On Inventory
In the beginning of the recorded history of batteries, there was no formal distinction between rechargeable, or secondary, cells and non-rechargeable batteries, or primary cells¹.
As electrochemical engineering evolved it was seen that a design choice could be made: store less energy per unit mass/volume, but improve the reversibility of the battery. Remember in a traditional closed battery there is no change in the mass of the cell during operation: rather mass is redistributed in the cell to enable the desired redox reactions between the positive and negative electrode.
The choice between designing a primary and secondary battery, then, is largely whether or not one is willing to sacrifice runtime for cycle life, or vice versa. Consider a cell phone battery vs. a TV remote battery. We cannot store enough energy in a cell phone battery to allow it to operate for 12 months without recharging, but we can store enough energy within a primary battery (e.g. “AA” cell), to enable the remote control to function for 12 months. But all batteries, primary or secondary by design, will reach a point where they cannot accept a sufficient amount of charge.
So overall we are left with this problem: in any battery it is not that the mass of the battery that decreases, it is that the active mass of the battery decreases at the same rate the inactive mass increases. We call this active mass electrochemical inventory, and the key to future batteries that can last 10 years or much, much longer is designing system in which the
- inventory does not decrease or
- the inventory can be re-established (i.e. converting the inactive mass back to active mass).
Permanent Inventory Loss
Lithium and lithium ion batteries, as we understand them and build them currently, have no mechanisms by which much of inactive inventory can be re-activated. There are a myriad of ways in which inventory can be lost, and while some can be reversed, others cannot be. And those irreversible losses are the ones that put a death sentence on the battery. In a lithium bearing battery inventory is lost both as a function of use and time.
For use, a rough analogy is an egg toss. The goal of an egg toss is to pass an egg back and forth as many times without breaking it. If the egg drops and doesn’t break, we can pick it up and recover the inventory. But if the egg breaks, either in our hand or on the ground, the game is over.
In any lithium bearing battery, each lithium ion/atom is an egg, and as we cycle the battery we toss the lithium between the positive and negative electrode. Just like the egg being tossed has a chance of breaking, each lithium ion moving through has a chance of finding itself in a place where it cannot be recovered.
In a lithium bearing system the limit of cycling is linked with the coulombic efficiency of a cycle, or, how much of the active material stays does what we want to do in a cycle. In a lithium bearing system, if the coulombic efficiency is less that 1, this currently indicates that lithium is lost from inventory.
What this means is that over time, per cycle, we lose more lithium from inventory, and the total lithium lost from inventory goes as
remaining capacity = initial capacity * coulombic efficiency^cycle
so for 100 cycles at 99% coulombic efficiency
0.99¹⁰⁰ =36% of the initial capacity
Remember, the mass of the battery has not changed, but the amount of charge it can store has decreased by almost 2/3’s with just 1% inventory lost per cycle. Put another way: your phone’s run time would diminish from 15 hours to 5hours over the course of a little over 3 months.
The challenge of lithium bearing systems becomes clear: assuming we want to run a battery once a day for 10 years (3650 cycles), to 80% of initial capacity:
0.8 = x³⁶⁵⁰ => x = 0.9999
Which means that we must lose than 1/100th of a percent of inventory per cycle, or an egg toss break rate of 1/10000. Pretty difficult.
And then there’s time: there are clear indications that if one keeps a lithium bearing battery charged, the SEI layer (those x’s in the electrolyte in my cartoon), grows independently of the use of a battery, consuming inventory irreversibly as it does so.
Yes: you are damned if you do, damned if you don’t. General Motors and Hughes Research Laboratory presented a detailed study of this a few years ago that is worth digging into.
Decoupling Coulombic Efficiency from Inventory
The focus on high voltage systems like lithium bearing systems and others that are unstable in water has implicitly conflated coulombic inefficiency with inventory loss. But before lithium ion batteries systems existed with coulombic efficiencies of 99% that retained 100% of their capacity for over 100 cycles. To make this work, the mechanism leading to the coulombic inefficiency has to not affect inventory.
In one example, when one uses water as an electrolyte and protons as an active species, it is a tractable, if difficult, task to recombine water which splits, for example, but if the split water can be recovered one can access the same amount of capacity per cycle
In another example, if a passivating film forms, blocking access to to sites and thereby reducing inventory, that film can be broken electrochemically in a special recharging step to recover inventory.
As exotic as the above scenarios sound the longevity and reliability of the modern lead acid starter battery is largely attributed to such tricks.
But within these systems there are still forms of irreversible inventory loss: if the battery breaks itself apart internally or forms unremovable passivation layers, no amount of electrochemical tomfoolery can reset the inventory.
Living Forever by Dying Everyday
I’ve been a bit dogged by this issue for a while now, and recently I’ve been asking my research group to consider a battery with a primary focus to never lose inventory.
Never is a strong word, but in a recent paper we demonstrated a system that can suffer massive losses in coulombic efficiency per cycle and still provide 100% of its rated capacity for over 1000 cycles and a year of use. We did this by purposely letting the battery short circuit and self discharge and designing these reactions such that we lose energy retention per cycle, but the active mass is still active.
A rough analogy is a leaky dam and turbine between two reservoirs. So long as all of the water leaks into the lower reservoir, it can be re-pumped to the higher reservoir. The trick is using the water fast enough through the turbine that less of it goes through the leak. We demonstrate that we apply this to a battery get up to 70% of the energy put into the battery out of battery 1000’s of times.
It’s not perfect, but if the goal is to have a cheap battery that lasts forever, it’s a effective, if counter intuitive, first step.
Going Forward
Putting this all together, there are two options to improve current lithium bearing batteries,
- do better than coulombic efficiency of 0.9999
- discover ways of recovering lost inventory
The nice thing here is that the two methods are not inherently opposed. In the case I outlined above, we relax the constraint on coulombic efficiency to maintain inventory, but that was cheating in many ways. An important, and largely unexplored, scientific challenge in battery is to figure out how to do both improvement simultaneously. There are no laws that say we can’t do both, yet.
¹Primary battery: a battery that has not been designed to accept current and is therefore used as a primary power source.
Secondary Battery: a battery that has been designed to accept current and is therefore not the primary power source but intermediate storage between the the primary power source (e.g. the wall socket, a solar panel, etc) and the device (e.g. your phone).
