Spin lattice relaxation molecular motion

Accordingly, the relaxation time of a C atom will increase the fewer hydrogen atoms it bonds to and the faster the motion of the molecule or molecular fragment in which it is located. From this, it can be deduced that the spin-lattice relaxation time of C nuclei provides information concerning four molecular characteristics ... 

Usually, nuclear relaxation data for the study of reorientational motions of molecules and molecular segments are obtained for non-viscous liquids in the extreme narrowing region where the product of the resonance frequency and the reorientational correlation time is much less than unity [1, 3, 5]. The dipolar spin-lattice relaxation rate of nucleus i is then directly proportional to the reorientational correlation time p... 

Given the specific, internuclear dipole-dipole contribution terms, p,y, or the cross-relaxation terms, determined by the methods just described, internuclear distances, r , can be calculated according to Eq. 30, assuming isotropic motion in the extreme narrowing region. The values for T<.(y) can be readily estimated from carbon-13 or deuterium spin-lattice relaxation-times. For most organic molecules in solution, carbon-13 / , values conveniently provide the motional information necessary, and, hence, the type of relaxation model to be used, for a pertinent description of molecular reorientations. A prerequisite to this treatment is the assumption that interproton vectors and C- H vectors are characterized by the same rotational correlation-time. For rotational isotropic motion, internuclear distances can be compared according to... 

Direct H—C dipole-dipole coupling dominating 13C relaxation (for protonated carbons) information about molecular shapes and motion are contained in the experimental spin-lattice relaxation times. 

There has been extensive effort in recent years to use coordinated experimental and simulation studies of polymer melts to better understand the connection between polymer motion and conformational dynamics. Although no experimental method directly measures conformational dynamics, several experimental probes of molecular motion are spatially local or are sensitive to local motions in polymers. Coordinated simulation and experimental studies of local motion in polymers have been conducted for dielectric relaxation,152-158 dynamic neutron scattering,157,159-164 and NMR spin-lattice relaxation.17,152,165-168 A particularly important outcome of these studies is the improved understanding of the relationship between the probed motions of the polymer chains and the underlying conformational dynamics that leads to observed motions. In the following discussion, we will focus on the... 

By assuming an Arrhenius type temperature relation for both the diffusional jumps and r, we can use the asymptotic behavior of /(to) and T, as a function of temperature to determine the activation energy of motion (an example is given in the next section). We furthermore note that the interpretation of an NMR experiment in terms of diffusional motion requires the assumption of a defined microscopic model of atomic motion (migration) in order to obtain the correct relationships between the ensemble average of the molecular motion of the nuclear magnetic dipoles and both the spectral density and the spin-lattice relaxation time Tt. There are other relaxation times, such as the spin-spin relaxation time T2, which describes the... 

Molecular motions in low molecular weight molecules are rather complex, involving different types of motion such as rotational diffusion (isotropic or anisotropic torsional oscillations or reorientations), translational diffusion and random Brownian motion. The basic NMR theory concerning relaxation phenomena (spin-spin and spin-lattice relaxation times) and molecular dynamics, was derived assuming Brownian motion by Bloembergen, Purcell and Pound (BPP theory) 46). This theory was later modified by Solomon 46) and Kubo and Tomita48 an additional theory for spin-lattice relaxation times in the rotating frame was also developed 49>. 

Woessner s equations thus permit prediction of spin-lattice relaxation times for the dipole-dipole mechanism, which can be of help in the assignment of 13C NMR spectra. Moreover, the calculations described can be applied to the problem of internal molecular motion. 

Differing 7j values for CH3, CH2, and CH carbon nuclei within a molecule can arise not only by methyl rotation or anisotropic molecular motion, but also from the segmental mobility of partial structures, even when the dipolar mechanism predominates. Thus the spin-lattice relaxation times of methylene carbon atoms in long alkane chains pass through a minimum at the middle of the chain. In the presence of heavy nonassociating... 

Strong intermolecular interactions such as hydrogen bonds or ion-dipole pairs restrict the motion of molecules and pertinent molecular segments. These interactions increase the correlation time zc and accelerate the 13C spin-lattice relaxation. Shorter 13C relaxation times can therefore also indicate the presence of such interactions. The Tj values of the C atoms of carboxylic acids, phenols, alcohols, and solvated molecular ions behave in this way. 

While the nuclei 3H and 13C relax predominantly by the DD mechanism, relaxation of a quadrupole nucleus such as deuterium essentially involves fluctuating fields arising from interaction between the quadrupole moment and the electrical field gradient at the quadrupole nucleus [16]. If the molecular motion is sufficiently fast (decreasing branch of the correlation function, Fig. 3.20), the 2H spin-lattice relaxation time is inversely proportional to the square of the quadrupole coupling constant e2q Q/H of deuterium and the effective correlation time [16] ... 

Water mobility from molecular reorientation and diffusion. Evidence for the motion of the water molecules in crystal structures is typically provided by XH NMR (Davidson and Ripmeester, 1984). At very low temperatures (<50 K) molecular motion is frozen in so that hydrate lattices become rigid and the hydrate proton NMR analysis suggests that the first-order contribution to motion is due to reorientation of water molecules in the structure the second-order contribution is due to translational diffusion. 2H NMR has been also used to measure the reori-entational rates of water and guest molecules in THF hydrate (Bach-Verges et al., 2001). Spin lattice relaxation rates (fy) have been measured during THF hydrate... 

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