# Energy density and Li-S batteries

Yesterday I created a new Shiny app for estimating the gravimetric energy density of Li-S cells based on ten different parameters of the materials that make up those cells. You can find the page describing it the app here (or you can jump straight to the app here.

I wrote some accompanying text giving some background to the app – more specifically about the gap between theory and practice and why wild promises surrounding new battery technologies never seem to come true. That page got a bit long, so I’ve split off that text into this post. It’s still a bit long, but I hope it can be of some interest!

Gravimetric energy density, or more properly specific energy – the amount of energy stored for a given mass – is one of the most important characteristics of a battery for any portable application, whether it’s for a laptop or an electric vehicle. It’s especially important for the latter, because the energies required to move something as heavy as a car over distances of hundreds of kilometers currently require exceptionally heavy batteries. This is one of the main motivations for research into new rechargeable battery chemistries which have much higher theoretical energy densities than Li-ion batteries, the current state-of-the-art.

The theoretical specific energy (hereafter referred to simply as energy density) of the lithium-sulfur (Li-S) battery system, for example, is given in various papers, review articles, news articles, etc, to be about 2,600 Wh/kg. This number comes from simply converting the Gibbs free energy of formation of Li2S (-432 kJ/mol) into the units of Wh/kg, and isn’t actually based on anything relating to the construction of a battery (it doesn’t consider, for example, an electrolyte, without which a battery can’t function). The real energy density of a battery is the energy released from the electrochemical reaction divided by the masses of everything in that battery – both electrodes, the separator, the electrolyte, the current collectors, and the packaging.

Most often, the number of interest is the energy density on the cell level, that is, the energy density of a single cell. This is of course much lower than the theoretical energy released from a perfectly efficient reaction of the reactants in that cell, because all the components besides the active materials (sulfur or lithium, in this case) do not contribute to the energy density, even if the battery can’t work without them. However, this fact hasn’t stopped a large number of researchers and journalists describing the system from writing things like:

The theoretical energy of the Li-S battery is 2,600 Wh/kg, which is much higher than for Li-ion batteries, currently 150-180 Wh/kg.

This is enormously misleading, and I am of the opinion that even unintentionally making these inappropriate comparisons – and the implicit wild promises of magic technology to come – does not do the reputation of the field any favours. Making cells with high energy densities is very hard: there are two companies that I know of (Sion Power and OXIS Energy) which have been developing these batteries long before the current rush of academic interest and currently produce real cells with energy densities of >300 Wh/kg. Both are claiming to be able to deliver 400 Wh/kg in the near future. For comparison, the highest energy Li-ion battery in production that I’m aware of is the 243 Wh/kg Panasonic NCR18650B.

I’m also of the opinion that many researchers in the field do not really appreciate what a remarkable achievement companies like Sion Power and OXIS have made in producing 300+ Wh/kg cells that can actually be recharged for more than a few cycles. One of the key conclusions I’ve come to in the time that I’ve been working in this field is that the more you work to make a cell that will actually have a high energy density, the more you realise the system really doesn’t want to work nicely under those conditions.

### Making a high-energy density battery is hard

What I mean by “a cell that will actually have a high energy density” is one where the dead weight – the weight in the cell which is not active lithium or sulfur, in this case – is minimised as far as possible. The electrolyte and current collectors are big contributors to this, but other electrode additives and any excess on the part of one of the electrodes also contribute. More importantly, the electrochemistry of the lithium-sulfur battery is extremely sensitive to many of these factors in ways that Li-ion batteries simply aren’t.

As far as I can see, the most serious issues regarding long-term rechargeability (cycle life) are a direct result of the instability of the negative electrode and destruction of the electrolyte. In most academic work when results from test batteries are reported, the electrode “loading” (the amount of sulfur on the positive electrode per unit area) is usually low, and the electrolyte and negative (lithium) electrode are in huge excess. This minimises the effect of capacity loss due to these serious issues. This is not an issue in itself: you can deliberately test cells in this way, so as to look at the stability of the positive electrode itself (in what we would typically call a half cell). However, in most cases it is not obviously deliberate: even though there are a number of papers now which have demonstrated how fundamentally important the electrolyte volume is, most papers in the recent past do not even report how much electrolyte was used. And from my own experience, I have so far only reviewed one or two articles on Li-S batteries where I have not had to ask the authors to include the electrolyte volume (or more specifically, the electrolyte/sulfur ratio). The thickness of the negative (lithium) electrode is reported even less frequently, and is also important. This situation of unreported experimental parameters does seem to be slowly improving, though.

It is also, simply, more convenient to make test batteries like this. For example, it is harder to coat thicker positive electrodes. Very thin Li foil (e.g. tens of µm thick) has also only recently become available, is difficult to work with and is relatively expensive. It is also not trivial to work with realistically small electrolyte-to-active material ratios for such test batteries either, because the volumes are usually very small (perhaps less than 30 µL, for batteries with a few mAh of capacity). For all these reasons, the rapid capacity fade that comes with having the combination of a low electrolyte volume, a thick positive electrode and a thin negative electrode, is usually not seen.

It is common now to see journal articles reporting test Li-S batteries as completing hundreds and hundreds of cycles with little capacity fade. This frequently comes with the implication, intended or not, that a major hurdle with the system has been cleared and we are well on our way to long-lived, high energy batteries with a dizzying range of applications. More disturbingly, I have seen a number of papers report relatively unremarkable results along with a statement to the effect of:

“We estimate that this corresponds to an energy density of 750 Wh/kg in a complete cell

or something similarly unsubstantiated, where this projection is made on the basis of assuming masses of other components which may not be realistically achievable. I do not know if those who would write this or similar things actually believe it, but certainly many readers would, and would assume it to be the truth, not least because these sorts of statements pass peer review. I know the urge and need to promote and spin one’s research is a strong one, but this is a bad habit that really needs to be kicked.

### This all sounds very bad!

I’m not trying to play down the potential of the lithium-sulfur system at all, in case that’s what it looks like. As much as I believe that wild, unrealistic promises are likely to eventually kill of interest from funding agencies and industry when those promises can’t be fulfilled, I also believe that direct and brutal criticism of these promises may also achieve the same result. I’m not going to say that a 500 Wh/kg Li-S battery is impossible. On the contrary, I think it’s quite realistic! I could tell you some values we need to reach in order to get there, although I couldn’t tell you how to actually get to them (that’s what research is for!). I will say that I’m fairly sure it’s not going to happen without better awareness of the limitations of our experiments and what conclusions can be drawn from them. It’s just as Feynman said (quoted on the top “Science” page on this site):

The first principle is that you must not fool yourself - and you are the easiest person to fool.