Spin-Lattice Relaxation Time Ti

The evolution of the projection of the magnetization (M) on the z axis (Mz) is described by the differential equation  

The probability to find the right component of the frequency of the molecular motion for correlation times higher or smaller than the optimum value are 

---

Experimental data on nitrogen obtained from spin-lattice relaxation time (Ti) in [71] also show that tj is monotonically reduced with condensation. Furthermore, when a gas turns into a liquid or when a liquid changes to the solid state, no breaks occur (Fig. 1.17). The change in density within the temperature interval under analysis is also shown in Fig. 1.17 for comparison. It cannot be ruled out that condensation of the medium results in increase in rotational relaxation rate primarily due to decrease in free volume. In the rigid sphere model used in [72] for nitrogen, this phenomenon is taken into account by introducing the factor g(ri) into the angular momentum relaxation rate... 

The process of spin-lattice relaxation involves the transfer of magnetization between the magnetic nuclei (spins) and their environment (the lattice). The rate at which this transfer of energy occurs is the spin-lattice relaxation-rate (/ , in s ). The inverse of this quantity is the spin-lattice relaxation-time (Ti, in s), which is the experimentally determinable parameter. In principle, this energy interchange can be mediated by several different mechanisms, including dipole-dipole interactions, chemical-shift anisotropy, and spin-rotation interactions. For protons, as will be seen later, the dominant relaxation-mechanism for energy transfer is usually the intramolecular dipole-dipole interaction. 

The temperature mapping method used in Ref. [8] is based on measurements of the spin-lattice relaxation time Ti of a suitable liquid such as ethylene glycol filling... 

The reason why one chose to follow the main liquid-crystalline to gel phase transition in DPPC by monitoring the linewidth of the various or natural abundance resonance is evident when we consider the expressions for the spin-lattice relaxation time (Ti) and the spin-spin relaxation time T2). The first one is given by 1/Ti oc [/i(ft>o) + 72(2ft>o)] where Ji coq) is the Fourier transform of the correlation function at the resonance frequency o>o and is a constant related to internuclear separation. The relaxation rate l/Ti thus reflects motions at coq and 2coq. In contrast, the expression for T2 shows that 1/T2 monitors slow motions IjTi oc. B[/o(0) -I- /i(ft>o) + /2(2u>o)], where /o(0) is the Fourier component of the correlation function at zero frequency. Since the linewidth vi/2 (full-width at half-maximum intensity) is proportional to 1 / T2, the changes of linewidth will reflect changes in the mobility of various carbon atoms in the DPPC bilayer. 

Morrow et al. measured the spin-lattice relaxation time Ti and quadrupole echo decay times T ) of headgroup deuterated d4-DMPC as a function of temperature and pressure to yield additional information about changes in the headgroup dynamics. Generally, motions in a LC phospholipid bilayer can... 

Fio. 18. Spin-lattice relaxation time Ti for silica gel (SG) and silica-alumina (SA) versus paramagnetic impurity content N. The straight line corresponds to the relation Ti oc (irS). 

Three parameters are readily obtainable from FiMR spectra which may be useful in studying binding interactions the chemical shift [jS], the linewidth (Av) or the apparent or effective spin-spin relaxation time (T2 ), and the spin-lattice relaxation time (Ti). C chemical shifts can reflect steric strain and change in the electronic environment within a molecule when it hinds to another species. Spin-lattice and spin-spin relaxation times can yield information on the lifetimes, sizes and conformations of molecular complexes. 

Polymer Dynamics. 13C spin-lattice relaxation times (Ti) were determined with either an inversion-recovery sequence (16) (for carbons observed by direct polarization) or with a modified cross-polarization experiment (17). 13C rotating-frame relaxation times (Tip(C)) were derived from measurements of the carbon signal that remained after a Tjp(C) hold time of... 

Birchall and Jolly used H NMR data for phosphine, arsine, and germane and some of their alkyl derivatives to determine the relative acidities in liquid ammonia Spin-lattice relaxation time (Ti) measurements for the H nuclei in PH3 are.reported by Armstrong and Courtney o) ... 

Other effects frequently encountered in inorganic systems that can severely affect line shape involve relaxation processes arising from interactions of nuclear quadrupole moments with electric field gradients. For quad-rupolar nuclei (I 1), the quadrupolar contribution to the spin-lattice relaxation time Ti is given approximately by... 

Clearly by working with typical spatial resolutions of approximately 30-50 pm, individual pores within the material are not resolved. However, a wealth of information can be obtained even at this lower resolution (53,54,55). Typical data are shown in Fig. 20, which includes images or maps of spin density, nuclear spin-lattice relaxation time (Ti), and self-diffusivity of water within a porous catalyst support pellet. In-plane spatial resolution is 45 pm x 45 pm, and the image slice thickness is 0.3 mm. The spin-density map is a quantitative measure of the amount of water present within the porous pellet (i.e., it is a spatially resolved map of void volume). Estimates of overall pellet void volume obtained from the MR data agree to within 5% with those obtained by gravimetric analysis. 

Table 3.20. 13C Spin-Lattice Relaxation Times Ti (s) of Saccharose in H20 and D20 at 42PC [166], "ch2oh...

Another way of using JH NMR to study the dynamics of phenyl protons in BPA-PC consists in selective deuteration of the methyl groups (BPA-d6-PC) [32]. Thus, the temperature dependence of the JH spin-lattice relaxation time, Ti, and spin-lattice relaxation time in the rotating frame, T p, has been determined, and is shown in Fig. 38. 

Table 4. Spin lattice relaxation time (Ti) of 2H of 90% ethanol and potentized homeopathic drugs in 90% ethanol. Figures in parentheses represent chemical shifts in ppm. Measurements were taken by a AMX-400 NMR spectrometer operating at 61.41 MHz at 22°C. Starting with the control other drugs are given in alphabetical...

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). ... 

If the motion of an acrylic polymer radical about the Cp bond is hindered, changing the temperature should lead to changes in the TREPR spectrum. This is indeed observed for all acrylic polymers we have examined to date. Simulation of the complete temperature dependence of TREPR spectra of acrylic polymer main-chain radicals should allow information regarding the conformational motion of the polymer in solution to be extracted, such as rotational correlation times, spin-lattice relaxation times (Ti), and activation energies for conformational transitions. 

Fig. 2.19. Temperature dependence of the NMR spin-lattice relaxation time, Ti, showing the minimum characteristic of hydrogen molecules (Carlos and Taylor 1982).

The first ist the strong dependence of observed CIDNP intensities on the nuclear spin lattice relaxation times Ti of the products. As is seen from Eqs. 

The total integrated intensities of all the silicons in the sample were usually reproducible to within 3% over the course of the reaction. The Si spin-lattice relaxation time, Ti, was 4.2 1.0 s, with a slight tendency for the more highly condensed species to exhibit times toward the lower limit of the uncertainty range. The pulse repetition period of 17.7 s ensured that the magnetization has recovered to 98 2% of its equilibrium value. 

---