Spin-lattice relaxation-time simulations

NMR 13C spin-lattice relaxation times are sensitive to the reorientational dynamics of 13C-1H vectors. The motion of the attached proton(s) causes fluctuations in the magnetic field at the 13C nuclei, which results in decay of their magnetization. Although the time scale for the experimentally measured decay of the magnetization of a 13C nucleus in a polymer melt is typically on the order of seconds, the corresponding decay of the 13C-1H vector autocorrelation function is on the order of nanoseconds, and, hence, is amenable to simulation. 

The spin-lattice relaxation time T can be determined from simulation by using the relationship169 of Eq. [70]... 

Figure 17 Spin-lattice relaxation times for six resonances along a PB chain. Trans and cis denote sp3 hybridized carbons in the respective monomer type, trans-trans, trans-cis, cis-cis, and cis-trans. They denote sp2 hybridized carbons in a trans-group with a transgroup as neighbor, a trans-group with a cis-group as neighbor, and so on. Open bars are for simulation, and filled ones for experiment. Values are shown for 273 K (short bars) and 400 K (longer bars).

Computational methods have been applied to study the conformations of free and metal-complexed oxathiacrown ethers 1-4 shown in Figure 6. The results were compared to variable temperature NMR and i spin-lattice relaxation time measurements <2001JP2988>. Theoretical studies included simulated 111 NMR spectra using PERCH and molecular modeling with PM3 semi-empirical quantum-chemical calculations. The NMR and the computational data both show that Ag+ coordinates equally well to S and O atoms, Bi3+ and Sb3+ prefer O atoms, and that Ptz+ and Pdz+ prefer exo-cyclic coordination only to the S atoms in this maleonitrile macrocycle. 

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. 

Sturz and DoUe measured the temperature dependent dipolar spin-lattice relaxation rates and cross-correlation rates between the dipolar and the chemical-shift anisotropy relaxation mechanisms for different nuclei in toluene. They found that the reorientation about the axis in the molecular plane is approximately 2 to 3 times slower than the one perpendicular to the C-2 axis. Suchanski et al measured spin-lattice relaxation times Ti and NOE factors of chemically non-equivalent carbons in meta-fluoroanihne. The analysis showed that the correlation function describing molecular dynamics could be well described in terms of an asymmetric distribution of correlation times predicted by the Cole-Davidson model. In a comprehensive simulation study of neat formic acid Minary et al found good agreement with NMR relaxation time experiments in the liquid phase. Iwahashi et al measured self-diffusion coefficients and spin-lattice relaxation times to study the dynamical conformation of n-saturated and unsaturated fatty acids. 

Naphthalene, in contrast to benzene, did not show any NMR-spectra line-width narrowing up to its melting temperature of 353 K. The mean experimental second moment was 9.1 compared to 10.1 G, estimated for the rigid crystal. Measurement of spin-lattice relaxation times indicated, however, also a slow reorientational jump motion about an axis normal to the molecular axis An activation energy of 105 kJ/mol was derived. Molecular dynamics simulations suggest that this reorientation about the axis of greatest inertia occurs with a frequency of 100 MHz within 20 K of fusion (353.6 K) Still, no plastic crystal behavior as found in cyclohexane and related compounds (see Sect. 3.1.1) is indicated for benzene or naphthalane, even close to the melting temperature. 

Figure 1. Compeirison of the spin lattice relaxation times determined from MD simulations and experiment for two different temperatures. The figure shows data for 12 different resonances (cis-cis for example indicates an carbon in a cis group next to another cis group, trans an sp carbon of a trans group)...

Figure 2. Conipaxison of the spin lattice relaxation times determined from MD simulations and experiment for the cis-cis (sp ) and the trans ( ) resonance as a function of inverse temperature. Also shown are results for the nuclear Overhauser enhancement which is a measure of the non>exponentiality of the observed relaxation...

FIG. 4 Temperature dependence of the spin lattice relaxation time for two different alkanes as seen in experiment (performed at 75 MHz carbon resonance frequency) and MD simulation [11],... 

Figure 5 (A) Plots of non-crystalline spin-lattice relaxation times T, of PE-SL samples ( ) and MQ-PE-SL (O) versus the reciprocal absolute temperature. (B) Intensity of non-crystalline peaks of a sample of PE-SL and MQ-PE-SL versus delay time r. The peak intensity was obtained from computer simulation of the partially relaxed dipolar-dephasing NMR spectra. Reproduced with permission of John Wiley Sons from Chen Q, Yamada T, Kurosu H, Ando I, Shioino T and Doi Y (1992) Journal of Polymer Science, Part B Polymer Physics 30 591.

The spin parameters for the hydroxyl radical were obtained from the EPR spectrum in ice conducted at a temperature of 77 K. Spin parameters for the 2-propanolyl radical can be obtained in a straightforward manner and all information has been extracted from the EPR spectrum. For the hydroxyl radical, the spin relaxation time was varied over the range 20-100 ps, and it was assumed that the spin-lattice relaxation time was equal to the spin-spin relaxation time (i.e. T = T2). Upon scavenging of the hydroxyl radical the spin relaxation of 2-propanol was not simulated as its relaxation time is known to be 2.7 x 10 s [7], which is longer than the timescale of the simulation (1 p.s). For all results presented an external static magnetic field of 0.33 T was used to reproduce experimental conditions. 

By modelling the TR MFE fluorescence decay curves in low-permittivity solvents using new simulation techniques, it has been shown that the spin-lattice relaxation time can be significantly decreased by this cross-combination effect, depending on the number of radical pairs in the spur. It is hypothesised that this effect acts as an extra source of spin relaxation in hydrocarbons where the recombination fluorescence is slowed down by an electron scavenger, such as hexafluorobenzene. It has also been hypothesised that different spin-lattice relaxation times are to be expected for photolytic and radiolytic pairs. 

The complexity of simulating an entire track structure from the IRT framework has been highlighted in this chapter. Although in the TR MFE decay curves the contribution of cross-recombination may have been overestimated, the results nonetheless highlight a distinctive correlation between cross-recombination and the spin-lattice relaxation time. Further work is now required to (1) incorporate a more realistic description of the magnetic interactions (in particular the exchange and dipole interactions) (2) use a realistic description for the track structure to describe the radiolysis of hydrocarbons, where the ERP effect can be properly understood in terms of the spatial distribution of the primary and secondary ion-pairs. 

The second separation method involves n.O.e. experiments in combination with non-selective relaxation-rate measurements. One example concerns the orientation of the anomeric hydroxyl group of molecule 2 in Me2SO solution. By measuring nonselective spin-lattice relaxation-rat s and n.0.e. values for OH-1, H-1, H-2, H-3, and H-4, and solving the system of Eq. 13, the various py values were calculated. Using these and the correlation time, t, obtained by C relaxation measurements, the various interproton distances were calculated. The distances between the ring protons of 2, as well as the computer-simulated values for the H-l,OH and H-2,OH distances was commensurate with a dihedral angle of 60 30° for the H-l-C-l-OH array, as had also been deduced by the deuterium-substitution method mentioned earlier. 

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