Linear is beautiful: a simple relationship provides guidance for optimal battery design

It isn’t often that simple relationships are found for complex problems in physics, but scientists pay attention when they are discovered.  This is especially true in the field of materials design, in which researchers try to create materials with specific properties tailored for certain uses – a light-emitting diode (LED) in our TV that always fluoresces green light, for example, instead of red.  TVs wouldn’t be very useful if we couldn’t predict which color would be emitting from our screens!  Clarifying relationships between key quantities central to device performance, like quantum dot size and fluorescent color in LEDs for example, is the best way to provide direction about what type of material to try next for a given purpose.

This is why a new computational study in Physical Review Letters is so exciting for battery research!  Graphite anodes intercalated with lithium are still the top contender for electrode design in the battery world, but we can still try to do better in terms of their energy density and recycling.  The key process in these electrodes is the intercalation and binding of lithium between graphite layers, transferring charge from the lithium to the graphite.  The problem is that experimentalists and theorists have found a host of varying binding energies (and therefore charge transfer) between Li and many carbon-based materials, such as graphene, graphene with defects and substitutions, carbon nanotubes, etc.  Until now, we haven’t been able to predict exactly which materials will promote the most charge transfer and thus increase capacity for lithium adsorption.

Now, scientists at Lawrence Livermore National Laboratory have found a linear relationship between two key quantities in battery design: lithium binding energy (measuring how strongly lithium is stuck to the anode substrate surface) and the work required to fill unoccupied electronic states (how much energy it takes to place an electron in the next available energy level).  We don’t often see such a simple relationship in nature, but we can use it to predict optimal materials for battery design that experimentalists can work on testing.  This is really an example of computational methods at their best, giving chemical insights at the atomic level that can inform experimentalists on which materials to probe and explore.

Figure courtesy of [1]

Figure courtesy of [1]

Here are the details.  As seen in the figure above, when Li (purple dot) adsorbs on a graphene surface (hexagonal lattice), it sits on top and donates electrons (yellow) to the graphite (hexagonal lattice).  The yellow in the graph above shows where these donated electrons like to go (electron density).  Graphite is known for its delocalized electrons, and you can see that they spread out across the lattice.  From this model and calculation, researchers can calculate the binding energy of such a configuration, basically indicating how much energy is stored in the interaction between the graphene and the Li.  High binding energy means a much higher concentration of Li can be adsorbed, leading to better battery capacity.

Figure courtesy of

Figure courtesy of

The other quantity calculated in the article is the work required to fill in higher energy electronic states of the graphene.  This requires some Quantum Physics 101 to understand.  Every material has a set number of electrons, and, depending on the geometry of the material and the types of elements used, these electrons occupy very specific quantum states with designated energy levels.  These levels fill up from lowest to highest with electrons until you run out of electrons!  Once you run out, there are still possible energy levels above them, but just no electrons to fill them.  When Li intercalates, however, it donates electrons to the graphite.  These new, excess electrons must then occupy these higher energy states that are available because all the lower-lying ones are filled by the graphite electrons.  We can calculate how much energy is required to fill these originally unoccupied states, and that’s the work calculated in this paper.

Both the binding energy and this filling work are excellent quantities to keep track of because they can be easily calculated!  So the researchers did just that for a host of different substrates for the Li beyond graphite – single layer graphene, graphite with defects, carbon nanotubes of various chirality (radius/size), strained graphite, etc. – and found a linear relationship between binding energy and work. This isn’t intuitive because these values depend on several quantities, including Coulomb interactions between the ions in the lattice of the anode material and between electrons.  None of these interactions necessarily have to follow linear relationships as well (but they do!).

Figure courtesy of [1]

Figure courtesy of [1]

Here’s an example of some of the relationships they found – all linear but with different slopes and intercepts.  The y-axis is the binding energy, the x-axis the work described above.  The upper left graph shows that increasing Li concentration leads to increased binding energy and decreased filling work, predicted by a linear line (in red).  The top right shows a similar relationship for various levels of strain, middle left for defect types, middle right for graphene cluster sizes, bottom left for different nanotube sizes.

This principle of linearity can now be implemented for quick screening of materials to use in anodes.  With the slopes of the above relationships in hand, we can quickly determine what the binding energy and work will be for a given carbon-based anode and determine if it will be better or worse, in terms of capacity at least, than current designs.  It’s really a great method of bookkeeping and a big jump in understanding just what anode structures suit battery performance best.



Liu, Y., Wang, Y., Yakobson, B., & Wood, B. (2014). Assessing Carbon-Based Anodes for Lithium-Ion Batteries: A Universal Description of Charge-Transfer Binding Physical Review Letters, 113 (2) DOI: 10.1103/PhysRevLett.113.028304

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