Silicate density relaxation

From a fit of Equation (10) to spatially resolved relaxation curves, images of the parameters A, B, T2, q M2 have been obtained [3- - 32]. Here A/(A + B) can be interpreted as the concentration of cross-links and B/(A + B) as the concentration of dangling chains. In addition to A/(A + B) also q M2 is related to the cross-link density in this model. In practice also T2 has been found to depend on cross-link density and subsequently strain, an effect which has been exploited in calibration of the image in Figure 7.6. Interestingly, carbon-black as an active filler has little effect on the relaxation times, but silicate filler has. Consequently the chemical cross-link density of carbon-black filled elastomers can be determined by NMR. The apparent insensitivity of NMR to the interaction of the network chains with carbon black filler particles is explained with paramagnetic impurities of carbon black, which lead to rapid relaxation of the NMR signal in the vicinity of the filler particles. 

For explaining the apparent contradictory results concerning the restricted dynamics in intercalated and exfoliated PLSNs, Lu and Nutt [2003] proposed a model with three different relaxation domains and three different relaxation rates. The relaxation properties differ depending on the extent to which the iayered silicates are exfoliated, the strength of interactions between silicate layers and polymer matrices, the grafting density, and the ceramic content. The authors concluded that a system with fully exfoliated silicate dispersion and strong interactions is expected to exhibit slow relaxation behavior (high Tg), whereas a system with intercalated silicates and weak interaction should display fast relaxation dynamics (low Tg). 

We measured the temperature-dependance of the spin-lattice relaxation time, for various alumino-silicate aerogels, corresponding porous glasses and crystalline counterparts. The purpose of these experiments is threefold (i) to compare the relaxation response of these very porous amorphous materials to the general one of more classical glasses, (ii) to see whether fractons, whose vibrationnal amplitudes are large, contribute to relaxation mechanisms, (iii) to follow - through variations of the density - the dependance of this dynamical property on the structural parameters, (iv) to test the theoretical predictions about relaxation in disordered systems proposed by R. Orbach and S. Alexander. 

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