Rapid Screening of Electrolyte Rate Performance via Electrode Tortuosity and the McMullin Number

1. Preface

This paper presents a rapid, practical method to evaluate lithium-ion electrolyte performance by linking electrolyte rate capability with electrode sheet tortuosity and the McMullin number. Combining symmetric-cell electrochemical impedance spectroscopy (EIS) with electrode tortuosity measurement enables quantification of how pore microstructure (pore size, throat diameter, connectivity) and electrolyte properties (viscosity, wettability) govern ion transport and battery rate behavior. The approach accelerates electrolyte R&D by providing an early screening metric that correlates with full-cell rate tests.

2. Introduction: Why Electrode Tortuosity Matters for Electrolyte Rate Performance

The electrolyte is the ionic highway inside a lithium-ion cell. Fast charge and discharge requires rapid Li\(^+\) transport through: (1) the bulk liquid phase, (2) desolvation and crossing the SEI membrane, and (3) porous electrode pathways to active particles. The microstructure of electrode coatings — especially pore connectivity and geometric complexity — determines the actual path Li\(^+\) must follow. This geometric impediment is captured by electrode tortuosity (\(\tau\)), commonly defined as the squared ratio of actual transport path length to straight-line coating thickness: \(\tau = (L’/L)^2\).

Because direct porosity measurement is often complex in production settings, the MacMullin number (\(N_m = \tau/\varepsilon\)) — the tortuosity-to-porosity ratio — is widely used as a convenient, physically meaningful descriptor of effective ion transport resistance inside porous electrodes. (Note: some literature variants spell it McMullin number or mcmullin number; all refer to the same concept, named after R. A. MacMullin.)

For a battery to achieve excellent rate performance, the electrolyte needs high lithium-ion transport capacity, and the speed of that transport is directly related to electrolyte performance.^[1] As shown in Figure 1, the charging process involves four stages: (1) solvated lithium forms and diffuses under concentration and potential gradients; (2) at the SEI interface, solvated Li⁺ undergoes desolvation; (3) desolvated Li⁺ transports through the SEI membrane; and (4) Li⁺ diffuses through the active material body to form an intercalation compound.^[2,3]

Fig. 1. (a) Schematic of lithium-ion battery charging process — four stages governing electrolyte rate performance: solvation/diffusion, SEI desolvation, SEI transport, active material intercalation; (b) Energy barrier profile at each stage^[3,4]

3. Principle: From EIS to MacMullin Number

The effective ionic conductivity in a porous electrode, \(\sigma_{eff}\), links bulk electrolyte conductivity \(\sigma\), porosity \(\varepsilon\), and electrode tortuosity \(\tau\) through the Bruggeman-type relation that underpins the MacMullin number:

\(\sigma_{eff} = \sigma \frac{\varepsilon}{T}\)

Rearranged, the MacMullin number equals \(N_m = \tau/\varepsilon = \sigma/\sigma_{eff}\). Practically, \(\sigma_{eff}\) is obtained from EIS on a symmetric cell (two identical electrodes separated by the same porous coating):

1. Assemble a symmetric cell and run EIS (frequency sweep, e.g., 100 kHz to 0.01 Hz).

2. Fit the low-frequency intercepts to extract ionic resistance \(R_{ion}\) of the electrode coating from the Nyquist plot.

3. Compute \(\sigma_{eff}\) from geometry: \(\sigma_{eff} = d / (R_{ion} \cdot A)\), where \(d\) is coating thickness and \(A\) is electrode area.

4. Calculate MacMullin number: \(N_m = \sigma / \sigma_{eff}\) (with \(\sigma\) from bulk electrolyte conductivity measurement).

This electrochemical route captures not only electrode geometry but also real wetting and electrolyte microphysics (viscosity, surface tension, solvation effects), making Nm a robust predictor of in-cell rate behavior — and a faster alternative to full-cell rate cycle tests for initial electrolyte screening.

4. Test Conditions & Methods

4.1 Test Equipment

Symmetric cell assembly and EIS testing used the IEST EIC1400 Electrode Sheet Tortuosity Tester & Separator Ion Conductivity Tester (Figure 2), which integrates four battery assembly fixtures and provides four-channel simultaneous EIS testing. Specifications: pressure range 0–20 kg; frequency range 100 kHz–0.01 Hz.

