Bq field

Bq field along the -axis, the resonant frequency V is defined by... 

Longitudinal magnetization This is the magnetization directed along the z-axis parallel to the Bq field. 

The above spectral densities can be modified for the occurence of chain flexibility, and for the director being oriented at dLD w.r.t. the external BQ field in the L frame. For CD bonds located in the flexible chain, the effect of DF is reduced due to an additional averaging of the time dependent factor (/f g) by conformational transitions in the chain. Consequently, the spectral densities given in Eqs. (60)-(62) are modified by replacing Soc%0(Pm,q) by the segmental order parameter YCD of the C-D bond at a particular carbon site on the chain.146,147 As observed experimentally,148,149 the spectral densities in a flexible chain show a SqD dependence when DF dominate the relaxation rates. The general expression of Jm(co 0LD) due to DF in uniaxial nematic phases is given by... 

Fig. 2. The different stages of a field-cycling experiment. Spins are pre-polarized in a relatively high static magnetic field (Bq). The relevant magnetization then decays to its equilibrium value in the field Bq according to the longitudinal relaxation time of interest (at a frequency equal to yBQl2n). For sensitivity reasons, magnetization is read again in the Bq field (a n/2 pulse yielding an fid Acq).

Ti in (5) is precisely the quantity that has to be measured (the longitudinal relaxation time which prevails for the Bq field). Mz( i) is measured in the higher magnetic field in order to benefit from a larger signal (let us recall that, in a general way, the NMR signal is proportional to where B is the... 

In FFC relaxometry, the most conspicuous pulser-controlled device (apart from the RF excitation channel) is the magnet system. In other words, we generate Bq field pulses of considerable amplitude, often switching the magnet field between zero and a maximum value of over 1 T, and we rigorously synchronize such Bq pulses with the RF signal-excitation and/or preparation pulses. This, moreover, does not exclude the possibility to control other devices as well. 

Accurate measurements of the frequency-resolved transverse spin relaxation T2) of Rb NMR on single crystals of D-RADP-x (x = 0.20, 0.25, 0.30, 0.35) have been performed in a Bq field of 7 Tesla as a function of temperature. The probe head was placed in a He gas-flow cryostat with a temperature stability of 0.1 K. To obtain the spin echo of the Rb - 1/2 -o-+ 1/2 central transition we have used the standard (90 - fi - 180y -ti echo - (2) pulse sequence with an appropriate phase-cycling scheme to ehminate quadrature detection errors and unwanted coherences due to pulse imperfections. To avoid sparking in the He gas, the RF-field Bi had to be reduced to a level where the 7T/2-pulse length T90 equalled 3.5 ps at room temperature. 

Suppose that a pulse Fourier transform proton NMR experiment is carried out on a sample containing acetone and ethanol. If the instrument is correctly operated and the Bq field perfectly uniform, then the result will he a spectrum in which each of the lines has a Lorentzian shape, with a width given hy the natural limit 1/(7tT2). Unfortunately such a result is an unattainable ideal the most that any experimenter can hope for is to shim the field sufficiently well that the sample experiences only a narrow distribution of Bq fields. The effect of the Bq inhomogeneity is to superimpose an instrumental lineshape on the natural lineshapes of the different resonances the true spectrum is convoluted by the instrumental lineshape. 

Figure 7.3.1.1 Schematics of two different RF coil geometries showing the coil and the sample tube position relative to the Bq field (a) saddle-type (b) solenoidal...

Figure 3.9. (a) The Bq field strength required for two different nuclei to attain the same spin state energy gap AE. (b) Resulting field-sweep NMR spectrum. 

Thus, as the Bq field increases, the difference in energy between the two spin states increases, as illustrated in Figure l-4b. Appendix 1 provides a complete derivation of these relationships. 

NMR is a valuable structural tool because the observed resonance frequency vq depends on the molecular environment as well as on y and Bq. The electron cloud that surrounds the nucleus also has charge, motion, and, hence, a magnetic moment. The magnetic field generated by the electrons alters the Bq field in the microenvironment around the nucleus. 

