Ionic liquids Stokes-Einstein equation

The Walden rule is interpreted in the same manner as the Stokes-Einstein relation. In each case it is supposed that the force impeding the motion of ions in the liquid is a viscous force due to the solvent through which the ions move. It is most appropriate for the case of large ions moving in a solvent of small molecules. However, we will see here that just as the Stokes-Einstein equation applies rather well to most pure nonviscous liquids [30], so does the Walden rule apply, rather well, to pure ionic liquids [15]. When the units for fluidity are chosen to be reciprocal poise and those for equivalent conductivity are Smol cm, this plot has the particularly simple form shown in Figure 2.6. 

Figure 1.4 Comparison of the acmal case of diffusion in an ionic liquid and the model from which the Stokes-Einstein equation is derived.

This work, along with all other diffusion studies in ionic liquids, depends on the validity of the Stokes-Einstein equation and here lies the main discrepancy with the analysis of most difhision coefficient data in ionic liquids. To be strictly accurate, the distance term, R, in Eqnation 1.3 should be replaced by the correlation length, which is only really equivalent to the radius of the diffusing species when the size of the diffusing particle is large conpared with the solvent particles [27]. Eqnation 1.3 was initially derived to describe the random movement of... 

Classical diffusion can be described by Equation 1.3 when the radius of the sphere is small conpared with the mean free path. With ionic liquids, the mean free path can be less than the radius of the ion, and hence the ion can be considered as moving via a series of discrete jumps where the correlation length is a measure of the size of the hole into which the ion can junp. Appreciating why deviations from the Stokes-Einstein equation occur shows why a model based on holes becomes appropriate. The approximate nature of the Stokes-Einstein equation is often overlooked and is discussed in detail by Bockris and Reddy [5, p. 379]. There are numerous aspects that need to be taken into account, including that it is derived for non-charged particles, it is the local viscosity rather than the bulk that is required, and the ordering effect of the ions exhibits an additional frictional force that needs to be explained. 

The Stokes-Einstein equation [77] is generally applicable for molecular liquids and ILs, at least semi-quantitatively, for analyzing the diffusion coefficient D. Water is ubiquitous in the environment. It was shown that water induced accelerated ion diffusion compared to its effect on neutral species in ionic liquids [78]. We also observed that IL conductivity is significantly increased when [Bmim][BF4] is... 

The conductivity of ionic liquids can be modeled in the same manner as the viscosity, i.e. despite the high ionic strength of the liquid, ionic migration is limited by the availability of suitably sized voids [130]. Since the fraction of suitably sized holes in ambient temperature ionic liquids is effectively at infinite dilution, migration should be described by a combination of the Stokes-Einstein and Nernst-Einstein equations. This is explained in greater detail in Chapter 11.3 on process scale-up but it is sufficient to say that an expression can be derived for the conductivity, k... 

This equation was deduced in Section 4.4.8. It is of interest to inquire here about its degree of appiicabiiity to ionic liquids, i.e., fused salts. To make a test, the experimental values of the self-diffusion coefficient D and the viscosity tj are used in conjunction with the known crystal radii of the ions. The product D r//T has been tabulated in Table 5.22, and the plot of D tj/T versus 1/r is presented in Fig. 5.31, where the line of slope k/6n corresponds to exact agreement with the Stokes-Einstein relation. ... 

Harris KR (2010) Relations between the fractional stokes- einstein and nemst- einstein equations and velocity correlation coefficients in ionic liquids and molten salts. J Phys ChemB 114 9572-9577... 

---