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. 

Figure 3.6-4 The Walden plot of the molar conductivity and viscosity data in Tables 3.6-3-3.6-5. The line represents the linear regression fit of the data.

Another conceptual tool used in the study of glassy systems is the Walden plot [177]. Its use is based on the observation that if ions in an ionic system move independently, then the product of their viscosity and conductivity should... 

This equation is known as Walden s rule. The constant is called the Walden product. Although the salt contents of bulk ILs are very high (about 3-7 mol L-1), the Walden plots for a variety of ILs are similar to that of a conventional diluted system [113]. This observation indicates that ILs are ionized effectively, even in the bulk. However, ILs also contain ion aggregates which do not contribute to the ionic conductivity. Recent research shows more specifically how much ILs are ionized [114]. 

Equilibrium MD simulations of self-diffusion coefficients, shear viscosity, and electrical conductivity for C mim][Cl] at different temperatures were carried out [82] The Green-Kubo relations were employed to evaluate the transport coefficients. Compared to experiment, the model underestimated the conductivity and self-diffusion, whereas the viscosity was over-predicted. These discrepancies were explained on the basis of the rigidity and lack of polarizability of the model [82], Despite this, the experimental trends with temperature were remarkably well reproduced. The simulations reproduced remarkably well the slope of the Walden plots obtained from experimental data and confirmed that temperature does not alter appreciably the extent of ion pairing [82],... 

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.

The Walden plot is of the equivalent conductivity against the log of the fluidity (inverse viscosity) and is shown in Figure 5. The Walden plot is a way to represent the ionicity of the ILs, with those having good ionicity likely to have other related good properties, such as high ionic conductivity. 

The ion—ion spacing in ideal ILs can be represented using the molar volume, It was previously shown on the Walden plot in Figure 5 that PILs are not ideal and instead may have some association of the ions and/or incomplete proton transfer from the acid to the base. Hence, Fm only gives an indication of the ion—ion spacing for PILs. These PILs had generally lower molar volumes than had been seen for the AILs reported by Angell et al. ... 

A nonstoichiometric mixture was produced from a poly-oxometalate and a heteropolyadd to make a proton conductor with the general formula of H3 xM POM. On the Walden plot, this mixture is above the line predicted by the classical Walden rule and in the superionic liquid region, indicating conduction is occnning by a more efficient conduction mechanism than the Walden mechanism, possibly by the Grotthus mechanism. ... 

From the compiled vapor pressure and conductivity data, the evaporation enthalpy and the activation enthalpy for proton conduction were calculated as a function of composition. The critical temperature according the Vogel-Tammann-Fulcher law was determined from the viscosity data and compared with glass transition temperatures from other studies using NMR spectroscopy. A correlation between dynamic viscosity and molar conductivity was found. As expected, a considerable decoupling between ionic conduction and viscous flow can be determined from a Walden plot, which is based on proton-hopping mechanisms in phosphoric acid. 

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 ... 

An alternative approach has been to explain deviations from the Walden plot as arising from... 

As a qualitative means to investigate the ionic nature of acid-base systems, various techniques have been employed such as one- or two-dimensional nuclear magnetic resonance (NMR) spectroscopy [31], infrared (IR) spectroscopy [32], the Walden plot [33], the ratio of molar conductivities AjmpMNMR (determined by electrochemical impedance spectroscopy and pulse-field-gradient spin-echo NMR, respectively) [34], Some of these will be discussed below. 

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