Measuring Spin Relaxation

CPMG sequence In 1954, it was shown by Carr and Purcell (Cpmg) that performing a simple modification of Hahn s spin-echo method can reduce the influence of diffusion on T2. In the CPMG sequence the general sequences of pulses can be described as [90°, r, 180°, 2t, 180°, 2t,.. .], so for example, if a r pulse is applied at 3t, then a spin-echo will develop at 4t (obviously with a reduced intensity due to spin-spin relaxation). This method is much faster and more efficient than the one described earlier, which allows for repeated refocusing of the spin echo. 

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T2 measurements usually employ either Carr-Purcell-Meiboom-Gill (CPMG) [7, 8] spin-echo pulse sequences or experiments that measure spin relaxation (Tlp) in the rotating frame. The time delay between successive 180° pulses in the CPMG pulse sequence is typically set to 1 ms or shorter to minimize the effects of evolution under the heteronuc-lear scalar coupling between 1H and 15N spins [3]. 

The measured spin relaxation parameters (longitudinal and transverse relaxation rates, Ri and P2> and heteronuclear steady-state NOE) are directly related to power spectral densities (SD). These spectral densities, J(w), are related via Fourier transformation with the corresponding correlation functions of reorientional motion. In the case of the backbone amide 15N nucleus, where the major sources of relaxation are dipolar interaction with directly bonded H and 15N CSA, the standard equations read [21] ... 

Massi et al measured spin relaxation in the rotating frame Rip to characterize chemical exchange kinetic processes occurring on ps-ms time scales. The new two-dimensional experiment allow the use of weak r.f. fields between 150 and 1000 Hz. The new experiments also extend the capability of the Rip technique to study exchange processes outside the fast exchange limit. 

Experimentally determined charge relaxation rates at room temperature compared to the theoretical values (Muller-Hartmann 1981), which have been scaled by the measured spin relaxation rates References for the values of and the valence have been summarized by Zirngiebl (1986) and by Zimgiebl and Guntherodt (1990). ( A means corresponds to .)... 

The spin-spin relaxation time, T, defined in the Bloch equations, is simply related to the width Av 2 Lorentzian line at the half-height T. Thus, it is in principle possible to detennine by measuring... 

Meiboom S and Gill D 1958 Modified spin-echo method for measuring nuclear relaxation times Rev. Sci. Instrum. 29 688-91... 

For example, if the molecular structure of one or both members of the RP is unknown, the hyperfine coupling constants and -factors can be measured from the spectrum and used to characterize them, in a fashion similar to steady-state EPR. Sometimes there is a marked difference in spin relaxation times between two radicals, and this can be measured by collecting the time dependence of the CIDEP signal and fitting it to a kinetic model using modified Bloch equations [64]. 

Figure B2.4.6. Results of an offset-saturation expermient for measuring the spin-spin relaxation time, T. In this experiment, the signal is irradiated at some offset from resonance until a steady state is achieved. The partially saturated z magnetization is then measured with a kH pulse. This figure shows a plot of the z magnetization as a fiinction of the offset of the saturating field from resonance. Circles represent measured data the line is a non-linear least-squares fit. The signal is nonnal when the saturation is far away, and dips to a minimum on resonance. The width of this dip gives T, independent of magnetic field inliomogeneity.

ESR can detect unpaired electrons. Therefore, the measurement has been often used for the studies of radicals. It is also useful to study metallic or semiconducting materials since unpaired electrons play an important role in electric conduction. The information from ESR measurements is the spin susceptibility, the spin relaxation time and other electronic states of a sample. It has been well known that the spin susceptibility of the conduction electrons in metallic or semimetallic samples does not depend on temperature (so called Pauli susceptibility), while that of the localised electrons is dependent on temperature as described by Curie law. 

Now we proceed to comparison between measured tj and The main basic formula extracting the relaxation time t0i2 from spin relaxation times is well known [83, 39]... 

