When less is more: Scaling law explains why ultrathin materials get stronger as they get thinner

June 14, 2026 dialog When less is more: Scaling law explains why ultrathin materials get stronger as they get thinner Sadie Harley Scientific Editor Robert Egan Associate Editor One of the most fascinating aspects of physics is that nature often behaves in ways that seem completely counterintuitive. A good example comes from ultrathin materials. If I take a sheet of material and make it thinner and thinner, most people would expect it to become weaker. After all, there is less material left to bear a load. Yet over the last decade, experiments and simulations have repeatedly shown something surprising: when certain materials become extremely thin—only a few nanometers or even a few atomic layers thick—they can become dramatically more resistant under extreme mechanical loading. This phenomenon has been observed in systems as different as graphene, graphene oxide, and ultrathin polymer films. The effect was clear, but the reason behind it remained unclear. Why should materials with completely different chemistry and structure all exhibit a similar trend? That question motivated our recent study, published in PNAS. Rather than focusing on the chemical details of individual materials, I approached the problem from a more fundamental perspective. I asked whether there might be a universal mechanical principle that all these systems share. The answer turned out to be "yes". The key idea comes from a concept known as nonaffine elasticity. In real materials, atoms and molecules do not simply follow an externally imposed deformation in a perfectly orderly way. They also undergo additional collective motions that help the material relax internal forces and stress. These motions generally make a material softer. An analogy is a crowd of people trying to make room in a busy train station. If everyone is free to move around, pressure can be relieved through many different rearrangements at various length scales. But if movement becomes spatially restricted, the crowd becomes effectively stiffer and less able to adapt. Something similar happens in ultrathin materials. When a material is confined to an extremely small thickness, many long-wavelength collective deformation modes simply cannot exist anymore. The material loses some of the pathways that normally allow it to deform. As a result, it becomes mechanically stiffer. What surprised me most was that this effect follows a remarkably simple mathematical law derived from microscopic atomic motions and dynamics. Our analysis shows that the confinement-induced increase in stiffness scales with the inverse cube of the thickness. In practical terms, reducing the thickness by a factor of two increases the confinement contribution by roughly a factor of eight. Even more remarkably, the same scaling law describes data from graphene, graphene oxide, and polymer thin films despite their enormous differences in composition and structure. This suggests that the phenomenon is not primarily about chemistry. Instead, it emerges from a universal aspect of elasticity itself. I find this particularly exciting because it transforms what appeared to be a collection of unrelated observations into a single physical picture. Often in science, the most satisfying discoveries are not those that reveal something entirely new, but those that show that seemingly different phenomena are actually manifestations of the same underlying principle. Beyond its fundamental interest, understanding how confinement alters mechanical properties could help guide the design of future materials that are both lightweight and mechanically robust. Many emerging technologies—from flexible electronics to advanced coatings and nanoscale devices—rely on structures whose dimensions are measured in nanometers. In such systems, the traditional intuition developed from bulk materials can become misleading. More broadly, this work highlights an idea that I find central to modern materials physics: when matter is reduced to very small dimensions, entirely new rules, often counterintuitive, can emerge. The nanoscale is not simply a smaller version of the macroscopic world. It is a regime where geometry, confinement, and collective motion can fundamentally reshape material behavior. In this case, the lesson is a simple one: Sometimes, less really does become more. This story is part of Science X Dialog, where researchers can report findings from their published research articles. Visit this page for information about Science X Dialog and how to participate. Publication details Alessio Zaccone et al, General inverse-cube thickness scaling of projectile penetration energy in ultrathin films, Proceedings of the National Academy of Sciences (2026). DOI: 10.1073/pnas.2609202123 Journal information: Proceedings of the National Academy of Sciences Alessio Zaccone received his Ph.D. from the Department of Chemistry of ETH Zurich in 2010. From 2011 till 2014 he was an Oppenheimer Research Fellow at the Cavendish Laboratory, University of Cambridge. After faculty appointments at Technical University Munich (2014–2015) and at University of Cambridge (2015–2018), he has been an associate professor and then a full professor and chair of theoretical physics in the Department of Physics at the University of Milano since 2022. Awards include the ETH Silver Medal, the 2020 Gauss Professorship of the Göttingen Academy of Sciences, the Fellowship of Queens' College Cambridge, and an ERC Consolidator grant "Multimech." Research contributions include the analytical solution to the jamming transition problem (Zaccone & Scossa-Romano PRB 2011), and the analytical solution to the random close packing problem in 2D and 3D (Zaccone PRL 2022). He is the author of the book "Theory of Disordered Solids", Springer, 2023.