Showing papers on "Relaxation (NMR) published in 1970"
TL;DR: By producing a train of absorption or dispersion signals (continuous wave magnetic resonance) or free induction decays (pulsed magnetic resonance), it is possible to save time in spin-lattice relaxation measurements as mentioned in this paper.
Abstract: By producing a train of absorption or dispersion signals (continuous‐wave magnetic resonance) or free induction decays (pulsed magnetic resonance) it is possible to save time in spin‐lattice relaxation measurements due to the fact that it is not necessary to wait for equilibrium magnetization before initiating the train. The relaxation time may be calculated from the train according to a simple rapidly converging iteration.
795 citations
TL;DR: In this paper, it was shown that the nuclear magnetic relaxation of the longitudinal and transverse components of a spin I are different, but each is the sum of I decaying exponential terms if I is an integer, or the sum I + ε+ ε−12 decaying exponential term if I was half an odd integer, if the relaxation is produced by quadrupole interactions for which the correlation time is not short compared to the Larmor period.
Abstract: Results are presented of calculations showing that the nuclear magnetic relaxation of the longitudinal and transverse components of a spin I are different, but each is the sum of I decaying exponential terms if I is an integer, or the sum of I + 12 decaying exponential terms if I is half an odd integer, if the relaxation is produced by quadrupole interactions for which the correlation time is not short compared to the Larmor period. Expressions for the exponents and coefficients are given in detail for the case I = 32. If the correlation time is short, the expressions reduce to the simple exponential decays calculated by previous investigators.
400 citations
TL;DR: In this paper, the theory of dielectric relaxation in a model polar liquid is developed and applied to experimental data, where a permanent point dipole moment undergoes rotational Brownian motion in the cavity.
Abstract: The theory of dielectric relaxation in a model polar liquid is developed and applied to experimental data. The model is a spherical Onsager cavity, with a uniform dielectric background described by the high frequency limit e∞ and containing a permanent point dipole. The dipole moment undergoes rotational Brownian motion in the cavity. Dielectric friction on the rotating dipole is taken into account and leads to a frequency‐dependent relaxation time. Earlier theoretical results, obtained first by Klug, Kranbuehl, and Vaughn and by Fatuzzo and Mason, are rederived. When the rotational Brownian motion is spherically isotropic, approximate Debye relaxation is found. When the rotational Brownian motion of the dipole is restricted to a constant angle with respect to some fixed axis, approximate Davidson–Cole relaxation is found. Experimental data on glycerol and i‐amylbromide are analyzed this way.
387 citations
TL;DR: In this article, the effect of proton decoupling on carbon-13 magnetic resonance spectra is treated in detail with the Solomon formulation for multiply irradiated spin systems, and the factors affecting the nuclear overhauser enhancement are discussed in terms of competition between the dipole-dipole relaxation mechanism essential to the Overhauser effect and other relaxation processes.
Abstract: The effect of proton decoupling upon carbon‐13 magnetic resonance spectra is treated in detail with the Solomon formulation for multiply irradiated spin systems. The factors affecting the nuclear Overhauser enhancement are discussed in terms of competition between the dipole–dipole relaxation mechanism essential to the Overhauser effect and other relaxation processes. Using a density matrix formulation, it is exhibited that the maximum Overhauser effect (achieved when the dipolar mechanism dominates) is independent of the number of hydrogen atoms interacting with a relaxing carbon‐13 nucleus. On the other hand, if the molecular tumbling motion is isotropic and the dipole–dipole mechanism dominates the relaxation process, then to a first approximation T1 can be shown to depend inversely upon the number of directly bonded hydrogen atoms. Expressions for treating an AMX three‐spin system are given also, and the effect of the third spin is discussed. The highly symmetric adamantane molecule provides an excell...
252 citations
TL;DR: It may be concluded that the enzyme probably provides three ligands for Mn(II) and thus the conformational changes previously detected by protein difference spectroscopy due to the binding of a divalent metal ion may be rationalized.
171 citations
TL;DR: The rotational energy transfer in collisions between homonuclear diatomic molecules and the rotational relaxation time in diatomic gases have been investigated using Parker's model for the intermolecular potential as mentioned in this paper.
