Showing papers on "Relaxation (NMR) published in 1969"

Nuclear Spin–Lattice Relaxation in Axially Symmetric Ellipsoids with Internal Motion

Abstract: The calculation of the nuclear‐magnetic‐resonance spin–lattice relaxation time has been extended to include molecules which approximate an axially symmetric ellipsoid and have internal motion about an axis at any constant angle to the symmetry axis of the ellipsoid. The calculation is carried out explicitly for two models of internal motion. These are, random reorientation among three equivalent positions 120° apart, and rotational diffusion.

Rotational Diffusion of Spherical‐Top Molecules in Liquids

Abstract: The extension of the classical rotational diffusion model proposed by Gordon in his study of linear molecules is applied to the evaluation of the reorientational correlation functions, their Fourier transforms, and correlation times for fluids composed of spherical‐top moelcules. The reorientational correlation times τθ(j), describing the time correlation of a jth‐order spherical harmonic, are expressed as functions of the correlation time τJ for the angular momentum of the molecules. These expressions are valid for all values of ωτJ, where ω is the root‐mean‐square angular frequency (kT / I)1 / 2 for a spherical‐top molecule with moment of inertia I. In the Debye limit (ωτJ ≪ 1), τθ(j) ≫ τJ, and τθ(j) are proportional to τJ−1 / ω2; in the perturbed‐free‐rotor limit (ωτJ ≫ 1), τθ(j) is proportional to τJ and is of comparable magnitude. τθ(j) goes through a minimum value when τθ(j), τJ, and ω−1 are approximately equal. Magnetic spin relaxation due to motional modulation of anisotropic spin–rotational...

Self-Modulation, Self-Steepening, and Spectral Development of Light in Small-Scale Trapped Filaments

Abstract: The spectral broadening associated with light propagating in self-trapped filaments through liquids with large optical Kerr constants is studied. In particular, we treat the influence of a nonzero orientational relaxation time and of linear dispersion upon the phase (and amplitude) development of the light as it interacts with the optically nonlinear medium. Relaxation introduces Stokes-anti-Stokes asymmetry, even in the absence of pulse steepening. The spectrum is compressed, and the degree of interference in various portions of the spectrum is altered. The effect of dispersion is apparently much less important, particularly in the case where propagation distances are short compared with the shock distance. However, dispersion combined with a finite relaxation time does introduce an exponential gain in the forward direction. For a small nonlinearity, the peak gain is equal to the stimulated Rayleigh gain in the backward direction; but it falls off with increasing nonlinearity, because of the Stokes-anti-Stokes interaction.Spectra computed for a picosecond pulse and for a 100% sinusoidally modulated light beam of infinite extent are compared. Because of its periodicity, the latter possesses a fine structure and is influenced differently by the orientational relaxation.Comparison of the experimental results with the theoretical calculations for the cases of a zero and a nonzero relaxation time indicates that pulses of the order of 5-10 psec in extent could give rise to the observed spectra. Possible sources of such pulses (or a sequence of such pulses) are discussed.

Coherent Resonance Fluorescence Excited by Short Light Pulses

Abstract: Fluorescence produced by resonant coherent light pulse passing through medium assuming infinite relaxation times and negligible pulse attenuation

Effect of a Magnetic Field on the Superparamagnetic Relaxation Time

Abstract: The relaxation time for the fluctuations in the direction of the magnetization vector is calculated for very fine, single-domain ferromagnetic particles which have a uniaxial (shape or crystalline) anisotropy. A magnetic field is assumed to be applied parallel to the easy magnetization axis, and the relaxation time is computed for various magnitudes of this field. It is found that the commonly used approximation for high-energy barriers is about as justified as in the case of zero magnetic field, down to barriers of the order of $\mathrm{kT}$.

Electronic Relaxation in Large Molecules

Abstract: In this paper we consider the problem of the radiative decay of electronically excited states of a large molecule. We have considered both intramolecular vibronic coupling and the interaction with the radiation field. Compound states for a system of decaying indistinguishable levels are constructed using the Fano method. General expressions for the radiative decay rate are derived and applied for the statistical limit of intramolecular vibronic coupling. On a time scale shorter than a typical intramolecular recurrence time the radiative decay is exponential, and the reciprocal lifetime consists of independent contributions of radiative and nonradiative components. The experimental implications of these results for large and medium‐size molecules are discussed.

