Home
All posts

· Electrode manufacturing

Solving the electrode calendering U-shape puzzle

Companion note to the preprint Capturing the calendering U-shape in lithium-ion electrode thermal conductivity. arXiv:2607.11521 · PDF

Lithium-ion cells depend on calendered electrodes for volumetric energy density. Predicting what compression does to through-plane thermal conductivity (λeff) turns out to be harder than it looks. On first thought, a monotone relationship is expected: press harder, conductivity should rise.

Measurements disagree. Through-plane conductivity drops through the early stages of calendering and only recovers at high compaction. This produces a U-shape with a clear minimum. Porosity-only closures cannot produce this relation. Because static contact models still rise, the initial drop must come from a mechanism that offsets contact growth. This is the loss of favorable particle orientation for through-plane heat flow, so one useful transport pathway is being lost during early compaction. Note: For the quasi-isotropic NMC cathode, contact-network evolution reproduces the curve. Early damage to the contact/bridge network is followed by recovery or interlocking at higher compaction.

The physics of particle reorientation

The missing mechanism is graphite anisotropy. Conductivity within the graphene planes is high; perpendicular to them it is poor, by more than an order of magnitude. Compression brings particles closer, but it also rotates them, laying the flakes flat against the current collector.

Flat flakes present their poor through-plane axis to the direction heat must travel. Early calendering therefore trades a shrinking pore volume for a worsening particle orientation, and orientation wins. Once most flakes are already aligned, further reorientation contributes less. At that point, growing particle-particle contact starts to dominate and the curve turns upward.

The draft captures this with a calendering-aware Zehner–Bauer–Schlünder closure: a compression-indexed contact term φ(Π) on a Knudsen-corrected ZBS base, with the orientation effect entering as a bounded correction rather than a free-floating fit parameter. Across 27 calendering states the mean absolute percentage error falls from 31.1% to 4.5%.

What that number is and is not. 4.5% MAPE is in-sample across 27 states of one anode chemistry. It shows the closure can represent the U-shape; it does not establish that it transfers to other formulations, cathodes, or coating thicknesses. Held-out validation across chemistries is the obvious next test, and the honest reason to call this a draft.

Where does the accuracy come from? The draft's ablation (Table 3) answers per component. M0 is the zero-fit ZBS reference, M1 adds a fitted constant contact fraction, and M2 adds the process-dependent φ(Π) term. The figure below shows the measured error of each stage, per electrode family.

Grouped bar chart of mean absolute percentage error for three closure stages across four electrode families and their average. The full process-dependent closure M2 reduces the average error from 31.1 percent at the zero-fit stage to 4.5 percent. M0 · zero-fit M1 · constant contact M2 · φ(Π) 10% 20% 30% 40% 50% 1.8 5.4 1.4 9.4 4.5 graphite(thin) graphite(thick) NMC622 NMC811 average MAPE over all calendering states, per closure stage
Measured, not schematic: ablation MAPE from Table 3 of the draft. The constant contact fraction (M1) removes most of the offset (31.1% → 13.5% on average); the process-dependent φ(Π) term (M2) is what reproduces the U-shape and brings the average to 4.5%.

Interactive · Calendering

Compress the electrode. Particles flatten and rotate toward the horizontal; porosity falls monotonically. The dot tracks the calendering-aware prediction, which dips before it recovers (unlike the two monotone baselines).

0%
Porosity ε
45.0%
λeff (through-plane)
0.60 W/mK

Curves are schematic functional forms chosen to reproduce the qualitative behaviour of each closure, not the fitted model or the measured data. Read the shapes, not the values.

Cross-section of an electrode: graphite particles flatten and align as the press plate descends. Through-plane conductivity versus compaction for three closures. Only the calendering-aware model produces a minimum. 0% 60% Compaction Π 0.2 2.0 λ_eff (W/mK) Porosity-only Static contact Calendering-aware ZBS

The minimum appears when two monotone effects act against each other. Two monotone processes (falling porosity and worsening orientation) cross in their influence on the same transport path. Any closure that carries only one of them is forced to be monotone, and will be wrong on one side of the minimum or the other.