Imagine a highway jammed with bumper-to-bumper traffic, all cars crawling. A motorcycle weaves through the gridlock, moving far faster than the overall traffic flow. At the molecular level, a similar phenomenon occurs in glass-forming liquids. As the liquid cools and becomes more viscous, most molecules slow down, but a few take shortcuts and diffuse much faster than expected. This breakdown of the classical Stokes-Einstein relation known as decoupling has puzzled scientists for decades.
A common explanation was that decoupling arises from dynamic heterogeneity, which indicates the spontaneous formation of clusters of fast-moving and slow-moving particles that emerge as a liquid cools toward its glass transition. However, a new study published in National Science Review turns this assumption on its head.
Dynamic heterogeneity is not the cause of decoupling, but rather a symptom. The true origin lies much earlier in the high-temperature liquid, where molecular motion is relatively simple and homogeneous.
An international team led by researchers from the Chinese Academy of Sciences, Nanjing University, the National Institute of Standards and Technology, and Wesleyan University conducted extensive molecular dynamics simulations on more than a dozen different glass-forming systems. These ranged from simple atomic mixtures such as the well-known Kob-Andersen model to complex polymeric materials, including polymer-additive composites, star polymers with variable numbers of arms, and knotted ring polymers of varying complexity.
In all systems, they observed a universal power-law relationship between two characteristic timescales, the structural relaxation time, which relates to viscosity and momentum diffusion, and the peak time of the non-Gaussian parameter, which relates to mass diffusion. The power-law exponent known as the decoupling exponent quantifies how strongly these processes are decoupled.
The key insight came when the team applied the string model of glass formation, an extension of the classical Adam-Gibbs theory. The string model predicts that the decoupling exponent below the onset temperature of glass formation is determined by the ratio of the high-temperature activation free energies for mass and momentum diffusion. To test this, they analyzed data from all systems and found that the measured decoupling exponent matched the predicted ratio with remarkable accuracy.
This means that the seeds of decoupling are already present at high temperatures, where there is minimal dynamic heterogeneity. As the liquid is cooled and collective molecular motion becomes more pronounced, the difference in activation energies is amplified but its origin remains unchanged.
This can be understood through a simple analogy of two runners starting on flat terrain with different natural speeds. When they move to high altitude, the thinner air makes the race harder for both, and the initial speed gap becomes even more apparent. Yet, the outcome was already determined on the plain.
The finding resolves a long-standing puzzle in condensed matter physics. For years, researchers observed that decoupling seemed to correlate with the growth of mobile and immobile particle clusters upon cooling, leading to the natural assumption that these clusters caused the decoupling. The new study shows that this correlation is coincidental rather than causal.
The implications extend beyond fundamental physics. Decoupling plays a critical role in phase-change memory materials, where fast diffusion enhances crystallization; battery electrolytes, where ion transport efficiency depends on the balance between diffusion and viscosity; pharmaceutical stability, where molecular mobility determines shelf life; and atmospheric science, where aerosol particle diffusion affects cloud formation.
Because the key activation parameters can be determined from relatively short simulations at high temperatures, the team suggests that machine learning methods could help rapidly screen new materials for their decoupling behavior, opening a pathway toward predictive design of advanced materials.
The research was supported by the National Natural Science Foundation of China and used computing resources at the Changchun Institute of Applied Chemistry.
