Glass Transition — Kauzmann Entropy Crisis

Where does the liquid's excess entropy go? VFT viscosity divergence, fragility, and the ideal glass paradox

Glass T_g / T_m
T_Kauzmann / T_m
η at T_g (Pa·s)
Fragility index m

Physics

VFT equation: log η = A + B/(T − T₀). Near T_g viscosity exceeds 10¹² Pa·s (structural relaxation > 100s).

Kauzmann (1948): extrapolating supercooled liquid entropy below T_g crosses crystal entropy at T_K — the liquid would have fewer microstates than the crystal. Paradox avoided by glass transition.

Fragility (Angell): strong liquids (SiO₂) follow Arrhenius; fragile liquids (o-terphenyl) show super-Arrhenius behaviour (VFT). RFOT theory: T_K is a true thermodynamic transition.