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We rarely think about how liquids flow—why honey is thick, water is thin or how molten plastic moves through machines. But for scientists and engineers, understanding and predicting the viscosity of materials, especially polymers, is essential.

Viscosity governs how substances deform and flow under stress, which in turn affects how they are processed, how they behave in industrial pipelines, in environmental settings, or in consumer products, and how they respond to changing temperatures.

Traditionally, to calculate the viscosity of a liquid or polymer melt based on molecular simulations on computers, people rely on a method called the Green–Kubo formalism. It works by tracking how internal stresses fluctuate and decay over time inside a simulated material at thermodynamic equilibrium.

This approach is widely used in molecular dynamics simulations and is well established at high temperatures, where everything is fluid and relaxed and thermodynamic equilibrium is a good assumption.

But as we cool these systems toward the so-called glass transition—a point where the material begins to behave more like a solid—things start to get messy. Molecules move sluggishly. Stress correlations take a long time to decay. Simulations drag on for unrealistically long times, and the Green–Kubo method begins to fail. We're left with uncertainty right where the physics gets most interesting.

This motivated me to take a different path—one that doesn't rely on waiting for a system to relax. Instead, I decided to listen to how the material vibrates. In particular, I published a paper in 2023 that established a new mathematical relation between viscosity and the vibration spectrum of atoms and molecules in a material.

With my collaborators Ankit Singh and Vinay Vaibhav at the University of Milan, and with Tim Sirk at the U.S. Army Research Laboratory, in a paper just in the Journal of Chemical Â鶹ÒùÔºics, I introduced a new atomistic method for computing viscosity that builds on that 2023 theoretical framework.

That , published in Â鶹ÒùÔºical Review E, showed how the flow and elasticity of liquids and disordered solids—like glasses and polymers—can be understood through something called non-affine lattice dynamics, or NALD. It describes how atoms and molecules deviate from ideal, uniform motions when the material is deformed. These non-affine motions are the hallmark of disorder, and they turn out to be crucial in determining how materials resist flow.

In this new study, we took that theory and applied it to real atomistic simulations of polymers. Specifically, we used the Kremer–Grest model, a well-known, coarse-grained representation of polymer chains. We then computed how the atoms vibrate around their equilibrium positions—the full spectrum of vibrational modes.

From this, using the NALD formalism, we were able to calculate how the material responds to stress at different frequencies. This gives us a spectrum of shear moduli—essentially, a fingerprint of how stiff or soft the material is at various timescales.

From the low-frequency end of this spectrum, we extracted the viscosity. What's remarkable is that this approach works all the way down to temperatures near the glass transition, where traditional methods become unreliable. In fact, the vibrational information encodes everything we need to know about how the material flows, without needing to simulate long-time relaxation at all.

Another striking result is that all vibrational modes matter—not just the soft ones. It's the entire landscape of atomic motion, from fast local jiggles to slower collective movements, that contributes to viscosity. This offers deep physical insight into what makes a material flow—or resist flow.

We benchmarked our predictions against conventional Green–Kubo calculations and also against non-equilibrium simulations in the high temperature regime where both these techniques are still reliable. The agreement was excellent across a wide temperature range, without adjustable parameters, but our method maintained its accuracy and efficiency even near the glass transition, where no other method can produce meaningful results.

This has major implications. For one, it opens the door to a more predictive, physically grounded approach to understanding viscosity in fluids and soft matter. It also allows us to compute flow properties in regimes that were previously inaccessible—critical for designing materials that need to function under extreme conditions.

And from a fundamental perspective, it gives us a new way to see how atomic-scale structure and motions translate into macroscopic flow. It also opens doors to predictive design of soft materials and polymers based on their vibrational characteristics, and to new non-destructive, mechanical testing based on vibrational spectroscopy.

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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 being on the faculty of Technical University Munich (2014–2015) and of University of Cambridge (2015–2018), he has been a full professor and chair of theoretical physics in the Department of Â鶹ÒùÔºics 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 interests range from the statistical physics of disordered systems (random packings, jamming, glasses and the glass transition, colloids, nonequilibrium thermodynamics) to solid-state physics and superconductivity.