Water self-diffusion coefficient

FIG. 26 Observed water self-diffusion coefficients as a function of the protein concentration (g protein/g water) for micellar casein dispersions ( ), for acid gels (O), and for rennet gels ( ) [reproduced with permission from Mariette et al (2002)]. 

FIG. 28 Water self-diffusion coefficient plotted as a function of weight fraction of solids for samples of sucrose, instant 1 dent starch, and a 1 1 sucrose/starch mixture at 20 °C. The corresponding weight fractions at the DSC Tg equal to 20 °C are given for reference [reproduced with permission from Kou et al. (1999)]. 

Metais, A. and Mariette, F. 2003. Determination of water self-diffusion coefficient in complex food products by low field h-1 PFG-NMR Comparison between the standard spin-echo sequence and the T-l-weighted spin-echo sequence. J. Magn. Reson. 165, 265-275. 

Proton mobility (D J and water self-diffusion coefficient (D q) as a function of the water volume fraction (X ) in Nafion and SPEEKK, where X, = volume of water in membrane divided by volume of wet membrane. (From Kreuer, K. D. 2001. Journal of Membrane Science 185 29-39.)... 

Water self-diffusion coefficients (Dh o) have been determined by pulse field gradient NMR for Nation (Nil/) , BPSH, and SPEEKK and have been shown to increase with increasing acid and water content. At high water contents, the values for PEMs approach the corresponding value for pure water. This is due to the increase in volume fraction of free water. At low water content, however. Nation exhibits greater Dnp values than either BPSH or SPEEKK. In corranon with the observations for EOD, this has been attributed to the smaller channels in aromatic-based polymers, leading to a considerably lower dielectric constant for the water in the channels. 

The reduction of the long-range diffusivity, Di by a factor of four with respect to bulk water can be attributed to the random morphology of the nanoporous network (i.e., effects of connectivity and tortuosity of nanopores). For comparison, the water self-diffusion coefficient in Nafion measured by PFG-NMR is = 0.58 x 10 cm s at T = 15. Notice that PFG-NMR probes mobilities over length scales > 0.1 /rm. Comparison of QENS and PFG-NMR studies thus reveals that the local mobility of water in Nafion is almost bulk-like within the confined domains at the nanometer scale and that the effective water diffusivity decreases due to the channeling of water molecules through the network of randomly interconnected and tortuous water-filled domains. ... 

Figure 2. Conductivity diffusion coefficient (mobility) of protons and water self-diffusion coefficient of aqueous solutions of hydrochloric acid (HCl), as a function of acid concentration (molarity, M) (data are taken from ref 141).

Figure 9. Proton conductivity diffusion coefficient (mobility) and water self-diffusion coefficient of Nation 117 (EW = 1100 g/equiv), as a function of temperature and the degree of hydration n = [H20]/[—SOsH]). ...

Another descriptor of the mobility of water molecules in contact with the clay layers is the water self-diffusion coefficient. A fine recent review summarizes the theoretical and practical aspects of measurement by spin-echo nmr methods of this parameter (36) The plot of the decrease in the water self-diffusion coefficient as a function of C, the amount of suspended clay, for the same samples, is again a straight line going through the origin. By resorting once more to a similar analysis in terms of a two-state model (bound and "free water), one comes up (25) with a self-diffusion coefficient, for those water molecules pinched in-between counterions and the clay surface, of 1.6 10 15 m2.s 1,... 

Water in skeletal carbonates bound Hp and OH , 106-107,109 liquid Hp in fluid inclusions, 106 Water molecules at day interface, modes of reorientation, 403-404 Water self-diffusion coefficient, measurement, 404-405 Weathering, definition, 4 Wintergreen, triboluminescent spectra, 255259... 

Sposito and co-workers employed a rigid framework for the clay lattice that has been used successfully to predict rf(001) layer spacing, interlayer structure, and water self-diffusion coefficients [62-80], Calculated layer spacings and thermodynamic properties, as well as interlayer water configurations and interlayer-species self-diffusion coefficients are in agreement with available experimental data. 

Zawodzinski et al. [64] have reported self-diffusion coefficients of water in Nafion 117 (EW 1100), Membrane C (EW 900), and Dow membranes (EW 800) equilibrated with water vapor at 303 K, and obtained results summarized in Fig. 36. The self-diffusion coefficients were deterinined by pulsed field gradient NMR methods. These studies probe water motion over a distance scale on the order of microns. The general conclusion was the PFSA membranes with similar water contents. A, had similar water self-diffusion coefficients. The measured self-diffusion coefficients in Nafion 117 equilibrated with water vapor decreased by more than an order of magnitude, from roughly 8 x 10 cm /s down to 5 x 10 cm /s as water content in the membrane decreased from A = 14 to A = 2. For a Nafion membrane equilibrated with water vapor at unit activity, the water self-diffusion coefficient drops to a level roughly four times lower than that in bulk liquid water whereas a difference of only a factor of two in local mobility is deduced from NMR relaxation measurements. This is reasonably ascribed to the additional effect of tortuosity of the diffusion path on the value of the macrodiffusion coefficient. For immersed Nafion membranes, NMR diffusion imaging studies showed that water diffusion coefficients similar to those measured in liquid water (2.2 x 10 cm /s) could be attained in a highly hydrated membrane (1.7 x 10 cm /s) [69]. 

