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