Self diffusion coefficient of water

The self-diffusion coefficient of water in Nafion, as measured by PFG is shown in... 

For comparison purposes, the proton mobility. Do (for Nafion solvated with water), which is closely related to the self-diffusion coefficient of water, is also plotted. At low degrees of hydration, where only hydrated protons (e.g., H3O+) are mobile, it has a tendency to fall below the water diffusion coefficient (this effect is even more pronounced in other polymers), which may be due to the stiffening of the water structure within the regions that contain excess protons, as discussed in Section 3.1.1. . Interestingly, the proton mobility in Nafion solvated with methanol (Da(MeOH) in Figure 14a) is even lower than the methanol self-diffusion (Z ieon). This may... 

Figure 5. Experimental self-diffusion coefficient of water molecules in NaX as a function of reciprocal temperature, (a) Mean diameter of the zeolite crystals 3 pm ...

Self diffusion coefficients can be obtained from the rate of diffusion of isotopically labeled solvent molecules as well as from nuclear magnetic resonance band widths. The self-diffusion coefficient of water at 25°C is D= 2.27 x 10-5 cm2 s 1, and that of heavy water, D20, is 1.87 x 10-5 cm2 s 1. Values for many solvents at 25 °C, in 10-5 cm2 s 1, are shown in Table 3.9. The diffusion coefficient for all solvents depends strongly on the temperature, similarly to the viscosity, following an Arrhenius-type expression D=Ad exp( AEq/RT). In fact, for solvents that can be described as being globular (see above), the Stokes-Einstein expression holds ... 

Fig. 2.11. Self-diffusion coefficients of water ( ), sodium ions ( ), dodecyisul-fate ion ( ) and micelles ( ) in SDS solutions. Data from Refs.37-110- 2>...

For B = A, the tracer diffusion coefficient equals the self-diffusion coefficient, D lba= Dla- 1° Table 6-6 the self-diffusion coefficient of water and some diffusion coefficients of organic solutes in water at infinite dilution calculated with Eq. (6-31) are compared with experimental values (Reid et al., 1987). The experimental value for sucrose is from Cussler (1997). 

If the hydroxonium ions migrated only hydrodynam-ically A° 85 cm2 would be expected, which value can easily be derived by using the -> Stokes law and the known values of the -+ self-diffusion coefficient of water, the radius of the ion and the - viscosity. (See also proton, - Eigen complexes, - Zundel complexes, charge transfer, - Dahms-Ruff theory.)... 

NMR and used it to determine the pore size distribution of mesoporous silicates. They also derived the self-diffusion coefficient of water in MCM-41 and MCM-48 [94,107]. Llewellyn et aL [109] found that MCM-41 exhibits a type V water adsorption isotherm indicating an initial repulsive character followed by capillary condensation at higher pressures. 

The self diffusion coefficient of water enclosed in the pores of the three-dimensional MCM-48, determined by using NMR spin-echo measurements, was found to be signifrcantly larger than that of MCM-41. The high degree of ordering and the three dimensional, interconnected pore system, leads to a high self diffusion coefficient of molecules enclosed in the pores of MCM-48 (82). 

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]. 

Table 8. Self-diffusion coefficients of water in Nafion 117 (T = 30 °C) as a function of glycerol pre-treatment temperature.

Interactions between oppositely charged micelles in aqueous solutions spontaneously form vesicles. The self-diffusion coefficient of water and 2H relaxation of 2H-labeled dodecyl trimethyl ammonium chloride of the dodecyl trimethyl ammonium chloride-sodium dodecyl benzenesulfonate systems show that in these mixtures there is limited growth of the micelles with changes in composition. The vesicles abruptly begin to form at a characteristic mixing ratio of the two surfactants. The transition is continuous.205 Transformation from micelle to vesicle in dodecyl trimethyl ammonium chloride-sodium perfluoro-nonanoate aqueous solution has been studied by self-diffusion coefficient measurements, and it was found that at a concentration of 35 wt% with a molar ratio of 1 1, the self-diffusion coefficient of the mixed micelles is far smaller than that of the two individual micelles.206 The characteristics of mixed surfactant... 

Very recently, a novel Fourier transform NMR method was employed by Lindman, et al. (21) to obtain multicomponent self-diffusion data for some single phase microenulsion systems. Because of the large values obtained for the self-diffusion coefficients of water, hydrocarbon, and alcohol, over a wide range of concentrations, the authors concluded that there are no extended, well-defined structures in these systems. In other words, the Interfaces which separate the hydrophobic from the hydrophilic regions appear to open up and reform at a short time scale. 

Selected Examples. - Pulsed magnetic field gradient (PFG) NMR is today a routine method for the determination of self-diffusion coefficients. However, a remaining goal is the improvement of the precision of the method. The best procedure for the determination of accurate diffusion coefficients by PFG NMR is a calibration with a sample of precisely known D value. Thus Holz et al presented temperature-dependent self-diffusion coefficients of water and six selected molecular liquids. The gained accurate self-diffusion data are suited for an elaborate check of theoretical approaches in the physics of molecular liquids. Price et al examined the translational diffusion... 

FIGURE 10 Self-diffusion coefficients of water across the gel layer of an HPMC tablet after 3 hours of hydration. The x axis is as shown in the original. (Reprinted with permission from ref. 17, Copyright 1996, Plenum.)... 

Table III. Self-Diffusion Coefficients of Water in 1200 EW Nafion (7).