As shown by Zawodzinski et al., the dramatic uptake of water upon preswelling the membrane in glycerol at elevated temperatures (Fig. 27) substantially affects the transport properties in the membrane. In Table 8, the H intradiffusion coefficient is given for several different water contents. The water self-diffusion coefficient increases to 1.7 x 10 cm /s as the water content reaches the exceptionally high level of A = 80 (liquid water has a self-diffusion coefficient of 2.2 x cm /s at the same temperature). 

We have studied a variety of transport properties of several series of 0/W microemulsions containing the nonionic surfactant Tween 60 (ATLAS tradename) and n-pentanol as cosurfactant. Measurements include dielectric relaxation (from 1 MHz to 15.4 GHz), electrical conductivity in the presence of added electrolyte, thermal conductivity, and water self-diffusion coefficient (using pulsed NMR techniques). In addition, similar transport measurements have been performed on concentrated aqueous solutions of poly(ethylene oxide)... 

Figures 2-4 show the thermal and ionic conductivity, and water self-diffusion coefficient measured in these same systems. Also shown are the transport properties of PEO solutions of molecular weights ranging from 200 to 14,000 (12). The predictions of the Hanai and Maxwell relations are indicated, which were calculated on the assumption that the ionic conductivity or self-diffusion coefficient of the water or suspending electrolyte is equal to that of the pure liquid and that of the oil and emulsifier combined is zero. Also shown are similar results from the PEO solutions of various molecular weights. The thermal conductivity of the microemulsions and PEO solutions are shown in separate figures because the limiting thermal conductivity at zero water content is slightly different (0.27 times that of water for the microemulsion, vs. 0.31 for the PEO).

Figure 4. Water self-diffusion coefficient D of the micro-emulsions and PEO solutions, normalized to that of the pure liquid water. The need for the additional factor (1-p) is described in the text. Also shown are predictions of the Maxwell and Hanai equations.

The striking observation is that the ionic conductivity and water self-diffusion coefficient, but not the thermal conductivity, deviate significantly from the predictions of the mixture theories. This could arise from structural effects, such as a gradual transition from 0/W to W/0 structure with decreasing water content. We argue instead that these deviations principally result from hydration effects, and not from structural properties of the microemulsions. This would be expected because of the similarity of the data from the microeraulsions and PEO, in which structure effects would be quite different. 

Effect of Microemulsion Structure on the Transport Properties. It appears from the discussion above that the reduction in the ionic conductivity and water self-diffusion coefficient is primarily attributable to hydration effects, not principally to changes in the structure of the microemulsion with higher phase volume. 

Figure 5. Water self-diffusion coefficients in a variety of ionic and nonionic microemulsions. The compositions of these microemulsions are given in Reference 2.

Thus, by measuring oil and water self-diffusion coefficients, it was quite easy to establish whether oil or water or none of them are confined to discrete domains, i.e. to droplets . In the first work on microemulsion structure by self-diffusion [46], using both tracer techniques and NMR spin-echo measurements, it was clearly shown that microemulsions can indeed be bicontinuous over wide ranges of composition, which is manifested by both... 

C. Connectivity of Solvent Domains from Oil and Water Self-Diffusion Coefficients... 

From the oil and water self-diffusion coefficients we can thus easily decide whether a given microemulsion is of the discrete oil-in-water (O/W), discrete water-in-oil (W/O), or bicontinuous type. Thus we have for the three cases (Z>o denoting the neat solvent value) ... 

Figure 8 Relative self-diffusion coefficients of water and oil as a function of temperature for a sample containing 16.6 wt% C12E5 and roughly equal volumes of water and tetradecane. The opposite temperature dependences of water and oil clearly show that the structure evolves as a function of temperature at constant composition. The simultaneous increase in the oil and decrease in the water self-diffusion coefficients indicate a decrease in the interfacial film mean curvature with increasing temperature. (Data taken from Ref. 42.)...

Tapping mode atomic force microscopy Water molecules per acid site, H2O/SO3H Fickian diffusion coefficient of water Self-diffusion coefficient of water Proton mobility Electroosmotic drag coefficient Bulk membrane proton resistance Uncompensated resistance Glass transition temperatme Water volume fraction... 

Fig. 26 Water self-diffusion coefficient (Dh2o) and proton mobility (Da) as a function of the water volume fraction in Nafion and sulfonated polyetherketone [134]...

For the purpose of macroscopic transport of water, self-diffusion coefficients of water are converted to Fickian diffusion or the chemical diffusion... 

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