In battery continuum modelling, few parameters are as universally accepted—and as fundamentally flawed for modern cells—as a Bruggeman exponent of 1.5. While it is widely understood that tortuosity and porosity are distinct structural metrics, the industry consistently defaults to this idealized constant to bridge the gap between them. To understand why modern battery parameterization fails at high C-rates, we must first look at where this number comes from, and why it cannot survive the realities of physical electrode manufacturing.
The Origin of the 1.5 Assumption
The textbook Bruggeman exponent of 1.5 stems from a very specific theoretical geometry. It inherently assumes a system composed of monodisperse spheres arranged in a loose random packing.
The problem is that real electrodes look nothing like this. Modern calendered electrodes are engineered with different particle size powders and fibrous carbon nanotube networks, completely violating the mono disperse sphere assumption. More critically, the error introduced by this assumed exponent grows as the electrode is compressed, meaning the empirical relation fails exactly where accuracy matters most.
The Measurement Challenge
If the empirical assumption is flawed, the logical alternative is direct measurement. However, physically evaluating tortuosity in a real-world electrode is exceptionally difficult. Physical characterization techniques are expensive, time-consuming, and struggle to accurately resolve the nanoscale carbon-binder domain (CBD). Furthermore, these techniques only provide a static snapshot of an uncycled electrode. They cannot predict how tortuosity will change non-linearly when the active material breathes and expands in service, generating squeeze pressure that crushes the interstitial voids against a rigid casing.
Solving Parameterization Through Digital Twins
The solution to the parameterization bottleneck is abandoning empirical guesswork in favor of deterministic microstructural modeling. Rather than extrapolating transport metrics from a generic formula, advanced computational platforms now construct spatially resolved digital twins of the specific electrode under design.
Once the physical reality of the internal structure is accurately represented in a virtual environment, transport pathways can be explicitly tested. By simulating the movement of virtual random walkers directly within the unoccupied pore network, the true ionic tortuosity can be explicitly measured from their trajectories. Crucially, this same computational approach can be applied to the solid skeleton to measure electronic tortuosity, entirely removing the need for assumed contact exponents.
Conclusion
Parameterizing a battery model with a Bruggeman exponent of 1.5 is designing for a state that does not exist. By replacing static assumptions with direct computational measurements through a reconstructed digital twin, battery engineers can accurately predict transport limits even in heavily compressed, highly heterogeneous electrodes. It is time for cell design to reflect the physical reality of the microstructure, rather than the idealized mathematics of random sphere packing.
Kerem Buğra Batuş, Cell Design & Process Development
At AION Engineering, we accelerate lithium-ion cell development using AI-driven design and advanced technologies, delivering innovative, sustainable energy solutions for a better future