Untitled - Technische Universiteit Eindhoven

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