Magnetic susceptibility transversal

Here k is the Fermi wave vector determined from the value of the hole concentration p assuming a spherical Fermi surface, m is the hole effective mass taken as 0.5/no (mo is the free electron mass), is the exchange integral between the holes and the Mn spins, and h is Planck s constant. The transverse and longitudinal magnetic susceptibilities are determined from the magnetotransport data according to x = 3M/dB and xh = M/B. 

Experimental studies of filled rubbers are complicated by several things, such as the effect of the magnetic susceptibility of the filler, the effect of free radicals present at the surface of carbon black, the complex shape of the decay of the transverse magnetisation relaxation of elastomeric materials due to the complex origin of the relaxation function itself [20, 36, 63-66], and the structural heterogeneity of rubbery materials. 

Since its first description in 1971 [35], gel-phase NMR was applied to peptide chemistry by Manatt and coworkers [36, 37], These authors used 13C NMR to determine the extent of chloromethylation of crosslinked polymers and 19F NMR to monitor protection-deprotection reactions. These two nuclei are the most commonly used in these types of studies, mainly because of their significant chemical shift dispersion, which can alleviate in part the resolution loss due to the non ideal linewidth obtained in the gel state. Apart from restricted molecular motion, that shortens T2 because of an efficient transverse relaxation, other sources of line-broadening derive from magnetic susceptibility variations within the sample (due to the physical heterogeneity of the system) and residual dipolar couplings. 

However, only isotropic solids will be considered such as cubic crystals or randomly textured polycrystals, for which the magnetic susceptibility becomes equivalent to a scalar. In a powder with random crystallite orientation, M of the aggregate is in the direction of H, since those components of M transverse to H in the individual crystallites cancel on average. However, the mean value of M for a powder is the mean value of the principal susceptibilities, which are equal in magnitude. Hence, in a powder, x = ( t. + A + Tz)(Nye, 1957). 

We summarize as follows The longitudinal and transverse magnetic susceptibilities characterizing the solid-state process are approximately described by [55]... 

Substituting Eqs. (5.55) and (5.57) into (5.41) we obtain the longitudinal and transverse components of the complex magnetic susceptibility, namely... 

We now evaluate the magnetic susceptibility in a transverse external field directed along the x axis (the z axis as above, is oriented along the anisotropy field). We confine ourselves to the case of small a, that is acritical value of a at which the characteristic frequency of precession of the magnetic moment vanishes. 

G. Meslin said that potassium dichromate is paramagnetic. He found that the magnetic susceptibility of the powder is 0-13 x 10 mass unit and G. Quincke gave for a soln. of the dichromate between 18° and 20°, 0-76 Xl0 mass unit. J. Forrest measured the variations in the parallel and transverse components of the magnetization of the crystals. P. Weiss and P. Collet found the paramagnetism of a sohi. of the dichromate is constant between 14° and 50° and the subject was discussed by P. Weiss, L. A. Welo and A. Baudisch, and S. Berkman and H. Zocher. W. G. Hankel and H. Lindenberg found that the crystals exhibit pyroelectricity in that when warmed the (OOl)-face is usually positively electrified, and the (OOf)-face negatively electrified—the reverse behaviour is rare. 

Fig. 26. Decay times Tpu) to 1/e of the initial value of the free-induction signals in melts of linear polyethylene at 150 "C as a fimction of molecular mass. The horizontal broken line (a) indicates the instrumental homogeneity limitation determined with a water sample at 30 °C (see Fig. 25). The motional averaging region (b) is characterized by a strong molecular mass dependence equivalent to that of the proper (effective) transverse relaxation time (see Fig. 19d). It is therefore attributed to the combined influence of components B and C. The plateau (c) reached at high molecular masses reflects the unaveraged effect of internal field inhomogeneities corresponding to a full width at half maximum of the resonance line of about 7 ppm. This value can be estimated on the basis of the magnetic susceptibility of polyethylene relative to that of empty voids [152]...

---