Thermodynamic aspect of the glass transition

A new characterization of the thermodynamic transition underlying the glass transformation is proposed. The definition incorporates both the continuous nature of the transition from supercooled liquid to amorphous solid as well as history dependent effects. Contrary to usual approaches of considering differences of thermodynamic quantities between the (metastable) equilibrium liquid and a glass, viz. δX> ≡ Xe − Xg, the present characterization of the glass transition is based on differences between a supercooled liquid-amorphous solid branch and the stable crystalline solid, that is, ΔX ≡ Xℓ −Xc. For the hard-sphere and the soft-sphere models, the present general definition of the glass transition reduces to δ(Cp) → O+ as T → T+g which implies a minimum in the excess entropy δS. However, for more general pair potentials, for instance, Lennard-Jones model, δ(Cp) 0 at tthe transition point, albeit small. This behavior suggests that the glass transition is indeed dictated by the repulsive part of the potential.