Relaxation (NMR)

Abstract: The dispersion and absorption of a considerable number of liquid and dielectrics are represented by the empirical formula e*−e∞=(e0−e∞)/[1+(iωτ0)1−α]. In this equation, e* is the complex dielectric constant, e0 and e∞ are the ``static'' and ``infinite frequency'' dielectric constants, ω=2π times the frequency, and τ0 is a generalized relaxation time. The parameter α can assume values between 0 and 1, the former value giving the result of Debye for polar dielectrics. The expression (1) requires that the locus of the dielectric constant in the complex plane be a circular arc with end points on the axis of reals and center below this axis.If a distribution of relaxation times is assumed to account for Eq. (1), it is possible to calculate the necessary distribution function by the method of Fuoss and Kirkwood. It is, however, difficult to understand the physical significance of this formal result.If a dielectric satisfying Eq. (1) is represented by a three‐element electrical circuit, the mechanism responsible...

Abstract: 1. Elements of Resonance.- 2 Basic Theory.- 3. Magnetic Dipolar Broadening of Rigid Lattices.- 4. Magnetic Interactions of Nuclei with Electrons.- 5. Spin-Lattice Relaxation and Motional Narrowing of Resonance Lines.- 6. Spin Temperature in Magnetism and in Magnetic Resonance.- 7. Double Resonance.- 8. Advanced Concepts in Pulsed Magnetic Resonance.- 9. Multiple Quantum Coherence.- 10. Electric Quadrupole Effects.- 11. Electron Spin Resonance.- 12. Summary.- Problems.- Appendixes.- A. A Theorem About Exponential Operators.- B. Some Further Expressions for the Susceptibility.- D. A Theorem from Perturbation Theory.- E. The High Temperature Approximation.- F. The Effects of Changing the Precession Frequency - Using NMR to Study Rate Phenomena.- G. Diffusion in an Inhomogeneous Magnetic Field.- H. The Equivalence of Three Quantum Mechanics Problems.- I. Powder Patterns.- J. Time-Dependent Hamiltonians.- K. Correction Terms in Average Hamiltonian Theory - The Magnus Expansion.- Selected Bibliography.- References.- Author Index.

Abstract: A new general technique for the investigation of exchange processes in molecular systems is proposed and demonstrated. Applications comprise the study of chemical exchange, of magnetization transfer by inter‐ and intramolecular relaxation in liquids, and of spin diffusion and cross‐relaxation processes in solids.

Abstract: The necessary coordination of the motions of different parts of a polymer molecule is made the basis of a theory of the linear viscoelastic properties of dilute solutions of coiling polymers. This is accomplished by use of the concept of the submolecule, a portion of polymer chain long enough for the separation of its ends to approximate a Gaussian probability distribution. The configuration of a submolecule is specified in terms of the vector which corresponds to its end‐to‐end separation. The configuration of a molecule which contains N submolecules is described by the corresponding set of N vectors. The action of a velocity gradient disturbs the distribution of configurations of the polymer molecules away from its equilibrium form, storing free energy in the system. The coordinated thermal motions of the segments cause the configurations to drift toward their equilibrium distribution. The coordination is taken into account by the mathematical requirement that motions of the atom which joins two submolecules change the configurations of both submolecules. By means of an orthogonal transformation of coordinates, the coordination of all the motions of the parts of a molecule is resolved into a series of modes. Each mode has a characteristic relaxation time. The theory produces equations by means of which the relaxation times, the components of the complex viscosity, and the components of the complex rigidity can be calculated from the steady flowviscosities of the solution and the solvent, the molecular weight and concentration of the polymer, and the absolute temperature. Limitations of the theory may arise from the exclusion from consideration of (1) very rapid relaxation processes involving segments shorter than the submolecule and (2) the obstruction of the motion of a segment by other segments with which it happens to be in contact. Another possible cause of disagreement between the theory and experimental data is the polydispersity of any actual polymer; this factor is important because the calculated relaxation times increase rapidly with increasing molecular weight.

Abstract: Abragam and Pound's method for the calculation of the longitudinal relaxation time ${T}_{1}$ has been extended to the transverse relaxation time ${T}_{2}$. Explicit calculations have been carried out for a pure dipole-dipole interaction, showing that for an interacting pair of like spins, or for nuclei in paramagnetic solution, ${T}_{1}$ is exactly equal to ${T}_{2}$ in the extreme narrow case. For a pair of interacting unlike spins, it is shown that the longitudinal components of the magnetic moments do not have simple exponential decays. This gives rise to a steady and transient Overhauser effect. The transverse components, however, have in all cases, simple exponential decay defined by a single relaxation time ${T}_{2}$. A set of modified Bloch's equations is found, giving the correct equation of motion of the macroscopic magnetic moments of such a system of pairs of unlike spins.The equality of ${T}_{1}$ and ${T}_{2}$ has been verified in paramagnetic solutions, and a nuclear Overhauser effect has been observed in anhydrous hydrofluoric acid. If one assumes that the extreme narrow case corresponds to the actual motion, the experimental results are not consistent with the picture of a pure dipole-dipole interaction between the hydrogen and fluorine nuclei of a molecule without taking into account the effect of the other molecules.