Spin echo measurement

It may be noted that refocusing occurs only in the heteronuclear system, i.e., when a selective 180° pulse is applied. Field inhomogeneities or differences of chemical shift cause an additional fanning out of the magnetic vectors which can be eliminated by the application of the 180° pulse to the X nucleus. This is important for practical purposes since the Larmor frequency of the X nucleus is not normally identical to the carrier frequency Vq, as assumed in the above discussion. 

In heteronuclear systems the pulse sequence is modified so that 180° pulses are simultaneously applied to both types of nuclei (A and X). By using selective detection, i.e., A- X (observe A, decouple X), one obtains spectra in which the phases of the signals are dependent on time t and the magnitude of the coupling constants. 

This allows the FID of the echo sequence for A spins to be recorded with the X spins decoupled. It results in the refocusing of chemical shifts but does not refocus the coupling constants. To refocus the coupling constants without affecting the chemical shifts for a CH system, one uses the sequence 

The application of the 180° pulse to would then result in changing of the spin labels of Mh and Mh and a refocusing of the doublet after a time t. 

2 Attached Proton Test by Gated Spin-Echo (GASPE) 

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The mathematical description of the echo intensity as a fiinction of T2 and for a repeated spin-echo measurement has been calculated on the basis that the signal before one measurement cycle is exactly that at the end of the previous cycle. Under steady state conditions of repeated cycles, this must therefore equal the signal at the end of the measurement cycle itself For a spin-echo pulse sequence such as that depicted in Figure B 1.14.1 the echo magnetization is given by [17]... 

Figure 20. Pulse sequence for spin echo measurements of selfdiffusion coefficients. (Reprinted from Ref. 106 with permission from Z. Naturforschmg.)...

We are now going to compare the results of mode analysis with measurements of viscosity on polyethylene melts. With the aid of Eq. (30), which links the viscosity to the relaxation times, we can predict the viscosity using the results of spin-echo measurements and compare it with the viscosity measurement... 

Detailed analyses of a combination of n3Cd and 31P MAS-NMR and spin-echo measurements and 113Cd-31P SEDOR experiments led to the conclusions that,... 

Fig. 3.11 Dynamic structure factor for a PB melt at 353 K (M =l,600) obtained from simulation (lines) and neutron spin echo measurements (symbols). The Q-values are given adjacent to the respective lines. (Reprinted with permission from [55]. Copyright 2000 Elsevier)...

Mays and Brady 17) have published preliminary measurements of water adsorbed on rutile (Ti02) at 77°K, 195°K and 300°K for several different coverages. Zimmerman and co-workers 18) have made extensive magnetic resonance (spin-echo) measurements of protons of water vapor adsorbed on silica gel. Transverse and longitudinal relaxation times have been measured at room temperature at many different surface coverages and a two-phase behavior of the adsorbed water has been observed. 

Diffusion and Pulsed Gradient Spin Echo Measurements... 

Because field-gradient spin-echo measurements of D depend on no driving force such as a concentration, temperature, or velocity gradient, etc., they reflect Brownian motion of the molecules in the laboratory reference frame, and are usually referred to as self-diffusion. These attributes are further discussed in Sections 2 and 3. 

The reproducibility of spin-echo measurements is a sensitive function of the temperature stability of the sample during measurement. Changes in temperature affect both the unattenuated echo height (mainly via T2) and the degree of attenuation (via D). 

Statements b and c follow from the spin echo measurements. 

Hahn, E. L., and D. E. Maxwell Spin echo measurements of nuclear spin... 

Supported non-framework elements, as well as substituted or doped framework atoms, have been important for zeolite catalyst regeneration. By incorporating metal atoms into a microporous crystalline framework, a local transition state selectivity can be built into the active site of a catalytic process that is not readily attainable in homogeneous catalysis. The use of zeolites for carrying out catalysis with supported transition metal atoms as active sites is just beginning. The local environment of transition metal elements as a function of reaction parameters is being defined by in situ Mossbauer spectroscopy, electron spin echo measurements, EXAFS, and other novel spectroscopic techniques. This research is described in the second part of this text. 

The negative sign indicates relative shielding. Obtained from spin-echo measurements. 

Fig. 2. Fit of the displacement for diffusion with memory to NMR spin-echo measurements in polymers. The data corresponds to the spin-echo signal from polysulfane-poly-butadiene copolymer in different solvents comprising a mixture of trichloroethane (TCE) and octane. The fits were obtained using Eq. (83).

The self diffusion coefficient of water enclosed in the pores of the three-dimensional MCM-48, determined by using NMR spin-echo measurements, was found to be signifrcantly larger than that of MCM-41. The high degree of ordering and the three dimensional, interconnected pore system, leads to a high self diffusion coefficient of molecules enclosed in the pores of MCM-48 (82). 