This conclusion is supported by the experimental result " given by the pulsed-NMR measurement that the spin-spin relaxation time T2 is considerably shorter for the gel than that for the matrix mbber vulcanizate, which of course, indicates that the modulus is considerably higher for the gel than for the matrix mbber. More quantitatively, Maebayashi et al. measured the acoustic velocity of carbon gel by acoustic analysis and concluded that the compression modulus of the gel is about twice that of matrix mbber. Thus, at present, we can conclude that the SH layer, of course without cross-linking, is about two times harder than matrix cross-linked mbber in the filled system. 

NMR Spectroscopy. All proton-decoupled carbon-13 spectra were obtained on a General Electric GN-500 spectrometer. The vinylldene chloride isobutylene sample was run at 24 degrees centigrade. A 45 degree (3.4us) pulse was used with a Inter-pulse delay of 1.5s (prepulse delay + acquisition time). Over 2400 scans were acquired with 16k complex data points and a sweep width of +/- 5000Hz. Measured spin-lattice relaxation times (Tl) were approximately 4s for the non-protonated carbons, 3s for the methyl groups, and 0.3s for the methylene carbons. 

This simple theoryis based on the expectation that, to a reasonable degree of approximation, proton-proton, dipolar contributions to the measured spin-lattice relaxation-rate are pairwise additive and decrease as a simple sixth power of the interproton distance. The simplified version of the dipole-dipole mechanism is summarized in the following two equations for spin i coupled intramolecularly with a group of spins j... 

The main objectives of this article are (i) to give an account of the simple theory related to spin-lattice relaxation-rates, in a language that is directed, as far as possible, to the practising chemist rather than to the theoretician (ii) to caution against uncritical use of this simple theory for systems that are strongly coupled, or undergoing anisotropic reorientation, or both (hi) to introduce the pulse n.m.r. experiments that are used to measure spin-lattice relaxation-rates, and to stress the precautions necessary for accurate... 

By measuring the proton relaxation times, and T,p, it is possible to estimate the mobility of polymer chains within the cell wall (11). Proton spin relaxation editing (PSRE) is a method of expressing these results. It separates the components seen in a conventional CP-MAS C spectra into low-mobility and intermediate-mobility components. If PSRE is applied to a experiment (12) the mobility of the... 

The most significant results obtained for complexes of iron(II) are collected in Table 3. The data derive from laser Raman temperature-jump measurements, ultrasonic relaxation, and the application of the photoperturbation technique. Where the results of two or three methods are available, a gratifying agreement is found. The rate constants span the narrow range between 4 x 10 and 2 X 10 s which shows that the spin-state interconversion process for iron(II) complexes is less rapid than for complexes of iron(III) and cobalt(II). 

Exponential decay often occurs in measurements of diffusion and spin-relaxation and both properties are sensitive probes of the electronic and molecular structure and of the dynamics. Such experiments and analysis of the decay as a spectrum of 7i or D, etc., are an analog of the one-dimensional Fourier spectroscopy in that the signal is measured as a function of one variable. The recent development of an efficient algorithm for two-dimensional Laplace inversion enables the two-dimensional spectroscopy using decaying functions to be made. These experiments are analogous to two-dimensional Fourier spectroscopy. 

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. 

Since it was proposed in the early 1980s [6, 7], spin-relaxation has been extensively used to determine the surface-to-volume ratio of porous materials [8-10]. Pore structure has been probed by the effect on the diffusion coefficient [11, 12] and the diffusion propagator [13,14], Self-diffusion coefficient measurements as a function of diffusion time provide surface-to-volume ratio information for the early times, and tortuosity for the long times. Recent techniques of two-dimensional NMR of relaxation and diffusion [15-21] have proven particularly interesting for several applications. The development of portable NMR sensors (e.g., NMR logging devices [22] and NMR-MOUSE [23]) and novel concepts for ex situ NMR [24, 25] demonstrate the potential to extend the NMR technology to a broad application of field material testing. 

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