Abstract: The rotational‐translational energy transfer in collisions between homonuclear diatomic molecules and the rotational relaxation time in diatomic gases have been investigated classically. Using Parker's model for the intermolecular potential, numerical solutions were obtained for the rotational‐energy transfer in individual collisions. The method of solution for the collision trajectories has been combined with a Monte Carlo integration procedure to evaluate the transport properties for diatomic gases. The formal kinetic‐theory expressions derived by Wang Chang, Uhlenbeck, and Taxman for the transport coefficients of gases with internal energy states were used. Results are presented for the shear viscosity, thermal conductivity, and rotational relaxation time in N2 which compare favorably with experimental values. Results are included for both a coplanar and three‐dimensional collision model. Approximate solutions for the rotational‐energy transfer in coplanar collisions and the rotational relaxation time ...
158 citations
TL;DR: In this article, a description of nuclear spin-spin and spin-lattice relaxation is presented for a system of two coupled nonequivalent spin−12 nuclei subject to mutual dipole-dipole interaction and interactions with external magnetic species.
Abstract: A description of nuclear spin–spin and spin–lattice relaxation is presented for a system of two coupled nonequivalent spin−12 nuclei subject to mutual dipole–dipole interaction and interactions with external magnetic species Expressions are derived for the six transition probabilities linking the four energy levels, in terms of an internal dipole–dipole relaxation parameter TD, external relaxation parameters TXA for nucleus A and TXB for nucleus B, and the degree of correlation (C) between the interactions of A and B with external magnetic species These molecular relaxation parameters are related to the initial rates of recovery of the NMR signal intensities after a selective pulse has rotated the magnetization vector of a chosen line through π radians in the rotating frame of reference A small general‐purpose computer has been used to control these pulse experiments and to program a synthesizer to provide the required stable audiofrequency signals Measurements have been made on the high‐resolution pr
150 citations
TL;DR: The longitudinal and transverse nuclear magnetic relaxation of a system of three identical spin-12 nuclei at the corners of an equilateral triangle with respect to a molecule which undergoes rotational Brownian motion has been calculated on the assumption that the relaxation is due to dipole-dipole interactions between the three nuclei as discussed by the authors.
Abstract: The longitudinal and transverse nuclear magnetic relaxation of a system of three identical spin‐12 nuclei at the corners of an equilateral triangle which undergoes hindered rotation with respect to a molecule which undergoes rotational Brownian motion has been calculated on the assumption that the relaxation is due to dipole–dipole interactions between the three nuclei, including the effects of cross correlations. The longitudinal relaxation is in general the sum of three decaying exponentials. If the rotational Brownian motion is rapid compared to the Larmor frequency, the longitudinal and transverse relaxations are both proportional to A1exp(s1t) + A2exp(s2t). For a molecule of arbitrary shape, the expressions for the coefficients A1 and A2 and the negative exponents s1 and s2 are quite complicated. The expressions simplify somewhat for the case of a symmetric top molecule, and even more for the case of a spherical molecule. It is shown for a molecule of arbitrary shape that, if the hindered rotation is...
143 citations
TL;DR: In this article, a theoretical description of stochastic magnetic resonance is given based on the phenomenological Bloch equations, and its application to the enhancement of sensitivity is analyzed and it is compared with conventional spectroscopy and with pulse-Fourier Spectroscopy.
143 citations
TL;DR: In this article, a number of expressions for angular momentum and reorientation correlation times are derived based on the similarity of the time dependences of the torque and the force exerted on the molecule of interest.
Abstract: In this paper a number of expressions for angular momentum and reorientation correlation times are obtained. The inverse of the angular momentum correlation time is related to a sum of two terms, one of which involves the shear viscosity of the medium and the other of which describes the precessional relaxation of the molecule. The derivation is based on the similarity of the time dependences of the torque and the force exerted on the molecule of interest. The reorientation correlation time is related to the angular momentum relaxation time in the diffusion and the near‐diffusion limits. The expressions obtained here have been confirmed by a number of ESR experiments.
TL;DR: In this article, temperature-dependent nuclear magnetic resonance relaxation times of quadrupolar nuclei in several symmetric top molecules (as neat liquids) are reported, and the success of the hydrodynamic calculation, the agreement with all available reorientational rates determined by dielectric relaxation, and semiquantitative "χ test" are used to confirm that these motions are indeed in the diffusion limit.
