Larmor frequencies

The population of nuclei located in energy state E2, is slightly less numerous than that in the more stable state E. Expression 15.5 calculates the ratio of these two populations (Boltzmann distribution equilibrium). 

From an analytical point of view, a nuclide can be identified if AE, in a field 

A basic experiment consist of irradiating the nuclei present in a magnetic field with a source of electromagnetic radiation of variable frequency v with a propagation direction perpendicular to the external field. Absorption will occur if  

The energy of this photon must exactly match the energy difference between the two states. Expression 15.4 leads to the fundamental relation of resonance (15.7)  

The radiofrequency which induces the exchange between the two levels is equal to the Larmor frequency at which the spin vector rotates about the average direction of the z-axis. Larmor, an Irish physicist whose work preceded that of NMR has shown, by an independent reasoning that o), the angular rotation frequency of the spin vector about the z-axis, has a value of  

---

Here Ti is the spin-lattice relaxation time due to the paramagnetic ion d is the ion-nucleus distance Z) is a constant related to the magnetic moments, i is the Larmor frequency of the observed nucleus and sis the Larmor frequency of the paramagnetic elechon and s its spin relaxation time. Paramagnetic relaxation techniques have been employed in investigations of the hydrocarbon chain... 

Lariam [51773-92-3] Lariat ethers Laricinan Larmor frequency... 

Figure 8 Effects of spin diffusion. The NOE between two protons (indicated by the solid line) may be altered by the presence of alternative pathways for the magnetization (dashed lines). The size of the NOE can be calculated for a structure from the experimental mixing time, and the complete relaxation matrix, (Ry), which is a function of all mterproton distances d j and functions describing the motion of the protons, y is the gyromagnetic ratio of the proton, ti is the Planck constant, t is the rotational correlation time, and O) is the Larmor frequency of the proton m the magnetic field. The expression for (Rjj) is an approximation assuming an internally rigid molecule.

Chemical shift relates the Larmor frequency of a nuelear spin to its ehemieal environment The Larmor frequency is the preeession frequency Vg of a nuclear spin in a static magnetic field (Fig. 1.1). This frequency is proportional to the flux density Bg of the magnetic field vglBg = const.)... 

It is convenient to reference the chemical shift to a standard such as tetramethylsilane [TMS, (C//j)4Si] rather than to the proton fC. Thus, a frequency difference (Hz) is measured for a proton or a carbon-13 nucleus of a sample from the H or C resonance of TMS. This value is divided by the absolute value of the Larmor frequency of the standard (e.g. 400 MHz for the protons and 100 MHz for the carbon-13 nuclei of TMS when using a 400 MHz spectrometer), which itself is proportional to the strength Bg of the magnetic field. The chemical shift is therefore given in parts per million (ppm, 5 scale, Sh for protons, 5c for carbon-13 nuclei), because a frequency difference in Hz is divided by a frequency in MHz, these values being in a proportion of 1 1O. ... 

Figure 1.1. Nuclear precession nuclear charge and nuclear spin give rise to a magnetic moment of nuclei such as protons and carbon-13. The vector n of the magnetic moment precesses in a static magnetic field with the Larmor frequency vo about the direction of the magnetic flux density vector Bo...

Before the application of a pulse, only equilibrium magnetization exists, directed toward the z-axis corresponding to the zero coherence level for all coherence pathways. When the pulse is applied, two coherence levels, + 1 and —1, are created during the evolution period that evolve into M and respectively, where [Pg.74]

The frequency with which a nucleus precesses around the applied magnetic field is called its Larmor frequency or Larmor processional... 

We can use the angular frequency of TMS as the reference frequency of the rotating frame. Deducting this from the Larmor frequency of the signal will leave only the differential frequency (or, in other words, the chemical shift) associated with the magnetization vector of the signal. 

The amplitude represents a circular motion of the magnetization vector along the [Pg.81]

Greatly enhanced sensitivity with very short measuring time is the major advantage of PFT (pulse Fourier transform) experiments. In the CW (continuous wave) experiment, the radiofrequency sweep excites nuclei of different Larmor frequencies, one by one. For example, 500 s may be required for excitation over a 1-KHz range, while in a PFT experiment a single pulse can simultaneously excite the nuclei over 1-KHz range in only 250 jits. The PFT experiment therefore requires much less time than the CW NMR experiment, due to the short time required for acquisition of FID signals. Short-lived unstable molecules can only be studied by PFT NMR. 

Hence it is clear that if the two delay periods before and after the 180° pulses are kept identical, then refocusing will occur only when a selective 180° pulse is applied. This can happen only in a heteronuclear spin system, since a 180° pulse applied at the Larmor frequency of protons, for instance, will not cause a spin flip of the C magnetization vectors. 

In order for relaxation to occur through Wj, the magnetic field fluctuations need to correspond to the Larmor precession frequency of the nuclei, while relaxation via requires field fluctuations at double the Larmor frequency. To produce such field fluctuations, the tumbling rate should be the reciprocal of the molecular correlation time, i.e., f), so most efficient relaxation occurs only when voT, approaches 1. In very small, rapidly tumbling molecules, such as methanol, the concentration of the fluctuating magnetic fields spectral density) at the Larmor frequency is very low, so the relaxation processes Wj and do not occur efficiently and the nuclei of such molecules can accordingly relax very slowly. Such molecules have... 

Five different types of peaks can occur in 3D spectra. These are illustrated in an ABC spin system, in which the Larmor frequencies of the three nuclei are v,, Vg, and v, -, and the coherence transfers are associated with two different mixing processes, M, and Mj ... 

The basic principle underlying the development of images is simple (Lauterber, 1973). Consider a body cavity containing two pools of water in different quantities. In a uniform magnetic field, the NMR spectrum will consist of a single peak, since all the water molecules will process at the same frequency, irrespective of their spatial location. If, however, a linear field gradient is applied in the x -direction, the Larmor frequency of the water will increase linearly across the sample as a function of the x -coordinate, thereby creating a one-dimensional profile, or spectrum, of the sample (Fig. 7.21). 

Larmor frequency The nuclear precession frequency about the direction of Bo. Its magnitude is given by yBo/27T. 

Precession A characteristic rotation of the nuclear magnetic moments about the axis of the applied magnetic field Bo at the Larmor frequencies. Preparation period The first segment of the pulse sequence, consisting of an equilibration delay. It is followed by one or more pulses applied at the beginning of the subsequent evolution period. 

Often the electronic spin states are not stationary with respect to the Mossbauer time scale but fluctuate and show transitions due to coupling to the vibrational states of the chemical environment (the lattice vibrations or phonons). The rate l/Tj of this spin-lattice relaxation depends among other variables on temperature and energy splitting (see also Appendix H). Alternatively, spin transitions can be caused by spin-spin interactions with rates 1/T2 that depend on the distance between the paramagnetic centers. In densely packed solids of inorganic compounds or concentrated solutions, the spin-spin relaxation may dominate the total spin relaxation 1/r = l/Ti + 1/+2 [104]. Whenever the relaxation time is comparable to the nuclear Larmor frequency S)A/h) or the rate of the nuclear decay ( 10 s ), the stationary solutions above do not apply and a dynamic model has to be invoked... 

---