Glasses are non-crystalline but solid states of matter in which molecules and atoms are not arranged into a regular crystal lattice, but rather in a disordered pattern. Glassy materials are widely used in various settings, for instance, in the synthesis of pharmaceuticals and the development of electronics or optical devices.
When studying movement and changes in various materials and substances, physicists commonly rely on the so-called Arrhenius model. This is a mathematical framework introduced by Svante Arrhenius in 1889, which can be used to calculate how temperature affects the speed of a heat-activated chemical reaction or physical process.
Past studies have shown that when the Arrhenius model is applied to molecular glasses, it yields unrealistically small pre-exponential factors. Pre-exponential factors are values that describe the intrinsic timescale of the movement of molecules without considering temperature effects.
Researchers at University of Silesia and the Naval Research Laboratory in Washington, DC, have gathered new evidence that could explain this well-documented inconsistency of the Arrhenius model.
Their paper, published in Physical Review Letters, introduces an updated physical framework that could be used to describe gradual molecular rearrangements in glasses and other disordered materials.
“The inspiration for this work came from a problem that had been present in the field for decades, but which many researchers had gradually learned to accept,” Marzena Rams-Baron, first author of the paper, told Phys.org.
“When scientists analyze molecular motions in glasses using the Arrhenius equation, they often obtain pre-exponential factors that are clearly nonphysical, sometimes many orders of magnitude smaller than what should be possible from a molecular point of view. For a long time, we also did not have a convincing explanation for this inconsistency.”
Solving an established inconsistency of the Arrhenius model
The idea behind this study came to the researchers while they were studying a series of carefully designed molecules containing internally rotating fragments, called molecular rotors. In these systems, selected parts of the molecule can rotate relative to the rest of the molecular structure.
“These systems were almost ideal model compounds because we knew exactly which molecular fragment was rotating,” said Rams-Baron.
“Surprisingly, although the rotors were structurally very similar, the experimentally determined pre-exponential factors varied by nearly seven orders of magnitude. At that point, it became clear to us that the problem could not simply originate from molecular structure alone. Almost exactly at that moment, we came across a largely forgotten theoretical paper published by the French physicist Brot in the late 1960s.
“He suggested that activation energy might not actually be constant, as assumed in conventional Arrhenius analysis, but instead could change with temperature. This can only be resolved by constant-volume experiments.”
The researchers showed that this idea, introduced by Claude Brot over 80 years ago, could explain the anomalous Arrhenius parameters observed in molecular glasses. They thus set out to test this concept experimentally using the molecular systems they designed.
“Our primary objective thus became to determine whether the long-standing ‘Arrhenius paradox’ could finally be resolved by separating intrinsic thermal effects from density-related effects hidden in conventional measurements,” explained Rams-Baron.
“The key idea was realizing that temperature and density are inseparable in ordinary experiments when relaxation times are measured as a function of temperature at ambient pressure conditions.”
When a material is cooled at constant pressure, not only does its temperature change, but also how tightly its underlying molecules are packed together. If the density of molecules also changes, then the activation energy would be influenced by both thermal and molecule density-related effects.
“To separate these effects, we combined broadband dielectric spectroscopy with pressure-volume-temperature (PVT) measurements,” said Marian Paluch, co-author of the paper.
“This allowed us to reconstruct the relaxation times under constant-volume (or isochoric) conditions. In simple terms, we asked: what happens if the density is kept fixed while the temperature changes? Once we did this, the paradox essentially disappeared.”
The team’s experiments showed that the activation energy in molecular glasses is not constant, but rather it decreases linearly as the temperature decreases. Notably, this is precisely what Brot had predicted decades ago.
“This means that the anomalous pre-exponential factors observed in conventional Arrhenius analysis are not mysterious or nonphysical after all; they arise because density effects are hidden inside standard measurements,” said Paluch.
Informing future condensed matter physics research
The recent work by Rams-Baron and her colleagues explains why conventional Arrhenius fitting approaches tended to yield unrealistic activation energies when applied to molecular glasses. In addition, it proposes an alternative framework that could be better suited for analyzing thermally activated processes in condensed matter.
“Our paper provides a physical explanation for a long-standing inconsistency in the interpretation of rotational dynamics in molecular glasses,” said Rams-Baron.
“Instead of invoking abstract entropy corrections, we show that apparently unrealistic Arrhenius parameters can be transformed into meaningful molecular quantities when density effects are properly included.”
The researchers believe that their study could also have implications for the study of other materials beyond molecular glasses. In fact, it could enable the introduction of more reliable approaches for studying chemical and physical processes in various materials and compounds, including polymers, various solids and even pharmaceuticals.
“Our results suggest that, in systems where molecular dynamics is sensitive to density changes, the experimentally determined activation parameters may contain hidden density-related contributions,” explained Paluch. “Consequently, some current approaches used to describe molecular mobility, relaxation behavior, or material stability may require correction or reinterpretation.”
The results gathered by Paluch and her colleagues might eventually inform the design of materials with more predictable thermal and mechanical properties. Before that, however, the researchers plan to further explore the phenomenon they observed, to understand whether it is universal or is only relevant to specific materials or scenarios.
“Our paper is only the beginning,” added Rams-Baron. “While it solved one paradox, it also opened many completely new questions. In the near future, we want to understand how universal this phenomenon is and what molecular factors determine the sensitivity of rotational barriers to density changes.”
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Publication details
Marzena Rams-Baron et al, Resolving the Arrhenius Paradox by Isochoric Analysis of Rotational Barriers in Molecular Glasses, Physical Review Letters (2026). DOI: 10.1103/jpnz-xfbj.
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Molecular glasses solve long-standing Arrhenius paradox (2026, June 2)
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