The rules of the road for ions

For the past 5 years, chemical engineer Ankur Gupta of the University of Colorado Boulder has wondered what rules govern the diffusion of ions through the winding nanoscale tunnels within a supercapacitor. Each twist and turn changes how the capacitor charges and discharges. Understanding how these features influence ions’ behavior could allow scientists to fabricate next-generation energy storage devices with use-specific properties.

Now Gupta and his team have derived the mathematical rules of the road for ions traveling through these long pores and, he says, brought scientists one step closer to realizing supercapacitors’ full potential (Proc. Natl. Acad. Sci. U.S.A. 2024, 10.1073/pnas.2401656121).

The team was surprised to realize that the math governing ion movement mirrors the equations governing electrical circuits, known as Kirchhoff’s laws. These laws are usually used to calculate electric potentials and predict electrons’ movement through circuits. But when ions replace electrons in the mathematical functions, “you change that electrical potential into an effective electrochemical potential,” Gupta says. With that simple tweak, the laws can predict ions’ movement.

Although Gupta’s model can take the geometric complexity of real materials into account, it cannot predict how specific ions’ chemical properties will affect diffusion. “The sizes of cations and anions can impact kinetics,” physical chemist Yat Li writes in an email. His research at the University of California, Santa Cruz, focuses on designing functional materials like supercapacitors. The model “holds promise for guiding next-generation 3D structural designs aimed at high-energy and power-density energy storage,” he writes, but it will not be fully predictive until it considers the electrolyte in conjunction with pore geometry.

Gupta is well aware of this limitation and says his group is working to incorporate ions’ chemical properties into the model. Despite this, he says he’s excited to finally have something to hand to experimentalists before they start fabricating new materials. “Our hope is that this will improve how we understand supercapacitors, how we make them, and eventually, optimize their performance,” he says.