For decades, physicists studying how molecules move inside glasses have encountered a stubborn mathematical problem: the Arrhenius equation, a cornerstone of chemical kinetics, kept producing wildly unrealistic results. Researchers at the University of Silesia and the Naval Research Laboratory in Washington, DC, have now solved this puzzle, resurrecting an overlooked theory from the 1960s and opening a new understanding of how disordered materials behave.
Glasses—materials where molecules and atoms lack the orderly arrangement of crystals—are everywhere. They form the base of pharmaceuticals, optical devices, and electronics. When scientists measure how molecules move within these glasses and plug their findings into the Arrhenius model, developed by Swedish chemist Svante Arrhenius in 1889, something goes systematically wrong. The calculations produce pre-exponential factors—values describing the intrinsic timescale of molecular motion—that are sometimes many orders of magnitude too small to be physically possible. Researchers gradually accepted this inconsistency as simply the way things worked, but Marzena Rams-Baron and her team decided to ask why.
The breakthrough came while studying carefully designed molecules with rotating fragments—molecular rotors. Structurally similar rotors should produce similar results, yet their 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," Rams-Baron explained. The team then rediscovered a largely forgotten 1960s theoretical paper by French physicist Claude Brot, who had suggested something radical: the activation energy guiding molecular motion might not be constant, as Arrhenius assumed, but instead could change with temperature—an effect detectable only through constant-volume experiments.
The key insight was recognizing that conventional experiments, which measure relaxation times at ambient pressure while cooling materials, conflate two independent effects. When temperature drops, not only does the material get colder, but its molecules also pack more densely together. These density-related effects had been invisibly baked into every measurement, distorting the true activation energy. The researchers set out to test Brot's century-old hypothesis experimentally by separating intrinsic thermal effects from these hidden density effects.
Their work, published in Physical Review Letters, introduced an updated physical framework for describing how molecular rearrangements unfold in glasses and other disordered materials. By designing experiments that could hold volume constant while varying temperature—or vary pressure while holding temperature fixed—the team demonstrated that Brot had been right all along. The "Arrhenius paradox" was not a flaw in how physics works, but a misunderstanding of what the traditional equation was actually measuring.
The implications reach far beyond textbook curiosity. Glasses appear in countless applications where thermal stability and relaxation times matter—from drug formulations that must remain stable in storage to polymer films in electronics. A correct understanding of how temperature and molecular motion relate could improve predictions about material longevity, help engineers design more stable compounds, and deepen the fundamental physics of disordered systems. What had been accepted as an unsolvable mystery for decades, Rams-Baron reflected, was simply waiting for someone to ask the right question about density's hidden role.