Lithium Battery Research
Li Ion Battery Aging, Degradation, and Failure
Stephen J. Harris  sjharris(at)


Tortuosity in Li-ion battery porous electrodes

Martin Ebner and Vanessa Wood
ETH Zurich



Failure Statistics NEW!

Internal Pouch T NEW!


Diagnostic studies on NCA/Gr cells

Tortuosity of Porous Electrodes

Mechanics of Silicon Anodes

Nanoparticle Morphology Evolution

The Materials Project

Li Transport
in Graphite Electrode


Strain Maps

X-Ray Tomography

LiCoO2 Particle 1

Molecular Dynamics

Tin Oxide Nanowires

Neutron Imaging

Dendrites and Fracture


Publications by Stephen J Harris


The tortuosity (τ) of the pore structure in a lithium ion battery is a parameter that describes the influence of the morphology of the electrode on the effective transport properties of lithium ions in the electrolyte. Knowing the tortuosity of a porous electrode makes it possible to ascertain whether performance limitations in a battery stem from its microstructure.

Tortuosity of porous electrodes has traditionally been difficult to quantify. Recently, advances in 3D visualization techniques such as x-ray tomographic microscopy and focused-ion beam scanning electron microscope tomography have made it possible to determine the tortuosity of porous electrodes [1]. To calculate tortuosity, a sub-volume of a porous electrode is visualized and numerical diffusion simulations are performed. These techniques that enable the direct visualization of the microstructure provide extensive insights into porous electrodes and the effect of their structure on battery performance. For example, it was possible to determine that active particle shape and orientation has the most important impact on electrode tortuosity [2].

However, methods to obtain quantitative microstructure representations are experimentally and computationally expensive. Furthermore, certain materials pose challenges for 3D imaging in terms of size and contrast. Therefore, it is beneficial to consider how tortuosity can be estimated based on easily obtainable information such as particle shape and size distributions.
We developed an open source software application "BruggemanEstimator" that allows a user to estimate the tortuosity of a porous electrode (It is available for download at “BruggemanEstimator” uses the Differential Effective Medium approximation to determine the Bruggeman exponent (α) that relates the tortuosity (τ) to the porosity (ε) via τ = ε-α and requires only two microscope images (top and cross sectional view of an electrode) as input. These images, which can be easily acquired with a scanning electron or optical microscope, are used to extract a sampling of active particle shapes as well as the orientation of the particles within the electrode. A paper provides a detailed discussion of the methodology and validation of the program [3].

Relevant References: (PDFs of all references can be found at:
[1] M. Ebner, F. Geldmacher, F. Marone, M. Stampanoni, and V. Wood. “X-Ray Tomography of Porous, Transition Metal Oxide Based Lithium Ion Battery Electrodes,” Advanced Energy Materials,3, 845 (2013).
[2] M. Ebner, D.-W. Chung, R. E. Garcia, and V. Wood. “Tortuosity Anisotropy in Lithium-Ion Battery Electrodes,” Advanced Energy Materials,4, 1614 (2014).
[3] M. Ebner and V. Wood “Tool for Tortuosity Estimation in Lithium Ion Battery Porous Electrodes” Journal of the Electrochemical Society, 162, A3064 (2015).