The operation of battery management systems requires that the transient conditions experienced by a battery cell in electrified vehicle applications can be accurately described through battery modeling [1]. Reliable data on the transport properties of electrolyte solutions, as functions of both salt concentration and temperature, are a prerequisite for accurate electrochemical modeling. Complicating the acquisition of such reliable data is the fact that Li-ion battery (LIB) electrolyte solutions can experience large concentration polarizations during battery operation, due to fairly low values of the Li⁺ cation transference number (t⁺) and the salt diffusivity (D), particularly during battery operation at high charge/discharge rates or at low temperatures. While modern computerized instrumentation makes specific conductivity and viscosity measurements routine, this is not the case for diffusivity and transference number measurements. In order to determine the latter two transport properties, we apply the in situ magnetic resonance imaging (MRI) technique [2] for the in-operando visualisation of the steady-state ion concentration in LIB electrolytes during the application of a constant current. Our results confirm that the concentration gradient developed is proportional to the applied current (Fig. 1) as described by the diffusion-migration equation under steady-state conditions (Eqn. 1), where i is the current density and F is the Faraday constant. Taking into account that ∂c/∂x  is the salt concentration gradient obtained from imaging, the task of determining t⁺(c) and D(c) is reduced to measuring of the concentration dependence of the diffusivity D(c). We showed previously that salt diffusivity can be accurately determined as the harmonic mean of the cation and anion diffusion coefficients as measured by pulsed-field gradient NMR (PFG NMR) [3]. By combining the PFG NMR and MRI techniques into one experiment, we can determine the salt concentration and the salt diffusivity of the electrolyte during the application of a constant current (Fig. 2). It can be readily seen that the diffusion coefficient has a significant dependence on the salt concentration, with the values of D measured at opposite ends of the cell varying by more than 60%. This conclusion is in good agreement with our previous results obtained by in situ, slice-selective NMR diffusion measurements [4]. On the other hand the lithium transference number varies less with salt concentration [3]. From the experimentally derived D and concentration profiles one obtains t⁺= 0.31 ± 0.03, by using Eqn. (1).

References:

(1)   T.R. Tanim, C.D. Rahn, and C.-Y. Wang, J. Dynamic Syst. Meas. and Control, 137, article # 011005 (2014).

(2)   C.E. Muir, B.J. Lowry, and B.J. Balcom, New J. Phys., 13, article # 015005 (2011).

(3)   A.K. Sethurajan, S.A. Krachkovskiy, I.C. Halalay, G.R. Goward, and B. Protas, J. Phys. Chem. B, 119, 12238 (2015).

(4)   S.A. Krachkovskiy, A.D. Pauric, I.C. Halalay, and G.R. Goward, J. Phys. Chem. Lett., 4, 3940 (2013).