Thermodynamic stability of amorphous morphologies

Determine whether the amorphous morphologies in the charged binary fluid are thermodynamically stable equilibrium states or merely long-lived metastable states, beyond the resolving capability of the two-mode harmonic approximation.

Background

The paper studies a charged binary fluid whose tendency toward macroscopic phase separation competes with screened electrostatic repulsion. Numerical simulations produce disordered amorphous morphologies, including labyrinthine patterns in two dimensions and tubular and shell-like structures in three dimensions. The authors compare these configurations with ordered lamellar and droplet phases using free-energy estimates and find that amorphous states can have comparable, and in some cases lower, free energies. However, the two-mode harmonic approximation used for the analytical phase diagram includes only homogeneous, charge-separated, lamellar, and hexagonal-droplet patterns, and therefore cannot represent amorphous states directly.

The unresolved issue is whether the amorphous configurations correspond to genuine thermodynamic equilibrium phases stabilized by frustration and entropy, or whether they are long-lived metastable transients that would eventually decay into another morphology. Resolving this question requires an approach capable of comparing amorphous states with ordered phases at equilibrium, rather than relying solely on finite-time simulations and an approximation that excludes amorphous structures by construction.