Liquid molar ionic conductivities

For liquid electrolytes, ionic conductivity, self-diffusivity, and viscosity are three key properties. Though originally based on dilute aqueous electrolyte solutions, the Walden rule [52] has been proposed as a tool to provide insight to the proton transfer and ion association. The rule suggests that the molar cmiductivity of an electrolyte, A, is proportional to the fluidity, which can be expressed as the inverse of the shear viscosity i/. In other words, the product of the molar conductivity and viscosity of an electrolyte is a constant, as shown in (3.10). 

Such a chemical approach which links ionic conductivity with thermodynamic characteristics of the dissociating species was initially proposed by Ravaine and Souquet (1977). Since it simply extends to glasses the theory of electrolytic dissociation proposed a century ago by Arrhenius for liquid ionic solutions, this approach is currently called the weak electrolyte theory. The weak electrolyte approach allows, for a glass in which the ionic conductivity is mainly dominated by an MY salt, a simple relationship between the cationic conductivity a+, the electrical mobility u+ of the charge carrier, the dissociation constant and the thermodynamic activity of the salt with a partial molar free energy AG y with respect to an arbitrary reference state ... 

One-dimensional ion conduction is achieved for columnar liquid crystalline ionic liquids 10a,b [29]. In the macroscopically ordered states of these columnar materials, ionic conductivities parallel to the columnar axis (ay) is higher than those perpendicular to the axis (ox)- For example, compound 10b shows the conductivities of 3.1 X 10 S cm (ay), 7.5 x 10 S cm (cJx), and anisotropy (ay/ Qx) of 41 at 100°C. These materials function as self-organized electrolytes. They dissolve a variety of ionic species such as lithium salts. Compound 10b containing LiBp4 (molar ratio of LiBp4 to 10b 0.25) exhibits the conductivities of... 

What is the stmcture of neat ionic liquids. Even though the stmcture of liquids, such as water, has been studied for many years, the study of room-temperature ionic liquids is still in its infancy [58]. Purified [BMIM][PFj], probably the most studied IL, has been shown to be purely monophasic, with no aggregates, but to have a local stmcture [47]. Imidazolium groups are positioned in pairs with a plane-to-plane separation of 4.5 A. The stmcture of ILs is also characterized by a degree of anion-cation association. Thus, in [EMIM][NTf2] and [BP][NTf2], the self diffusion coefficients of the anions and the cations measured by pulsed-gradient spin-echo N M R are superior to the diffusion coefficients deduced from the molar conductivity, which demonstrates the existence of ion pairs which cannot contribute to the ionic conduction [53]. 

Subsequently, this empirical law has been linked to the ionic conduction model in liquid electrolytes involving electrophoretic and relaxation effects, which are found to be very strong in concentrated solutions (see section 4.2.2.1). For a 1-1 strong electrolyte solution, the molar conductivity of an ion is shown in the following equation ... 

Now ionic conduction in a full cell actually occurs in a region of length kfs = 1 - 21h, where is the effective thickness of the inner region, next to the electrode, into which ions cannot fully penetrate. Because of the finite size of ions, the minimum steric but not necessarily electrical value of Ih is an ionic radius. Except for unrealistically thin cells, the distinction between 4 and I is not important for most circuit elements and will usually be neglected hereafter. It should be mentioned, however, that in the study of thin (sometimes monomolecular) membranes in the biological field, using high-molarity liquid electrolyte electrodes, the distinction may be important. We may now write the expression for as... 

The conductance of an electrolyte solution is a property that determines the extent of movement of all ionic species in the solution upon the application of an electric field, resulting in the flow of the current through the solution. A complementary property is defined, the trans-ferance number, which expresses the relative extent to which only one kind of ion contributes to the charge transport. The conductance is the sum of the ionic conductances, whereas the transferance numbers depend on their ratio. Conductance yields unique information as to the nature of the structure of electrolytes, their equilibria and the ionic composition of liquids. Conductance depends on concentration and on external parameters, temperature and pressure. The concentration dependence of conductance indicates the ion-ion interactions such as the ion-pair formation and dissociation equilibria. On the other hand, the limiting values of the molar conductance (conductance/concentration) obtained by extrapolation for an infinitesimal dilution are functions only of the ion-solvent interactions. 

Electronic and ionic conduction processes in a liquid are influenced by the presence of solutes. These may have been added on purpose or they might represent impurities. Various measures for the concentration of a solute in a liquid are in use. For discussions within the framework of the kinetic theory, concentrations are given as number density of particles or as molar quantities. As a relative measure the mole fraction, X, is used. If a solution contains n moles of component A, ne moles of component B, n moles of component C, and so on, then the mole fraction of component A is given as... 

TABLE 34.9 Ionic Conductivity of Some 1 Molar Organic Liquid Electrolytes Used in Secondary Lithium Battery Systems... 

The viscosity of a liquid is closely related to the ion mobility, and the ionic conductivity of ILs is, to some extent, dependent on the viscosity. Over a relatively broad temperature range, the ionic conductivity of many ILs is inversely proportional to their viscosity. The product of the molar conductivity (A J and viscosity (ri), A r), varies over a relatively narrow range, about 500 200 ms cm cP/mol. This shows that their viscosity has a great influence on their ionic conductivity. 

Figure 12 compares the Arrhenius plot of the ionic conductivity of a LiC104 (IM), EC-DEC liquid electrolyte in comparison with that of a P(EO)ioLia04+10 wt% nano-particle SiOa composite membrane swelled (300 wt%) in an EC(25 % molar)-DEC solvent mixture. The conductivity of the two systems are comparable, reaching at 20 °C the values of 2.5x10" S cm" for the liquid electrolyte and 2.1x10" S-cm" for the swelled membrane [31]. 

Ionic liquid System Cation Anion(s) Temperature, (X Conduc- tivity (k), mS cm Conduc- tivity method Viscosity (n), cP Viscosity method Density (p), gcm Density method Molar conductivity fAJ, cm iT mor Walden product (An) Ref. 

Table 8.2 lists the conductivities, transport numbers and molar conductivities of the electrolyte A = olc, and ions Xj = t+A for a number of melts as weU as for 0.1 M KCl solution. Melt conductivities are high, but the ionic mobilities are much lower in ionic liquids than in aqueous solutions the high concentrations of the ions evidently give rise to difficulties in their mutual displacement. 

Ionic liquids with discrete anions have a fixed anion structure but in the eutectic-based liquids at some composition point the Lewis or Bronsted acid will be in considerable excess and the system becomes a solution of salt in the acid. A similar scenario also exists with the incorporation of diluents or impurities and hence we need to define at what composition an ionic liquid is formed. Many ionic liquids with discrete anions are hydrophilic and the absorption of water is found sometimes to have a significant effect upon the viscosity and conductivity of the liquid [20-22], Two recent approaches to overcome this difficulty have been to classify ionic liquids in terms of their charge mobility characteristics [23] and the correlation between the molar conductivity and fluidity of the liquids [24], This latter approach is thought by some to be due to the validity of the Walden rule... 

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