Redox without Redox

Recently Braga et. al. published Alternative Strategy for a Safe Rechargeable Battery in Energy and Environmental Science. This is a subtle title for a work, if reproducible and truly invoking the mechanism described in the article, will have a lasting impact on the battery community. As described, however, it seems to violate key concepts in thermodynamics, namely the conservation of energy.

The big idea is motivated halfway through the paper. The claim is that of anomalous capacity at the cathode:

The measured capacity was much greater than the capacity of the sulfur in the cathode, but it corresponds to 90.1% of the capacity of the lithium anode, which is much greater than the capacity of the sulfur. We therefore conclude that the sulfur acts as a redox center determining the voltage of the cell at which electrons from the anode reduce the Li+ at the electrolyte/cathode interface to plate lithium rather than reducing the sulfur, so long as the voltage remains above 2.34 V; below 2.34 V, the S8 molecules are reduced to Li2Sx (1 < x < 8 ) and the lithium on the anode becomes exhausted after 28 days in the cell of Fig. 1. The cell reaction was no longer reversible after this full discharge. At voltages V > 2.34 V, the cell is rechargeable and the sulfur is not reduced. The Fermi level of the lithium plated on the carbon–copper composite cathode current collector is determined by the Fermi level of the cathode current collector, whereas the Fermi level of the lithium anode remains that of metallic lithium, but the cell voltage is determined by the energy of the redox couple of the unreduced redox center.

In short: the potential of the cathode is set by the chemical species of the cathode interface, but the capacity of the cathode is set by the lithium anode. If this is correct this is a big deal, as described further along:

These illustrations demonstrate that the ability to plate/strip an alkali-metal anode in contact with a Li-glass or Na-glass electrolyte allows a totally unconventional strategy for the design of a rechargeable battery in which reversible plating of an alkali metal from the anode onto the cathode current collector gives a battery cell having a capacity determined by the amount of alkali metal used as the anode rather than the solid-solution range of the working ion in a host cathode lattice. The voltage is limited by the difference in the chemical potential of the alkali-metal anode and that of the cathode current collector, but it is determined by a cathode redox energy (if one is needed) that is above the Fermi level of the metallic cathode current collector. Without a redox center, the voltage is V = 3.5 V.

Long story short the effective energy density of a battery, if this can be utilized to its full extent, approaches 8x the current energy density of lithium ion cells (based on our current understanding of electrodes the projected ranges is somewhere between 2 and 5 times modern lithium ion capacity).

This is because in standard battery design the capacity of the battery is determined by the mass of the anode and cathode. The striking claim in this paper is that there effectively just needs to be an “image” of an oxidizing species in this reaction, and that is enough to drive a significant discharge capacity limited only by the amount of reductant available.

Another way to think about this: it’s like having an air electrode without the need for breathing air in or out: just the mere scent of air is enough to drive the cathodic potential. Another analogy: it’s like having an air fuel ratio that is exceptionally fuel rich yet reacting almost all of the fuel nonetheless.

More importantly: what they’re proposing is analogous to saying that the fuel doesn’t really react, it just gives off the enthalpy of reaction while remaining fuel and not turning to H2O and CO2.

Everything I understand about chemistry and thermodynamics says this is impossible. Can the limit really be the total capacity of the anode without any thought to the configuration of the cathode? Figure 4 in the paper suggests a mechanism and opens a bunch of questions. Below are my notes for working through this:

To be specific, the claims are:

1. Upon discharge, in a normal reaction (e.g. every other battery, ever), the total charge of the oxidizing species has to balance the the total charge of the reducing species
2. Upon discharge, in the proposed reaction, the oxidizing reaction is just the exact opposite of the reducing reaction (lithium plates on the cathode and strips on the anode) but the potential of the oxidation reaction is set by the lithium, while the potential of the reduction reaction is set by the sulfur “redox center”
3. In the paper S, MnO2, and Fe(CN)4- are used as redox centers, and anomalous capacity is observed on all three.

The problem with the above is that, according to statewise analysis, there is no net chemical change in anything in the cell:

• Lithium is replated as lithium → ∆G =0
• The sulfur doesn’t change → ∆G = 0
• The copper doesn’t change → ∆G = 0
• Thus: no net reaction, so no energy should be released.

As described in the paper, all that is changing is the position of the reactants, not the chemical state. If nothing changes oxidation state, no energy can be released.

My open questions, from my current read of the paper:

1. Why does this work at all? Why does lithium plate at the cathode at a potential determined by the sulfur?
2. By the same token, why doesn’t the sulfur reduce?
3. What is the real structure / morphology of the cathode lithium? The SEM does not elucidate the physical nature of the deposit.
4. Once lithium exists on both sides of the cell, why is there any potential difference at all? (we’ve accidentally plated lithium on cathodes before and the potential is typically zero as a result) After all, the net reactions are the stripping and plating of lithium.

