Theory 004/Physics & Matter /Glass physics
Glass Transition Tracks an Entropy Ratio
Two glasses with equal entropy behave differently. The split between what is stored in arrangements and what in vibrations may be the variable.
The glass transition temperature scales with the ratio of configurational to vibrational entropy rather than with any single entropy, so compositions with the same total entropy can have different transition temperatures.
01The evidence
The glass transition is associated with a fall in configurational entropy toward a small value, and the ratio of configurational to vibrational entropy varies widely across glass formers.
02The tension
Models use total entropy or configurational entropy alone, and both fail to collapse data across chemically different glasses. The failure is absorbed into a fragility parameter.
03The mechanism
Vibrational entropy is stored in the phonon spectrum; configurational entropy is stored in the number of accessible arrangements. Their ratio measures how much of the system's freedom is in rearrangements rather than in vibration.
A system with a low ratio has little configurational freedom to lose, so it rigidifies at a lower temperature. That predicts the transition temperature should track the ratio rather than either term.
04What this is not
Those models use configurational entropy alone. This uses its ratio to vibrational entropy, which predicts differences at equal configurational entropy.
05Predictions
- P1Transition temperature should collapse onto the ratio across chemistries.
- P2Compositions matched on configurational entropy but differing in vibrational should differ.
- P3Pressure should shift the ratio and the transition together.
06Refutation
Data collapsing on configurational entropy alone would make the ratio redundant.
07What it changes
It would give glass design a single structural variable.