Abstract: Temperature‐dependent nuclear magnetic resonance relaxation times of quadrupolar nuclei in several symmetric top molecules (as neat liquids) are reported. These include 51V and 35Cl in VOCl3, 11B and 35Cl in BCl3, and 14N and 35Cl in CCl3CN; sufficient in each case to calculate the molecule's complete rotational diffusion tensor as a function of temperature. These results, along with previously reported results for other symmetric top molecules, are discussed. It is found that for small molecules in the liquid phase rotational motions which reorient an electric dipole invariably proceed by small‐step Brownian diffusion and that the rates of such reorientations can be calculated with good accuracy by hydrodynamic (microviscosity) theory. The success of the hydrodynamic calculation, the agreement with all available reorientational rates determined by dielectric relaxation, and the semiquantitative “χ test” are used to confirm that these motions are indeed in the diffusion limit. On the other hand, strong in...
TL;DR: In this article, the authors measured the proton spin lattice relaxation time at 19.00 MHz as a function of temperature in the range 25°-500°C for a series of samples in the α, β and γ phases of titanium hydride.
TL;DR: In this paper, it was shown that the behavior at very low and very high frequencies can be described in terms of apparent relaxation times, which differ by approximately 50% from the temperature dependence predicted by Parker, but the magnitudes are larger by a factor of 2.
Abstract: In his well‐known theory, Parker assumes that the rotational relaxation of diatomic gases may be described by a single relaxation time which is calculated for the special case of initially nonrotating molecules. In the present theory the evolution of the rotational distribution function is described by a diffusion‐equation approximation to the master equation. This equation is linearized and solved for the case of acoustic waves. The results indicate that the absorption and dispersion of acoustic waves cannot be described by a single relaxation time. However, the behavior at very low and very high frequencies can be described in terms of “apparent relaxation times” which differ by approximately 50%. The temperature dependence of the apparent relaxation times is similar to that predicted by Parker, but the magnitudes are larger by approximately a factor of 2.
TL;DR: In this article, the paramagnetic term of the nuclear magnetic shielding constant, σ p, was calculated from the chemical shift of nuclear resonance, which provides a general method for estimating spin-rotation interaction constants.
Abstract: Spin-rotation interaction constants, c, are calculated from the paramagnetic term of the nuclear magnetic shielding constant, σ p, using a relationship originally due to Ramsey. Calculated values show excellent agreement with experimental determinations from molecular beam measurements. Since σ p can be easily estimated from the chemical shift of the nuclear resonance this provides a general method for estimating spin-rotation interaction constants. Chemical shift anisotropies allow the components c ⊥ and c ‖ of the spin-rotation interaction tensor to be determined. Generally both components have the same sign and are of similar magnitude. The r.m.s. value of the spin-rotation interaction constant, required to calculate nuclear spin-lattice relaxation times, is not expected to differ appreciably from average values obtained from molecular beam measurements or magnetic shielding. Values for the molecular angular velocity correlation time, τ sr, calculated directly from nuclear spin-lattice relaxation times...
TL;DR: In this paper, the Fourier inversion of vibrational band contours was used to show that the rotational motion in a large variety of liquids, some of them strongly associated, occurs by a jump of the order of a molecular diameter after a trapping time of 10−11−10−10 sec.
Abstract: It is shown experimentally (Fourier inversion of vibrational band contours) that the molecular orientational motion in some representative common liquids [methylene chloride (CH2Cl2), methyl iodide (CH3I), chloroform (CHCl3), cyclohexane (C6H12)] appears to consist of angular jumps of the order of 20° to 60°. During a jump, which is completed in times of the order of 0.4 × 10−12 sec, the molecules are observed to rotate as if they were in their vapor phase, regardless of whether or not the orientational motion involves the tilting of a permanent dipole moment or of the size of the molecule. The infrared data are compared with results from nuclear magnetic relaxation studies. It is seen that the rotational motion in liquids, as it is observed by these techniques, is not sensitive to molecular association, weak hydrogen bonding, etc. On the basis of the extended Torrey model of intermolecular spin–lattice relaxation, it appears that molecular translational diffusion in a large variety of liquids, some of them strongly associated, occurs by a jump of the order of a molecular diameter after a trapping time of the order of 10−11–10−10 sec. As far as can be predicted, liquids which obey a classical diffusion model of very small diffusion steps would be the exception rather than the rule. The possibility is discussed that a dimer is the diffusing entity in acetic acid.
