Glycerol is a fragile glass-former with glass transition temperature and melting point

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Crystal structure, bonding and diffraction · Crystal structure, bonding and diffraction

Solid State Physics, Ch Solids without a lattice: glasses and quasicrystals

Problem

Glycerol is a fragile glass-former with glass transition temperature Tg=190 KT_g = 190\,\mathrm{K} and melting point Tm=291 KT_m = 291\,\mathrm{K}. Calorimetry gives a fusion entropy ΔSm=62.0 J mol−1 K−1\Delta S_m = 62.0\,\mathrm{J\,mol^{-1}\,K^{-1}} and an excess liquid-over-crystal heat capacity ΔCp=80.0 J mol−1 K−1\Delta C_p = 80.0\,\mathrm{J\,mol^{-1}\,K^{-1}}, closely constant over the supercooled range studied. A Vogel-Fulcher fit to the viscosity of supercooled glycerol gives T0=130 KT_0 = 130\,\mathrm{K}. ((a)) Using ΔS(T)=ΔSm−∫TTmΔCp/T′ dT′\Delta S(T) = \Delta S_m - \int_T^{T_m} \Delta C_p/T'\, dT' with ΔCp\Delta C_p taken constant, find the Kauzmann temperature TKT_K at which the extrapolated excess entropy of the supercooled liquid over the crystal would reach zero. ((b)) State the two standard responses to the resulting paradox, and say whether the relation between TKT_K, T0T_0 and TgT_g found here decides between them.

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