# Elastic energy of graphene: new idea for (non-chemical) battery

Is it possible to build a battery using the elastic property of graphene?

Here is the stress-strain curve of graphene. Image source: https://www.researchgate.net/figure/Stress-strain-curves-of-defect-free-graphene_fig2_313777746

Based on the figure, with 0.1 m^3 graphene fiber, by applying 80 GPa force, graphene fiber will stretch about 10%, then 80 GPa * 0.1 m^3 * 10% * 0.5 = 400 MJ energy is stored. The energy can be released by winding the fiber to the gear.

As a comparison, a standard car with 65 liters of gasoline contains the energy of 65L * 0.77 kg/L * 45 MJ/kg = 2252.25 MJ, while the efficiency of a gasoline car is roughly 25%.

1. What is the limitation of this approach?
2. If it works, is any other material better than graphene? For example, materials such a rubber band which can be stretched 700%.

Elastic and plastic deformation of graphene: https://arxiv.org/pdf/0907.0501.pdf

• recent update: "A CNT spring made of bundles of densely packed 1 nm diameter SWCNTs stretched to a 10% strain is predicted to have an energy density of 3.4×10^6 kJ/m3" from wikipedia (en.wikipedia.org/wiki/Carbon_nanotube_springs). Aug 1 '20 at 6:30

The basic problem is that there is no practical way to apply the required force to stretch the grapheme.

Suppose you pack the $$0.1$$ m$$^3$$ of graphene in to a cubical box with sides of about $$0.5$$ m. The area of two opposite faces forming your "spring" is 0.25 m. The force acting on that area is $$0.25 \times 80 \times 10^9$$ N = $$2 \times 10^{10}$$ N = about 20 million tons force.

Designing a "recharging system" to apply that much force to recompress the graphene, and making the box strong enough to withstand it, would be an "interesting engineering challenge".

You might also think about what would happen if the device failed mechanically when it was fully charged. It would release the same amount of energy as burning a full tank of gasoline, but in a few microseconds. That could have quite an big impact on the local environment … bad pun intentional.

Actually, this would make a nice problem about work and energy for a first-level dynamics course. Calculate the amount of energy stored in the "spring", and ignoring air resistance, find the height which the car would reach if an explosive failure launched it vertically upwards :)

There is no way round this fundamental "leverage" problem. It works exactly the same as any other lever. If you need a force $$F$$ to move the car say 500 km (comparable with what a full tank of petrol could do) but you want to store it in a spring that moves say 50 mm, (i.e. 10% of the length of the 0.5 m cube) the force on the spring needs to be 500,000/0.05 = 10 million times bigger than the force it takes to propel the car. The product of force $$\times$$ distance must be the same, for the movement of the car and the movement of the spring driving it.

• I think the force is not a big issue. We could just consider a single bundle graphene fiber (super long) with 0.5 m^3 volume and wind the "stretched" graphene fiber into a cylinder, while the diameter of the bundle could be adjusted so that the tension force is reasonable. The main problem might be that 80GPa tension force is not able to reach due to the defects of the fiber. Besides Carbon materials, other materials are not easy to reach GPa tension force. Jul 20 '19 at 19:50
• "80GPa tension force" doesn't even mean anything. The units of tension are not GPa. If you really want to make a grapheme based energy storage device, consider an electrical battery or a supercapacitor, not trying to power a car with high tech elastic band. Jul 20 '19 at 23:02
• excellent analysis, @alephzero. Jul 21 '19 at 7:26
• Some research here, while it is still far from practice. "Benefits and challenges of mechanical spring systems for energy storage applications" (core.ac.uk/download/pdf/82374665.pdf) Jul 22 '19 at 20:06