Characteristic temperatures of glassy behaviour in a simple liquid

Abstract

A model for the metastable liquid in terms of holes present in the amorphous structure is considered using the classical density functional theory (DFT). For a one component Lennard-Jones liquid we obtain the temperature dependence of the free volume v_f in the metastable state. A temperature T₀, similar to that of the characteristic transition of the free volume theory, is identified by extrapolating v_f(T) to zero. The Kauzmann temperature T_K is also obtained here by extrapolating the entropy difference between the supercooled state and that of the crystal to zero. We compare the temperatures T₀ and T_K obtained in our model with other two characteristic temperatures for glassy behaviour, namely (a) the dynamic transition temperature T_c of the mode coupling theory (MCT) and (b) the glass transition temperature T_g which was obtained by Leonardo et al (2000 Phys. Rev. Lett. 84 6054) from studying the violation of the fluctuation-dissipation theorem. All the four temperatures, obtained from independent routes, are located with respect to the melting temperature T_m in a manner which is in agreement with experiments.