The forgotten equation helps scientists track and control carbon dioxide shifts

To manage atmospheric carbon dioxide and turn the gas into a useful product, Cornell scientists dusted off an ancient electrochemical equation—now 120 years old. The group aims to thwart the consequences of global warming and climate change by applying this long-forgotten idea in a new way.

The calculation—named the Cottrell equation by chemist Frederick Gardner Cottrell, who developed it in 1903—can help today’s researchers understand the many reactions carbon dioxide can take on when electrochemistry is applied and pulsed on a laboratory bench.

Their work is published March 27 in the journal ACS catalyst.

said lead author Rileigh Casebolt DiDomenico, a PhD student at the Smith School of Chemistry and Biochemical Engineering, at Cornell Engineering under the direction of Professor Tobias Hanrath.

The electrochemical reduction of carbon dioxide offers an opportunity to convert the gas from an environmental liability into a feedstock for chemical products or as a means of storing renewable electricity in the form of chemical bonds, as nature does.

“If we have better control over reaction, then we can make whatever we want, when we want to do it,” DiDomenico said. “The Cottrell equation is the tool that helps us get there.”

In simple terms, the equation depicts a change in the measured electrochemical current over specific signals to time during an experiment. What this means in the laboratory is that the carbon dioxide is exposed to various applied potentials that are stepped up or down, or pulsed, and these in turn generate a current that is associated with the products formed from the reduction of the carbon dioxide.

De Domenico first came across this ancient equation when he was a PhD student in a class taught by Hector Aberoena, Professor of Chemistry and Chemical Biology in the College of Arts and Sciences, Emil M.

Intrigued after Abruña mentions it in class, DiDomenico implements Cottrell’s equation into its carbon dioxide reduction work. It altered the electrochemical values ​​(such as the applied potential) or the time scale, to generate other gas-derived products.

For example, the equation enables a researcher to define and control experimental parameters for taking carbon dioxide and converting it into useful carbon products such as ethylene, ethane, or ethanol.

At first, Di Domenico thought she had strange results, but later confirmed that she had done the experiments correctly.

“I was trying to change the pulse coil to make ethylene specifically by applying what I was learning in class to see if it would fit,” DiDomenico said. “I realized that this was actually a way we could identify a mechanism for reducing carbon dioxide into a useful product.”

Many researchers today use advanced computational methods to provide a detailed atomic picture of the processes on the catalyst surface, but these methods often involve several subtle assumptions, which complicates direct comparison with experiments, said senior author Tobias Hanrath, Marjorie L. Hart Professor ’50. in Engineering, at the Smith School of Chemical and Biomolecular Engineering.

“The beauty of this old equation is that it has very few assumptions,” Hanrath said. “If you put empirical data in, you get a better sense of reality. It’s an old classic. That’s the part that I thought was beautiful.”

Abruña enjoyed seeing the equation in action. “This equation describes what happens when one imposes a potential step, so it switches from one voltage to another, and then looks at the resulting transient current,” he said. “By analyzing the results, you can glean important and interesting mechanical information and details. Only if you are not an expert in electrochemistry like me, you probably don’t know much about it.

“The carbon dioxide reduction people are much more into the distribution of products, or the engineering aspects of that,” Aproena said. “Here we’re using a very simple model that works amazingly well. It’s almost embarrassingly good.”

DiDomenico said, “Because it’s older, the Cottrell equation has been a forgotten technique. It’s classic electrochemistry. Just bringing it back to the front of people’s minds is great. And I think this equation will help other electrochemists study their own systems.”