Diffusion coefficient of the cation

D+, D = aqueous diffusion coefficients of the cation and anion, respectively, cm2/sec... 

Diffusion measurements in neat ILs can reveal information on the internal structure of fhese media and on ionic association. But due to the high viscosities of mosf ILs, sfrong gradients or quite long diffusion times are necessary. With this technique, it was found that most IL cations diffuse faster than their corresponding anions [39], but the molecular size of anions and cations did not correlate well with their diffusion coefficients. In addition to this, the diffusion coefficients of the cations were strongly anion-dependent [40]. 

Of the four coefficients L, Lhh, aA, and ah, only three are independent. In order to determine them, we need a third experimental transport parameter which is chosen to be the tracer diffusion coefficient of the cations. The transport coefficient LAA, in terms of >A is (see Section 5.2)... 

We note that (Dy v) is proportional to the self-diffusion coefficient of the cations in AO near the surface. 

Pertinent calculations have been carried out by R. Schlogl and M. Schodel (146). They considered a cation exchange membrane and a uniunivalent electrolyte. A constant concentration of active groups was assumed to occur across the whole membrane, as well as constant activity and diffusion coefficients. For simplification of the calculations it was assumed that the diffusion coefficients of the cation and the anion have... 

Figure 5.3 depicts the Arrhenius plots of the apparent self-diffusion coefficient of the cation (Dcation) and anion (Oanion) for EMIBF4 and EMITFSI (Figure 5.3a) and for BPBF4 and BPTFSI (Figure 5.3b). The Arrhenius plots of the summation (Dcation + f anion) of the cationic and anionic diffusion coefficients are also shown in Figure 5.4. The fact that the temperature dependency of each set of the self-diffusion coefficients shows convex curved profiles implies that the ionic liquids of interest to us deviate from ideal Arrhenius behavior. Each result of the self-diffusion coefficient has therefore been fitted with VFT equation [6].

As is seen, when the temperature rises, a considerable decoupling of the Li ions in liquid LiCl seems to take place. Decoupling of the cations is likely to help cationic self-diffusion more than cationic conductance, because in self-diffusion cations must interchange positions while in conductance they may move in parallel. In fact, corresponding to the temperature dependence of n in molten LiCl, an increase of D+/Ta (D+ = self-diffusion coefficient of the cations, A = equivalent conductance) with absolute temperature T has been observed for all molten alkali halides checked (30). (Also work is in progress at Mainz to check LiCl.)... 

Fig. 5 Arrhenius plots of the diffusion coefficients of the cations squares) and anions (circles) of a pure (closed) and a 97% pure (open) sample of [bmim]PF6 [36]. Reproduced with permission...

Here, p represents the density of the solid (mol/cm ) and and i soiunon the diffusion coefficients of the cation in the solid and the electrolyte, respectively. 

Huang, Kwei, and Reiser have estimated the diffnsion coefficient of some cations from the dissolution rate and the width of the penetration zone. Using the observed dissolution rate R (200 A/s) and an estimated penetration width d of 20-100 A, the authors have estimated the diffusion coefficient of the cations in novolac resins to be on order of... 

Figure 10. (a) Distribution curves for a 2.5 X 10 M solution of several fluorides and of HCl. Growth rate 5 microns a second. No stirring. No relation exists between the apparent distribution coefficients fk computed from the slope of the cation curve) and the diffusion coefficients of the cations... 

Examples of the use of sulphidation to verify oxidation theory has been provided also by Wagner. In Chapter 3, the parabolic rate constant was derived from first principles using the simplifying assumption that cations and electrons were the only mobile species involved. It was assumed that the anions migrated so slowly that they could be considered to be immobile. Wagner has considered the mobilities of all three species (cations, anions, and electrons) and expressed the rational rate constant in terms of the self-diffusion coefficients of the cation and anion species, as in Equation (6.1),... 

Schottky defects as major defects and Frenkel defects as minor defects, the effective diffusion coefficient of the cation can vary from Dm,Io... 

The parabolic oxidation constant in this case is proportional to the diffusion coefficient of the cation vacancies and to their concentration at the oxide-gas interface. 

Here, Dj is the diffusion coefficient of the cation interstitials, K = Fe/RT, where e is the electric field strength inside the barrier layer, and T is the temperature. The continuity equation is... 

The tracer diffusion coefficients for cations, anions, and water are shown as a function of salt concentration in Table 4.4. From the table, it can be seen that the diffusion coefficients for the ions and water molecules decrease with increasing salt concentration, and close analysis of the data in Table 4.4 indicates that, for the Csl solution, the decrease in diffusion coefQcients with concentration is the smallest and largest for the LiCl solution. In both cases, as the concentration increases, the diffusion coefficients of the cation and anion become more nearly alike. A similar observation has been made in previous studies of aqueous solutions of NaCl and KCl at high concentrations (Allen and Tildesley 1987 Chowdhuri and Chandra 2001 Koneshan and Rasaiah 2000). As for the systems containing large ions (e.g., Cs+, Rb+, and I" ions) with weaker electric fields, the observed decrease of ion diffusivity also can be explained in terms of inCTeased ion pairing, which slows down the movement of ions and water molecules bound to them. 

If the formation of reaction products has resulted from cationic anti-diffusion, the rate constant is proportional to the diffusion coefficient of the cation which is not too active. If the diffusion occurs according to the defect mechanism, the cation which is not too active would be directly in proportion with the concentration of cation defects. It is obvious that the diffusion of the cation proceeds at a faster rate, and with a stronger response in the non-stoichiometric phase that is in defect of metal ion, and has a high concentration of cation defects than that in stoichiometric phase. 

Furthermore, assuming that the diffusion coefficients of the cation and the anion are the same, D, = D, the relaxation rate can be rewritten for a z z-type electrolyte of concentration c as... 

Transference numbers are defined as ratio of ion motion to electrolyte motion. One possibility to calculate the transference number of a cation is the quotient of diffusion coefficient of the cation divided by difiusion coefficient of cation plus diffusion coefficient of anion ... 

The ionic conductivity was also evaluated by the GK approach. However, as the mechanism of charge transport in these systems is related with the process of self-diffusion of the ions it is also possible to relate electric conductivity with the diffusion coefficients of the cation and the anion, known as the Nernst-Einstein relation (NE) (Hansen McDonald, 1986) ... 

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