Transverse magnetisation

Relaxation refers to all processes which regenerate the Boltzmann distribution of nuclear spins on their precession states and the resulting equilibrium magnetisation along the static magnetic field. Relaxation also destroys the transverse magnetisation arising from phase coherenee of nuelear spins built up upon NMR excitation. 

Spin-spin relaxation is the steady decay of transverse magnetisation (phase coherence of nuclear spins) produced by the NMR excitation where there is perfect homogeneity of the magnetic field. It is evident in the shape of the FID (/fee induction decay), as the exponential decay to zero of the transverse magnetisation produced in the pulsed NMR experiment. The Fourier transformation of the FID signal (time domain) gives the FT NMR spectrum (frequency domain, Fig. 1.7). 

FID Free induction decay, decay of the induction (transverse magnetisation) back to equilibrium (transverse magnetisation zero) due to spin-spin relaxation, following excitation of a nuclear spin by a radio frequency pulse, in a way which is free from the influence of the radiofrequency field this signal (time-domain) is Fourier-transformed to the FT NMR spectrum (frequency domain)... 

Figure 7.1 Most modern NMR techniques are based on the fact, that the phase (p of the precessing transverse magnetisation M t) kann be measured. By use of the Fourier transformation the phase provides access to NMR spectra, images, and parameters of translational motion like velocity v and acceleration a. Spectroscopic parameters as well as components of translational velocity and acceleration can be used for generating contrast in NMR imaging. In the drawing the magnetisation M(t) has been generated from Mz by use of a 90° pulse of the B1 radio-frequency (rf) field in y direction...

Mx is the quantum operator associated with the transverse magnetisation. With regard to the proton magnetic relaxation, the probe determined by the end-to-end vector r, is substituted for any chemical unit attached to the chain segment. The observation is thus delocalised over the space scale defined by the distance r = 5 nm. From the spectroscopy point of view, HD represents a dispersion of non-coherent broadening frequencies and... 

Network Structure Analysis by Means of NMR Transverse Magnetisation Relaxation... 

Experimental studies of filled rubbers are complicated by several things, such as the effect of the magnetic susceptibility of the filler, the effect of free radicals present at the surface of carbon black, the complex shape of the decay of the transverse magnetisation relaxation of elastomeric materials due to the complex origin of the relaxation function itself [20, 36, 63-66], and the structural heterogeneity of rubbery materials. 

H NMR transverse magnetisation relaxation experiments have been used to characterise the interactions between NR, isoprene rubber, BR, EPDM and polyethylacrylate rubbers with hydrophilic silica and silicas modified with coupling agents [124-129]. These studies showed that the physical interactions and the structures of the physical networks in rubbers filled with carbon black and rubbers filled with silicas are very similar. In both cases the principal mechanism behind the formation of the bound rubber is physical adsorption of rubber molecules onto the filler surface. 

Figure 10.15 The decay of the transverse magnetisation (points) for ethylene-octene copolymer at different temperatures [136]. The decay was measured using the solid-echo pulse sequence. The solid lines represent the result of a least-squares adjustment of the decay using a linear combination of Weibull and exponential functions. The dotted lines represent the relaxation component with a long decay time. In the experiments the sample was heated from room temperature to 343 K (70 °C)...

Simon and co-workers [71-75] later developed a variation of this model of T2 relaxation in which the faster decay process arises from an inter-crosslink component of the network, in which motion is rapid and anisotropic and does not eliminate completely the dipolar interactions. The rapid motion, described by a correlation time Tf, occurs simultaneously with a slower isotropic motion of the complete inter-crosslink segment described by the correlation time xs. The longer relaxation decay arises from dangling chain ends and is exponential in nature. The total decay of transverse magnetisation if then given by ... 

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