Dear Buddhi,

when looking at the derivation of the Butler-Volmer equation, k is defined as a constant, and it does not change with the concentration of the reactants and products (i.e., the SOC, in a battery), because is a property of the reaction per se. The dependence of the kinetics on the SOC is instead given in the definition of the exchange current density (equation 2.25).

To have a clearer picture, look at this well-explained derivation of the BV (from page 54 on): http://mocha-java.uccs.edu/ECE5710/ECE5710-Notes03.pdf

Best,

Alessandro

Many thanks Alessandro Innocenti for your informative reply.

Yes it can be seen that 'k' is a property of the particular reaction. I got a second question now, how do we explain the large variations in the EIS semi-arch at extreme SOCs such as 0% or 100% compared to EIS at other SOCs (like 50%)?

isn't this due to a change in the reaction rates (becoming sluggish) at these extreme SOCs due to more difficult lithiation or delithiation at these SOCs, and this sluggishness is represented by a variation in the 'k' at these extreme SOCs?

I understand that exchange current density (i0) depends on the SOC, and at extreme SOCs, i0 is smaller compared to 50% SOC, which will give larger EIS semi-arches at extreme EIS. But, some EIS can not be explained with change in the i0 alone.

Much appreciate some input for this.

Dear Buddhi,

I know that the kinetic semicircle variation can be really huge in some systems when the SOC is at the extremes and that the concentration variation is not enough to explain all the change, I observed it too in some experiments. But the reaction rate k should be the same if the reaction is the same along the de-/lithiation of the material. But maybe if the nature of the reaction changes, k may also vary during the operation of the battery! But I am thinking more of a stepwise process, than a continuous variation. It comes to my mind the lithium intercalation in the graphite, which proceeds in separate stages with different stoichiometries of lithium in the graphite. Or in some cathode materials, where different redox centers react with lithium along the charge and discharge processes according to the voltage region, like LNMO. But please check some literature about it because it is just an idea I am having now, and I am not 100% sure of its physical background! :)

If you want to have a more empirical approach, you can try to add a kind of linear or exponential correction factor to the i0 and see if there is a trend according to the type of cathode, anode, cycling conditions, etc.

Maybe you can give a look at the paper Article Modeling the impedance versus voltage characteristics of LiN...

Btw, I had recently the opposite problem, with a particular material I studied with impedance which had basically no variation of the kinetic semicircle with the SOC, and I had to use a constant i0 to have to best fit.

EIS is really strange sometimes!

Good luck with your experiments and your work on this interesting topic! :)

Best,

Alessandro

Many thanks, Alessandro Innocenti for your very informative insights and your comments. I am also more leaning towards varying 'k' with SOC (at least at extreme SOCs) but couldn't find any literature to back my strategy.

Thanks again!

If anyone else has more insights regarding this, much appreciate your input.