Effective Ionic Resistance in Battery Separators
Authors: Hattendorff Johannes , Landesfeind Johannes , Ehrl Andreas , Wall Wolfgang A. , Gasteiger Hubert A. 
Published: February 2020

A key to understanding the limitations of lithium ion batteries and for modelling battery performance is the knowledge of ohmic losses in the porous battery components. In the electrolyte filled pores of a separator, ohmic losses arise from ionic resistivity. In a porous electrode they originate from the network of ionic and electronic resistances.
We apply impedance spectroscopy to measure the high frequency resistance of separators and other battery components. In the literature, many values for effective ionic resistance of separators can be found [1,2,3,4], but their usefulness is sometimes diminished by unclear definitions of tortuosity as well as by the frequent lack of experimental details such as cell setup, electrolyte, and temperature. In general the high frequency resistance (HFR) of a porous separator can be described by:
HFR = d τ/ε 1/(A κ) + Rcontact ,
where d is the thickness, ε is the porosity, τ is the tortuosity, κ is the conductivity of the electrolyte and A is the area. We aim to give a theoretical background on HFR measurements in general and discuss setups that allow us to measure the ionic resistance (and thus tortuosity) in a porous separator with high accuracy. We will discuss sources of error such as contact resistance, Rcontact, and inductive noise, showing how 4-point-probe measurements, proper shielding of the cables, and well-defined geometry can substantially decrease measurement errors.
With regards to determining the tortuosity of porous separators, two measurement setups have been applied. The first consists of two Cu blocks with a defined effective area. The separators are placed between the blocks and wetted with electrolyte for measurement. The other approach uses a three layer Cu/separator/Cu pouch bag cell with 2x2 cm² electrodes, filled with electrolyte and vacuum sealed. The HFR between the Cu electrodes is then measured carefully in an electrolyte of EC:EMC 3:7 (wt%) with 1M LiPF6 and 2 wt% vinylene carbonate (LP572, BASF) at 25°C.
Some results for several layers of a 20 µm PP/PE/PP trilayer separator similar to Celgard C480 are shown in Figure 1. Repetitive measurements yield very similar results and also the two completely different setups do not deviate by more than a few percent. The slope of a linear regression fit gives the ionic resistance of one separator layer, amounting to 1.566 Ω cm2. From this and the porosity of ε = 0.47, we can calculate a tortuosity of τ = 3.41 or an equivalent MacMullin number of 7.26. We will present data for a range of typical battery separators, showing that the commonly used Bruggeman estimation of the tortuosity (τ = ε-0.5 equating to τ = 1.46 for this separator) is not valid for typical separators, as shown before in literature [5]. We hope that this updated separator data will be helpful for battery modelling in the future.
In our contribution, we will also present an impedance based method to quantify the ionic resistance in porous electrodes and its dependence on electrode morphology and compression.

References:

[1] P. Arora and Z. Zhang, Chemical Reviews, 104 (10), 4419-4462 (2004).
[2] K. Abraham, Electrochim. Acta, 38 (9), 1233-1248 (1993).
[3] K. K. Patel, J. M. Paulsen, J. Desilvestro, J. Power Sources, 122, 144-152 (1993).
[4] D. Djian, F. Alloin, S. Martinet, H. Lingnier, J. Y. Sanchez, J. Power Sources, 172, 416-421 (2007).
[5] I. V. Thorat, D. E. Stephenson, N. A. Zacharias, K. Zaghib, J. N. Harb, and D. R. Wheeler, J. Power Sources, 188 (2), 592-600 (2009).

Acknowledgment:

Funding for J. H. was provided by the BMBF (Federal Ministry of Education and Research, Germany), ExZellTUM project, grant number 03X4633A. J. L. also gratefully acknowledges the funding by the Bavarian Ministry of Economic Affairs and Media, Energy, and Technology for its financial support under the auspices of the EEBatt project.

Figure 1: Measurement of area specific high frequency resistance for multiple layers of polymer separator in two different setups and linear fit through 11 data points and linear regression line (R2 = 0.998).

Figure 1