How Temperature Affects Electrode Performance: Optimization Directions from Tortuosity Changes

1. Background: Electrode Tortuosity and Its Role in Battery Performance

Electrode tortuosity is a key parameter that quantifies the complexity of internal ion transport pathways within an electrode. It characterizes the ratio of the actual migration path of lithium ions through the pore network to the theoretical straight-line distance. Research confirms a direct correlation between electrode tortuosity and battery rate performance and cycle life: lower tortuosity means more efficient ion transport, enhancing fast-charging capability. Conversely, excessively high or unstable tortuosity increases polarization, accelerates capacity fade, and degrades cycle stability.

Temperature is a critical environmental variable that affects electrode tortuosity through two competing mechanisms. First, rising temperature reduces electrolyte viscosity, which—per the Stokes–Einstein relation—lowers ionic resistance and improves ion mobility through the pore network. Second, elevated temperature can degrade electrode microstructure: polymer binder chains soften, pore geometry changes, and differential thermal expansion between the active material coating and the current collector can cause delamination. Understanding the temperature–tortuosity relationship therefore provides both theoretical guidance for electrolyte formulation and a practical method for rapidly assessing electrode thermal stability.

2. Test Conditions & Methods

2.1 Test Equipment

Electrode tortuosity was measured using the IEST multi-channel ionic conductivity test system (EIC2400M-T), shown in Figure 1. The system provides:

• Four independent test channels, each with individual temperature control (range: 10–80 °C)
• High-purity argon atmosphere for electrochemical stability
• Multi-channel electrochemical impedance spectroscopy (EIS) testing of symmetric cells simultaneously
• Pressure range: 10–50 kg; frequency range: 100 kHz–0.01 Hz

Figure 1. IEST EIC2400M-T multi-channel ionic conductivity and electrode tortuosity test system — four independent temperature-controlled channels (10–80 °C), simultaneous EIS, 100 kHz–0.01 Hz frequency range

2.2 Test Sample

Graphite negative electrode sheets (graphite anode).

2.3 Test Procedure

Symmetric cells were assembled in the fixture sequence: electrode → separator → electrode → chamber sealed → quantitative electrolyte injected into each channel → wetting period completed → EIS data automatically collected by software → tortuosity derived by fitting and calculation.

2.4 Calculation Method — MacMullin Number

MacMullin Number Calculation Method:

\[
\tau = \frac{R_{ion} \cdot A \cdot \varepsilon \cdot \sigma}{d} \tag{1}
\]

\[
N_m = \frac{\tau}{\varepsilon} = \frac{R_{ion} \cdot A \cdot \sigma}{d} \tag{2}
\]

Where: \(\tau\) = tortuosity; \(R_{ion}\) = ionic resistance (\(\Omega\)) from EIS; \(A\) = electrode area (cm²); \(\varepsilon\) = electrode porosity; \(\sigma\) = electrolyte conductivity (S/cm); \(d\) = electrode thickness (cm).

To extract \(R_{ion}\) from the Nyquist plot (Figure 2): extend the low-frequency segment until it intersects the real axis; subtract the high-frequency real-axis intercept; multiply by three. This difference—3× the separation of the two real-axis intercepts—equals the electrode ionic resistance of the coating. Substituting \(R_{ion}\) into the equation above yields the MacMullin number and thus characterizes electrode tortuosity at each temperature.

Figure 2. Nyquist plot of a symmetric cell EIS spectrum

3. Results: How Temperature Affects Electrode Ionic Resistance and MacMullin Number

Figure 3. EIS spectra at (a) 25 °C, (b) 45 °C, (c) 60 °C, (d) 80 °C — arc compression reflects decreasing ionic resistance; MacMullin number derived from each spectrum

Fitting the EIS spectra at each temperature yields the ionic resistance values and corresponding MacMullin numbers shown in Table 1. Two clear regimes emerge:

25 °C → 45 °C: substantial improvement. The MacMullin number drops from 18.58 to 13.50—a decrease of 27.34%—reflecting a major reduction in electrode ionic resistance. The dominant mechanism is the temperature effect on electrolyte conductivity: as temperature rises, electrolyte viscosity decreases. Per the Stokes–Einstein relation, ion migration rate is inversely proportional to viscosity, so lower viscosity increases lithium-ion mobility and reduces the resistance of ion transport through the electrode pore network.

45 °C → 80 °C: near-plateau behavior. Further temperature increases produce almost no additional MacMullin number reduction (−0.14% at 60 °C; +1.7% at 80 °C). Despite continued electrolyte viscosity reduction at higher temperatures, two structural degradation mechanisms counteract the transport benefit:

• Binder softening: PVDF binders soften above approximately 60 °C, causing pore collapse and reduced pore diameter. This increases pore tortuosity and ion pathway length, partially offsetting the viscosity-driven resistance reduction.
• Differential thermal expansion: Mismatch between the thermal expansion coefficients of the active material coating and the metal current collector generates interfacial stress. At elevated temperatures this can cause localized delamination, creating electrochemically dead zones where electrolyte access is permanently blocked.

Figure 4. Line Chart of MacMullin Number Changes at Different Temperatures

This competing mechanism demonstrates that electrolyte viscosity optimization alone cannot overcome high-temperature performance limits. Electrode thermal stability— specifically binder thermal resistance and coating adhesion to the current collector—must be addressed in parallel.

4. Conclusion and Design Implications

Temperature significantly affects electrode ionic resistance and MacMullin number in graphite anodes, but the relationship is non-linear. The transition from a steep improvement regime (25–45 °C) to a plateau (45–80 °C) provides two actionable engineering insights:

• Optimal wetting temperature window: The 35–45 °C range offers the best viscosity reduction with minimal structural risk, suggesting this as the preferred temperature window for electrolyte injection and wetting during cell manufacturing. Temperatures above 45 °C provide diminishing returns on wetting improvement while increasing structural risk.
• High-temperature electrode design priorities: For batteries targeting operation above 45 °C, the MacMullin number plateau indicates that material-level improvements are required—not just electrolyte formulation changes. Specifically, three development directions are supported by these data:
  • Electrolyte formulations with superior high-temperature viscosity stability and reduced decomposition at elevated temperatures
  • Electrode processes with enhanced resistance to thermal deformation—improved binder anchoring and current-collector surface treatment to prevent delamination
  • Binder systems with higher softening temperatures than standard PVDF, such as cross-linked PVDF variants, polyimide binders, or SBR/CMC systems with improved thermal stability

Tortuosity testing across a temperature range provides a rapid, non-destructive method for ranking electrode thermal stability: materials whose MacMullin number continues to fall above 45 °C have better thermal structural stability than those that plateau or increase early.

5. FAQs