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17.4 Bulk Properties  599


                  5


                  4
                κ / (mS/cm)  3



                  2

                  1

                   0     5     10     15    20     25
                                 trial number

               Figure 17.16  Specific conductivity κ of LiBOB in
                               ◦
               EC/PC/DMC/EA at −25 C measured at compositions sug-
               gested by a simplex algorithm, showing results for subse-
               quent trials.
               will change, as DRS is able to estimate the concentration of ion-pairs and other
               aggregates of ions in highly concentrated solutions. Such measurements will help
               to resolve the transference number controversy reported [528]. In the literature,
               the conductivity receives the majority of attention because it is easy to measure.
               But for a full characterization, ionic transference numbers are required for an
               understanding of charge transport by ions in rechargeable lithium-ion batteries.
               An electrolyte with n species needs n(n − 1)/2 concentration-dependent transport
               properties, where n is the number of independent species [435].
                Concentration gradients which develop across a lithium-ion cell during current
               flow are defined by the value of the lithium transference number. Precipitation of
               the salt at the anode or depletion of electrolyte at the cathode with resulting cell
               failure are possible consequences at sufficiently high currents. A low or negative
               transference number thus leads to poor high-rate performance and entails a limit on
               the cell’s power output. A high lithium-ion transference number can significantly
               reduce the effects of concentration polarization, and thus decrease the potential
               waste in the cell. Several definitions of transference numbers exist:
                For a completely dissociated electrolyte, the transference number of an ion is ‘the
               number of faradays of electricity carried by the ion concerned across a reference
               plane, fixed with respect to the solvent, when one faraday of electricity passes across
               the plane’ [436].
                So it can be written as
                             I ±  ∧ Q ±  ∧ Λ ±
                           =   =     =                                   (17.59)
                      t ±
                             I    Q    Λ
                    t + + t − = 1                                        (17.60)
               with I ± , Q ± , and Λ ± as the current, charge, and ionic conductivity of the cation or
               anion, respectively, that is, carried by that ion.
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