Diffusion and Relaxation Phenomena in Ice

Abstract: The underlying mechanisms of several rate processes in ice are examined through cross comparisons of the processes with each other and with experimental observations. The assumption that the migration of orientational defects (Bjerrum faults) is the common origin of dielectric and elastic relaxation leads to a predicted ratio of dielectric‐to‐elastic relaxation time of 32, in close agreement with experiment. The conclusion that a separate process is responsible for diffusion is based on a comparison of diffusion and dielectric relaxation data. The faster diffusive motion controls the thermal equilibration of the proton spins as well as the magnetic resonance linewidths; an interstitial migration appears to be the mostlikely diffusion mechanism.

Quasielastic Rayleigh Scattering in Nematic Liquid Crystals

Abstract: Using a light-beat laser spectrometer, we observe the relaxation of the thermally excited fluctuations of anisotropy in the nematic phase of $p\ensuremath{-}\mathrm{azoxyanisole}$. We identify the two low-frequency purely dissipative modes recently predicted. A first study of the angular dependence of the width of these modes allows a determination of three among the six viscosity coefficients introduced by Leslie.

Formation of Excited States by recombining Organic Ions

Abstract: It is often supposed that the recombination of radical ions gives triplet and singlet states in the ratio 3:1, but this is not always true, especially in the case of geminate recombination. The possibility of changing the ratio by means of magnetic fields is discussed.

Influence of resonant and foreign gas collisions on line shapes

Abstract: In the limit of a dipole-dipole interaction between neutral atoms and the binary-collision approximation, we present a theory of pressure broadening in which the multiplet structure of the atomic levels is considered. The appropriate Schr\"odinger equations for the collision problem are numerically integrated to obtain solutions for both resonant and foreign gas broadening. The presence of radiation fields is neglected in the first half of the paper, where the collisional time rate of change of the density matrix is found. The pertinent collisional decay parameters are extracted from these equations. The ratios of the parameters of the average magnetic dipole to electric quadrupole moment obtained were 1.21\ifmmode\pm\else\textpm\fi{}0.02 for the relaxation of the entire ensemble in resonant broadening, 0.966\ifmmode\pm\else\textpm\fi{}0.012 for the relaxation of the initially excited atoms in resonant broadening, and 1.12\ifmmode\pm\else\textpm\fi{}0.02 for the relaxation of the initially excited atoms in foreign gas broadening. In the second half of the paper, the collisional broadening results are incorporated in a systematic evaluation of (i) spectral profiels (effects arising from the velocity and recoil of the emitting atom are neglected), (ii) Hanle-effect line shapes, and (iii) laser phenomena. For the case of resonant broadening, the radiation trapping process is reviewed and its influence on line shapes discussed. Finally, a detailed comparison of the theory with experimental findings as well as with previous theoretical results is made. We conclude that the dipole-dipole interaction is sufficient to explain most cases of resonant and some cases of foreign gas broadening.

Nonexponential Relaxation of Three‐Spin Systems in Nonspherical Molecules

Abstract: The longitudinal and transverse nuclear magnetic relaxation of a system of three identical spin‐12 nuclei in equivalent positions at the corners of an equilateral triangle fixed perpendicular to the axis of a symmetric‐top molecule is calculated on the assumptions that :(1) The relaxation is due to the dipole–dipole interactions between the three spins, including the effects of cross correlations, (2) the motion of the molecule can be treated as anisotropic rotational Brownian motion, and (3) the correlation time is short. The relaxation is found to be the sum of two decaying exponentials. The deviation from a simple exponential decay is greatest when the rotational diffusion about the symmetry axis is rapid compared to the rotational diffusion about an axis perpendicular to the symmetry axis.

Nuclear Magnetic Relaxation Studies of Internal Rotations and Phase Transitions in Borohydrides of Lithium, Sodium, and Potassium

Abstract: Proton spin–lattice relaxation times, T1, have been measured as a function of temperature for KBH4, NaBH4, and LiBH4. For NaBH4 and KBH4, 23Na and 11B relaxation measurements were also made. In all cases, the magnetization recovery is approximately exponential. Correlation times, τc, derived from the T1 data were used to calculate activation energies, V, for BH4− ion reorientations. For the cubic phase of KBH4, V = 14.8 ± 0.4 kJ/mole (3.55 ± 0.1 kcal/mole) (± always refers to rms error) from measurements on proton and 11B. For NaBH4, V was found to be 11.2 ± 0.5 and 14.8 ± 0.7 kJ/mole (2.7 ± 0.1 and 3.5 ± 0.2 kcal/mole) for the high‐ (cubic) and low‐temperature (tetragonal) phases; an anomaly in τc was observed at temperatures slightly below the phase transition, and may be interpreted as a relatively sudden change in V associated with the phase transition. In LiBH4, a rather broad minimum was observed for the proton T1 vs temperature; this has been interpreted as due to two inequivalent BH4− tetrahedra w...

