Relaxation measurement

Following the application of a pulse or pulses to an NMR sample and the acquisition of whatever data are of interest, time is required for the system to return to some level of equihbrium. Two fundamental relaxation processes govern the return of a perturbed spin system to equihbrium. These processes are spin—lattice or Tj relaxation, and spin—spin or T2 relaxation. A variety of means are available to measure both of these fundamental processes [27, 29, 31]. We will limit the discussion here to the former. 

Spin—lattice relaxation is the time constant for the recovery of magnetiTation along the z-axis in a NMR experiment. Various methods are available for the measurement of spin lattice relaxation times. The interested reader is referred to the series of monographs echted by Levy on Carbon-13 NMR spectroscopy [44, 45] for more details. The energy transfer between nuclear moments and the lattice , the three-dimensional system containing the nuclei, provides the mechanism to study molecular motion, e.g. rotations and translations, with correlation times of the order of the nuclear Larmour frequencies, tens to hundreds of MHz. We will limit our chscussion here to the simple inversion-recovery Tj relaxation time measurement experiment, which, in addition to providing a convenient means for the quick estimation of Tj to establish the necessary interpulse delay in two-dimensional NMR experiments, also provides a useful entry point into the discussion of multi-dimensional NMR experiments. 

To establish interpulse delays for two-dimensional NMR experiments, it is frequently convenient to run a very quick proton Tj relaxation measurement. Given the sensitivity of modem spectrometers, this can usually be done with only a single or a few transients for each of the r values in the series, and typically requires 10 min or less. By visual inspection, the Tj relaxation time can be estimated from the r value at which response intensity is zero. A knowledge of the Tj relaxation time is also useful for establishing mixing times for NOESY and ROESY experiments. 

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Another application of the knowledge of is to employ it for the interpretation of another relaxation measurement in the same system, an approach referred to as the dual spin probe teclmique. A rather old, but... 

Canet D, Levy G C and Peat I R 1975 Time saving in C spin-lattice relaxation measurements by inversion-recovery J. Magn. Reson. 18 199-204... 

Attard J J, Carpenter T A, Flail L D, Davies S, Taylor M J and Packer K J 1991 Spatially resolved T. relaxation measurements in reservoir cores Magn. Reson. Imaging 9 815-19... 

The H-NMR shift and relaxation measurements have been performed in cooperation with Prof Dr. 

Another resonant frequency instmment is the TA Instmments dynamic mechanical analy2er (DMA). A bar-like specimen is clamped between two pivoted arms and sinusoidally oscillated at its resonant frequency with an ampHtude selected by the operator. An amount of energy equal to that dissipated by the specimen is added on each cycle to maintain a constant ampHtude. The flexural modulus, E is calculated from the resonant frequency, and the makeup energy represents a damping function, which can be related to the loss modulus, E". A newer version of this instmment, the TA Instmments 983 DMA, can also make measurements at fixed frequencies as weU as creep and stress—relaxation measurements. 

Stress-relaxation measurements, where stress decay is measured as a function of time at a constant strain, have also been used extensively to predict the long-term behavior of styrene-based plastics (9,12). These tests have also been adapted to measurements in aggressive environments (13). Stress-relaxation measurements are further used to obtain modulus data over a wide temperature range (14). 

The influence of the thermal history on the location and intensity of the a peak of PTEB can be observed in Fig. 18. It can be seen that the intensity of this relaxation measured on both E" and tanS bases decreases considerably on passing from the liquid crystalline sample... 

Dielectric relaxation measurements of polyethylene grafted with acrylic acid(AA), 2-hydroxyethyl methacrylate (HEMA) and their binary mixture were carried out in a trial to explore the molecular dynamics of the grafted samples [125]. Such measurements provide information about their molecular packing and interaction. It was possible to predict that the binary mixture used yields a random copolymer PE—g—P(AA/HEMA), which is greatly enriched with HEMA. This method of characterization is very interesting and is going to be developed in different polymer/monomer systems. 

This model does not say anything about the mechanism of triple-helix formation, because even in the case of an AON mechanism, nucleation may take place at many positions of the chains and may lead to products the chains of which are staggered. The AON model is based on the assumption that these products are too instable to exist in measurable concentration. As already mentioned, Weidner and Engel142 succeeded in proving by relaxation measurements of al CB2 that the kinetics of in vitro triple-helix formation is governed by more than one relaxation time. This rules out an AON mechanism, but the fitting to the experimentally found equilibrium transition curves nevertheless showed good accommodation and AH° computed from these curves could be confirmed by calorimetric measurement. 

Chemical relaxation techniques were conceived and implemented by M. Eigen, who received the 1967 Nobel Prize in Chemistry for his work. In a relaxation measurement, one perturbs a previously established chemical equilibrium by a sudden change in a physical variable, such as temperature, pressure, or electric field strength. The experiment is carried out so that the time for the change to be applied is much shorter than that for the chemical reaction to shift to its new equilibrium position. That is to say, the alteration in the physical variable changes the equilibrium constant of the reaction. The concentrations then adjust to their values under the new condition of temperature, pressure, or electric field strength. 

Storer model used in this theory enables us to describe classically the spectral collapse of the Q-branch for any strength of collisions. The theory generates the canonical relation between the width of the Raman spectrum and the rate of rotational relaxation measured by NMR or acoustic methods. At medium pressures the impact theory overlaps with the non-model perturbation theory which extends the relation to the region where the binary approximation is invalid. The employment of this relation has become a routine procedure which puts in order numerous experimental data from different methods. At low densities it permits us to estimate, roughly, the strength of collisions. 