Translational self-diffusion and rotation of the water molecules. Since the above two models fail to explain the data, one may think of a model which combines both, and which is certainly more realistic. We h ve2tr e< such a possibility with p = 0.95 and D 1.6 x 10 cm /s. This last value is the long range self-diffusion coefficient of water in this membrane, measured by radioactive tracers. We found that no fit is possible with these values whatever D is chosen. As for the preceeding section, we find that the fiE improves considerably if we take either p or Dt as parameters. With Dt fixed, we should increase p to 3 A, as above, and with p fixed, we should increase D to 10 cm /s. These results suggest that one should think of a model which contains these two features. The simplest one is a model where the water molecules, more precisely the protons, are restricted to diffuse (diffusion goejjficient D) in a sphere of radius a, where we expect D 10 cm and a 3 S. 

The "barrier-effect" also reduces the average translational self-diffusion of protons and is most acute in this case with low coverages. The presence of high concentrations of solute, the physical obstruction of the pore surfaces, and the presence of almost impermeable barriers (such as the liquid-air surface) will result in a pure steric effect reducing the self-diffusion coefficient of water molecules. This is termed the barrier effect... 

The self-diffusion coefficient of water was determined by the same method. The contrast arises from a small amount of H2O added to D2O. The self diffusion is not influenced by the swollen gel. 

Figure 18 Concentration dependence of the self-diffusion coefficients of water (open symbols) and ammonia (filled symbols) without co-adsorbed hydrocarbons (A, A) and with 0.8 molecules per cavity of co-adsorbed /i-butane - d, (O, 0). and butene - dg (n, 12% butene-1, 56% /ran5-butene-2, 32% r -butene-2), respectively. (From Ref. 110.)...

Neutron scattering data for Li- and Na-vermiculite, on the other hand, gave no indication of water protons being immobile on the neutron scattering time scale.This result is consistent with the behavior of water molecules in aqueous solution, since the residence time in the primary solvation shell of a monovalent cation is about 10" s, well within the time scale probed by neutrons. However, as shown in Table 2.4, the self-diffusion coefficients of water molecules on Li- and Na-vermiculite were found to be much smaller than the bulk liquid value at 298 K. These data suggest that, even in the two-layer hydrate, the solvating water molecules exhibit only about 5 per cent of the mobility they have in the bulk liquid phase and about 10 per cent of that in the primary solvation shell of a monovalent cation in aqueous solution (Dg 1.3 x 10" m s" ) . This reduction in water molecule mobility is evidently produced by interactions with the charge distribution on the siloxane surface. 

Figure 7 Relative self-diffusion coefficients of water and oil plotted as a function of temperature in a three-component system, Ci2E5-water-tetradecane, at constant (16.6 wt%) surfactant concentration. Note the symmetry around the balanced temperature (here approximately 47°C) corresponding to zero spontaneous curvature. (Data taken from Ref 42.)...

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.)...

Figure 9 Relative self-diffusion coefficients of water and oil as a function of the oil volume fraction

Figure 10 Variations of self-diffusion coefficients of water, oil, surfactant, and cosurfactant in a salinity scan for a five-component microemulsion, SDS-butanol-water- NaCI-toluene. The experiments were performed with excess solvent(s) in the so-called Winsor sequence.The system...

Figure 11 Relative self-diffusion coefficients of ( ) water and (A) oil as a function of the oil content in a four-component microemulsion, AOT-water-NaCl-isooctane.The system is tuned by temperature at constant salinity. (Data taken from Ref. 45.)...

Figure 13 Relative self-diffusion coefficients of water and oil as a function of the surfactant mixing ratio in a five-component microemulsion consisting of Ri20CH2CH2S04Cai/2-/-R80CH2CH(0H)CH20H-water with 8 wt% CaCh and decane. Here R12 refers to a dodecyl (C12H25) chain and /-Rg to an isooctyl ((CHj)jC(CH2)4] chain. The system is tuned by the surfactant mixing ratio (Data taken from Ref 47.)...

Figure 15 Self-diffusion data at 25 C in the toluene-water-alcohol-sodium dodecyl sulfate system (weight ratios 12.5 35.0 35.0 17.5) as a function of increasing chain length of the alcohol. The filled circles correspond to alcohol diffusion coefficients normalized by the diffusion coefficient of neat alcohol, which removes the trivial molecular weight dependence. Note that the self-diffusion coefficient of water decreases by more than two orders of magnitude as the cosurfactant is changed from butanol to decanol. (Data taken from Ref 95.)...

Figure 20 Double-water experiment, the aqueous analogy of the double-oil experiment, performed on an AOT microemulsion as a function of temperature. The polar solvent is a 5% A-methyl formamide (NMF) solution in heavy water (D2O). The ratio of the water (here measured as trace impurities of HDO) and NMF diffusion coefficients is monitored as a function of temperature (c). Also shown as (a) the individual self-diffusion coefficients of water (O). NMF ( ), and AOT ( ) and (b) the relative diffusion coefficient of water. Kq = 1.73 is the diffusion coefficient ratio in the pure water-NMF mixture and is indicated as a broken line in (c). The phase boundary at 75"C is indicated as a vertical broken line. The behavior with increasing temperature is completely analogous to that of the nonionic system (Fig. 19) and illustrates a transition from reverse micelles to a bicontinuous structure via growing droplets that become attractive. (Data from Ref 49.)... 

Eccles, C.D., Callaghan, P.T., and Jenner, C.F., Measurement of the self-diffusion coefficient of water as a function of position in wheat grain using nuclear magnetic resonance imaging, Biophys. J., 53 75, 1988. 

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... 

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

---