Spin echo measurements on metal complexes have been reviewed extensively by Mims and Peisach [267]. One use of this technique has been to study anion binding at paramagnetic metal centers. When cupric ion is substituted for ferric ion in transferrin, a pattern corresponding to the weak coupling for in C-doped bicarbonate indicates that bicarbonate is bound directly to the metal ion [269]. Thus, a modulation pattern detected by spin echo can confirm that adducts with a weakly coupled nuclear spin are bound directly to the metal site. 

In this subsection, the theoretical background for SANS and neutron spin-echo measurements carried out with o/w- and w/o-droplet microemulsions will be presented. According to Milner, Safran and others, shape fluctuations in droplet microemulsions can be described in terms of spherical harmonics [42-44]. This offers the possibility to calculate a dynamic structure factor S(q,w) or its Fourier transform, i.e. the intermediate scattering function I(q,t) for the problem, which can be used to analyse dynamical measurements by neutron spin-echo spectroscopy [45]. For the scattering from thin shells I(q,t) was calculated [43]... 

Thus, by measuring oil and water self-diffusion coefficients, it was quite easy to establish whether oil or water or none of them are confined to discrete domains, i.e. to droplets . In the first work on microemulsion structure by self-diffusion [46], using both tracer techniques and NMR spin-echo measurements, it was clearly shown that microemulsions can indeed be bicontinuous over wide ranges of composition, which is manifested by both... 

Allerhand and Gutowsky (1964) also report Ea = 14-0 + 0-9 kcal mole-1 and log A = 10-9 + 0-6 for the barrier in AA-dimethylcarbamyl chloride from spin-echo measurements. 

Modification to the probe-head design for high-pressure spin-echo measurements... 

The major advantages of the diaphragm-cell method are its low cost and its slightly superior accuracy (under ideal conditions). It is also possible to use the technique to look at diffusion in complex mixtures which are problematical by NMR. In order to obtain a valid spin-echo measurement for a particular species in a mixture, it is necessary to resolve a signal in the spectrum, with no underlying peaks. However, this may be overcome by isotopic substitution (that is, by deuteration) of a sample. Where this is not a problem, NMR is again the preferred technique, because the diffusion coefficient of all species in a mixture can potentially be obtained in one experiment. ... 

In Fig. 4, we plot the volume dependences of the diffusivities of various model systems, all calculated for argonlike particles, and for the laboratory system methyl cyclohexane, which seems to be representative. Data for the latter are available for two temperatures from the accurate nuclear magnetic resonance (NMR) spin-echo measurements of Jonas et al. To group the data for different systems for better comparison of their behavior, we have obtained a reducing parameter for each liquid by taking advantage of the observations of Batchinski and Hildebrand that fluidities , and diffusivities D of highly fluid molecular liquids vary linearly with volume. 

R. L. Void and R. R. Void, "Spin-echo measurements of long-range coupling constants in some simple esters," J. Magn. Resonance 13, 38-44 (1974). 

Note that in some cases direct measurement using PFG NMR of this quantity by increasing A to large values may be hindered by loss of signal intensity due to nuclear relaxation during the spin-echo measurement. The effective diffusivity is related to the bulk diffusion coefficient through the relation... 

No direct information on the phase memory or quantum coherence time 7m has yet been obtained from magnetization detected EPR investigations. In one study, a spin echo measurement was attempted on frozen solutions of [Ni(hmp)(dmb)Cl]4 in toluene dichloromethane (1 1) at 5.5 K, but no echoes were observed. An upper limit of Tm = 50 ns was deduced from this observation [132]. For homogeneously... 

Use of a surfactant allows solubilization of the polyoxometalate cluster K6[Vi5As6042(H20)] 8H20 (V15) in the organic solvent chloroform. Spin echo measurements revealed a phase memory time of Tm = 340 ns, which was attributed to resonances in the 5 = 3/2 excited state of the cluster [166]. No quantum coherence was detected in the pair of 5 = 1/2 ground states [151]. By measurement of the z-magnetization after a nutation pulse, and a delay to ensure decay of all coherences, Rabi oscillations were observed. From the analysis of the different possible decoherence mechanisms, it was concluded that decoherence is almost entirely caused by hyperfine coupling to the nuclear spins. 

The FID decays rapidly in solid samples, for which spin echo measurements are better suited. 

Self-Diffusion. The self-diffusion coefficient D of liquid PH3 and PD3 in sealed tubes was determined by spin echo measurements of the nuclei H, h, and ip from 139 K to ambient temperature. Numerical values for both phosphanes are given by D(cm2/s) = 5.18x10" exp(-413/T) at temperatures up to 200 K. Above this temperature, D rises faster with temperature to reach 1.5x10 cm /s at 293 K. Attempts to correlate D and the viscosity t failed except at the lowest temperatures [11]. The self-diffusion constant of plastic crystalline PH3 was estimated for a vacancy diffusion mechanism on the basis of the spin-lattice relaxation time. The increase from D = 2x10" to 1x10" cm /s between 103 and 138 K is typical for a plastic crystal. A diffusion activation energy of 19 kJ/mol was estimated [12]. 

SPIN-ECHO MEASUREMENT OF THE SELF-DIFFUSION COEFFICIENT IN METHANE. 

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