TL;DR: In this article, a general theory of non-radiative intramolecular decay in large molecules is formulated using the methods of solid state physics and the harmonic approximation, and the predicted dependence of the decay rate on the energy gap Δ E between electronic origins gets characteristic forms in two limiting cases: the string electronic-vibrational coupling case (gaussian in Δ E, Arrhenius-type barrier climbing between electronic states, small isotope effect) and the weak coupling case(nearly exponential variation with Δ E, domination by the highest frequency modes and marked deuter
TL;DR: In this paper, the deuteron and nitrogen spin-lattice relaxation times of acetonitrile-d3 were measured as a function of pressure up to 2 kbar at 23°C using the NMR pulse method.
Abstract: The deuteron and nitrogen spin–lattice relaxation times of acetonitrile‐d3 have been measured as a function of pressure up to 2 kbar at 23°C using the NMR pulse method. Since the quadrupole coupling constants for nitrogen and deuterons in acetonitrile‐d3 are known, the experimental T1 data were interpretable in terms of the rotational diffusion constants for motion perpendicular and parallel to the symmetry axis, D⊥ and D‖, respectively. In agreement with our previous results the calculated activation volumes show that ΔV‡(D⊥) is much larger than ΔV‡(D‖).
TL;DR: In this article, the authors measured the relaxation times of CO2 in an atmosphere of N2, Ne, He, D2 and H2 and showed that during the approach to equilibrium the relaxation time changes in the way to be expected from the change in the translational temperature.
Abstract: times and that during the approach to equilibrium the relaxation time changes in the way to be expected from the change in the translational temperature. These observations have been confirmed by infrared measurements on shock heated CO2 (Hodgson & line i969) and are consistent with recent laser fluorescence measurements on the rate of deactivation of the asymmetric stretching mode (Hocker, Kovacs, Rhodes, Flynn & Javan i966; Moore, Wood, Ho & Yardley i967). In the present paper results are given for the relaxation times of C02 in an atmosphere of N2, Ne, He, D2 and H2. The object of these experiments was to measure relaxation times over a wide range of temperatures for these collision partners. The results give some insight into the relative importance of the effeets of the reduced masses and force fields at different temperatures. They provide the grounds for testing current calculations of relaxation times and help in the understanding of the collision processes important in the CO2 laser.
TL;DR: In this paper, the nuclear magnetic relaxation times for rubber, polybutene-1, polyethylene, polyvinyl chloride, polychlorotrifluoroethylene and polycarbonate were reported.
Abstract: Nuclear magnetic relaxation times T2, T1, and T1ρ are reported for natural rubber, polybutene-1, polyethylene, polyvinyl chloride, polychlorotrifluoroethylene, polyethylene terephthalate and polycarbonate. The measurements cover the temperature range form 77 K to above the melting or glass transition regions. All seven polymers exhibit glass transition effects. Methyl group reorientations are observed at low temperatures. An additional ethyl side group motion and a crystalline rotator phase (>50°) are observed in polybutene-1. Other mechanisms are discussed. Good agreement is found between mechanical, dielectric and n.m.r relaxation frequencies.
TL;DR: In this article, it was found that the line shape and integrated intensity depend on the pH and on the type and concentrations of counteranions in the solution, which is interpreted in terms of the formation of monosubstituted complexes which give signals too broad to observe.
Abstract: ESR measurements of aqueous solutions of Fe3+ containing various electrolytes were made at X‐ and Q‐band frequencies. It was found that the line shape and integrated intensity depend on the pH and on the type and concentrations of counteranions in the solution. Addition of LiCl and NH4NCS result in reduction in the integrated intensity and subsequent disappearance of the ESR signal. This is interpreted in terms of the formation of monosubstituted complexes which give signals too broad to observe. From the results, formation constants have been calculated. Successive addition of NH4F results in the formation of complexes of the type [Fe(H2O)6−nFn]3−n having different ESR linewidth ranging from 10 to 1000 G. There is a strong reduction in the linewidth on going from X‐ band to Q‐band frequencies. The results are explained in terms of electronic relaxation via the modulation of the zero field splitting (zfs) parameter. From the analysis of the data it was possible to derive values for the zfs interactions an...
