Sodium ions self-diffusion coefficients

Most of the current applications of perfluorosulfonate membranes involve electrochemical cells in which concentrated electrolyte solutions are employed, often at elevated temperatures. Relatively little diffusion data are available under these conditions, although a larger amount of membrane resistance and other operating data have been published. Sodium ion self-diffusion coefficients have been measured in various Nafion membranes in concentrated NaOH solutions at elevated temperatures (23). This... 

Thus, it is suspected that strong contact ion pairing in the case of the carboxylate is responsible for the low sodium ion diffusion coefficients and high diffusional activation energies. For the sulfonate, sodium ions that function as exchange-site counterions may be less strongly bound than for the carboxylate case, resulting in more facile sodium ion self-diffusion in the polymer. 

Table I. Sodium Ion and Cesium Ion Self-Diffusion Coefficients, 25°C...

Spiegler has used the friction model to describe a system consisting of sodium ions (1), chloride ions (2), water (3) and a charged matrix (4). He neglects the interaction of the sodium ions with the chloride ions. Then five independent measurements are needed to calculate the friction coefficients. Spiegler chose to be measured the self-diffusion coefficient... 

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

Williams et al,92) have investigated the diffusion of the sodium ion in NMA solutions of NaCl at 40 °C. The values of the diffusion coefficient for the Na+ ion were found to be equal to approximately half the value of the self-diffusion coefficient for pure NMA. This suggests a solvation which is equivalent to three or four molecules of NMA coordinated to the sodium ion. 

The self-diffusion coefficients of sodium and cesium ions have been measured for perfluorinated sulfonate (Nafion ) and carboxylate membranes of similar structure. The exchange-site con-... 

Self-diffusion coefficients for sodium ion, cesium ion, and water in these polymers are shown in Fig. 9, as Arrhenius plots from 0 to Diffusion of sodium ion and water is remarkably similar... 

The self-diffusion coefficient of sodium ion is plotted in Fig. 11 vs. the reciprocal of absolute temperature for the perfluorosulfo-nate and perfluorocarboxylate membranes which were discussed in Section Here though, the membrane environment con-... 

Tracer self-diffusion coefficients for sodium ion and cesium ion have been measured for 1200 equivalent weight Nafion membranes 04-7). Results obtained at 25°C are listed in Table I, along with... 

The self-diffusion coefficient for iodide ion was also measured at 25°C in the first sample of 1200 EW Nafion, before aging 04). The result, 9 10 8 cm2 sec"1, indicates that this anion is more mobile than cesium ion, but less than a sodium ion. This is also somewhat unusual. In general, co-ion diffusion coefficients are seen to be larger than those of counterions in ion exchangers, because no electrostatic attractions to the polymer phase exist. (The membrane concentration is only 5 x 10 3 mol L 1 though, reflecting the effects of Donnan exclusion processes (4 ).)... 

In order to interpret the Na" " and Cs" " diffusional results in terms of this model, it is assumed that both cations would be able to diffuse readily in both the ionic clusters and interfacial regions. Cesium ion would experience a more tortuous diffusion path compared to sodium ion, and thus would have a smaller measured self-diffusion coefficient. The insensitivity of this diffusion coefficient to increasing water sorption may then be because most of this water serves to increase the size of ionic clusters, which would have a relatively minor overall effect on the diffusion path length. 

Membrane Diffusion in Nonaqueous Solvent Environments. Self-diffusion coefficients of Na+ and Cs+ for 1200 EW Nafion membranes in dilute methanol and acetonitrile solutions have been measured (5). Arrhenius plots of these results are shown in Figure 7 along with corresponding results for aqueous experiments activation energies of diffusion are listed in Table IV. Diffusion coefficients of Na+ in methanol and water-equilibrated membranes are very similar, and the activation energy of diffusion for the methanol system is only slightly higher than the respective value for Na+ in pure methanol solvent, 12.9 kJ mol 1 (27). Thus a solution-like diffusion mechanism is inferred for both solvent systems. Cesium ion diffusion in the methanol equilibrated membrane is much slower than sodium ion diffusion in fact the... 

Water, sodium ion, and hydroxide ion concentrations have been measured within the membrane phase as a function of bulk caustic solution concentration and temperature. These internal membrane concentrations are important because of their influence on the membrane polymer morphology, structural memory, plasticity and the resultant effects on its internal resistance, viscoelasticity and material transport. In addition, the self-diffusion coefficient of the sodium ions in various Nafion membranes has been measured as a function of temperature and external caustic concentration... 

Light transmission L. L. Schramm and J.C.T. Kwak, op. cit. Electrophoretic mobility P. Bar-On, I. Shainberg, and I. Michaeli, Electrophoretic mobility of montmorillonite particles saturated with Na/Ca ions, J. Colloid Interface Sci. 33 471 (1970). Intrinsic viscosity I. Shainberg and H. Otoh, op. cit. Chloride exclusion volume J. E. Dufey, A. Banin, H. G. Laudelout, juid Y. Chen, Particle shape and sodium self-diffusion coefficient in mixed sodium-calcium montmorillonite. Soil Sci. Soc. Am. J. 40 310 (1976). 

The variation of the self-diffusion coefficient of sodium and cesium counter-ions as a function of a is reported in Figure 3. The equivalent conductances of the same solutions are reported in Figure 4. 

Diffusion coefficients provide two kinds of information. First, their absolute magnitudes, combined with membrane sodium ion concentrations, are useful indicators of the temperature dependence of ionic self-diffusion and thereby they yield the activation energy for diffusion. They thereby provide insight into the nature of the diffusion mechanism (16). When activation energies are measured for various types of related membranes, the influence of different membrane structural design features can thus be separated and determined directly. 

Diffusion of an ion which is a primary component of a glass, as discussed above, is termed self-diffusion. We can also measure diffusion of an ion which is not present in the glass, e.g., potassium diffusion in a sodium silicate glass. The results of such measurements for a set of R20-3Si02 glasses, where R is Na, K, Rb, or Cs, reveals that the diffusion coefficient is always greatest for the ion which is the component of the glass. The diffusivity of the impurity ions decreases as the difference... 

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