A new look at mesoscopic dynamics of molecular liquids

Imagine a glass of water or a bottle of ethanol. These are molecular liquids, substances where molecules are free to move but are still closely packed, interacting with each other through forces like hydrogen bonds or weaker attractions. Scientists have long been fascinated by how these molecules move and interact, especially at scales that are neither as small as individual atoms nor as large as the bulk liquid we see with our eyes. This intermediate scale, known as the mesoscopic scale, is where intriguing behaviours emerge, and a recent study ¹ sheds new light on these dynamics, revealing surprising universal patterns in how molecules in liquids move collectively and individually.

Exploring molecular liquids with neutron scattering

To understand this research, let’s first consider what happens in a liquid at the mesoscopic scale. This scale involves distances of about 6 to 60 nanometres—much larger than the size of a single molecule but not yet in the realm where the liquid behaves like a uniform fluid, as described by hydrodynamics. At this scale, the liquid’s structure is relatively uniform, meaning the arrangement of molecules doesn’t vary much over these distances. Scientists study this scale using a technique called neutron scattering, which is like shining a special kind of light on the liquid to watch how its molecules wiggle and jostle.

Neutron scattering comes in two flavours: coherent and incoherent. Coherent scattering tells us about collective motion—how groups of molecules move together, like a crowd swaying in sync. Incoherent scattering, on the other hand, tracks individual molecules, similar to following a single person’s steps in that crowd. The researchers used a sophisticated version of this technique, called neutron spin echo, to study five different liquids: glycerol, methanol, tetrahydrofuran (THF), propylene carbonate, and tributyl phosphate. These liquids vary in their molecular sizes and the types of forces holding them together, from strong hydrogen bonds in glycerol to weaker van der Waals forces in THF.

Simply relax

What they found was remarkable. For collective motion, the way groups of molecules relax—or return to a stable state after being disturbed—follows a simple pattern. This relaxation happens through a process that doesn’t depend on the distance scale within the mesoscopic range. Picture a group of dancers who, after a sudden move, settle back into their rhythm at the same pace, whether they’re spread out over a small or slightly larger area. This process is exponential, meaning it decays smoothly over time, and its timing is linked to something called stress fluctuations—tiny variations in the forces between molecules that ripple through the liquid.

This finding wasn’t entirely new; earlier studies on water and THF hinted at this behaviour. But the researchers showed it’s universal, appearing in all five liquids despite their different molecular interactions. They suggest this universal behaviour stems from a fundamental principle: the conservation of momentum. When molecules interact through direct forces, their collective motion cancels out certain diffusive effects at the mesoscopic scale, leading to this consistent relaxation time.

A nondiffusive relaxation process

Now, let’s turn to the individual molecules. You might expect that, at the mesoscopic scale, a single molecule’s motion would be dominated by diffusion—the random wandering we associate with particles in a liquid, like pollen grains jiggling in water. Diffusion is indeed a major player, but the researchers uncovered something unexpected. The individual motion of molecules also shows a fast, local relaxation process that mirrors the collective one. This process happens on a short timescale and doesn’t vary with distance, much like the collective relaxation.

To make sense of this, the researchers developed a model that describes individual motion as a combination of two processes: the slow, diffusive wandering and a quicker, local motion tied to the same stress fluctuations seen in collective dynamics. This local motion is like a molecule briefly rattling in a temporary “cage” formed by its neighbours before breaking free to diffuse. The timing of this local motion closely matches the collective relaxation time, suggesting that the same underlying forces—those stress fluctuations—are at play.

This discovery challenges a common assumption that individual molecular motion at the mesoscopic scale is purely diffusive, especially at high temperatures where molecules are more energetic. Instead, the study shows that stress fluctuations influence both collective and individual motions, even in warm liquids. The researchers also found that the spatial extent of this local motion shrinks as the liquid cools toward its glass-transition temperature, the point where it becomes a rigid, glassy solid. This hints at a connection to the physics of glass formation, where molecular motion slows dramatically.

To dig deeper, the researchers analysed how the strength of molecular vibrations and local motions changes with temperature. Vibrations, which are tiny oscillations of molecules, grow stronger with heat, as expected. The local motion, however, has a larger spatial extent and seems to vanish near the glass-transition temperature, reinforcing its link to the liquid’s ability to flow or freeze.

A hidden unity in the dance of molecules in liquids

The implications of this work are profound. By showing that a nondiffusive relaxation process governs both collective and individual motions at the mesoscopic scale, the study offers a new lens on how liquids behave. This could impact fields from materials science, where understanding liquid dynamics helps design better polymers or glasses, to biophysics, where similar principles govern the behaviour of biological fluids. The use of neutron spin echo, with its ability to separate collective and individual motions, was key to this breakthrough, highlighting the power of advanced experimental techniques in uncovering hidden patterns in nature.

In essence, this research reveals a hidden unity in the dance of molecules in liquids. Whether they’re moving in sync or wandering alone, molecules at the mesoscopic scale are influenced by the same stress fluctuations, creating a universal rhythm that transcends the specifics of each liquid. It’s a reminder that even in the chaotic world of liquids, there’s an underlying order waiting to be discovered.

Author: César Tomé López is a science writer and the editor of Mapping Ignorance

Disclaimer: Parts of this article may have been copied verbatim or almost verbatim from the referenced research paper/s.