To questions 1,2 and 4 a capacitance argument is presented, briefly, in the paper, but I am not convinced by the argument provided. If the lithium is lithium and sulfur is sulfur at the end of the experiment, regardless of where they are in the cell, no net reaction has taken place and therefore no energy can be released.

This isn’t to say I don’t believe the experimental result: I just don’t think the proposed mechanism justifies the first law violation motivated above. The sulfur may not be reducing, but something else must be in a stoichiometric balance to the oxidizing lithium to provide the results described in the paper.

This is not the first time “anomalous capacity” has been measured or ascribed to a system: more often than not it is O2 leaking into the cell, or even more often, mis-measurement of redox species. The relatively stable cycling and shelf life indicate the former may not be the case, and the quality of the group and journal indicate that the latter would not be the case.

More likely is that the electrolyte is participating in redox, something proposed and demonstrated by Amatucci’s group with LiI about ten years ago. There’s all sorts of stuff that might want to redox in that separator……

A healthy dose of grounding is required here, and there may be another explanation for the anomalous capacity, but this is a result worth trying to reproduce because if the result is correct the mechanistic understanding can be improved.

UPDATE 2017–03–21:

In a computer world interview Professor Goodenough said of the above questions:

“In this case, scientists wonder how it is possible to strip lithium from the anode and plate it on a cathode current collector to obtain a battery voltage since the voltage is the difference in the chemical potentials (Fermi energies) between the two metallic electrodes,” Goodenough stated. “The answer is that if the lithium plated on the cathode current collector is thin enough for its reaction with the current collector to have its Fermi energy lowered to that of the current collector, the Fermi energy of the lithium anode is higher than that of the thin lithium plated on the cathode current collector.”

This raises two interesting questions:

1. How much lithium has to exist on both electrodes before the potential difference is that of lithium vs. lithium? The answer to this is very little. Electrodeposited lithium on copper, at room temperature, forms a thin alloy, and then once this alloy is formed the interface, and fermi level, becomes that of pure lithium. This interlayer, at most, is on the order of 10 nm, and is more likely 1 or 2 atomic layers and less than 1 nm.
2. Based on that amount, what is the practical capacity accessible lithium that can be deposited per unit area of current collector/“redox center” before the super capacity effect is diminished? Well, let’s assume 10 nm.

So 10 nm of lithium per cm² is

capacity_Li = 3800 mA*h/g #always and forever
rho_Li = 0.534 g/cm^3 #ditto 
d_Li = 10 nm #assume best case scenario
d_Li*rho_Li * capacity_Li in µA*h/cm^2 => 2.03 µA*h/cm^2

So the capacity available in this coin cell, based on the copper surface area, would be 2.0 µAh/cm². Let’s assume this effect can be applied to a large surface area electrode like porous carbon (and let’s also assume that the lithium doesn’t intercalate into the carbon), and we get a 100 fold increase in surface area. This is now 200µAh per cm² of electrode.

The capacity of the cathode in the paper is 1000x that of the cathode that is motivated by thin lithium. More importantly, modern lithium ion cathodes deliver 3.6 mAh/cm², or 10 to 1000x the capacity I calculated above for the thin lithium. (Remember that Dr. Goodenough invented the modern lithium ion cathode.)

So I don’t think the thickness of the lithium can resolve what is claimed in the paper. In reality what happens as this layer forms is that the potential rapidly drops, and no such potential drop was seen in the paper.

UPDATE 2017–04–20:

Online and off I’ve had a few questions about why, specifically, this mechanism constitutes a first law violation.

If we assume that the battery is a closed but not isolated system (mass cannot enter or leave, but heat can enter or leave), we can use the closed form of the first law where:

Q - W = ∆U = ∆G

Where

• Q is heat (positive if entering the system by convention)
• W is work (positive if leaving the system by convention)
• ∆G is change in the free energy of the system which for a closed chemical system can be set equal to ∆U because PdV = VdP = 0, so ∆U = ∆G = µdn

The above analysis indicates that as described ∆G = 0 so ∆U = 0.

The system is not endothermic, if anything, due to transport overpotentials Q should be less than 0, but to give the system the benefit of the doubt we’ll set Q = 0.

So

• Q = 0 (no heat in or out)
• W > 0 (the system does work on the LED)
• ∆U = 0

Thus, Q - W ≠∆U, violating the first law of thermodynamics.

If we allow for the heat generation inherent in any real electrochemical operation, Q < 0, so

• Q < 0 (heat out)
• W > 0 (work out)
• ∆U = 0

So in a real system the first law violation is exaggerated because the left hand side is more negative (something negative + something negative is more negative), so once again

Q - W ≠ ∆U.