Ionic liquids Walden plots

A linear regression was performed on the data, giving a slope of 1.08, an intercept of 1.922, and = 0.94. The fit of the data to the linear relationship is surprisingly good when one considers the wide variety of ionic liquids and the unloiown errors in the literature data. This linear behavior in the Walden Plot clearly indicates that the number of mobile charge carriers in an ionic liquid and its viscosity are strongly coupled. 

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 2.7 is a composite representation of the transport properties of ionic liquids of different types intended to show the relation between Walden behavior and the temperature dependence of conductivity. In Figure 2.7a we show, in this Walden representation, an alternative set of data emphasizing proton transfer salts (protic ELs). The plot in this case terminates at the universal high T limit for fluidity implied by Figure 2.3, 10" poise. 

Figure 2.10 Dependence of the cohesion of salts of weakly polarizable cations and anions, assessed by Tg value, on the ambient temperature molar volume hence on interionic spacing [(r -i- r) V ]. A broad minimum in the ionic liquid cohesive energy is seen at a molar volume of 250 crrPnmr, which corresponds to an interionic separation of about 0.6nm, assuming face-centered cubic pacidng of anions about cations. The lowest Tg in the plot should probably be excluded from consideration because of the non-ideal Walden behavior for this IL (MOMNMgE BF ) [15]). The line through the points is a guide to the eye. The data for open triangles are from Sun, Forsyth, and MacFatlane [42].

The relationship between conductivity and viscosity may be viewed through the use of a Walden plot (log A versus log (1// )) [61]. Plotting the molar conductivity (A) instead of the absolute conductivity (k), to an extent, normalizes the effects of molar concentration and density on the conductivity and, thus, gives a better indication of the number of mobile charge carriers in an ionic liquid. Fig. 3.6-4 shows the Walden Plot for the data in Tables 3.6-5-3.6-8. Data for each of the various types of ionic liquids (haloaluminates, non-haloaluminate imidazoliums, ammoniums, other ionic liquids) were plotted separately on the graph. However, as is clearly shown in Fig. 3.6-4, no difference in the behavior of any of the types of ionic liquids was observed. 

Fig. 3.6-4 The Walden plot of the molar conductivity and viscosity data in Tables 3.5-4—3.5-8. ( ) haloaluminate ionic liquids, (A) non-haloaluminate imidazolium ionic liquids, (V) ammonium ionic liquids, (o) other ionic liquids. The line represents the ideal 1 1 Walden...

The Walden plot of the log(equivalent conductivity) versus log(fluidity) can be used to show how good an ionic liquid is (see section 3.2). Using this method, PILs have generally been shown as poor ionic liquids, though it is not possible to differentiate whether this is due to incomplete proton transfer, aggregation, or the formation of ion complexes. 

Figure 5. Walden plot of log(equivalent conductivity) against log-(fluidity). This plot uses the same designation of symbols as in Figure 4. The PILs are classified using the scheme of Angell and co-workers,with the solid line indicating good ionic liquid behavior, while below the line indicates poor ionic liquid behavior.

Schreiner C, Zugmann S, Hartl R, Gores HJ (2010) Fractional Walden rule for ionic liquids examples from recent measurements and a critique of the so-called Ideal KQ line for the Walden plot. J Chem Eng Data 55 1784-1788... 

Protic or aprotic Ionic Liquids [21]. Protic ionic liquids (PILs), as all other protic solvents can give away protons and, more important, can form hydrogen bonds. As a result, they are not necessarily fully dissociated and can be distUlated more easily (though still xmder extreme conditions) than aprotic Ionic Liquids (AlLs). Further, they are considered to be poor ILs in the sense that their electrical conductivity is lower than what is predicted by the Walden plot. FAN is a representative example of a PIL. 

Figure 1.3 Walden plot Pipper and modified Walden plot Howerl for a variety of ionic liquids. For the upper curve. tA is the ideal Walden plot line for KCl. IBl is the Walden plat taking account of ionic size, and ICl is the Walden plot if the conductivity...

Schreiner et al. recendy published a critique of the use of the Walden rule with ionic liquids [17]. They suggested that use of the enpirical approach from Stokes, Equation 1.7. explains the observed deviations from the so-called ideal Walden plot, since each salt will have a different value of C and a ... 

Fig. 3.4 Walden plots for proton conductors. The ideal line is for 0.1 mol KCl. Data for sulfuric acid, phosphoric acid, and the pseudo-ionic liquid of methylimidazole and acetic acid were taken from...

Fig. 7.11 The Walden rule for the ionicity of Walden plot log(A) versus og(rf ) of the Li[N(Tf)2]/ MAc DES at A)LiTFsi =1/4 filled circle and Pyrrolidinium nitrate protic ionic liquid [HPyr][NO ] and its mixture with propylene carbonate ([HPyr][N03] + PC) hinaiy mixtures as a function of the temperature at Xpu.=0.25 filled triangle, 0.10 open square, 0.22 filled square, 030 Reverse filled triangle, 0.50 open diamond, 0.80 open circle, 1. Reproduced from [40] with permission from Elsevier...

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