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538  17 Liquid Nonaqueous Electrolytes

                                                          −
                        −
                    (OTf ), bis(trifluoromethylsulfonyl)imide (TFSI ), and bis(fluorosulfonyl)imide
                                                                 −
                    or inorganic anions such as hexafluorophosphate (PF 6 ) and tetrafluoroborate
                        −
                    (BF 4 ).
                    17.2.3.1 Physical Chemical Properties
                    17.2.3.1.1 Viscosity  ILs are much more viscous than common molecular
                    solvents, with viscosities ranging from optimal values between 10 and 50 mPa s
                    up to several thousand mPa s at room temperature [121, 122]. Viscosity generally
                    strongly depends on temperature and is determined by the nature of the anions and
                    cations used [123]. For example, for ILs with equal anions, the viscosity increases
                    with alkyl chain length of the cation, whereas for a given cation, the viscosity
                    does not increase exactly with anion size. Viscosity is also greatly affected by
                    impurities [124] (most commonly water), and therefore data reported, especially in
                    the early literature, may be not correct. Traces of water, which are present even in
                    hydrophobic ILs or other cosolvents, reduce the viscosity of the ILs, decreasing it
                    more strongly for cosolvents with higher dielectric constants, while the presence of
                    chloride impurities causes a sizeable increase in viscosity even at low concentrations
                    [124]. Addition of lithium salts to yield electrolytes in RTILs increases viscosities
                    in the case of common cations with aliphatic alkyl chains. The high viscosity can
                    influence the rate dependence of the discharge capacity [125].

                    17.2.3.1.2 Conductivity  ILs are sometimes expected to have high conductivities
                    because of their purely ionic nature. However, the conductivity of common aprotic
                                                    −1
                    ILs is usually in the range 0.1–18 mS·cm , so being significantly lower than those
                    of aqueous electrolytes, but higher than those of common organic solvent-based
                    electrolytes [121–123]. This is because of their high viscosities and large ion sizes
                    resulting in low ion mobility.
                      Conductivity is related to viscosity by Walden’s rule, that is, their product is
                    approximately constant, see also Section 17.4.5.3. The fractional Walden rule,
                              0
                                                −1

                          log(  ) = log(C ) + α· log(η )                       (17.2)
                              m

                    where α and C are constants and
                                     κ·M
                           0
                            = κ·V m =                                          (17.3)
                           m
                                      ρ
                    where κ is the specific conductivity, M the molar mass of an IL, ρ its density,
                    and V m the molar volume. The rule is a useful tool to estimate its viscosity from
                    easily accessible conductivity as a function of temperature. Plots according to
                    Equation 17.2 are linear. Different ILs show nearly the same slope α but different

                    log (C )-values. The deviation from the so-called ideal Walden rule is used as a
                    measure of ion–ion interaction. For details and a critique of this approach see
                    Ref. [126] and the literature cited therein. Temperature dependence of viscosity
                    may be interpreted in terms of Angell’s fragility concept [520–522]. This approach
                    is based on the deviation from a classical Arrhenius plot. Strong liquids such as
                    SiO 2 show nearly Arrhenius-behavior, caused by highly coordinating molecules,
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