A free-energy landscape picture and Landau theory for the dynamics of disordered materials

TL;DR

This paper develops a theoretical framework combining free-energy landscapes and Landau theory to explain the complex relaxation dynamics of disordered materials, emphasizing entropy effects and internal-energy maxima.

Contribution

It introduces a novel approach applying Landau's theory with nanothermodynamics to disordered systems, highlighting entropy's role and internal-energy maxima in dynamics.

Findings

Explains VTF-like relaxation rates and time-temperature superposition.

Provides a unified picture for relaxation time distribution and heterogeneity.

Shows entropy dominates thermal behavior in disordered systems.

Abstract

Landau's theory of phase transitions is adapted to treat independently relaxing regions in complex systems using nanothermodynamics. The order parameter we use governs the thermal fluctuations, not a specific static structure. We find that the entropy term dominates the thermal behavior, as is reasonable for disordered systems. Consequently, the thermal equilibrium occurs at the internal-energy maximum, so that the minima in a potential-energy landscape have negligible influence on the dynamics. Instead the dynamics involves normal thermal fluctuations about the free-energy minimum, with a time scale that is governed by the internal-energy maximum. The temperature dependence of the fluctuations yields VTF-like relaxation rates and approximate time-temperature superposition, consistent with the WLF procedure for analyzing the dynamics of complex fluids; while the size dependence of the fluctuations provides an explanation for the distribution of relaxation times and heterogeneity that are found in glass-forming liquids, thus providing a unified picture for several features in the dynamics of disordered materials.