The actual field present at a given nucleus thus depends on the nature of the surrounding electrons. This electronic modulation of the Bq field is termed shielding, which is represented quantitatively by the Greek letter a. The actual field at the nucleus becomes B]ocai and may be expressed as Bq(1 - cr), in which the electronic shielding ct normally is positive. The variation of the resonance frequency with shielding has been termed the chemical shift. 

The system of units depicted in Figure 1-7 and used throughout this book has been developed to overcome the fact that chemical information often is found in small differences between large numbers. An intuitive system might be absolute frequency—for example, in Hz. At the common field of 7.05 T, for instance, all protons resonate in the vicinity of 300 MHz. A scale involving numbers like 300.000764, however, is cumbersome. Moreover, frequencies would vary from one Bq field to another (eq. 1-3). Thus, for every element or isotope, a reference material has been chosen and assigned a relative frequency of zero. For both protons and carbons, the substance is tetramethylsilane [(CH3)4Si, usually called TMS], which is soluble in most organic solvents, is unreactive, and is volatile. In addition,... 

This expression for the frequency differences, however, still depends on the magnetic field Bq. In order to have a common unit at all Bq fields, the chemical shift of nucleus i is defined by... 

As seen in the H spectrum of meffiyl acetate (Figure 1-7), the 8 value for the C—CH3 protons is 2.07 ppm and that for the O — CH3 protons is 3.67 ppm. These values remain the same in spectra taken at a Bq field of either 1.41 T (60 MHz) or 21.2 T (900 MHz), which represent the extremes of spectrometers currently in use. Chemical shifts in Hz, however, vary from field to field. Thus, a resonance that is 90 Hz from TMS at 60 MHz is 450 Hz from TMS at 300 MHz, but always has a 8 value of 1.50 ppm (8 = 90/60 = 450/300 = 1.50). Note that a resonance to the right of TMS has a negative value of 8. Also, since TMS is insoluble in water, other internal standards are used for this solvent, including 3-(trimethylsi-lyI)-l-propanesulfonic acid [(CH3)3Si(CH2)3S03Na] and 3-(trimethyIsilyl)propionic acid [(CH3)3SiCH2CH2C02Na] (sodium salts). 

Modem spectrometers vary the B frequency while the Bq field is kept constant. An increase in shielding (a) lowers the right side of eq. 1-3, so that vq must decrease in order to maintain a constant 5q. Thus, the right end of the spectrum, as noted before, corresponds to lower frequencies for more shielded nuclei. The general result is that frequency increases... 

Figure 6-39 Diagram of a Bq field gradient along the z direction. (Reproduced from F. J. M. van de Yen, Multidimensional NMR in Liquids, VCH, New York,...

In the absence of Bq, all orientations of the nuclear magnets in space have the same energy. The Bq field, however, interacts with the nuclear magnets to alter their energies as a function of /,. Because energy is a scalar quantity, it is obtained by the scalar or dot product of the magnetic moment and the external magnetic field that is,... 

Quadrupole effects are due to the interaction of the nuclear quadrupole moment (caused by a non-spherical distribution of charge on the nucleus) with the electric field gradient at the nucleus. Quadrupole effects cause peak broadening, displacement of the peak from the isotropic (true) chemical shift, and distortion of the peak shape. These effects decrease in magnitude with the square of the Bq field strength, and spectra of quadrupolar nuclides are usually recorded at the highest field available. 

R159 M. Piotto, Applications of Bq Field Gradients to the Study of Natural Products by NMR , p. Pl/211... 

The calculation is simplified considerably by transforming the Bloch equations into a coordinate system which rotates with the rf magnetic field vector (2.2.12) around the 2-axis of the laboratory frame. In this rotating frame the magnetic field including the rf field component appears static, but the magnitude of the Bq field in z-direction is changed, and (2.2.10) turns into... 

In related techniques, the homogeneous magnetic field of standard NMR magnets is degraded, for instance, by a Maxwell coil pair [Tanl], or pulsed Bq field gradients are... 

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