The same information may be obtained from purely rotational far infrared spectroscopy (FIR) and depolarized Rayleigh spectra. Dielectric relaxation measurements are also used for the same goal, most successfully in combination with far-infrared data. The absorption coefficient of a periodic electric field... 

One-dimensional nuclear Overhauser effect (NOE), relaxation measurements in native D. gigas Fdll, and analysis of temperature depen-... 

In proton-relaxation experiments, R, values are used extensively, whereas 7, values are more frequently reported for C relaxation measurements. Although there is no special merit in this preference for C 7, values, the pairwise additivity of relaxation contributions in proton-relaxation experiments is more clearly apparent for the relaxation rates. 

Nevertheless, the overall structural problem can be solved from combined n.O.e. and single-selective relaxation-measurements through the evaluation of individual cross-relaxation terms, (Ty. According to Noggle and Shirmer, the n.O.e. value is a function of the cross-relaxation between spins i and j and the relaxation contributions of the neighboring protons to spin i, that is. 

III. Spin-Lattice Relaxation Measurements 1. Experimental Methods... 

The second separation method involves n.O.e. experiments in combination with non-selective relaxation-rate measurements. One example concerns the orientation of the anomeric hydroxyl group of molecule 2 in Me2SO solution. By measuring nonselective spin-lattice relaxation-rat s and n.0.e. values for OH-1, H-1, H-2, H-3, and H-4, and solving the system of Eq. 13, the various py values were calculated. Using these and the correlation time, t, obtained by C relaxation measurements, the various interproton distances were calculated. The distances between the ring protons of 2, as well as the computer-simulated values for the H-l,OH and H-2,OH distances was commensurate with a dihedral angle of 60 30° for the H-l-C-l-OH array, as had also been deduced by the deuterium-substitution method mentioned earlier. 

R,1S isomer. However, this proposal is tentative, because X-ray diffraction has shown that another specimen of asperlin, possessing a different crystalline form, has structure 49b. It should be noted that 1 tumbles somewhat anisotropically, with D /D = 1.3, as deduced from C relaxation measurements. If, however, the anisotropic motion of 1 were not properly corrected for, the largest error in the measurement of its interproton distances would not exceed 4%. 

Transient measnrements (relaxation measurements) are made before transitory processes have ended, hence the current in the system consists of faradaic and non-faradaic components. Such measurements are made to determine the kinetic parameters of fast electrochemical reactions (by measuring the kinetic currents under conditions when the contribution of concentration polarization still is small) and also to determine the properties of electrode surfaces, in particular the EDL capacitance (by measuring the nonfaradaic current). In 1940, A. N. Frumkin, B. V. Ershler, and P. I. Dolin were the first to use a relaxation method for the study of fast kinetics when they used impedance measurements to study the kinetics of the hydrogen discharge on a platinum electrode. 

Methods and Basic Relations for Relaxation Measurements of Spin-State... 

In a solution where a nonzero volume change between the electronic isomers, HS and LS, is encountered, the position of the spin equilibrium will depend on pressure. The volume change, usually denoted here AF°, may be obtained from the study of the pressure dependence of equilibrium properties such as the magnetic susceptibility or the electronic spectrum. In favorable cases, A F° values may be derived from the amplitude of sound absorption observed in ultrasonic relaxation measurements of a spin equilibrium as will be shown in the... 

Results of relaxation measurements on spin-state equilibria in solution are available for complexes of iron(II), iron(III), and cobalt(II). The results comprise values of relaxation time r, rate constants for the forward and reverse reactions feLH activation parameters AH and AS for the two opposed... 

Table 16, Diiferences of molar volume AV° between LS and HS isomers of spin transition complexes on the basis of solution relaxation measurements and pressure studies...

R. Y. Dong, M. Bloom 1970, (Determination of spin-rotation constants in flu-orinated methane molecules by means of nuclear spin relaxation measurements), Can. J. Phys. 48, 793. 

The 50.31 MHz 13C NMR spectra of the chlorinated alkanes were recorded on a Varian XL-200 NMR spectrometer. The temperature for all measurements was 50 ° C. It was necessary to record 10 scans at each sampling point as the reduction proceeded. A delay of 30 s was employed between each scan. In order to verify the quantitative nature of the NMR data, carbon-13 Tj data were recorded for all materials using the standard 1800 - r -90 ° inversion-recovery sequence. Relaxation data were obtained on (n-Bu)3SnH, (n-Bu)3SnCl, DCP, TCH, pentane, and heptane under the same solvent and temperature conditions used in the reduction experiments. In addition, relaxation measurements were carried out on partially reduced (70%) samples of DCP and TCH in order to obtain T data on 2-chloropentane, 2,4-dichloroheptane, 2,6-dichloroheptane, 4-chloroheptane, and 2-chloroheptane. The results of these measurements are presented in Table II. In the NMR analysis of the chloroalkane reductions, we measured the intensity of carbon nuclei with T values such that a delay time of 30 s represents at least 3 Tj. The only exception to this is heptane where the shortest T[ is 12.3 s (delay = 2.5 ). However, the error generated would be less than 10%, and, in addition, heptane concentration can also be obtained by product difference measurements in the TCH reduction. Measurements of the nuclear Overhauser enhancement (NOE) for carbon nuclei in the model compounds indicate uniform and full enhancements for those nuclei used in the quantitative measurements. Table II also contains the chemical... 

Yuan P, Marshall VP, Petzold GL, Poorman RA, Stockman BJ. Dynamics of stromelysin/inhibitor interactions studied by 15N NMR relaxation measurements Comparison of ligand binding to the SrS3 and S -Sy subsites. J Biomol NMR 1999 15 55-64. 

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