Susceptibility corrections volume

The theory of the susceptibility corrections in solid state NMR experiments with oriented membrane samples has been described. To determine the necessary corrections, a general analysis is presented for the demagnetizing field of a layered sample of rectangular block geometry, with the normal of the layers parallel to the main field or tilted about an axis of the block. The correction to the line position of the block sample was found to be approximately equal to that of the spheroid which can be inscribed into the block, and for which the correction is well known. It was shown that sample and support materials contribute to that average according to their volume filling factors. 

Medium effects include that of bulk susceptibility, which depends on the geometry of the sample and the composition of the solution. For a perfectly spherical sample, the nuclear magnetic shielding contribution a of the bulk susceptibility is zero. For other shapes a susceptibility correction is needed because of polarization of the sample near the liquid surface. For an infinitely long cylinder, oriented with the cylindrical axis perpendicular to the direction of the magnetic field as in an electromagnet, the frequency shift due to bulk susceptibility of a pure solvent (as for a molecule observed in infinite dilution) is related to the molecular magnetic susceptibility x, or the volume susceptibility Xv of the solvent by... 

The gas to be tested may be drawn or forced at the rate of a few cubic centimeters per minute through the test chamber, which in present models has a volume of about 4 ml., or it may be introduced after evacuating the test chamber. The instrument indicates correctly the magnetic susceptibility of the gas in the test chamber within a few seconds the main delay in reading the instrument is caused by the time required to introduce the gas. 

Magnetic Susceptibility Measurements. Magnetic susceptibilities were measured by the Faraday method and were accurate to 2%. Samples, usually as powders, were placed in a cylindrical Teflon boat having an internal volume of 0.30 cc. Measurements were made at 2963, 4357, 5724, 7077, and 8243 G, and at temperatures 77°-295°K. It was possible to correct for ferromagnetic impurities from any field dependent effects. 

For the definition of AN, see Eq. (2-11). All S values have been extrapolated to zero concentration and corrected for differences in volume susceptibilities. 

In general, two different solvent effects on NMR spectra can be distinguished (a) shifts due to a difference in the bulk volume magnetic susceptibility x of the solute and the solvent (b) shifts arising from intermolecular interactions between solute and solvent molecules. Since the bulk susceptibility effect depends on the shape of the sample and, therefore, is not of chemical interest, some form of correction for it is applied. For two... 

Shifts extrapolated to infinite dilution, referred to w-hexane and corrected for the difference in volume susceptibilities between -hexane and the respective solvent. 

In comparing the work of Schneider and co workers to that of Huggins, Pimentel, and Shoolery, we should note a different use of reference standards. Schneider and Reeves discuss their use of an external reference sample (1705). In this use, it is generally assumed that the volume susceptibilities of solution components are additive. This assumption is made doubtful by the existence of solvent-solute complex formation. Huggins et al, on the other hand, use an internal reference, i.e., a reference solute dissolved in the solution of interest. Thus a correction for bulk diamagnetic susceptibility is obviated by putting the solute in the same mag netic environment as the species of interest. 

The Fermi liquid as well as the Hartree-Fock theory, however, can hardly account for the observed temperature dependence of the spin susceptibility obtained at constant volume - namely, corrected for thermal dilatation of the sample - which shows a monotonic but sizable growth as the temperature increases (Fig. 8) [53, 54, 58]. This variation turns out to be much faster than the one expected from the H-F theory, which only predicts a F (T) with a very slow temperature dependence that is spread out over on a temperature scale [58, 59]. 

Most problems with this procedure have involved tracer impurities and the separation of bound and free labeled fractions. Several separation techniques have been used, including equilibrium dialysis, membrane ultrafiltration, and steady-state gel filtration. Their deficiencies include a requirement for a large sample volume, the need for complicated correction of sample volume changes that occur during the separation, and difficulties of collecting and measuring radioactivity in numerous fractions of each sample. Equilibrium dialysis has been used most often in the past, but serious errors often arise from the sample dilution required by this method. Symmetrical dialysis of undiluted samples is reported to be less susceptible to tracer contamination and dilution effects. Ultrafiltration also appears to overcome these problems and to obviate errors caused by dilution. 

Ref. 84, 15N spectra of labelled compounds, originally referred to external gaseous NH3, recalculated with NH3 (neat liquid) shift of +381-93 ppm from neat CH3N02 corrected for liquid volume susceptibilities. 

Ref. 86, 15N spectra of 15N(CH3)3 shifts corrected for liquid volume susceptibility, originally referred to gaseous (CH3)3N, recalculated with (CH3)3N (neat liquid) shift, +368-59 from CHjN02, ref. 61, see also Table VII. 

In these equations cl is the density in g cm-3 and M is the molecular weight. X is called the gram susceptibility and /m is called the molar susceptibility. When a value of is obtained from the measured volume susceptibility, k, it can be corrected for the diamagnetic contribution and for the TIP to give a corrected molar susceptibility, Xm"> which is the most useful quantity in drawing conclusions about electronic structure. 

Thus, to recapitulate, one first makes a direct measurement of the volume susceptibility of a substance from which Xm is calculated, and in accurate work is corrected for diamagnetism and TIP. From this corrected molar susceptibility and the temperature of the measurement, equation 19-12 enables one to calculate the magnetic moment of the ion, atom or molecule responsible for the paramagnetism. 

The demagnetisation correction is applicable only to the volume susceptibility. This requires an accurate determination of the sample volume, which may not be trivial. Normally the amount of the sample is determined by weighing and it refers to the sample mass. The determination of the volume is less accurate and more complex for powders. 

Strong diamagnetic materials exhibit a volume susceptibility close to the limit of x = — 1 (dimensionless). These obey perfect diamagnetic screening due to a superconducting current and in fact they are superconductors. Thus the measurement of magnetic susceptibility serves as a convenient and fast identification of superconductivity, even for powder materials (the Meissner effect). However, due to the considerable susceptibility value, the demagnetisation effect becomes substantial and thus a correct determination of... 

Ferrofluid suspension viscosity Hydrodynamic-to-magnetic volume fraction Scalar moment of inertia density Vortex viscosity Initial magnetic susceptibility LMM approximation correction... 

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