNR inevitably leads to a broadening of the lines as such a function hastens the decay of the signal. In this section we will consider the opposite case, where the weighting function is designed to narrow the lines in the spectrum and so increase the resolution. 

Sample spinning.The rotation, using an air bearing, of the NMR tube/spin-ner assembly, used to average, on the NMR time scale, the strength of the applied magnetic field experienced by molecules in the sample solution. Sample spinning narrows the line widths of the peaks we observe and is almost exclusively employed in the collection of 1 -D spectra. 

It has been shown that, instead of an exponential function as in the case of 3-D system, in a pure 1-D system motional narrowing leads to G (t) exp (-/ ). Such a time dependence is intermediate between the static case (no motion), which gives a Gaussian G(t) exp (- F), and the 3-D motional narrowing, G(t) exp (- /). This shows that motion is less efficient in one dimension than in three dimensions in narrowing the line. 

The band width will be determined by the rate of atomic motion of the resonating nucleus, which, in turn, is determined by the relaxation times ti and f2. The larger these relaxation times (i.e., the faster the motion), the narrower the line widths. 

Ironically, too perfect a crystal may cause problems the line width in an X-ray diffractogram is dependent inter alia on its perfection. The more perfect a crystal is, the narrower the lines. However, if these lines are too narrow, then their detection may give rise to problems. Thus, a happy medium must be reached. 

When a specimen is stressed, one can think of continuous lines of force running through the material the stronger the force, the more the lines. If the specimen has constant cross section, the stress, which can be represented as the number of line of force per area, will be constant throughout the specimen. If the specimen narrows, the lines of force become more concentrated and the stress increases in that region. If there is a hole in the specimen, the lines will tend to flow aroimd the hole and become more concentrated in its vicinity. These lines become even more concentrated in the vicinity of a sharp discontinuity such as a square hole or a crack. (This is why portholes and hatches in the bulkheads of ships are roimd or oval. The windows in the Comet aircraft were square.)... 

Unfortunately, for systems with a number of different carbon nuclei, there is usually extensive overlap of the CSA signals, and the analysis of the powder pattern is difficult, if not impossible. Therefore, other techniques that partially narrow the lines must be used. Three different experiments can be used to determine chemical-shift anisotropies for powders ... 

The dipolar decoupling (DD)-CP-MAS C-NMR spectra of a glassy poly(ethyl-ene terephthalate) (PET), a PET sample annealed for 76 h at 200°C, and a solution-crystallized PET sample are compared in Fig. 9.14 [38]. The spectra show substantial differences that reflect the differences in the conformations and molecular packing of the chains. An increase in the crystallinity narrows the lines by limiting the number of conformational sequences to long sequences rather than to a series of short, disordered ones. 

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