Transverse spin relaxation time

Measurements of i N iH -NOEs, and longitudinal and transverse spin relaxation times can provide supplementary information on the globular PrP domain in the form of data on the internal mobility along the polypeptide chain (Peng and Wagner, 1992). Furthermore, realtime... 

In liquid crystals the proton resonance line width and the related effective transverse spin relaxation time T2 depend on the angle 9 between the magnetic field and the director n, which is described approximately... 

There is a second relaxation process, called spin-spin (or transverse) relaxation, at a rate controlled by the spin-spin relaxation time T2. It governs the evolution of the xy magnetisation toward its equilibrium value, which is zero. In the fluid state with fast motion and extreme narrowing 7) and T2 are equal in the solid state with slow motion and full line broadening T2 becomes much shorter than 7). The so-called 180° pulse which inverts the spin population present immediately prior to the pulse is important for the accurate determination of T and the true T2 value. The spin-spin relaxation time calculated from the experimental line widths is called T2 the ideal NMR line shape is Lorentzian and its FWHH is controlled by T2. Unlike chemical shifts and spin-spin coupling constants, relaxation times are not directly related to molecular structure, but depend on molecular mobility. 

Relaxation is an inherent property of all nuclear spins. There are two predominant types of relaxation processes in NMR of liquids. These relaxation processes are denoted by the longitudinal (Ti) and transverse (T2) relaxation time constants. When a sample is excited from its thermal equihbrium with an RF pulse, its tendency is to relax back to its Boltzmann distribution. The amount of time to re-equilibrate is typically on the order of seconds to minutes. T, and T2 relaxation processes operate simultaneously. The recovery of magnetization to the equilibrium state along the z-axis is longitudinal or the 7 relaxation time. The loss of coherence of the ensemble of excited spins (uniform distribution) in the x-, y-plane following the completion of a pulse is transverse or T2... 

In Eqs. (4)-(7) S is the electron spin quantum number, jh the proton nuclear magnetogyric ratio, g and p the electronic g factor and Bohr magneton, respectively. r//is the distance between the metal ion and the protons of the coordinated water molecules, (Oh and cos the proton and electron Larmor frequencies, respectively, and Xr is the reorientational correlation time. The longitudinal and transverse electron spin relaxation times, Tig and T2g, are frequency dependent according to Eqs. (6) and (7), and characterized by the correlation time of the modulation of the zero-field splitting (x ) and the mean-square zero-field-splitting energy (A. The limits and the approximations inherent to the equations above are discussed in detail in the previous two chapters. 

Another important parameter that influences the inner sphere relaxivity of the Gd(III)-based contrast agents is the electronic relaxation time. Both the longitudinal and transverse electron spin relaxation times contribute to the overall correlation times xa for the dipolar interaction and are usually interpreted in terms of a transient zero-field splitting (ZFS) interaction (22). The pertinent equations [Eqs. (6) and (7)] that describe the magnetic field dependence of 1/Tie and 1/T2e have been proposed by Bloembergen and Morgan and... 

T, Transverse (spin-spin) relaxation time for x,y-magnetization... 

By spin-spin relaxation, the nuclei relax to equilibrium among themselves (i.e. precession occurs without phase coherence). The vectors dephase (Fig. 1.5 (b) - Fig. 1.5 (a)), and the components of transverse magnetization, Mx and My, decay to zero as a result (transverse relaxation). The spin-spin relaxation time T2 is thus also referred to as the phase memory time or the transverse relaxation time. 

Longitudinal and transverse relaxations have been assumed by Bloch et al. [6] to be first-order rate processes. Following this assumption, the increase of Mz to M0 and the decay of Mx and My to zero may be expressed in terms of spin-lattice and spin-spin relaxation times, T, and T2 ... 

In several previous papers, the possible existence of thermal anomalies was suggested on the basis of such properties as the density of water, specific heat, viscosity, dielectric constant, transverse proton spin relaxation time, index of refraction, infrared absorption, and others. Furthermore, based on other published data, we have suggested the existence of kinks in the properties of many aqueous solutions of both electrolytes and nonelectrolytes. Thus, solubility anomalies have been demonstrated repeatedly as have anomalies in such diverse properties as partial molal volumes of the alkali halides, in specific optical rotation for a number of reducing sugars, and in some kinetic data. Anomalies have also been demonstrated in a surface and interfacial properties of aqueous systems ranging from the surface tension of pure water to interfacial tensions (such as between n-hexane or n-decane and water) and in the surface tension and surface potentials of aqueous solutions. Further, anomalies have been observed in solid-water interface properties, such as the zeta potential and other interfacial parameters. 

Elsewhere (31), we have discussed Browns measurements (14) on the transverse proton spin relaxation time as a function of temperature. His data suggest anomalous changes around 18°, 42°, and 60°C. Simpson and Carr (138) have also observed an anomaly near 40°C. on the basis of their spin relaxation studies. Simpson (137), in particular, reviewed other evidence for anomalies in this temperature range and noted that... 

The transverse relaxation is often called spin-spin relaxation and its relaxation rate is expressed by the inverse of the spin-spin relaxation time T2. However, these seems to be misleading, because the transverse relaxation is induced not only by electron spin-electron spin interaction, and the observed kinetics of the relaxation cannot always be expressed by a single exponential function. 

There is one other type of relaxation process that must be mentioned at this point. After irradiation ceases and B, disappears, not only do the populations of the m = + and m = states revert to the Boltzmann distribution, but also the individual nuclear magnetic moments begin to lose their phase coherence and return to a random arrangement around the z axis (Figure 2.1a). This latter process, called spin-spin (or transverse) relaxation, causes decay of MJ>y at a rate controlled by the spin-spin relaxation time T2. Normally, T2 is much shorter than T. A little thought should convince you that if T2 < Th then spin-spin (dephasing) relaxation takes place much faster than spin-lattice (Boltzmann distribution) relaxation. 

Eigure 12.5 presents TR ESR and ET ESR spectra obtained under photolysis of DAR (Scheme 12.1). One can observe a broadened signal of benzoyl radical in the ET ESR (or a signal of much lower apparent intensity). The intensity of the signals in CW TR ESR is determined by polarization, longitudinal (spin lattice) relaxation time Ti and by the rate of chemical disappearance of r. The intensity of signals in ET ESR is determined by polarization, and phase memory time Tm, which includes Ti, transverse (spin-spin) relaxation time T2, and a rate of chemical disappearance of r. Broad ESR components have short Tm, and they are difficult to observe. Broadening of components in spin adducts is ascribed to a hindered rotation around a Cp bond or cis-trans isomerization (Scheme 12.4). ... 

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