TL;DR: A spin-echo NMR study of the dimethyldodecylamine oxide–deuterium oxide system is carried out—a system in which anisotropic ordered structures exist and one for which considerable X-ray and continuous wave NMR data are available.
Abstract: NUCLEAR magnetic resonance (NMR) spectroscopy is one of the most promising techniques to be recently applied to the study of lipid, protein and water interactions in biological and other ordered and semi-ordered systems. NMR studies of the water in many hydrated biological systems have been interpreted in terms of the existence of “structured”, “ice-like” or “bound” water1–6. Likewise, line broadening in ordered liquid crystalline and biological systems has often been taken as an indication of restriction of molecular motion7–13. We should like to point out some possible pitfalls in interpreting the results of limited relaxation or line width data in terms of changes in molecular mobility arising from specific interactions, in systems which are not isotropic liquids and are not always homogeneous. We have carried out a spin-echo NMR study of the dimethyldodecylamine oxide–deuterium oxide system—a system in which anisotropic ordered structures exist and one for which considerable X-ray and continuous wave NMR data are available9,14. This system is an ideal one for the study of the effects of molecular ordering and anisotropy on the measured NMR parameters because the structure can be changed from isotropic to anisotropic simply by a slight change in composition or temperature.
TL;DR: The results of neutron activation, spectrochemical analysis and EPR measurements show that the amount of paramagnetic ions present in samples of protein solutions cannot be responsible for the decrease of T1 with respect to pure water.
TL;DR: In this paper, the authors carried out an exact study of the relaxation of a single magnetic impurity embedded in a linear quantum chain and obtained a rigorous result for the expectation value of any spin in the chain.
Abstract: We carry out an exact study of the relaxation of a single magnetic impurity embedded in a linear quantum chain. We obtain a rigorous result for the expectation value of any spin in the chain, and find that it relaxes to its equilibrium value as ${t}^{\ensuremath{-}1}$.
TL;DR: In this paper, the frequency dependence of the proton relaxation times in aqueous solutions of manganese carboxypeptidase A and pyruvate kinase has been measured and analyzed.
TL;DR: In this paper, the effect of pressure on the reorientational and translational motions of molecular liquids investigated was investigated and the intermolecular T1 was found to follow the changes in the viscosity with pressure.
Abstract: The pressure dependence of the proton spin–lattice relaxation times has been measured at 23°C in liquid benzene and its mixtures with benzene‐d6 up to 600 bar, and in liquid chlorobenzene and its mixtures with chlorobenzene‐d5 up to 2000 bar. The separation of the intramolecular and intermolecular contributions to proton dipolar relaxation allowed us to study the effect of pressure on the reorientational and translational motions of the molecular liquids investigated. As predicted by the Bloembergen–Purcell–Pound (BPP) theory the intermolecular T1 were found to follow the changes in the viscosity with pressure. On the other hand, the experimental pressure dependence of the intramolecular T1 in benzene differs widely from the BPP theoretical prediction due to the relatively free rotation about the C6 axis in benzene. Removal of the C6 axis and introduction of a dipole in chlorobenzene result in agreement between theoretical and experimental intramolecular T1 pressure dependences. As an example of a molecul...
TL;DR: In this article, it was shown that the dominant electronic relaxation in solutions of Cr3+ and Fe3+ hydrates is due to modulation of the zero-field splitting interaction.
Abstract: ESR intensities and linewidths at X band and linewidths at Q band of [Cr(H2O)6]3+ and [Fe(H2O)6]3+ in water‐glycerol mixtures are reported. At X band the linewidth increases with glycerol concentration and there is a concommitant decrease in the integrated intensity of the ESR line. The linewidth at Q band is independent of the glycerol content of the solvent. The results are interpreted in terms of the general theory of electronic relaxation. It is shown that the dominant electronic relaxation in solutions of Cr3+ and Fe3+ hydrates is due to modulation of the zero‐field splitting interaction. This interaction and its time dependence result from collisions of the hydrated complex with solvent molecules. Using equations derived for relaxation by rotational tumbling, a correlation time of about 5 × 10−12 sec in water is found for both complexes. The decrease in the integrated intensity with increasing viscosity at X band is due to the smearing out of all but the 12 → − 12 transitions. At Q band the Cr3+ res...