Relaxation time analysis

All carbon resonances of pure PMMA, PS(OH), and their blends showed single-exponential decays in both Ti and Tjp. The Tj and Tjp values for the main resonance lines are shown in Figs. 13 and 14, respectively. For each of PMMA and PS(OH) containing different amounts of hydroxyl, the protons attached to different carbons have similar relaxation times, which indicates that the spin diffusion equalizes the relaxation rates of all protons. In addition, the Tj and Tip values for PS(OH) show a gradual decrease and increase, respectively, as the hydroxyl content in PS(OH) is increased. The difference in either Tj or Tj between PMMA and PS(OH) is substantial, encouraging the gathering of information about the phase structure of their blends by NMR relaxation time analysis. 

Richard S., Querleux B., Bittoun J., Idy-Peretti L, Jolivet 0., Cermakova E., Leveque J.-L. (1991). In vivo proton relaxation times analysis of the skin layers by magnetic resonance imaging.Ujj sL.Denna, 97,120-125. 

Motions shorten spin-lattice relaxation times. Analysis can provide insight into molecular motions. Dynamics of a radicals can be studied by analysis of contributions due to rotational modulation of hyperfine and Zeeman anisotropies. 

For polyacrylamide there are two rheological effects which can be explained in terms of its random coil structure. Firstly, it was discussed above that polyacrylamide is much more sensitive than xanthan to solution salinity and hardness. This is explained by the fact that the salinity causes the molecular chain to collapse, which results in a much smaller molecule and hence in a lower viscosity solution. The second effect which can be explained in terms of the polyacrylamide random coil structure is the viscoelastic behaviour of this polymer. This is shown both in the dynamic oscillatory measurements and in the flow through the stepped capillaries (Chauveteau, 1981). When simple models of random chains are constructed, such as the Rouse model (Rouse, 1953 Bird et al, 1987), the internal structure of these bead and spring models gives rise to a spectrum of relaxation times, Analysis of this situation shows that these relaxation times define response times for the molecule, as indicated in the simple Maxwell model for a viscoelastic fluid discussed above. Thus, because of the internal structure of a flexible coil molecule, one would expect to observe some viscoelastic behaviour. This phenomenon is discussed in much more detail by Bird et al (1987b), in which a range of possible molecular models are discussed and the significance of these to the constitutive relationship between stress and deformation rate and deformation history is elaborated. 

Joe T and Albrecht A C 1993 Femtosecond time-resolved coherent anti-Stokes Raman spectroscopy of liquid benzene a Kubo relaxation function analysis J. Chem. Phys. 99 3244-51... 

The tliree-line spectrum with a 15.6 G hyperfine reflects the interaction of the TEMPO radical with tire nitrogen nucleus (/ = 1) the benzophenone triplet caimot be observed because of its short relaxation times. The spectrum shows strong net emission with weak E/A multiplet polarization. Quantitative analysis of the spectrum was shown to match a theoretical model which described the size of the polarizations and their dependence on diffrision. 

Bain A D and Duns G J 1994 Simultaneous determination of spin-lattioe (T1) and spin-spin (T2) relaxation times in NMR a robust and faoile method for measuring T2. Optimization and data analysis of the offset-saturation experiment J. Magn. Reson. A 109 56-64... 

For small enough temperature steps (< lOK) during small step annealing the vacancy concentration practically remains constant and corresponds to the instantaneous aimealing temperature. This allows for an easy analysis of SRO-kinetics yielding SRO-relaxation times and SRO-activation enthalpies, which by usual interpretation correspond to H +Hf. 

When applied to the relaxation time of a polymer, dimensional analysis of Eq. (22) shows that the following scaling transformation should be written for tr ... 

Experimental data on nitrogen obtained from spin-lattice relaxation time (Ti) in [71] also show that tj is monotonically reduced with condensation. Furthermore, when a gas turns into a liquid or when a liquid changes to the solid state, no breaks occur (Fig. 1.17). The change in density within the temperature interval under analysis is also shown in Fig. 1.17 for comparison. It cannot be ruled out that condensation of the medium results in increase in rotational relaxation rate primarily due to decrease in free volume. In the rigid sphere model used in [72] for nitrogen, this phenomenon is taken into account by introducing the factor g(ri) into the angular momentum relaxation rate... 

In this case one determines the spectral intensity solely in the centre, not over the whole frequency range. Therefore the analysis often refers not to the spectrum as a whole, but to relaxation times Tg,i or and their dependence on rotational relaxation time tj [85]. This dependence contains much information and can be easier to interpret. It enables one to determine when free rotation turns into rotational diffusion. 

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. 

Some information concerning the intramolecular relaxation of the hyperbranched polymers can be obtained from an analysis of the viscoelastic characteristics within the range between the segmental and the terminal relaxation times. In contrast to the behavior of melts with linear chains, in the case of hyperbranched polymers, the range between the distinguished local and terminal relaxations can be characterized by the values of G and G" changing nearly in parallel and by the viscosity variation having a frequency with a considerably different exponent 0. This can be considered as an indication of the extremely broad spectrum of internal relaxations in these macromolecules. To illustrate this effect, the frequency dependences of the complex viscosities for both linear... 

Differential pulse voltammetry provides greater voltammetric resolution than simple linear sweep voltammetry. However, again, a longer analysis time results from the more sophisticated potential waveform. At scan rates faster than 50 mV/sec the improved resolution is lost. Because it takes longer to scan the same potential window than by linear sweep, an even longer relaxation time between scans is required for differential pulse voltammetry. 

The usefulness of NMR in such analysis is because the proton spin-relaxation time constants are different for different components, such as water, liquid fat and solid fat. For example, the signal from solid fat is found to decay rapidly while the liquid signals decay much slower. This phenomenon is the basis for an NMR technique to determine the solid fat content [20], However, as the relaxation time constant of water, for example, could depend on its local environment, such as protein concentration, it may overlap with that of oil and other components. As a result, it could be difficult to formulate a robust and universal relaxation analysis. It... 

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