Question about the Li -> Li+ + e- half cell reaction in a LiB battery

[hurreechunder]

Hi all - I have a question on the redox reactions in Li ion batteries. I'm not being able to figure out where the Li-> Li+ + e- half cell reaction is actualy happening.

Take the standard LCO reaction:

LiCoO2 + C6 -> LiC6 + CoO2 (in reality, only 50% of the Li reacts this way, but let's ignore that)
The thing is that the Li is present in the LCO cathode as Li+ and it is again intercalated in the graphite anode as Li+
So the only redox happening in the reaction is the oxidation of Co from 3+ to 4+ and the reduction of C6 from 0 to -1.

In the discharge cycle, the C6 is losing one electron and expelling the Li+ while the LCO cathode is accepting an electron as well as a Li+ ion to reduce Co from 4+ to 3+.
I can't figure out where in the half cell reactions we are ever getting Li -> Li+ + e- as the Li remains as Li+ all through. However, without this half cell reaction, an Li ion battery cannot get the 3.7 V that it does.
Any help would be appreciated.

 

[TeethWhitener]

However, without this half cell reaction, an Li ion battery cannot get the 3.7 V that it does.

Why not? The half reaction:
$$LiC_6 \rightleftharpoons C_6 + Li^+ + e^-$$
has a potential within a few tenths of a volt of the half reaction:
$$Li \rightleftharpoons Li^+ + e^-$$
See, e.g., p. 37 of the following slide deck:
http://www.tec.ch.tum.de/uploads/me...ures_-_Battery__Michele_P._for_Hubert_G._.pdf

 

[hurreechunder]

Thanks for the link. My question is precisely around that: in LiC6, the Li exists as an Li ion. It's not as if it's forming a covalent bond with the carbon. The electron in the outer shell of the Li atom is delocalised in the graphite, so it's actually Li+ and C6- forming an ionic bond. So on discharging, we should get C6- >> C6+e-. I don't know what this is, but I don't see why this should be identical to Li>Li+ + e-. In fact, in this case the reduction potential of the metal cation should not matter at all, as it exists as an ion throughout.
I'm clearly wrong here, the lithium must exist as lithium and not the ion...so what's the flaw in my reasoning?

 

[Borek]

It is not like Li exists as Li⁺ and whole LiC₆ is ionic. To quote DOI: 10.1103/PhysRevB.68.205111:

"Upon intercalation of Li ions into graphite, some fraction of the Li 2s valence electron density becomes delocalized on the carbon layers."

Note "some".

My bet is that LiC₆ is close to just Li, and the C₆ part is more of an inert "envelope" than a counterion.

 

[hurreechunder]

Thanks, Borek. Makes sense.

 

[TeethWhitener]

My bet is that LiC6 is close to just Li, and the C6 part is more of an inert "envelope" than a counterion.

There is actually significant electron transfer from Li to graphite, as evidenced by XPS.

The important point is that the half reaction for lithium de-intercalation has roughly the same voltage as the half reaction for lithium metal alone. The reason is well-explained in this paper (section II). The Gibbs free energy of the reaction (directly proportional to the voltage) ends up being $\Delta G=G_{LiC_6} + eU_{Li/Li^+}$, where $G_{LiC_6}$ is the intercalation energy and $eU_{Li/Li^+}$ is the energy associated with the lithium metal half reaction. It turns out that $G_{LiC_6}$ is quite close to zero at room temperature (in fact, the LiC₆ phase is thermodynamically unstable above about 300°C), so the majority of the formation energy is in the lithium half reaction. Therefore, the potential for the LiC₆ half reaction ends up being very close to the potential for the lithium metal half reaction.