Fig. 6. Rate-capacity retention curves for three electrolyte formulations at 0.5C–10C — Formula 2 (lowest Nm) achieves best 10C retention (93.92%); Formula 3 (highest Nm) shows lowest retention (89%)

Figures 5 and 6 and Table 1 demonstrate that the MacMullin number rank directly correlates with the rate performance rank of soft-pack batteries assembled with the same electrode sheets but different electrolytes. At 10C, the capacity retention is 90.55% (Formula 1), 93.92% (Formula 2), and 89% (Formula 3) — exactly matching the Nm rank (F2 < F1 < F3). This confirms that the electrode sheet McMullin number, measured by EIS tortuosity testing, can predict battery rate performance — enabling rapid electrolyte formulation screening without full cycle testing for each candidate.

6. Practical Implications for Electrolyte and Electrode R&D

• Rapid electrolyte screening: Measuring MacMullin number via symmetric-cell EIS provides a fast, low-material-consumption way to rank electrolyte candidates before committing to full-cell rate tests. This can shorten electrolyte development cycles significantly.

• Process optimization — wetting issues: Differences in McMullin number across electrolyte concentrations or formulations can reveal wetting problems (e.g., poor penetration into electrode nanopores) that are addressable by adjusting electrolyte viscosity, adding wetting agents, or tuning liquid-fill process parameters.

• Electrode design feedback: If MacMullin number remains high despite a well-optimized electrolyte, the bottleneck is electrode geometry — optimize electrode porosity, particle size distribution, or calendering pressure to reduce tortuosity.

• Battery simulation inputs: Nm serves as a compact, physically meaningful input parameter for porous-electrode models and multi-physics battery simulations to predict rate capability and internal resistance without full-cell experiments.

7. Limitations & best practices

• Geometry accuracy: Accurate coating thickness (\(d\)) and electrode area (\(A\)) measurements are critical when computing \(\sigma_{eff}\); calibrate thickness measurement regularly.

• Wetting interpretation: Electrochemical Nm reflects real wetting as well as geometry; a high McMullin number could result from incomplete electrolyte wetting into nanopores rather than from geometric tortuosity alone. Complement with FIB-SEM or X-ray CT imaging when geometric versus wetting contributions need to be separated.

• Reproducibility conditions: Maintain consistent test temperature and assembly pressure across measurements; both influence ionic conductivity and therefore the calculated MacMullin number.

8. Summary

This study assembled symmetric cells and pouch cells with three LiPF\(_6\) electrolyte formulations and demonstrated a clear correlation between electrode sheet McMullin number (\(N_m\)) — measured by EIS-based tortuosity testing — and battery rate performance at 0.5C to 10C. The MacMullin number rank (Formula 2 < Formula 1 < Formula 3) matched the rate capacity retention rank, confirming that \(N_m\) from symmetric-cell EIS can serve as a reliable, fast, non-destructive screening metric for electrolyte development. Beyond electrolyte screening, the electrode tortuosity test can be applied to study the effects of electrode formulation, porosity, active material particle morphology, separator type, and manufacturing process parameters on lithium-ion battery performance.

9. References

[1] Li N, Chen Z P, Ren W C, et al. Flexible graphene-based lithium ion batteries with ultrafast charge and discharge rates[J]. Proceedings of the national academy of sciences of the United States of America, 2012, 109 (43): 17360-17365.

[2] Yamada Y, Furukawa K, Sodeyama K, et al. Unusual stability of acetonitrile-based superconcentrated electrolytes for fast-charging lithium-ion batteries [J]. Journal of the American chemical society, 2014, 136(13): 5039-5046.

[3] Caiwl, Yao Y X, Zhu G L, et al. A review on energy chemistry of fast-charging anodes [J]. Chemical society reviews, 2020, 49 (12): 3806-3833.

[4] Yin ZG, Wu NN, Cao MH, et al. Progress of electrolyte for fast-charging lithium-ion batteries[J]. New Energy Progress, 2024, 12(2): 216-226.

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