What happens when you bring two negatively charged objects really close to each other? Repulsion would be the obvious answer, but what if there were positive charges in between? Recently, MIT researchers as part of the Center for Enhanced Nanofluidic Transport (CENT) published a theory in *Langmuir* which offered a comprehensive mathematical description for this fundamental problem. Their answer? It depends.

Curiously, a liquid solution loaded with ions, known as an electrolyte, can bring two negatively charged layers closer together when it is sandwiched in between. The new theory reports an attractive disjoining pressure that arises from electrostatic interactions. It becomes pronounced when the charged layers are only a few nanometers apart from each other. In those cases, like charges can appear to attract! The secret to this counterintuitive phenomenon lies in the ions confined between the layers.

“The positive ions in the solution are very strongly attracted to the negatively charged surface, and they can bridge across from one surface to the other,” explained Pedro de Souza, a graduate student advised by Martin Bazant, an applied mathematician and MIT chemical engineering professor. “They act as a glue between the two surfaces.”

Simple as it sounds, the mathematical description of the phenomenon is anything but straightforward. The starting point was an equation that Bazant, now affiliated with CENT, and co-workers wrote down in 2011. It describes the electric potential near a negatively charged surface, when positive ions approach it to overcompensate the surface charges, thus attracting more negative charges that reside behind them. This effect, known as overscreening, is not predicted by an established theory, but it is commonly seen in experiments.

Counter to intuition, Bazant’s modified equation, which takes overscreening into account, shows that ions may also feel slightly more comfortable when they are squeezed close together. In technical terms, the confinement of the ions lowers the free energy of the electrolyte.

Daniel Blankschtein, another MIT chemical engineering professor, has also investigated electrostatic interactions in a variety of novel materials through a combination of computer simulations and theory. Before CENT was funded last year, Blankschtein’s graduate student, Rahul Prasanna Misra initiated research to calculate the disjoining pressure using Bazant’s energy equation. However, it was the CENT collaboration that brought Blankschtein and Bazant together. De Souza then teamed up with Misra to complete the mathematical theory. The new team aimed to derive an equation for the force in the electrolyte between two charged surfaces that directly takes into account Bazant’s contribution.

The result of the derivation was enlightening indeed. They found that, as the ion which neutralizes the surface charges increases in valency—the number of charges per ion—the new theory predicted an attractive force. To validate this unusual effect, the authors were pleased to find an experimental study on the cohesive strength of cement paste.

“Cement is such a ubiquitous material and cement paste is mostly calcium silicate hydrate layers with calcium hydroxide salt solution as the electrolyte,” Misra said. “Experiments have already shown that the surfaces are negatively charged.”

That leaves the positive calcium ions, each bearing two positive charges, to act as the glue. In mathematical language, one additional term in the new equation flipped the sign of the overall prediction, matching the experimental observations.

The implication of their new theory goes far beyond cement paste. At the cutting edge of energy-efficient separation technology, CENT scientists have been looking deep into nanoscale pores that could trap, transport, and sieve particles in water. These microscopic actions, once clearly understood, will benefit applications ranging from seawater desalination to drug delivery inside our bodies.

As CENT director Michael Strano explains, “When fluids are confined to roughly 10 nanometer and smaller regions, we see very exotic phenomena that theory often fails to describe. But these very narrow conduits show up in technological applications, and we hope that they will form the basis for new low-energy separation processes. Imagine being able to sieve ions or impurities in water through chemical separations—that we currently rely on distillation to accomplish. You need very narrow pores.”

Uniquely, CENT contributes to the advancement of technology by outputting insightful scholarship that will guide researchers down the road. The center recently published a perspective article outlining the seven knowledge gaps that its researchers identified in the field. Closing these gaps requires not just more experiments, but the ingenuity of new and modified theories.

“The gold standard in science is to extrapolate from a theory and predict the outcome of an experiment,” said Strano. “In turn, every experiment that is compared with a prediction is a potential falsification of the theory. To show that you can now predict what you could not before means you have made demonstrable progress on a knowledge gap.”

Strano lauded Bazant and Blankschtein as linchpins of the center for their fundamental contribution that explained long-standing mysteries in nanofluidics.

“Our center is organized with a bottom-up strategy, where principal investigators self-assemble into groups and put mini-proposals together. These two groups found each other through this process,” said Strano.

He believes that this unique structure has accelerated the journey that a good piece of scientific theory takes towards validation or falsification by new simulations and experiments.

Misra echoes this belief. “Although professors Blankschtein and Bazant worked on related areas at MIT, it was the EFRC collaboration that gave us a common platform to work on interesting ideas.”

As a continuation of their collaboration, the two teams are working together to carry out a one-to-one comparison of the predictions of the new theory with simulations.