Diffusion coefficients of ions

Polymer gels and ionomers. Another class of polymer electrolytes are those in which the ion transport is conditioned by the presence of a low-molecular-weight solvent in the polymer. The most simple case is the so-called gel polymer electrolyte, in which the intrinsically insulating polymer (agar, poly(vinylchloride), poly(vinylidene fluoride), etc.) is swollen with an aqueous or aprotic liquid electrolyte solution. The polymer host acts here only as a passive support of the liquid electrolyte solution, i.e. ions are transported essentially in a liquid medium. Swelling of the polymer by the solvent is described by the volume fraction of the pure polymer in the gel (Fp). The diffusion coefficient of ions in the gel (Dp) is related to that in the pure solvent (D0) according to the equation ... 

Table 2.3 Self-diffusion coefficients of ions in aqueous solution at 25 °C ...

Baird et al. [350]). In the following analysis, the functional forms, p(E), which have been proposed (see below) to represent the field-dependence of the drift mobility are used for electric fields up to 1010Vm 1. The diffusion coefficient of ions is related to the drift mobility. Mozumder [349] suggested that the escape probability of an ion-pair should be influenced by the electric field-dependence of both the drift mobility and diffusion coefficient. Baird et al. [350] pointed out that the Nernst— Einstein relationship is not strictly appropriate when the mobility is field-dependent instead, the diffusion coefficient is a tensor D [351]. Choosing one orthogonal coordinate to lie in the direction of the electric field forces the tensor to be diagonal, with two components perpendicular and one parallel to the electric field. 

Ionic radii in the figure are measured by X-ray diffraction of ions in crystals. Hydrated radii are estimated from diffusion coefficients of ions in solution and from the mobilities of aqueous ions in an electric field.3-4 Smaller, more highly charged ions bind more water molecules and behave as larger species in solution. The activity of aqueous ions, which we study in this chapter, is related to the size of the hydrated species. 

T. Yoshinobu, T. Harada and H. Iwasaki, Application of the pH-imaging sensor to determining the diffusion coefficients of ions in electrolytic solutions, Jpn. J. Appl. Phys. Pt. 2 -Lett., 39 (4A) (2000) L318-L320. 

In most cases the only measured quantity is encounter diffusion coefficient of ions, D, is known. It is precisely z that is usually studied as a function of the recombination free energy at contact... 

If A is the effective surface area of the electrode and D the diffusion coefficient of ion, then the quantity of ions mx diffusing through the layer of the thiokness 8, in one second, at activity difference (a — o ), according to Fick, will be expressed by the equation ... 

Expansion of the blob. Because of attraction between ions and electrons, expansion of the blob is governed by the law of ambipolar diffusion. As a result out-diffusion of electrons is almost completely suppressed, but the diffusion coefficient of ions is increased by a factor of two. Thus, blob expansion proceeds very slowly and may usually be neglected in the problem of Ps formation. 

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

In the experiment described in Exercise 6 it was found that at a certain time the Geiger counter registered a maximum ion flux, i.e., the intensity of the radiation has a maximum with respect to time. It was also found that by placing the Geiger counter farther away from the electrode, the time at which the maximum occurs becomes longer, and the peak intensity of the maximum decreases rapidly. Justify this observation and evaluate its usefulness in experimentally measuring diffusion coefficients of ions. (Xu)... 

The assumed identity of the rates of hole diffusion and ionic diffusion is recalled. Thus, the final expression for the diffusion coefficient of ions in a fused salt is the same as that for holes, i.e., Eq. (5.98). 

Oelkers E. H. and Helgeson H. C. (1988) Calculation of the thermodynamic and transport properties of aqueous species at high pressures and temperatures aqueous tracer diffusion coefficients of ions to 1,000 °C and 5 kb. Geochim. Cosmochim. Acta. 52, 63—85. 

Miyoshi, H. Diffusion coefficients of ions through ion exchange membrane in Donnan dialysis using ions of different valence. J. Membr. Sci., 141, 101-110, 1998. 

Although amperometric detection of ionic species based on ITIES is feasible, the mechanical instability of a liquid-liquid interface is a major problem which has to be circumvented to develop a commercial ion sensing system. A lot of work has been done to gelify the organic phase in order to achieve a better handling of liquid-liquid systems [38]. Most publications related to IT reactions at a liquid-gel interface have shown that although the diffusion coefficients of ions in the gel are significantly reduced, the IT processes could still be used for amperometric detection. 

T. Ktari, C. Larchet and B. Auclair, Mass transfer characterization in Donnan dialysis, J. Membr. Sci., 1993, 84, 53-60 H. Miyoshi, Diffusion coefficient of ions through ion exchange membrane in Donnan dialysis using ions of different valence, J. Membr. Sci., 1998, 141, 101-110. 

Ritthichauy W Sugiyama T., Tsuji Y. (2002) Calculation of diffusion coefficient of ion in multicomponent solution for ion movement in concrete, 2002. Proceedings of Japan Concrete Institute, Tsukuba. 19-21 July 2002. Tokyo Japan Concrete Institute, p. 669-674. 

Section 5.5 dwelled on the transport of charged mixtures and the derivation of the basic transport equations. Recall that for an infinite diluted mixture, the transport of ions takes place due to their migration in the electric field, diffusion and convection. As in the Section 5.5, we limit ourselves to the study of a binary electrolyte mixture, for which (in the case of electrically neutral mixture) the distribution of reduced ion concentration is described by a convective diffusion equation, with the effective diffusion coefficient given by (5.96). The solution of Eq. (5.94) allows us to find the distribution of electric potential. In Eq. (5.98), we can form scalar products of both parts with dx, where x is the radius-vector, and then use the relation between diffusion coefficients of ions and their mobility D = ATi> . Integrating the resultant expression, we then find the potential difference Ap between two points of the mixture ... 

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