Neutralization of Isolated Ion Pair in Polar Media. I. Theory for the Yield of Solvated Electrons

Abstract: Motion of an isolated ion pair in a polar medium is described here through the Smoluchowski equation with a time‐dependent dielectric constant. The time dependence is taken as appropriate to constant charge rather than to constant external field. Explicit solution of the problem is obtained in the framework of prescribed diffusion. This solution, in the infinite time limit, gives the escape probability. The yield of escaped electrons is identified with the solvated electron yield. Known yields in various polar media are used to calculate the respective thermalization distances and effective dielectrc constants. Dielectric relaxation time is explicitly used in the present formulation. Two diffusion constants are used, one prior and one after relaxation. Calculated results are compared with experiment. Physical concepts derived from the present model relate to thermalization length, effective dielectric constant, and diffusion–relaxation length.

Rodlike and Random‐Coil Behavior of Poly(n‐butyl Isocyanate) in Dilute Solution

Abstract: The polymer chain configuration, molecular relaxation, and the dipole moment of poly(n‐butyl isocyanate), (–CO–NR–)n, where R = C4H9, have been studied by dielectric measurements of the polymer in dilute solution. The complex dielectric constant, e* = e′ − je″, was measured at room temperature over a frequency range 10−1–1 × 106 Hz for fractionated samples whose molecular weights cover a very broad range, 20 × 103–10 × 106. From observation of the dielectric relaxation time as a function of molecular weight we deduce that the low‐molecular‐weight molecule, Mw 106, the polymer chain configuration can be described as random coil. The relaxation time and dipole‐moment measurements indicate that there is a one‐to‐one correspondence between the end‐to‐end distance and...

Nuclear Magnetic Resonance Studies of Solutions of the Rare‐Earth Ions and Their Complexes. IV. Concentration and Temperature Dependence of the Oxygen‐17 Transverse Relaxation in Aqueous Solutions

Abstract: The concentration and temperature dependence of oxygen‐17 linewidths in solutions of rare‐earth perchlorates have been investigated. Empirical models are proposed to account for the observed behavior. An equation relating the apparent relaxation rate to the concentration and to the NMR parameters of the nuclei under conditions of fast chemical exchange has been derived. It was used in the interpretation of the experimental results. Lower limits have been estimated for the rate constants of water exchange between the aquo complexes of Tb3+, Dy3+, Ho3+, Er3+, and Tm3+ and the solvent. These are found to be in the range 0.3–2.6 × 107 sec−1 and to follow the trend of the ionic radii. The upper limit for the activation enthalpy of the exchange process is estimated to be 5 kcal/mole. The upper limits of the electron relaxation times are in the range 2.8–5.0 × 10−13 sec. The temperature dependence of the oxygen‐17 transverse relaxation rates in these systems is discussed in terms of the microdynamic behavior of the molecules in water and electrolyte solutions. The observed trends comply with a model according to which there are two kinds of water molecules differing in their activation enthalpies for rotation. The relative contribution of the “hydrogen‐bonded” and coordinated molecules prevails at lower temperatures, whereas that of the “free” molecules becomes pronounced at higher temperatures. It is suggested that spherically shaped samples be preferred for studies of 17O line width in paramagnetic solutions in order to minimize inhomogeneous broadening. It is shown that this may be a source of some inconsistencies found in the literature.

Nuclear magnetic shielding of hydrated alkali and halide ions in aqueous solution

Abstract: Various methods for the determination of the paramagnetic term of the shielding constant of alkali and halide ions in dilute aqueous solution are discussed. Values of the chemical shift of the hydrated ions, σp Maq+ and σp Xaq− , are obtained from solvent isotope chemical shifts of halide ions; spin relaxation rates of quadrupolar nuclei in dilute aqueous solution and from the concentration dependence of the chemical shift and relaxation rates of alkali and halogen nuclei in aqueous solutions of alkali halides.

