Info

1.15 g

Tobacco Mosaic Virus

40 x 106

336,500

2,130

20 g

we have a fixed area of land, and we not only have more houses to put in it but the houses are getting larger as well. In addition to the overlap problem, the peak height is reduced because the intensity is spread out over a larger range of frequencies. Because the "peak height" of the noise remains the same, the signal-to-noise ratio decreases and eventually the peak "disappears" in a sea of noise.

12.2.3 Chemical-Shift Anisotropy

Why does linewidth increase with molecular weight? One reason has to do with chemical-shift anisotropy (CSA, Chapter 2, Section 2.6), which is the dependence of chemical shift on orientation of the molecule with respect to the Bo field. We saw that chemical shifts in the benzene ring are particularly sensitive to orientation, but the same applies to the XH, 15N, and 13 C chemical shifts in an amide linkage and to a lesser extent at all positions in a protein. In the extreme case of a solid sample, the molecules are all fixed in their orientation and each resonance would be very broad because of the variation of chemical shift with orientation over the whole ensemble of molecules in the sample. In the solution state, small molecules are rapidly reorienting ("tumbling") all the time with no orientational preference ("isotropic" motion), so we see a single sharp line at the average chemical shift, just as we saw in fast exchange (Chapter 10, Section 10.2) when different environments are switched back and forth rapidly. As molecules get larger, though, they tumble more slowly and the lines begin to broaden due to incomplete averaging of the different orientations, just like exchange broadening. Because CSA (the range of variation of chemical shift with orientation) is measured in ppm, the actual variation in hertz gets larger as we go to larger Bo field. It is the variation in hertz that determines the tumbling rate necessary to average it to a sharp line: 1/(2.22 Av) is the NMR timescale for exchange coalescence, where Av is expressed in Hz. So if we try to get around the overlap problem by spending millions for a very high field (e.g., 900 MHz) instrument, we are also broadening our lines due to this CSA effect!

12.2.4 Dipole-Dipole Relaxation

Even if we consider only the dipole-dipole interactions, T2 is determined entirely by the tumbling rate of the molecule (Chapter 5, Fig. 5.14) and always decreases as the molecular size increases because the tumbling rate decreases. T2 relaxation is dominated by the ZQ pathway (aft ^ fta), and the population of molecules tumbling at this very slow rate gets larger and larger as the molecular size increases (Chapter 5, Fig. 5.13). Linewidth is inversely proportional to T2, so that even with perfect shimming the linewidth will increase steadily with molecular weight:

Molecular weight

Typical T2

Minimum Avi/2 (Hz)

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