Theory proves local equilibrium at interfaces

The behavior of materials where they connect and interact with other materials – the interface – is often a thorn in the side of scientists and engineers who want to understand and design systems that are well integrated and can function in a transparent with several components. In batteries, for example, the molecular processes that occur at the interfaces between the solid electrode and the liquid electrolyte can limit battery performance.

Through complex calculations and computer simulations, researchers at the Pritzker School of Molecular Engineering (PME) at the University of Chicago have developed a new theory for multicomponent interfaces that are far from equilibrium. The theory proves the long-held ‘local equilibrium’ hypothesis, the idea that although two substances may have very different temperatures or phases, their interface includes a small region where the system is in equilibrium. The research was published in the Proceedings of the National Academy of Sciences.

“We now have a framework that anyone can use and apply to any type of hardware to better understand interfaces,” said Professor Juan de Pablowho led the research with Philip Rauscher, a student at the University of Chicago, and their collaborator, Professor Hans Christian Oettinger of ETH Zuerich.

Prove local equilibrium
Professor de Pablo and his collaborators wanted to develop a theory describing exactly what happens at the interface of systems in disequilibrium. They chose to focus on systems involving two components and having two different phases with an interface between them.

Through computer calculations and simulations, the team took a model system – a mixture of a liquid and a gas with different temperatures – and developed a theory that describes what happens at their interface. It can describe, for example, a boiling liquid whose molecules escape into the adjacent vapour, a complex dance at the interface.

“We have found a stronger basis for understanding molecular transport in systems with interfaces,” said Phil Rauscher, PhD’20, a former postdoctoral researcher at UChicago and co-author of the paper. “We now have a thermodynamically rigorous way of describing these systems.”

A key hypothesis they proved is that of local equilibrium – a concept from thermodynamics stating that a small part of the interface will always be in equilibrium, even if the whole system is out of equilibrium.

“Seeing local equilibrium at an interface that is out of equilibrium was better than we could have hoped for,” Rauscher said. “It was a guess, but now we’ve proven it to be true.”

Immediate applications of the theory include, for example, gas absorption and extraction, which are used to separate gas mixtures and remove impurities in industry, thereby reducing emissions and ultimately resulting in less pollution.

“Now we want to extend the theory and apply it to more complex systems,” said de Pablo. “We want to demonstrate this theory for different classes of materials, and we hope that scientists and engineers in academia and industry can start using it to design and improve these systems.”

Other authors of the paper include Hans Christian Öttinger of ETH Zurich.

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Sharon D. Cole