Erratum: Shock‐Wave Study of Vibrational Energy Exchange between Diatomic Molecules

Abstract: The relaxation equation of the vibrational energy for a mixture of two diatomic gases is solved under the condition of Landau–Teller, considering the translation–vibration energy transfer (T–V) processes as well as the vibrational energy exchange (V–V) process. The solution shows that the relaxation of each of the component molecules proceeds as if it has two relaxation times. At the starting point of the relaxation process, both of the components begin to relax with their respective T–V relaxation rates, and then, the relaxation rate of one component, which has a smaller T–V relaxation time, decreases gradually, while the rate of the other component increases. Finally, both the components relax with the same rate toward their equilibrium states. The extent of coupling between the T–V processes of the two components is determined by the rate of the V–V process and by the concentration of two species in the mixture. Based on the preceding analysis, the vibrational relaxations of CO in CO–N2, CO–C2, CO–D2, and CO–H2 mixtures diluted in Ar are observed by the infrared emission of the CO fundamental behind shock waves, and the V–V collision probabilities are determined. The results agree with the SSH theory except in the case of CO–H2 collision. Theoretical calculation using the Morse‐type potential is also discussed for the near‐resonant V–V process between CO and N2.

Absorption and Dispersion in Porous and Anisotropic Polycrystalline Ferrites at Microwave Frequencies

Abstract: In polycrystalline ferrites the relaxation of ferromagnetic resonance is often considerably increased by the random variations in the orientation of the anisotropy fields in different grains and by the presence of pores. The magnitude of this relaxation has been calculated most often in terms of scattering to spin‐waves, and the theories have been tested experimentally by measurements of the ferromagnetic resonance linewidth as a function of frequency or sample shape. In this paper it is discussed how an effective linewidth W and shift S of the resonance field can be derived from a measurement of the tensor susceptibility χ+, over a wide range of the applied magnetic field at a given frequency. The measuring apparatus is described and experimental results are presented for Ni0.36Zn0.64Fe2O4 with porosities from 0.2% up to 19%, and for a dense material of NiMn0.05Fe1.95O4, at a frequency of 9005 MHz, and applied magnetic fields from 1500–8000 Oe. These results are compared with the predictions of the spin‐...

23Na nuclear magnetic resonance relaxation studies of sodium ion interaction with soluble RNA.

Abstract: Interactions between 23Na+ and soluble RNA in aqueous solution are studied with the use of 23Na nuclear magnetic resonance. At low concentrations of NaCl, the interactions obey a simple equilibrium model with a formation constant log (Kf)3 = 2.8 ± 0.3. The relaxation rate of the bound sodium is found to be T1B-1 = 222 ± 19 sec-1 compared to that of free sodium T1F-1 = 17.5 sec-1. At high NaCl concentrations, the system deviates from the model, possibly owing to aggregation of the soluble RNA.

Kinetics of denaturation of DNA

Abstract: The kinetics of denaturation of DNA have been studied by relaxation techniques. Examination of the terminal relaxation times for a variety of DNA's under a variety of conditions has shown that DNA denaturation is principally a hydrodynamically limited process. Measurements within the helix–coil transition have demonstrated that the experimentally measured terminal relaxation times are a function of the following: (1) position in the helix–coil transition; (2) ionic strength of the solvent; (3) solvent viscosity; (4) DNA concentration; (5) molecular weight; (6) number and position of single-strand breaks. The dependence of the terminal relaxation time on the above mentioned factors can be attributed to hydrodynamic effects. Thus a hydrodynamic model for DNA unwinding is required. The model which best fits the data involves the assumption of a rotational frictional coefficient independent of molecular weight. This assumption is suggested by the fact that the relaxation time is proportional to the first power of the molecular weight.

Nuclear spin–lattice relaxation in solid methane and its deuterated modifications

Abstract: The proton and deuteron spin–lattice relaxation time T1 has been measured in CH4, CD4, CHD3, CH3D, and CH4–CD4 mixtures and CH4–krypton mixtures as a function of temperature between 1.2 °K and 60 °...

AN INVESTIGATION ON THE Ta--H SYSTEM BY INTERNAL FRICTION MEASUREMENTS.

Abstract: The internal friction has been measured as a function of temperature in a series of tantalum-hydrogen alloys with atomic ratios varying from H/Ta⩽0.005 to 0.17. The temperature of the measurements cover the range (78÷450) °K; the vibration frequencies are included between 1.5·102 Hz and 1.0·105 Hz. Two anelastic relaxation peaksP1 andP2 have been observed near 100 °K and in the range (180÷300) °K, respectively. The behaviour of these peaks has been studied in connection with the phase compositions of the Ta-H system. The second relaxation effectP2 is found to be a suitable tool for investigating the phase diagram of the system; its activation energy is (0.38±0.05) eV and its limiting relaxation time 2·10−14 s.