Thermal Modeling

How radial thermal gradients drive degradation in cylindrical cells

The temperature at the jelly roll core and the can surface diverge under load. That gap is where capacity fade starts.

Abstract thermal gradient photography representing heat distribution in cylindrical cells

The jelly roll inside a cylindrical lithium-ion cell is not a thermally homogeneous object. During charging and discharging, electrochemical reactions generate heat in a distributed pattern across the electrode stack, and the thermal properties of the cell structure determine how that heat distributes spatially. For a cylindrical cell, the dominant spatial dimension is radial: heat must travel outward from the core to the can surface to escape, and the radial thermal conductivity of the electrode stack is significantly lower than the axial conductivity. The result is a radial temperature gradient that is a structural consequence of the cell geometry, not an anomaly.

What has become clearer from detailed degradation studies is that this radial gradient does not just describe the temperature distribution inside the cell. It actively drives differential degradation: the electrodes near the core age at a meaningfully different rate than the electrodes near the can surface, and that differential accumulates over hundreds of cycles into asymmetric capacity fade.

The geometry of heat in a jelly roll

A standard 18650 cell contains roughly 600 to 700 millimeters of electrode strip wound into a spiral with an outer diameter of 18 millimeters and a core mandrel diameter of 2 to 4 millimeters. The electrode stack cross-section is approximately 7 to 8 millimeters from the center to the can wall. Every layer of that spiral contributes heat during electrochemical operation, and the heat from the innermost layers must conduct outward through all the outer layers before reaching the can surface.

The key thermal property is radial conductivity, which for typical NMC/graphite cells is in the range of 0.3 to 1.0 W/m per Kelvin. This low value is determined primarily by the electrolyte-soaked separator material between electrode layers and the contact quality between layers under compression. Axial conductivity through the electrode tabs and collector foils is much higher, typically 20 to 50 W/m per Kelvin, but for a cell in a pack where cooling is applied to the can surface rather than the tabs, the axial pathway does not help remove the heat generated in the central layers of the spiral.

The resulting steady-state temperature profile under constant current load follows the solution to the radial heat equation for a hollow cylinder: the temperature rises from the can surface inward, with the gradient steepening as you approach the core. The exact profile depends on current, internal resistance distribution, and the thermal boundary condition at the can surface (which depends on how the pack is cooled).

Differential degradation: the SEI story

The most well-documented degradation mechanism linked to radial gradients is differential SEI growth on the graphite anode. SEI growth follows Arrhenius kinetics: the reaction rate scales with temperature according to an activation energy that has been measured in the range of 50 to 80 kJ/mol for common SEI-forming reactions in LiPF6-based electrolytes. This translates to roughly a doubling of growth rate per 8 to 12 degree Celsius temperature increase.

In a cell with a 10 degree Celsius core-to-surface gradient during fast charge, the innermost electrode layers experience consistently higher temperatures than the outermost layers. Over time, the SEI thickness on inner-layer anodes grows faster, the capacity of those layers is consumed more quickly by lithium trapping in the SEI, and the resistance of those layers increases. This shows up in cell-level measurements as capacity fade and increasing internal resistance, but the actual degradation is spatially concentrated at the core, not uniform across the electrode area.

This spatial concentration matters for two reasons. First, it means that surface impedance measurements (which interrogate the surface-adjacent electrode layers most directly) underestimate the actual state of the core-adjacent layers, particularly in older cells. Second, it means that degradation models assuming spatially uniform aging will mispredict the fade trajectory, particularly in the second half of cell life when the nonlinearity of core aging starts to dominate the overall capacity loss curve.

Lithium plating concentration at the core

A second gradient-driven degradation mechanism is more acute: lithium plating risk at the core. Lithium plating occurs when the anode potential drops to or below the lithium metal equilibrium potential during fast charge, meaning that lithium is deposited as metal on the anode surface rather than intercalating into the graphite. This is most likely to occur at high C-rates, high SoC, and low temperature, because all three conditions reduce the kinetics of lithium intercalation and push the anode to lower potential.

The radial temperature gradient creates a counterintuitive local condition: the core of the cell runs hotter on average, which helps kinetics. But the current distribution in the jelly roll is also non-uniform due to the different path lengths through the electrolyte for inner and outer electrode layers. In a tightly wound spiral, the effective ionic resistance from the inner electrode layers to the separator is slightly different from the outer layers. Combined with the thermal gradient, this creates a complex local electrochemical environment at the core that can, in some charging windows, be more favorable for plating than the surface-adjacent layers.

This is not a universal finding across all cell designs and operating conditions. We would not argue that core lithium plating is always worse than surface plating. The point is that the thermal and electrochemical non-uniformity in the cell creates a landscape of degradation risks that varies spatially, and a spatially uniform degradation model does not capture it accurately.

Observable signatures of radial-gradient-driven aging

If you are trying to diagnose whether radial gradient effects are contributing significantly to degradation in a cell or pack, there are a few signatures to look for in electrochemical characterization data.

The most informative measurement is differential capacity analysis (dQ/dV) at multiple C-rates. A cell with significant spatially non-uniform degradation will show peak position shifts and peak broadening that differ between low-rate and high-rate measurements more than a uniformly aged cell would. The reason is that the inner and outer electrode layers contribute to the total cell capacity at slightly different SoC windows due to their different resistance states, and this difference becomes more visible when you spread the measurement over time (low rate) versus compress it (high rate).

Electrochemical impedance spectroscopy (EIS) at multiple temperatures also carries information about spatial degradation heterogeneity, though interpreting it requires a model. The charge transfer resistance and Warburg diffusion elements in an EIS spectrum are weighted averages over the entire electrode area, but a cell with non-uniform aging has a distribution of those elements rather than a single value. This distribution broadens the features in the Nyquist plot in characteristic ways.

Implications for charge protocol design

Understanding radial gradient effects does not necessarily mean you need to model the full spatial temperature distribution inside every cell in real time. What it does mean is that your charge protocol limits should be derived from a model that accounts for the gradient, not from a surface-temperature-only measurement.

The practical outcome: charge protocols that reduce current not just based on surface temperature but based on estimated core temperature will decelerate the gradient-driven degradation mechanisms we described. The current reduction happens at the right time, for the right reason, based on the actual thermal state of the cell, rather than a conservative margin applied to the surface measurement.

Over the lifecycle of a two-wheeler pack that undergoes daily charge cycles, the compounding effect of protocol choices on cumulative degradation is substantial. A protocol that maintains the core within a tighter temperature envelope through each charge event, compared to one that allows the core to run 10 to 12 degrees Celsius above its surface, will see meaningfully slower capacity fade not because it is charging slower on average, but because it is distributing the aging more evenly across the electrode stack. That is the thermal gradient argument translated into pack longevity terms.

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