Theory Of Nuclear Magnetic Relaxation Research Articles

Collision Theory of Relaxation Processes. II. Diatomics

A theory of nuclear magnetic relaxation for gases composed of diatomic molecules is developed starting from a quantum Boltzmann equation. Formal expressions for the relaxation times and collision induced chemical shifts due to intramolecular spin–rotation and dipole–dipole interactions are given in terms of the relaxation times for rotational polarization. The form of the resulting equations agrees with the Bloom–Oppenheim theory while also giving expressions for the rotational-polarization relaxation times in terms of the transition operator for the collision process.

Nuclear Magnetic Relaxation of Polymer Solutions

A theory of nuclear magnetic relaxation of solutions of chain macromolecules is presented. The relaxation takes place because of the relative motion of segments of the polymer chain containing magnetic nuclei. The analysis is based on the Brownian motion of isolated polymer molecules using a model which has been applied previously for dynamic viscoelasticity and dielectric relaxation of polymer solutions. The relative motion of magnetic nuclei may be considered as arising from three sources: (a) the relative motion of pairs of atoms rigidly attached to a chain segment, (b) the relative motion of chain segments, and (c) the motion of atoms relative to a chain segment to which they are attached. Cases (a) and (b) are treated here.

Proton Magnetic Relaxation and Protein Hydration

WE have found that ovalbumin dissolved in water decreases the proton spin–lattice relaxation time T1 and proton spin–spin relaxation time T2 and we show that this effect is due to an increase of correlation time of part of the water molecules. The correlation time τ can be defined as the mean time of persistence of the angular position of a water molecule and is simply related1 to the Debye dielectric relaxation time τd, τ=τd/3. According to the theory of nuclear magnetic relaxation by Solomon2, T1 and T2 are functions of τ. In some cases τ can be expressed as a function of the macroscopic viscosity of the liquid1, but in the case of protein solutions such an explanation is not possible as was shown by Hennel et al.3.

Theory of Nuclear Magnetic Relaxation by Spin-Rotational Interactions in Liquids

The contribution of spin-rotational interactions to the nuclear magnetic relaxation of identical spin-\textonehalf{} nuclei at equivalent positions in spherical liquid molecules is calculated by use of the semiclassical form of the density-operator theory of relaxation, and the result is compared with the contributions of intra- and intermolecular dipole-dipole interactions. The angular velocity of a molecule is treated classically by assuming that it obeys an equation analogous to the Langevin equation that is postulated in treatments of translational Brownian motion. The change in orientation of a molecule is assumed to be due to isotropic rotational Brownian motion. By use of this model the correlation functions of components of the angular velocity of a molecule are calculated, and are found to have an exponentially decaying time dependence with a time constant (correlation time) ${\ensuremath{\tau}}_{1}$ that is quite different in its temperature dependence than the correlation time ${\ensuremath{\tau}}_{2}$ of the dipole-dipole interactions. In typical situations ${\ensuremath{\tau}}_{1}$ is much smaller than ${\ensuremath{\tau}}_{2}$. Use is made of this fact to evaluate the correlation functions of the functions of the orientation and angular velocity that occur in the tensor spin-rotational interactions. The result that ${\ensuremath{\tau}}_{1}\ensuremath{\ll}{\ensuremath{\tau}}_{2}$ explains the experimentally observed "quenching" of the relaxation effect of spin-rotational interactions in liquids, and the result that ${\ensuremath{\tau}}_{1}T$ increases as the temperature increases explains the experimentally observed temperature dependence of the relaxation effect of spin-rotational interactions in liquids.

Theory of nuclear magnetic relaxation in liquid-phase polymers

MEASUREMENT of the nuclear magnetic resonance relaxation times permits information to be obtained on molecular motion in a substance. In low-moleelflar-weight liquids, this motion is characterized by the time of correlation of the energy of the magnetic dipole-dipole interaction of the nuclei. However. it has been shown in a number of experimental investigations [1-3] that polymeric liquids, as was to be expected, are characterized by a broad correlation time spectrum. In this case, the problem of the theoretical calculation of the form of the spectrtun of the correlation time in liquid-phase polymers (solutiol~ and melts) arises. I f the task is set of determining tbe spectrum of the correla*ion time to a rough approximation and calculating the relaxation time to an order of magnitude, it is possible to restrict oneself to the calculation of the interaction of the magnetic nuclei in a single group, since this interaction makes the main contribution to relaxation. This offers a possibility of considering melt sand solutions of polymers simultaneously. At the same time, the molecular motion can be described by a very simple model. In order to calculate the relaxation time it is necessary to know the correlat, ion function of the dipole-dipoJe interaction. We shall limit ourselves, for simplicity, to polymers in which the distances between the magnetic nuclei in the groups are constant and similar. Under these conditions it is nob difficult to convince oneself, using the usual definition of the correlation function (see, for example, [4]) and the isotropic nature of the liquid, that the correlation function .f(t) has the form of a sum of N correlation functions of the individual groups: 1 ~¢ .f(t) = ~q~=ifq(t ), (l)

Nuclear Magnetic Relaxation in Antiferromagnetics, II

Theory of nuclear magnetic relaxation in antiferromagnetics treated in the preceding paper for non-magnetic ions is extended to the case of magnetic ions. Strong hyperfine interactions and quadrupole interactions are the distinctive feature of the problem. The line width and the relaxation rate are calculated by using the spin wave approximation at low temperatures and the model of Gaussian random modulation at high temperatures. Order estimations of T1 and T2 are made for several substances, which predict that the nuclear resonance will be difficult to detect above the Curie point because of the broadening due to the hyperfine interaction, while the resonance will become detectable at sufficiently low temperatures where the low frequency components of the local field spectra decrease remarkably. The effects of the quadrupole interaction are also discussed.