Linewidth in solids

Generally, however, linewidths in solid state spectra are grater than in solution. An example is shown in Fig. 48, which compares the solution spectrum (a above) of a bisphosphonate (the structure of which is shown in the Figure) with that in the solid state (b below). While the lines are much sharper in the upper spectrum, we can clearly see splittings in the solid state spectrum. Since the protons are decoupled, these must be due not to coupling but to nonequivalence. In the solid state the molecule becomes unsymmetrical due to... 

The principal dilTerence from liquid-state NMR is that the interactions which are averaged by molecular motion on the NMR timescale in liquids lead, because of their anisotropic nature, to much wider lines in solids. Extra infonnation is, in principle, available but is often masked by the lower resolution. Thus, many of the teclmiques developed for liquid-state NMR are not currently feasible in the solid state. Furthemiore, the increased linewidth and the methods used to achieve high resolution put more demands on the spectrometer. Nevertheless, the field of solid-state NMR is advancing rapidly, with a steady stream of new experiments forthcoming. 

M continually decreases under the influence of spin-spin relaxation which destroys the initial phase coherence of the spin motion within they z-plane. In solid-state TREPR, where large inliomogeneous EPR linewidths due to anisotropic magnetic interactions persist, the long-time behaviour of the spectrometer output, S(t), is given by... 

Many components of food are in the solid state and possess very short T2. The linewidths from solid components are generally too wide to be observed directly by solution state NMR methods. However, these components can be detected by the special techniques of solid state NMR. These techniques involve the use of cross polarization excitation (from 3H to 13C), high power 3H decoupling (to inhibit... 

So far, the majority of granular matter studies by NMR/MRI have used liquid state proton measurements in solid materials. Because proton signals are relatively insensitive to chemical environment through the chemical shift effect and because the physical environments are relatively similar in all liquids, the resonance frequency and the NMR linewidth are not good indicators of granular parameters such as particle density and velocity. 

We have referred to the various interactions which can cause line broadening in the solid state. One of these, which is normally not a problem in liquid state NMR, is due to the fact that the chemical shift itself is a tensor, i.e. in a coordinate system with orthogonal axes x, y and z its values along these axes can be very different. This anisotropy of the chemical shift is proportional to the magnetic field of the spectrometer (one reason why ultra-high field spectrometers are not so useful), and can lead in solid state spectra to the presence of a series of spinning sidebands, as shown in the spectra of solid polycrystalline powdered triphenylphosphine which follows (Fig. 49). In the absence of spinning, the linewidth of this sample would be around 75 ppm ... 

INPUT g-values git linewidth r, frequency v, field limits INPUT stepwidth in solid angle dcosB, dip spectral points n NULL absorption-array... 

The single-mode laser naturally gives less output power than a multimode laser with the same active volume since its induced emission is concentrated into a smaller frequency range. This loss in intensity, however, is much less than one would expect from the ratio of linewidths or from the reduction in oscillating mode number 3i. 32,41) jbis is due to the fact, that not only atoms with the exact transition frequency can contribute to the induced emission, but also those inside the homogeneous linewidth which is determined by collision processes in the case of gas lasers or by crystal line broadening in solid lasers... 

FIGURE 5. Reduction in linewidth in the Li solid state NMR spectrum of the dimer of ( )-2-lithio-l-phenyl-1-(o-hthiophenyl)pent-l-ene (90% Li) by various techniques (a) static Li H spectmm, halfwidth 6.3 kHz (b) Li H CP/MAS spectmm, rotational frequency 3 kHz (c) central transition in the Li H CP/MAS spectmm, halfwidth 130 Hz (d) central transition in the Li H CP/MAS spectmm with additional Li decouphng. The two Li resonances are separated by 1.25 ppm hneshape analysis yields half-widths of 92 and 81 Hz, respectively ... 

The sum must be made over all spin pairs in the proton-rich solid. In the absence of large-amplitude molecular motion this Hamiltonian describes a line shape of width of up to 100 kHz. In the presence of molecular motion the angular part of Equation 13.1 becomes time-dependent, and the partial averaging of this term results in reduced linewidths. In polymers the geometry of main-chain motion is limited by the structure of the polymer chain, and is inherently anisotropic. As a general rule, as the measurement temperature is increased the motion tends to become more isotropic in nature as the free volume increases, and the extent of averaging of the dipolar Hamiltonian increases. This... 

The narrow linewidths of liquids allow one to observe weak spin interactions such as the indirect spin-spin (/) coupling and the isotropic chemical shift (7>). In the solid state, however, linewidths are broadened considerably by much stronger interactions, involving mainly the dipole-dipole interaction (typically 10-100 kHz), chemical-shift anisotropy ( 1 kHz), the quadrupole interaction ( 250 kHz) and the effect of paramagnetic impurities. For these reasons the / and <5 interactions are generally not observed in solids.2... 

One can see from Eq. (3) that the van Vleck dipolar Hamiltonian is the product of a spatial part and a spin part. In liquids, the rapid isotropic molecular tumbling motion, which occurs at frequencies well above the dipolar linewidth, averages the spatial part (1—3 cos2 6tj) to zero, thus nulling the dipolar broadening. In solids, the spins are constrained to vibrate and rotate about their mean positions, resulting in an effective dipolar Hamiltonian which is generally non-zero, and consequently in... 

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