Untitled - Technische Universiteit Eindhoven

14 2. Coupled mass transfer and sol-gel reaction in a two-phase bulk system2.2.4 Correlation of relaxation times with viscosity in binary mixturesIn (simple) binary liquid mixtures the effective viscosity often depends on the composition,provided that the viscosities of the pure components, η A and η B , are not equal to eachother. Several mixture laws exist [60]. For example, the following mixture law wasintroduced by Grunberg and Nissan [61]:ln η mix = x ln η A + (1 − x) ln η B + Gx(1 − x), (2.18)where η mix is the effective viscosity of the mixture, x is the mole fraction of componentA, and G is an interaction parameter.The relaxation times will be a function of composition (through the proton fractionsbelonging to the components A and B) as long as T A 1,2 is higher or lower than T B 1,2. If, inaddition, η A is different from η B , the relaxation times can be correlated with the effectiveviscosity via the composition dependence. On a molecular level, one can expect, in caseη A ≠ η B , the diffusivities of the molecules to be a function of the composition. The higherthe viscosity, the lower are the diffusivities. This will affect the inter-molecular relaxation(see Eq. 2.9). As for intra-molecular relaxation, the effective correlation times of thespecies may depend on η mix as indicated by Eq. 2.11, but this is not always the case [62].2.3 Experimental section2.3.1 Chemicals and preparationTetra-methyl-ortho-silicate, Si(OCH 3 ) 4 , was obtained from Aldrich (>99% pure). Forthe oleic phase, n-hexadecane, or n-C 16 H 34 (obtained from Merck, >99% pure) was usedas a clean and well-defined hydrocarbon liquid which has a significant difference in T 1compared to water and TMOS. The viscosities of TMOS, n-hexadecane and mixtures ofTMOS and n-hexadecane were measured at 25 ◦ C with a rheometer (Contraves LS40).For the aqueous phase we used double-demineralized water.Several gel samples were prepared at ambient conditions with demineralized water andTMOS in different volume ratios. The initial volume fraction φ g T(hence, also the molefraction) of TMOS in the mixture was chosen to be a measure to characterize the final gelstate. It was found that for 2.5 vol% (or 0.31 mol%) of TMOS in water no gel was formed,even after several months. For 5.0 vol% and more (tested up to 50 vol%) a homogeneousgel formed. It was observed that after several weeks the high-concentration gels showed asmall degree of syneresis. Calibration solutions of methanol in demineralized water wereprepared as well.2.3.2 NMR apparatus and sequencesRelaxation times and T 1 -weighted images of the samples were recorded with a 4.7 TeslaNMR spectrometer operating at a frequency of 200 MHz for 1 H. The setup consists ofa super-conducting magnet (Oxford Instruments, Oxon, UK) with a vertical, narrowboreinsert (Doty, Columbia, USA) with an inner diameter of 40 mm. The insert has