Macroscopic nuclear magnetization

FIGURE 2.3 Precession of an ensemble of magnetic moments at random phase and their resultant vector sum M, which represents the macroscopic nuclear magnetization. 

In NMR experiments, the observables of interest are generally the components of the macroscopic nuclear magnetization, which are proportional to the ensemble average values of the components of the nuclear spin operator I, (ly), and If. The magnetization in the X-direction of an ensemble of nuclear spins, for example, is given by ... 

The RF signal is derived ultimately from a digital frequency synthesizer that is gated and amplified to provide a short intense pulse. Pulses have to be of short duration because of the need to tip the macroscopic nuclear magnetization by 90 or 180° and at the same time to provide uniform excitation over the whole of the spectral range appropriate for the nucleus under study. Thus for NMR, for example, where chemical shifts can cover more than 200 ppm, this requires 25 kHz spectral width on a spectrometer operating at 500 MHz for H, which corresponds to 125 MHz for To cover this range uniformly requires a 90° pulse to be < 10 J,s in duration. 

Fig. 6.3. Schematic representation of the macroscopic nuclear magnetization M processing about the magnetic field along the z-axis after being tipped from its equilibrium value along z by a radiofrequency field, Wi.

Examination of what happens when the 1H spins in the levitating objects are inverted is in progress. This work potentially provides another one of few examples in which the nuclear magnetization causes a macroscopic kinetic effect.38... 

Thanks to the extensive literature on Aujj and the related smaller gold cluster compounds, plus some new results and reanalysis of older results to be presented here, it is now possible to paint a fairly consistent physical picture of the AU55 cluster system. To this end, the results of several microscopic techniques, such as Extended X-ray Absorption Fine Structure (EXAFS) [39,40,41], Mossbauer Effect Spectroscopy (MES) [24, 25, 42,43,44,45,46], Secondary Ion Mass Spectrometry (SIMS) [35, 36], Photoemission Spectroscopy (XPS and UPS) [47,48,49], nuclear magnetic resonance (NMR) [29, 50, 51], and electron spin resonance (ESR) [17, 52, 53, 54] will be combined with the results of several macroscopic techniques, such as Specific Heat (Cv) [25, 54, 55, 56,49], Differential Scanning Calorimetry (DSC) [57], Thermo-gravimetric Analysis (TGA) [58], UV-visible absorption spectroscopy [40, 57,17, 59, 60], AC and DC Electrical Conductivity [29,61,62, 63,30] and Magnetic Susceptibility [64, 53]. This is the first metal cluster system that has been subjected to such a comprehensive examination. 

Figure 2. The revolution of macroscopic magnetization in a rotating frame of reference (a), application of additional magnetic field (BL) along x -axis as a 90° pulse which tips the macroscopic magnetization into the x y -plane (b), as they precess in the x y -plane, the macroscopic magnetization diminishes because nuclear magnets actually precess at slightly different frequencies which causes dephasing.

An important objective in materials science is the establishment of relationships between the microscopic structure or molecular dynamics and the resulting macroscopic properties. Once established, this knowledge then allows the design of improved materials. Thus, the availability of powerful analytical tools such as nuclear magnetic resonance (NMR) spectroscopy [1-6] is one of the key issues in polymer science. Its unique chemical selectivity and high flexibility allows one to study structure, chain conformation and molecular dynamics in much detail and depth. NMR in its different variants provides information from the molecular to the macroscopic length scale and on molecular motions from the 1 Hz to 1010 Hz. It can be applied to crystalline as well as to amorphous samples which is of particular importance for the study of polymers. Moreover, NMR can be conveniently applied to polymers since they contain predominantly nuclei that are NMR sensitive such as H and 13C. 

For pulsed n.m.r., the quantum-theoretical concept of 21 + 1 discrete, nuclear energy-levels (I is the spin-quantum number) produced by quantization of individual, nuclear, magnetic moments along the z axis is less useful than for c.w.-n.m.r., and therefore pulsed n.m.r. is usually described, both experimentally and theoretically, in terms of a continuum of extensive, spatial manipulations of the macroscopic magnetization-vector, in a classical, mechanical sense. 

At room temperature, these molecules occupy well-defined locations in their respective crystal lattices. However, they tumble freely and isotropically (equally in all directions) in place at their lattice positions. As a result, their solid phase NMR spectra show features highly reminiscent of liquids. We will see an illustration of this point shortly. Other molecules may reorient anisotropically (as in solid benzene). Polymer segmental motions in the melt may cause rapid reorientation about the chain axis but only relatively slow reorientation of the chain axes themselves. Large molecular aggregates in solution (such as surfactant micelles or protein complexes or nucleic acids) may appear to have solidlike spectra if their tumbling rates are sufficiently slow. There are numerous other instances in which our macroscopic motions of solid and liquid may be at odds with the molecular dynamics. Nuclear magnetic resonance is one of the foremost ways of investigating these situations. 

There are macroscopic (uptake measurements, liquid chromatography, isotopic-transient experiments, and frequency response techniques), and microscopic techniques (nuclear magnetic resonance, NMR and quasielastic neutron spectrometry, QENS) to measure the gas diffusivities through zeolites. The macroscopic methods are characterized by the fact that diffusion occurs as the result of an applied concentration gradient on the other hand, the microscopic methods render self-diffusion of gases in the absence of a concentration gradient [67]. 

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