Relating Concentration to Capacity

[mlnsai]

Hi Team,

For a 5 Ah cell (LGM50 - Chen2020 parameters),

The initial total lithium concentration turns out to be 0.289333815092399 mol which is around 7.754 Ah
(Ah = mol * F *(1/3600))

1. How can I relate it to arrive at 5Ah?
2. Also, the Total lithium concentration = Total Li in particles + Total Li in electrolyte => Does particles mean positive and negative electrode concentration combined?

However, I can relate the cell capacity of 5 Ah from capacities of negative and positive electrodes through their SOC ranges.

1. SOC range of negative electrode = 91.05 - 3.46 % = 87.59%
   Cell capacity = (SOC range) x Negative electrode capacity = 87.59 x 5.83 = 5.10 Ah

2. SOC range of positive electrode = 84.84% - 26.38% = 58.45%
   Cell capacity = (SOC range) x Positive electrode capacity = 58.45 x 8.741= 5.10 Ah

I hope I am correct.

Thanks in advance :)

[brosaplanella]

1. Your calculations below on the SOC range seem correct (not sure where the 7.754 Ah comes from). Baiscally, the 5 Ah is the nominal capacity (at a given C-rate) so the theoretical capacity you calculate below should be a bit higher (as it is).
2. Yes, the total Li in particles refers to both electrodes.

[mlnsai]

Thanks Ferran. That clears a lot.

However, the "Total Lithium [mol]" can be obtained from experiments. I converted that to capacity [A.h] using the formula i mentioned.

[A.h] = [mol] * self.param.F / 3600,

where, F is Faraday's number: 96485.3321 coulombs.

This is where i couldn't understand, how the cell capacity is around 5 Ah when the total Li is around 7.75 Ah (converted 0.28933 mol to Ah). Any lead would help me a lot.

Please have a look :)

[valentinsulzer]

Section 3.2.1 of this paper is a really nice explanation of how theoretical capacity can be calculated from electrode capacities, total lithium, and voltage limits.

Alternatively see Appendix B of this paper

[mlnsai]

That's great @tinosulzer . I will check these articles out. Thanks for the reply :) @brosaplanella