Echo decay

As an example figure B 1.14.13 shows the droplet size distribution of oil drops in the cream layer of a decane-in-water emulsion as determined by PFG [45]. Each curve represents the distribution at a different height in the cream with large drops at the top of the cream. The inset shows the PFG echo decay trains as a fiinction of... 

The characteristic time of the tliree-pulse echo decay as a fimction of the waiting time T is much longer than the phase memory time T- (which governs the decay of a two-pulse echo as a function of x), since tlie phase infomiation is stored along the z-axis where it can only decay via spin-lattice relaxation processes or via spin diffusion. 

ESE-detected EPR spectroscopy has been used advantageously for the separation of spectra arising from different paramagnetic species according to their different echo decay times. Furthemiore, field-swept ESE... 

The stimulated (tln-ee-pulse) echo decay may also be modulated, but only by the nuclear frequencies (0,2 and... 

An alternative 2D ESEEM experiment based on the four-pulse sequence depicted in figure B 1.15.12(B) has been proposed by Meliring and coworkers [40]. In the hyperfme sublevel correlation (HYSCORE) experiment, the decay of the echo intensity as a fimction of is governed by -relaxation, whereas the echo decay along the t2-axis is... 

Figure Bl.15.16. Two-pulse ESE signal intensity of the chemically reduced ubiqumone-10 cofactor in photosynthetic bacterial reaction centres at 115 K. MW frequency is 95.1 GHz. One dimension is the magnetic field value Bq, the other dimension is the pulse separation x. The echo decay fiinction is anisotropic with respect to the spectral position.

The vibrational echo experiments yielded exponential decays at all temperatures. The Fourier-transfonn of the echo decay gives the homogeneous lineshape, in this case Lorentzian. The echo decay time constant is AT, where is... 

Resolvable modulation is detected on a three-pulse echo decay spectrum of predeuterated 3-carotene radical (Gao et al. 2005) as a function of delay time, T. The resulting modulation is known as ESEEM. Resolvable modulation will not be detected for nondeuterated P-carotene radical since the proton frequency is six times larger. The modulation signal intensity is proportional to the square root of phase sensitive detection and interfering two-pulse echoes and suppressed by phase-cycling technique (Gao et al. 2005). Analysis of the ESEEM spectrum yields the distance from the radical to the D nucleus, a the deuterium coupling constant, and the number of equivalent interacting nuclei (D). The details related to the analysis of the ESEEM spectrum are presented in Gao et al. 2005. 

Three-pulse ESEEM spectrum of perdeuterated P-carotene imbedded in Cu-MCM-41 exhibits an echo decay with an echo modulation due to deuterons. The three-pulse ESEEM is plotted as a function of time, and curves are drawn through the maximum and minima. From ratio analysis of these curves, a best nonlinear least-squares lit determines the number of interacting deuterons, the distance (3.3 0.2A), and the isotopic coupling (0.06 0.2MHz). This analysis made it possible to explain the observed reversible forward and backward electron transfer between the carotenoid and Cu2+ as the temperature was cycled (77-300 K). 

In an NMR analysis of the effects of /-irradiation induced degradation on a specific polyurethane (PU) elastomer system, Maxwell and co-workers [87] used a combination of both H and 13C NMR techniques, and correlated these with mechanical properties derived from dynamic mechanical analysis (DMA). 1H NMR was used to determine spin-echo decay curves for three samples, which consisted of a control and two samples exposed to different levels of /-irradiation in air. These results were deconvoluted into three T2 components that represented T2 values which could be attributed to an interfacial domain between hard and soft segments of the PU, the PU soft segment, and the sol... 

NMR relaxometry Free induction decay (T2 ) or solid echo Spin echo decay (T2) Magnetization recovery curve (7)) Eads (1998)... 

Morrow et al. measured the spin-lattice relaxation time Ti and quadrupole echo decay times T ) of headgroup deuterated d4-DMPC as a function of temperature and pressure to yield additional information about changes in the headgroup dynamics. Generally, motions in a LC phospholipid bilayer can... 

Fig. 3 Temperature dependence of the transverse relaxation time Ti for D-RADP-20 as obtained from a bi-exponential fit to the Rb spin echo decay. The fact that T2 changes discontinuously at the phase transition clearly indicates the first order character of the transition...

