NEW PAPER KLAXON: 📢🥳
"The electrode tortuosity factor: why the conventional tortuosity factor is not well suited for quantifying transport in porous Li-ion battery electrodes and what to use instead"
nature.com/articles/s4152…
"The electrode tortuosity factor: why the conventional tortuosity factor is not well suited for quantifying transport in porous Li-ion battery electrodes and what to use instead"
nature.com/articles/s4152…
This paper is the result of two and a half years of collaborative work by Tuan-Tu Nguyen (@ttu13e), Arnaud Demortière (@ArnoDemortiere), Benoit Fleutot, Bruno Delobel, Charles Delacourt & me!
You should all follow the superb lead author Tu - @ttu13e
You should all follow the superb lead author Tu - @ttu13e
There are two classic approaches to measuring the pore-phase tortuosity factor electrochemically (one is time domain, the other is frequency). Hubert Gasteiger's group have some (many) killer papers on this.
And they often give similar answers... but not always - why?
And they often give similar answers... but not always - why?
Before we get to that:
Firstly, ignore geometric "path length" type tortuosities, they're a waste of time for real electrodes. Secondly, double ignore the Bruggeman correlation - Bruggeman didn't think it's relevant and neither should you. #ChangeMyMind
sciencedirect.com/science/articl…
Firstly, ignore geometric "path length" type tortuosities, they're a waste of time for real electrodes. Secondly, double ignore the Bruggeman correlation - Bruggeman didn't think it's relevant and neither should you. #ChangeMyMind
sciencedirect.com/science/articl…
Now, the conventional tortuosity factor that we all know and love (Laplace equation) is about transport *through* a system (i.e. in one side and out the other), but this is not what's happening in an electrode.
Figure showing "dead end" pores that don't help *through* transport.
Figure showing "dead end" pores that don't help *through* transport.
But, we all know that lithium ions _don't_ travel all the way *through* the electrode, but rather from the separator into the surfaces of the active material.
The conventional tortuosity factor would tell you any real electrode has tau=inf as there's a blocking foil on one side!
The conventional tortuosity factor would tell you any real electrode has tau=inf as there's a blocking foil on one side!
These 4 structures are cool. B, C & D have the same porosity and conventional tortuosity factor (and all have same McMullen number), but would they be equally good electrodes?
No way!
Our new metric \tau_e (the electrode tortuosity factor) is able to distinguish between them.
No way!
Our new metric \tau_e (the electrode tortuosity factor) is able to distinguish between them.
What about more realistic structures? Our tau_e solver is now built into TauFactor and can easily handle billion voxel volumes on your desktop.
Remember those "dead-end" pores? Clearly *all* pores are ultimately dead-ends in an electrode... doesn't mean they're not being used!
Remember those "dead-end" pores? Clearly *all* pores are ultimately dead-ends in an electrode... doesn't mean they're not being used!
Battery manufactures know that drying electrodes too fast gives you a "custard skin" of binder on the top. This is bad for cell performance but the conventional tortuosity factor can't tell whether this layer is at the top or bottom or just bad throughout.
\tau_e to the rescue!
\tau_e to the rescue!
We also explain the theory and the maths.
We are solving a large pore phase resistor network (connected to capacitors are the solid surfaces) in the frequency domain. Then finding the difference in resistance as frequency→ 0 and ∞.
We are solving a large pore phase resistor network (connected to capacitors are the solid surfaces) in the frequency domain. Then finding the difference in resistance as frequency→ 0 and ∞.
Conclusions:
* The conventional tortuosity factor is not the ideal metric for electrodes (but it's still good for separators).
* There are simplifications in \tau_e too... but you only get 1 metric to encode microstructural complexity in your 0/1/2D models... \tau_e should be it!
* The conventional tortuosity factor is not the ideal metric for electrodes (but it's still good for separators).
* There are simplifications in \tau_e too... but you only get 1 metric to encode microstructural complexity in your 0/1/2D models... \tau_e should be it!
Bonus perspective:
* Electrochemistry experiments like the eSCM are surely the best way to measure tortuosity factors (not indirectly via 3D imaging/simulations); however, 3D imaging allows us to explain, model and optimize.
* Electrochemistry experiments like the eSCM are surely the best way to measure tortuosity factors (not indirectly via 3D imaging/simulations); however, 3D imaging allows us to explain, model and optimize.
