A mathematical model could help researchers design improved materials for storing electricity. Efficient, inexpensive storage battery and capacitor materials are a critical piece of the effort to reduce carbon emissions in transportation and electric generation and distribution.

“Current batteries and other storage devices are a major bottleneck for transition to clean energy,” Daniel Tartakovsky, the Stanford professor who led the research effort, said. “There are many people working on this, Electric car charging in Amsterdam. Credit: Wikipediabut this is a new approach to looking at the problem.”

Nanoporous materials are generally used for energy storage. Even though these materials appear solid, they are characterized by microscopic holes. Designing these materials has been a trial-and-error process, where the designers attempt to arrange a material’s pore pattern and characteristics.

Tartakovsky and co-author Xuan Zhang developed their mathematical formula using microscopic material characteristics, such as pore structure, as decision variables, and optimizing macroscopic properties for two two-dimensional material-assembly templates and several operating conditions.

The mathematical model shows materials chemists how materials perform if the grains are arranged a certain way. The researchers hope to find materials that greatly improve energy storage, rendering rechargeable batteries unnecessary for devices like cell phones and electric vehicles. These materials will have to withstand both high power and high energy.