Water, self-diffusion coefficient solutions

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).

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.

RbCl interfacial water is due to a higher RbCl saturation solution concentration. The variation of interfacial water residence time is in excellent agreement with water self-diffusion coefficients. In bulk solutions, water molecules move faster when compared with water molecules at crystal lattice positions and interfacial water molecules as indicated by the short residence times and large diffusion coefficients. For water molecules in bulk KCl solution, the residence time (5.9 ps) and self-diffusion coefficient ( 2.5 X 10 m /sec) are very close to the values for pure water ( 5 ps and 2.5 x 10 mVsec, respectively) (Du and Miller 2007c Koneshan et al. 1998 Koneshan and Rasaiah 2000). 

Diamagnetic electrolyte solutions Intermolecular nuclear magnetic relaxation rate of proton in water molecules correlation times for molecular rotation in free water and hydrated water self diffusion coefficients of water molecules 84, 85... 

Nafion absorbs MeOH more selectively than water, and the MeOH diffusion flow is higher than the osmotic water flow in Nafion membranes. Diffusion coefficients of Nafion 117 determined by different techniques have been reported. Ren et al. measured MeOH diffusion coefficients in Nafion 117 membranes exposed to 1.0 M MeOH solutions using pulsed field gradient (PPG) NMR techniques. The MeOH self-diffusion coefficient was 6 x 10 cm S and roughly independent of concentration over the range of 0.5-8.0 M at 30°C. A similar diffusion coefficient was obtained for Nafion 117 at 22°C by Hietala, Maunu, and Sundholm with the same technique. Kauranen and Skou determined the MeOH diffusion coefficient of 4.9 x 10 cm for Nafion... 

In that case the self diffusion coefficient - concentration curve shows a behaviour distinctly different from the cosurfactant microemulsions. has a quite low value throughout the extension of the isotropic solution phase up to the highest water content. This implies that a model with closed droplets surrounded by surfactant emions in a hydrocarbon medium gives an adequate description of these solutions, found to be significantly higher them D, the conclusion that a non-negligible eimount of water must exist between the emulsion droplets. 

To dearly distinguish between these two modes of solvent penetration of the gel, we immersed poly(acrylamide-co-sodium methacrylate) gels swollen with water and equilibrated with either pH 4.0 HQ or pH 9.2 NaOH solution into limited volumes of solutions of 10 wt % deuterium oxide (DzO) in water at the same pHs. By measuring the decline in density of the solution with time using a densitometer, we extracted the diffusion coefficient of D20 into the gel using a least squares curve fit of the exact solution for this diffusion problem to the data [121,149]. The curve fit in each case was excellent, and the diffusion coefficients obtained were 2.3 x 10 5cm2/s into the ionized pH 9.2 gel and 2.4 x 10 5 cm2/s into the nonionized pH 4.0 gel. These compare favorably with the self diffusion coefficient of D20, which is 2.6 x 10 5 cm2/s, since the presence of the polymer can be expected to reduce the diffusion coefficient about 10% in these cases [150], In short, these experiments show that individual solvent molecules can rapidly redistribute between the solution and the gel by a Fickian diffusion process with diffusion coefficients slightly less than in the free solution. 

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). 

While the clathrate model is attractive, it is not correct to assume that the water is organized in some long-lived structure the observation that the self-diffusion coefficient for co-sphere water is larger than that for the solute rules this out. However, the rotational correlation time is shorter for ethanol and t-butyl alcohol in water (in the clathrate cage ) than in the pure liquid (Goldammer and Hertz, 1970 Goldammer and Zeidler, 1969). Nmr experiments show that in water the solvent dipole moments point away from the apolar groups (Hertz and Radle, 1973). 

Self-Diffusion Coefficients of Ions and Solvent Water (Dj in a 2.2 molal Ltl Solution Obtained from MD Simulation and Experiments at 305... 

Since the relaxation rate constant of 23Na+ depends strongly on the viscosity of the solution, we measured the self-diffusion coefficient of 23Na+ in glycerol/water solution, and found a relationship between the self-diffusion coefficient and the transverse relaxation rate constant on viscosity [Fig. 2-a]. Then, we have estimated the Sf g value of Na ion in the agar gel from the self-diffusion coefficient of Na ion in the agar gel using the observed relationship [Fig. 2-b]. 

Examples of Ihe deterniinalioii of self-diffusion coefficients in solids are Ihe diffusion of hydrogen ions and water molecules (labelled with T and O, respectively) in alums, of Cl (labelled with Cl) in AgCl, and of 1 (labelled with l) in Agl. Besides self-diffusion, many other diffusion coefficients of trace elements in metals, oxides, silicates and other substances have been determined by application of radio-tracers. Investigation of the migration of trace elements from solutions into glass revealed fast diffusion of relatively small monovalent ions such as Ag+. 

Experiments were carried out with Ionac MC 3470 to determine the self-diffusion coefficient values for H+ and Al + in the coupled transport. Data points were used from the experiment involving 2N acid sweep solution in Figure 34.24b, presented later. These values formed the basis for aluminum transport rate or flux (7ai) calculation at different time intervals. The equilibrium data generated in Figure 34.20b were used in conjunction with Equation 34.25 to determine the interdiffusion coefficient values. Local equilibrium was assumed at the membrane-water interface. Eigure 34.24a shows computed Dai,h values for this membrane. When compared with Dai,h values for Nafion 117, it was noticed that the drop in interdiffusion coefficient values was not so steep, indicative of slow kinetics. The model discussed earlier was applied to determine the self-diffusion coefficient values of aluminum and hydrogen ions in Ionac MC 3470 membrane. A notable point was that the osmosis effect was not taken into account in this case, as no significant osmosis was observed in a separate experiment. 

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... 

Physical Mechanisms. The simplest interpretation of these results is that the transport coefficients, other than the thermal conductivity, of the water are decreased by the hydration interaction. The changes in these transport properties are correlated the microemulsion with compositional phase volume 0.4 (i.e. 60% water) exhibits a mean dielectric relaxation frequency one-half that of the pure liquid water, and ionic conductivity and water selfdiffusion coefficient one half that of the bulk liquid. In bulk solutions, the dielectric relaxation frequency, ionic conductivity, and self-diffusion coefficient are all inversely proportional to the viscosity there is no such relation for the thermal conductivity. The transport properties of the microemulsions thus vary as expected from simple changes in "viscosity" of the aqueous phase. (This is quite different from the bulk viscosity of the microemulsion.)... 

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