Bulk susceptibility

Figure 4. Susceptibility of the energy moment at To — 2. The symbols are static Monte Carlo results [1] and the curve is obtained from a local thermodynamic approximation [1] using the bulk susceptibilities from a Lennard-Jones equation of state [90], (From Ref. 1.)...

Fig. 16. Single voxel STEAM spectra of the SOL muscle (top) and the TA muscle (bottom). Different fibre orientation in those muscles results in clearly different patterns of the lines in the spectra In SOL (feathered muscle with oblique fibres), IMCL and EMCL signals show lower frequency separation than in TA (spindle-shaped muscle) due to bulk susceptibility effects. Furthermore, in SOL the Cr2 doublet merges into one resonance, the Cr3 triplet is less resolved, and TAU is shifted towards TMA.

The reference compound can be added to the sample solution (internal reference) or kept separate from the sample in a sealed capillary (external reference, Fig. 2.36). If an external reference is necessary, a correction term accounting for the difference between the bulk susceptibilities of reference ( R) and sample solution ( s) must be added to the observed shift, dob5 ... 

Neither CS2 nor TMS are ideal standards. The 13C signals of CS2 and carbonyl carbons overlap, as do the 13C signals of cyclopropane and some methyl carbons with TMS (Fig. 3.3). Furthermore, the 13C resonance of TMS has been shown to suffer from solvent shifts of the order of + 0.1 to 1.5 ppm in common NMR solvents, even at infinite dilution [74]. This must be considered if 13C shifts relative to TMS of one compound in different solvents are to be compared. There are two alternative methods to overcome this problem one is to use cyclohexane as the internal reference cyclohexane was shown to have 13C solvent shifts lower than + 0.5 ppm [74], The other alternative is to use TMS as an external reference (Sections 1.9.3 and 2.8.5) and to make bulk susceptibility shift corrections according to eq. (1.44). 

Note that the squarylium dye, 9, has quite a large susceptibility. At 1% in PMMA, the bulk susceptibility is 13x10 14 m(18). At a hypothetical "100%", this susceptibility is comparable to the THG and DFWM susceptibilities of some polydiacetylenes, though this comparison must be viewed with some circumspection considering the difficulty in accounting for the differences in dispersion between different processes. 

When the data in Fig. 3.2 are fit to Eq. (3.10), the results yield A = 0 and f (y) = sin 3 y/ for I (11, ) [67, 68]. Using p-polarized input and output, the data fits to A/B = 1 and f y/) = cos 3 // for I (11, 11). With appropriate choices of the input and output polarizations and separate SH phase measurements, combinations of the four independent surface susceptibility elements and the bulk susceptibilities y and C contributing to A and B for this system were also determined. There is inherent difficulty in separating the bulk surface susceptibilities such that the bulk susceptibility y is always measured in a linear combination with a surface susceptibility element for any experimental geometry [82-84]. 

Table 3.1. Composition of the parameters, a, b, and c in terms of the surface and bulk susceptibility elements. P-polarized ( ) or s-polarized ( O) fundamental field, i = (x,y)...

ESR is subject to some serious limitations. For reasons which need not concern us, resonance may be difficult or impossible to observe if the paramagnetic centre has an even number of unpaired electrons. This means, for example, that ESR can make little contribution to the extensive chemistry of nickel(II). Another problem arises from interactions between paramagnetic centres in magnetically non-dilute samples the resonance may be very broad and uninformative. ESR is best performed on magnetically-dilute samples, which means that we cannot obtain the kind of information furnished by bulk susceptibility measurements about ferromagnetic and antiferromagnetic interactions. 

VanderHart and Campbell89 pointed out that the linewidth contributed by off-resonance irradiation can be effectively removed by TPPM (or its variants), but inhomogeneous contributions such as anisotropic bulk susceptibility,90 which... 

Relative to water as internal standard corrected for temperature (water) and bulk susceptibility (cyclohexane). 

We consider now the NLO response of a molecule to an electric field. The resulting equations will be found to be analogous to the ones derived for a bulk medium. Instead of bulk susceptibilities however, molecular polarizabilities of nth order appear. For the latter, by convention, the lower-case Greek letters in ascending order (a, 3, y,. ..) are used. Again, an electric field of the form defined in (16) is used. Similar to the macroscopic polarization (17), the expression (33) for the molecular dipole moment p t) contains linear and non-linear terms. 

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... 

Only shifts observed in excess of this amount may then be attributed to intermolecular interaction effects. Use of an internal standard provides an automatic compensation for the bulk susceptibility effect, but for comparison of shifts measured in this way in different solvents it must be kept in mind that the standard itself may be subject to solvent effects. These are minimized in and NMR spectroscopy by the use of tetra-methylsilane (TMS) as an internal standard. 

Effective second harmonic generation is attained in materials which have both high second-order molecular hyperpolarizability, p, and high second-order bulk susceptability, x - Molecular polarization is described by the field dependent molecular dipole moment, p (eq 1), expanded as a function of the applied field strength, E, which may be electric or optical (that is, electromagnetic) in nature. The field strength E is a vector, and Pq is the intrinsic dipole... 

The odd order susceptibilities are nonzero in all materials. However, owing to the fact that x is a third rank tensor, the second order susceptibility is nonzero only in noncentrosym-metric materials, that is, materials possessing no center of symmetry. The focus of this paper is on second order processes, and the relationships between the bulk susceptibility, second harmonic generation, and the linear electro-optic effect. For second harmonic generation, Xijl is symmetric in ij, leading to the relationship between the second harmonic coefficient dijk and the bulk second order susceptibility x 2)[i2l... 

Since the electro-optic coefficient rij is defined by the electric field dependence of the optical indicatrix, is related to the second order bulk susceptibility through i... 

Construction of a bulk material possessing a large bulk susceptibility requires not only molecular constituents with large microscopic susceptibilities but a noncentrosymmetric system where the orientation of the molecular species results in additivity of the molecular susceptibilities. 

For completeness, I mention the ° Pd Knight shift measured in micrometer-sized powders with 0 < x < 0.025 (64). The shift changes linearly with the bulk susceptibility as AKIAx = 41 mol emu In pure Pd, this value... 

The relatively small changes in chemical shift with pressure can be qualitatively explained in terms of changes in bulk susceptibility as most spectra in SCFs are obtained without internal lock. Large chemical shift ranges are a characteristic of metal NMR spectroscopy, and the changes observed on changing temperature, pressure or solvent are no more exaggerated in supercritical solvents than those observed with conventional solvents. 

Table 3 presents Mg line width and chemical shift data obtained as a function of the concentration of MgBr2 and MgCl2 [41]. Also included in Table 3 are the viscosities of the solutions investigated. The chemical shifts, when corrected for bulk susceptibility effects, vary over a total range of less than 1 ppm. 

Chemical shifts ( 0.1 ppm) relative to the signal for Mg(C104)2. extrapolated to infinite dilution. More positive values refer to lower shielding. Bulk susceptibility corrections have been made. 

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