Novel approach to numerical measurements of the configurational entropy in supercooled liquids

Significance When liquids are cooled sufficiently fast, they remain trapped in an amorphous metastable state called a “glass.” Due to their highly disordered structure at the microscale, however, glasses are characterized by a large multiplicity of metastable states. The configurational entropy represents a measure of their number and can be estimated in experiments and simulations via different, and sometimes inconsistent, approximations. Here we propose a novel method to compute the configurational entropy in a computer simulation. Compared with other approaches, the proposed numerical scheme allows one to obtain an observable that is conceptually closer to the theoretical definition and at the same time yields results in better agreement with experiments. The configurational entropy is among the key observables to characterize experimentally the formation of a glass. Physically, it quantifies the multiplicity of metastable states in which an amorphous material can be found at a given temperature, and its temperature dependence provides a major thermodynamic signature of the glass transition, which is experimentally accessible. Measurements of the configurational entropy require, however, some approximations that have often led to ambiguities and contradictory results. Here we implement a novel numerical scheme to measure the configurational entropy Σ(T) in supercooled liquids, using a direct determination of the free-energy cost to localize the system within a single metastable state at temperature T. For two prototypical glass-forming liquids, we find that Σ(T) disappears discontinuously above a temperature Tc, which is slightly lower than the usual estimate of the onset temperature for glassy dynamics. This observation is in good agreement with theoretical expectations but contrasts sharply with alternative numerical methods. While the temperature dependence of Σ(T) correlates with the glass fragility, we show that the validity of the Adam–Gibbs relation (relating configurational entropy to structural relaxation time) established in earlier numerical studies is smaller than previously thought, potentially resolving an important conflict between experiments and simulations.

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