Effect of relaxation processes

Fig. 12. Effects of relaxation processes, a) Frequency dispersion in CH. Due to the small vibrational heat capacity in CHt, a relatively small frequency shift is obtained, b) Broadening of the resonance curve in the pressure region where relaxation occurs...

MRI is non-invasive and gives the spatial distribution of a particular species, making it ideal for investigating the water uptake of degradable materials. The effect of relaxation processes on the acquired signal must be considered if quantitative data is to be obtained. 

The relaxation processes. The second perturbation term in equation (15.16) represents the effect of relaxation processes. At present we are concerned only with the excited-state density matrix and assume that the relaxation is due only to spontaneous emission. Since this is again an essentially random process, being triggered by the zero-point fluctuations of the vacuum radiation fields, the effect of can be represented as a rate process and we have... 

In this chapter we shall be concerned mainly with the principles of the technique, the effect of relaxation processes, and magnetic resonance transitions between Zeeman sub-levels. We shall therefore initially describe the experiments in terms of the populations of the ground state sub-levels. The discussion of the effects of phase coherence (Hertzian coherence) and experiments involving transverse pumping is reserved until section 17.8. Moreover the application of optical pumping methods to the investigation of hyperfine intervals and the measurement of nuclear moments is postponed until Chapter 18, as are the applications of this technique in devices such as magnetometers, atomic clocks, and masers. 

Figure 1. Effect of activation energy on width of relaxation process (AH > AH 2). 

Figure 2. Effect of a parameter (equation (2)) on width of relaxation process (a > c ).

It is mostly used to describe the effect of temperature on the dynamics of relaxation processes in glassy polymers. Rearranging Eq. (8), we obtain the relation between the activation energy AU (in kJ) and the temperature of relaxation, Tr(f), detected at frequency f ... 

Side processes often proceed more slowly than kinetic reactions, from which a first explanation follows slow relaxations are induced by the effect of side processes [1, 2],... 

The presence of relaxation processes affects the shape of the absorption lines. This is because the lifetimes of the spin levels are shortened if relaxation occurs and so their energy is made imprecise this is the so-called lifetime broadening effect. There are two processes responsible for this effect spin-lattice relaxation and spin-spin relaxation. 

Some practical cases are determination of residual stress in steel springs, the effect of mechanical loading on stress relaxation of machined and shot-peened nickel-base alloys,65 determination of residual stress level in turbine engine disks as they accumulate engine cycles,65 66 effect of manufacturing processes on residual stress, measurement of stress gradients in mechanical, electronic and structural components, effect of heat treatment on residual stress in steel coil springs, effect of variable heat treatment temperature on residual stress in iron alloys, measurement of stress in multiphase materials and composites and stress measurements at locations of stress concentrations. 

Magnetic-FFF has been studied in only a few works [45,273,274] dealing with the separation and retention of BSA in the presence of Ni(II) ions and retention of metal oxides. The comparison of experimental retentions with the theoretical model indicated [45] that in addition to the effect of the magnetic field on the macromolecules, other yet unknown parameters seem to be present. Furthermore, the investigation of metal oxide particles in magnetic-FFF indicated that the slow velocity of relaxation processes probably influences the quality of the separation [273]. Even the surface nature of particles plays a role in retention [274]. In summary, magnetic-FFF remains an immature technique. 

G. P. Johari, Dynamics of irreversibly forming macromolecules, in Disorder Effects in Relaxational Processes, R. Richert and A. Blumen, eds., Springer-Verlag, Berlin, 1994, p. 627. 

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