Entropy gets a bad rap. Typically associated with randomness and chaos, it can also correlate with freedom and diversity.

Cornell researchers found that, thanks to the latter qualities, entropy can help bind certain pairs of molecules faster and more robustly – an approach that could have broad applications in drug development and assembling nanoparticles to form new materials.

The study published May 5 in the Proceedings of the National Academy of Sciences. The lead author is Mohammed Alshammasi, Ph.D. ’26.

Leading the project was Fernando Escobedo, the Samuel W. and M. Diane Bodman Professor in Chemical Engineering in the Cornell Duffield College of Engineering.

Escobedo’s group conducts molecular modeling to study physical phenomena and materials at the mesoscale – that middle range between quantum mechanics and the larger continuum models. The goal is to understand how to design building blocks, such as polymers and nanoparticles, that can self-assemble into deliberate, useful structures.

The Escobedo Lab also uses its modeling capabilities as a form of molecular sleuthing to assist other researchers who are exploring experimental systems.

One such researcher was Chris Alabi, the Fred H. Rhodes Professor of Chemical Engineering in Duffield Engineering and co-author of the paper, who was looking into different chemistries that could create synthetic polymers that mimic DNA’s ability to generate selective binding between building blocks. A potential candidate was oligocarbamates, which are oligomers – short-length polymers typically made of chains of less than 20 monomers – that can be synthesized from renewable sources such as vanillin. Like DNA, oligocarbamates can be designed to have sequence-specific groups that bind in a complementary fashion, but unlike DNA, which only works in water, they can also function in different industrially relevant solvents. 

But when that binding process was scrutinized, the researchers were surprised to find that in some cases there had been a slight increase in entropy – the exact opposite of what normally occurs.

“That seemed strange to us,” Escobedo said. “When you have these two separate molecules, they have more degrees of freedom of motion. When they bind, you have reduced the total translational degrees of freedom by half. So this bound object should have less entropy than the two unbound molecules. It seemed that maybe there was some kind of error in the analysis or that the solvent molecules around them were playing an outsized role. There was some mystery.”

Entropy’s advocate

Escobedo is no stranger to entropy. From an engineering perspective, he is the misunderstood property’s advocate. 

In nature, two main forces essentially drive all phenomenon: energetics and entropy. Most chemists and engineers focus on the former, Escobedo said; for example, manipulating atoms to confer molecules with more or less affinity, or attract or repel each other.

“Energetic forces are not necessarily easy to calculate, but conceptually, their effects are more intuitive and easier to understand,” Escobedo said. “But entropic forces are not. They tend to be working in the background, so people don’t proactively engineer entropy in their systems. Sometimes they think they have to fight it because entropy is just trying to create disorder, chaos, which is not accurate, of course.” 

Escobedo’s team modeled the system and found that entropic change upon binding was indeed positive. The explanation was in the very shape of the molecules. Generally, oligomers wriggle freely in solution, “like a snake,” according to Escobedo. But his team found that one of the oligomers was forming a loop, with its two ends connecting, before binding with its partner. 

“It had this intramolecular interaction between two groups of the same chain that made it into a loop,” he said. “So it was more constrained.” 

When the two molecules attached, the looped one was forced to open up. It gained more range because it could then move more freely.

“In these polymers or oligomers, their entropy is mostly in their conformations. So the more conformations it has access to, the more freedom to move in different ways, the more entropy it has,” he said. “When it was looped, it has fewer configurations, and when the loop got released, it had more. So the entropy increase was due to this partner gaining more freedom to explore more conformations when bound.”

Escobedo compared entropic force binding to an ideal marriage.

“By marrying another person, in some ways, you are constraining yourself. You had more freedom before,” he said. “But the best marriage would be one where you had some constraints when single, and then as a couple you are able to enjoy a new type of freedom. If it’s too constraining, that’s not going to work that well.”

The result is a robust bond that forms much faster than when fighting entropy. This would be particularly useful for chemically engineering new pharmaceutical products and the ligand-mediated selective binding of nanoparticles into complex structures.

“This binding, or recognition, of two molecules is at the core of many processes, from biology to material science, and understanding general principles for how that happens, how that can be optimized, e.g., through strategic pre-constraining of the molecules before binding, is crucial,” Escobedo said. “When we design molecules, we need to design them thinking not just about the raw affinity through energetics, but also the entropy.”

Kenton Weigel, Ph.D. ’24 was also a co-author.

The research was supported by the Research and Development Center of Saudi Aramco and the National Science Foundation.