The excellent resolution of the 0-tensor components at W band has been used to measure the relaxation properties of QA in the Zn-substituted bRC of R. sphaeroides.m The experiment showed, in contrast to the respective ubiquinone radical in organic solution, an anisotropic relaxation behavior in the pulse high field ESE experiments. From the analysis of the T2 experiments a motional anisotropy of Q% in the protein pocket was deduced with a preferred libration about the C-O symmetry axis. Recently, similar experiments were also performed on Qb- in ZnbRCs. Compared to QA different echo decay time constants were found. A model was proposed in which the relaxation is related to reorientational fluctuations around the quinones specific H-bonds to the protein.142... 

Quadrupolar interactions can offer direct information on the dynamics of organics within zeolite crystals. Eckman and Vega (304) studied the 2H quadrupolar echo decay in perdeuterated p-xylene adsorbed on zeolite ZSM-5. The deuterium quadrupolar interaction usually dominates the spin Hamiltonian, so that the powder pattern can be used as a test for models of molecular motion. At -75°C and 25°C typical rigid-lattice spectra were obtained. At 100°C however, the resonance arising from the aromatic deuterons was motionally narrowed, while the methyl resonance was not, The authors conclude that p-xylene molecules reorient about an axis which passes through the C3 axes of the methyl groups. 

Fig. 12.6 The 3s —> ns and 3s — nd collisional broadening cross sections derived from tri-level echo decay data are shown plotted vs the principal quantum number of the upper state of the transition. The curved line corresponds to the calculation of Omont (ref. 16). The flat part of the line is also calculated by Alekseev and Sobelman (ref. 3). The errors shown are typical and represent the statistical error in the data (from ref. 7).

The methodology described in this procedure is limited to systems that do not contain free moisture. In cases when both oil and water signals are refocused after the second pulse (e.g., when free water is present), the spin-echo decay curve can be collected over varying x values. Log of the echo amplitudes versus x can be further analyzed to deconvolute the contribution of various components, in this example water and oil would result in a biexponential decay curve. Extrapolating each decay curve to X 0 gives the signals amplitudes due to the oil and the water fractions (A0 and Aw Fig. A1.3.4). 

Leisen, J., Schmidtrohr, K., and Spiess, H. W. (1993). Nonexponential relaxation functions above T(G) analyzed by multidimensional NMR and novel spin-echo decay techniques. Physica A 201,79-87. 

Adjust the t-axis of the experiment until the actual time point zero is at the maximum amplitude of the echo decay function. The now negative time part is usually disregarded. With mathematical procedures it is also possible to correct the phase of the time trace using the real and imaginary part of the data. In DeerAnalysis2008 both steps are done automatically but can also be adjusted. 

In the Cohen-Addad-Sotta model [23, 25] the Hahn-echo decay is expressed without the assumption of dangling chains by the expression ... 

Figure 7.8 The shape of the Hahn-echo decay in cross-linked elastomers is given by the line of diamonds. In the short-time limit the curve can be approximated by a Gaussian (broken line) and in the long time limit it follows an exponential (solid line) [30]...

Figure 7.23 Applications of the NMR-MOUSE to elastomer materials (a) T2 values for a curing series of carbon-black filled NR. Comparison of values obtained at high homogeneous field (DMX 300) and with the NMR-MOUSE, (b) cross-link series of unfilled SBR with different sulfur content, (c) T2 versus glass-transition temperature Tg of unfilled SBR by the CPMG and the steady-state CPMG methods, (d) normalized Hahn-echo decay curves for poly(butadiene) latex samples. Different decay rates are obtained for small medium and large cross-link densities...

Figure 7. Spin-echo decay of signals from...

Figure 2 Vibrational echo decay data for the asymmetrical CO-stretching mode of Rh(CO)2acac in DBP ( 2000 cm-1) at 3.4 K and a fit to a single exponential function. The data were taken using the Stanford Free Electron Laser. The decay constant is 23.8 ps, which yields a homogeneous linewidth of 0.11 cm-1. The absorption spectrum has a linewidth of 15 cm-1 at this temperature, demonstrating that the line is massively inhomogeneously broadened.

---