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2.4. Results and discussion 23Table 2.2: Results of the NMR calibration measurements for the gels (at T = 22 ± 2 ◦ C) andliquids (at T = 25 ± 1 ◦ C). T 2 was measured with an inter-echo time of 7.2 msand with a pulsed read-out gradient G = 100 mT/m. φ g Tis the volume fractionof TMOS mixed with water. R is the water/methanol molar ratio, and R eq is theequivalent molar ratio in case of full hydrolysis and condensation.substance T 1 [s] T 2 [s] ExponentR First Second Thirdwater 3.26 1.66TMOS 3.57 1.33methanol 4.09 0.42 1.16water-methanol 8.97 2.54 0.195 - 1.383.36 2.29 0.141 - 1.592.24 2.32 0.070 0.70 1.541.49 2.47 0.060 0.73 1.400.56 2.95 0.055 0.46 1.28gel (φ g T ) R eq0.05 38.6 2.71 0.120 0.25 0.500.10 18.0 2.34 0.065 0.18 0.530.15 11.2 2.15 0.045 0.24 0.580.20 7.7 2.03 0.038 0.31 0.620.25 5.7 1.90 0.029 0.30 0.660.35 3.3 1.70 0.027 0.22 0.660.40 2.6 1.69 0.026 0.29 0.640.50 1.6 1.70 0.029 0.32 0.66a discrete tri-exponential fit was performed on the spin-echo trains to quantify the exponents.A dominant component was found in the order of tens of milliseconds for each gelthat appeared to be almost independent on the read-out gradient used, so that in thiscase the observed T 2 is not influenced by molecular diffusion. Between φ g T = 0.25 and φg T= 0.50 T 2 is almost constant (about 30 ms). The multi-exponential relaxation behavior ofthe aqueous samples is not trivial. It clearly indicates that the different hydrogen speciesexhibit different relaxation rates. The mechanisms that cause the multi-exponential relaxationare discussed below.The hydrolysis reaction of TMOS leads to the formation of methanol. In the case offull hydrolysis and complete condensation, the molar water/methanol ratio can be inferredfrom the initial water/TMOS ratio. This is denoted as the equivalent ratio R eq and isgiven in Table 2.2 for the calibration gel samples. It is noted, however, that condensationfor these samples is not complete, since this would lead to a dense glass and separation ofthe liquids from the gel, which is not the case for the calibration gels. Water/methanolmixtures are known to exhibit anomalous thermodynamic properties, such as mixingentropy, viscosity etc. [68]. At the molecular scale the mixing of methanol with wateris incomplete leading to complex solution structures. This is due to the chain-like and
24 2. Coupled mass transfer and sol-gel reaction in a two-phase bulk system # 0 0 + 0! 0 + 0! 01 J A I E J O = K # 6 I Fig. 2.8: T 2 spectra measured at 25 ◦ C of water, methanol and a mixture of 50 vol% methanolin water.ring-like alignment of the methanol molecules surrounding the water molecules [69]. Thestructure is caused by hydrogen bonds on the one hand and repulsion among the methylgroups and water on the other.Additionally, a rapid exchange among the hydrogen nuclei from methanol hydroxylgroups and water molecules occurs. This explains the rather different relaxation spectraof the mixtures compared to either pure water or methanol. T 1 for a solution (1:1 volumeratio or 1:2.24 mole ratio) of methanol in water was measured to be 2.32 s at 25 ◦ C, whereasfor water T 1 = 3.26 s, and for methanol T 1 = 4.09 s. The T 2 spectra for water, methanoland the mixture (obtained with a CONTIN inversion of the CPMG data) are shown inFigure 2.8. Water shows a peak near T 2 = 1.66 s. Methanol has a bimodal distribution,which is attributed to the different relaxation mode of the methyl group protons and thehydroxyl protons, respectively. The area of the peaks indicates the relative proton densityof the species (in analogy with spectroscopic frequency or chemical shift measurements[70]). Interestingly, in the mixture a dominant peak arises near 70 ms, while the peaksat higher times resemble the methanol peaks. Based on the relative intensities of thepeaks and the known composition, it follows that (most of) the water hydrogen nucleihave a shifted relaxation mode towards a much lower time of about 70 ms. The hydrogenexchange among the hydroxyl species has an influence on the relative intensities andtimes as well. The separate relaxation behavior of the hydrogen species was confirmedby chemical shift-T 2 measurements (not presented here). T 1 and T 2 for water/methanolmixtures of various ratios are listed in Table 2.2.It is concluded that the strong contrast in T 2 of the gels with respect to pure water orTMOS is caused by the complex structure of methanol/water solutions, since the liquidsconstitute the main part of the wet gels. Additional shortening of T 2 and T 1 is due tothe geometrical confinement of the liquids in the gels and interaction of the liquids with
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148 Appendix B
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150 Appendix CwhereΩ A (θ) = −2
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158 Appendix EAs the saturations, d
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160 Bibliography[12] B. Vinot, R. S
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162 Bibliography[40] M. D. Mantle a
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164 Bibliography[70] F. J. M. van d
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166 Bibliography[97] K. Yoshida, A.
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168 Bibliography[127] G. W. Scherer
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170 Bibliography
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172 Summaryand gelation rates. The
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174 Samenvattingwaterfase. De T 1 v
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176 List of publications
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178 Dankwoordimmer opgewekte stemmi
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Prior to the speech, Harald Cramér
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