Accurate prediction of the lithium ion battery charge-discharge behavior is critically important in many battery applications¹, including for the high-power, high-energy battery packs used in electric vehicles. Accurate model predictions by, for instance, the classical porous electrode model developed by John Newman², require accurate electrolyte solution transport properties. In this work, the self-diffusivities of all species in LiPF₆/EC/DEC electrolyte solutions were characterized by PFG-NMR, and the protocol reported by Kim and Srinivasan³was used to evaluate the transport properties.

Experimental

All chemicals were purchased from BASF. LiPF₆ in EC/DEC (w/w 50:50) of different concentrations (1.5M to 0.1M) were prepared inside an argon-filled glove box and sealed in aluminum bottles before the PFG-NMR measurement.⁵

Diffusion coefficients (D) of the Li⁺, PF₆^- , and EC/DEC were measured by ₇Li ₁₉F and ₁H PFG stimulated echo NMR spectroscopy. Since resonances from EC, DEC are separated in one-dimensional ₁H spectra, separate diffusion coefficients could be measured. Experiments were performed at Larmor frequencies of 599.82 and 564.3 MHz for 1H and 19F, respectively, over the temperature range of 0 to 40 ^oC using a 14.1 T (600 MHz ₁H) NMR spectrometer (Agilent) equipped with a 5 mm z-gradient probe (Doty Scientific), which can generate a maximum gradient strength of approximately 31 T/m. The echo heights, S(g), recorded as a function of gradient strength, g, were fitted with the Stejskal-Tanner equation (equation 1),

RESULTS AND DISCUSSION

Shown in Figure 1 is the concentration dependence of self-diffusivity of LIPF₆/EC/DEC measured by PFG-NMR for Li⁺, PF₆^-, EC and DEC. Careful inspection of the data leads to several conclusions below:

I. the self-diffusivities of all species decrease as the concentration increases or the temperature decreases, which is expected from the Stokes-Einstein equation

II. the self-diffusivity values are ordered as follows EC≈DEC>PF₆^->Li⁺

III. the concentration dependence of self-diffusivity for PF₆^-is stronger than other species, especially at lower concentrations, e.g. 0.1 M to 1.0 M, while Li+ shows the weakest dependence.

The generalized-Darken relation (Equation 1) for translating self-diffusivities and of species i and j into binary diffusivities, D_ij, is given by equation (2):

where x_i, x_j, are component mole fractions. This relation was validated by Krishna and van Baten⁴. The resulting Fickian diffusivity values decrease as the concentration increases in a narrow range (3.7x10^-10 to 2.4x10^-10m²/s), and have similar magnitudes to these reported in EC/DEC or PC/EC/DMC as measured by electrochemical methods over a wide range of concentrations. Lundgren et al. ⁶ reported that the Fickian diffusivities of LiPF₆ in the same electrolyte decreased from 2.8x10^-10 m²/s to 2.0x10^-10 m²/s in the range of 0.5M to 1.5M, as measured by galvanostatic polarization experiments (red connected points, Figure 2); Valøen and Reimers ⁷ measured the Fickian diffusion coefficients of LiPF₆in a PC/EC/DMC mixture (10:27:63) (blue connected points, Figure 2).

Reference

1. L. Cai, R. E. White J. Power Sources14 (2011): 5985.

2. J. Newman, W. Tiedemann, Aiche Journal21 (1975), 25.

3. S. Kim, V. Srinivasan, J. Electrochem. Soc. 163(2016), A2977.

4. R. Krishna, J. M. van Baten, Ind. Eng. Chem. Res., 44(2005), 6939.

5. K. Han, N. Rajput, X. Wei, W. Wang, J. Hu, K. Persson, K. Mueller J. Chem. Phys., 141(2014), 104509.

6. H. Lundgren, M. Behm, G. Lindbergh, J. Electrochem. Soc., 162(2015), A413.

7. Lars Ole Valøena, and J. Reimersa, J. Electrochem. Soc., 152 (2005), A882.