Self-diffusion of Ions

The rate of self-diffusion of ions is commonly obtained from other transport quantities, such as the conductivity. It may, however, be determined directly by labeling the ions isotopically. It is then assumed that the slight mass difference between ions that 

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In both cases, ctj i depends on PO2- Figure 1.43 shows that eqn (1.167) is dominant in the pressure range I O2 > 10 atm and eqn (1.168) is dominant in the pressure range 02 < 10 atm. In the former case, CT , depends on temperature because ion mobility is temperature dependent. The relation between the ionic and electronic conductivity for solid electrolytes is shown schematically in Fig. 1.44. Since ionic conductivity originates from diffusion of ions in the solid phase, (Tio is closely related to the coefficient of self diffusion of ions ( X,o ) shown by the following equation... 

The simple model (Fig. 20) can be criticized because it cannot readily be quantified. However, it does account for a wide range of properties, such as the tendency for the partial molar heat capacity and the viscosity -coefficient to become more negative with increase in ion size (Fortier et al., 1974a McDowell and Vincent, 1974 Kay, 1968 1973). Kay has collated conductance and viscosity data and shown how these lead to a classification of ionic properties (Fig. 21). The effects of added salts on the self-diffusion of ions is consistent with the Frank-Wen structural model (Hertz et al., 1974). It is noteworthy that in D20, which is argued to be more... 

Anderko and Lencka find. Eng. Chem. Res. 37, 2878 (1998)] These authors present an analysis of self-diffusion in multicomponent aqueous electrolyte systems. Their model includes contributions of long-range (Coulombic) and short-range (hard-sphere) interactions. Their mixing rule was based on equations of nonequilibrium thermodynamics. The model accurately predicts self-diffusivities of ions and gases in aqueous solutions from dilute to about 30 mol/kg water. It makes it possible to take single-solute data and extend them to multicomponent mixtures. 

Self-diffusion of ions in silica has been measured both experimentally and computationally. Experimentally, Mikkelsen (Mikkelsen Jr. 1984) used SIMS (secondary ion mass spectroscopy) to measure the concentration profiles of labeled O deposited on silica to obtain the diffusion coefficient. Brebec et al (Brebec et al. 1980) used labeled Si and SIMS analysis for determining Si diffusion. Hetherington (Hetherington et al. 1964) used viscosity measurements of commercial silica to determine diffusion constants. Their experimental data are shown in Table 1, along with results from several computational studies. 

Rollet, A.L., Simonin, J.P., Turq, P., Gebel, G., Kahn, R., Vandais, A., Noel, J.P., Malveau, C., Canet, D. (2001) Self-diffusion of ions at different time scales in a porous and charged medium the Nafion membrane. The Journal of Physical Chemistry B, 105, 4503-4509. 

In binary ion-exchange, intraparticle mass transfer is described by Eq. (16-75) and is dependent on the ionic self diffusivities of the exchanging counterions. A numerical solution of the corresponding conseiwation equation for spherical particles with an infinite fluid volume is given by Helfferich and Plesset [J. Chem. Phy.s., 66, 28, 418... 

Diffusion of ions can be observed in multicomponent systems where concentration gradients can arise. In individnal melts, self-diffnsion of ions can be studied with the aid of radiotracers. Whereas the mobilities of ions are lower in melts, the diffusion coefficients are of the same order of magnitude as in aqueous solutions (i.e., about 10 cmVs). Thus, for melts the Nemst relation (4.6) is not applicable. This can be explained in terms of an appreciable contribntion of ion pairs to diffusional transport since these pairs are nncharged, they do not carry cnrrent, so that values of ionic mobility calculated from diffusion coefficients will be high. 

The fraction of vacancies in a crystal of NaCl, riy/N due to a population of Schottky defects, is 5 x 10-5 at 1000 K. In a diffusion experiment at this temperature, the activation energy for self-diffusion of Na was found to be 173.2 kJ mol-1. Determine the potential barrier that the diffusing ions have to surmount. 

The impedance factor is strictly empirical, accounting primarily for the geometry of the soil pore network bnt also for ion exclusion by negative adsorption from narrow pores, and for the increased viscosity of water near charged surfaces. It is similar for all simple ions and molecules. It can be measured by following the self diffusion of a nonadsorbed ion, such as Cl , for which C = 0lCl and hence D =... 

Manning, G. (1969b). Limiting laws and counterion condensation in polyelectrolyte solutions II. Self-diffusion of small ions. J. Chem. Phys. 51(3), 934—938. 

Alternative to fibers and 2D and 3D woven or nonwoven networks thereof formed as either self-supporting structures or as a hydrogel, it is possible to self-assemble peptides into thin self-assembled monolayers (SAMS) or multilayer structures. Such structures have been reported to act as membranes for controlled diffusion of ions and controlled movement of body fluids and contaminants (Ellis-Behnke et al., 2006, 2007 Holmes et al., 1999). Alternatively, various techniques have been put in place to provide coatings on various substrates ranging from tissue to metals and inorganics, for example, mica (Boden et al., 2002 Haynie, 2005,2007 Haynie and Zhi, 2007 Yoo et al., 2008). 

On a molecular scale there is no sharp boundary between hydrodynamically stagnant and movable solvent molecules. As discussed In sec. 2.2, the, say tangential, diffusion coefficient of water near many surfaces may be somewhat lower than in bulk, but it is not zero. The very existence of ionic conduction In the layer(s) adjacent to surfaces also points to non-zero mobility. Yet, phenomenologically such layers behave as immobilized. This looks like a paradox, but the phenomenon is encountered in other places as well. For Instance, a few percent of gelatin added to water may hydrodynamically immobilize the liquid completely, without markedly impairing ionic conduction or self-diffusion of dissolved ions. Macroscopic immobilization of a fluid is not in conflict with mobility on a molecular sceile. 

The self-diffusion of water itself provided proof of the above hypothesis, because ions due to hydration retarded it, but structure breakers could accelerate it. The plot of the self-diffusion parameter as a function of transition concentration fully confirmed the above-mentioned assumption. The transition concentration thus corresponded with that at which the maximum hydration occured. 

Figure 2.4 Self-diffusion of counter-ions, co-ions and non-electrolytes through an ion exchange membrane (monovalent ions).

The authors studied the solution chemistry of Zr in nitric, perchloric, hydrochloric and sulphuric acid by a combination of experimental techniques including self-diffusion measurement, ion-exchange, electromigration and pH measurement. 

In some experiments answers to scientific questions which require knowledge of the presence and concentration of a specific element or conqwund at a certain place and at a certain time can be obtained only through the use of a radioactive tracer. For exanq>le, self diffusion of metal ions in solutions of their salts cannot easily be studied by any other technique. However, in other cases the use of radioactive tracers is not necessary in principle but is justified by the greater convmience. In either type of investigation there are two assumptions implicit in such uses. 

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