Disordered Worm-Like Clusters in a Hexagonal Mesophase Former: Simulation and Thermodynamic Description

In microphase-forming systems, the loss of long-range order at the order-disorder transition does not necessarily imply the total disappearance of short-range structural organization. Instead, transient clusters locally resembling the ordered mesophase may persist within the isotropic phase. While the existence of such clusters is known, their statistical properties and their relationship to the thermodynamic signatures of the system have not been fully characterized. In this work, we address these questions for a binary mixture with isotropic Stillinger-Weber interactions that stabilizes a hexagonal mesophase by combining molecular dynamics simulations with thermodynamic modeling. A geometry-based algorithm is introduced to identify worm-like aggregates from particle configurations using a temperature-dependent B-B connectivity criterion. The resulting size distributions are monotonically decreasing and broaden markedly on approaching the order-disorder transition from above, showing that the disordered phase is not locally homogeneous but retains a population of finite worm-like fragments with persistent local compositional order. To rationalize these observations, we develop a minimal thermodynamic model based on a Flory-Huggins-type free energy, in which cluster formation is controlled by a single effective interaction parameter. The model reproduces the simulated size distributions over the explored temperature range using a single temperature-independent energetic parameter for a physically meaningful connectivity definition. Using this same parameter, fitted only to the structural distributions, the predicted disordering enthalpy closely matches that obtained directly from the simulations, providing an independent thermodynamic validation. Together, these results identify worm formation as the dominant energetic contribution in the isotropic phase and provide a direct link between microscopic cluster statistics and macroscopic thermodynamic behavior above the order-disorder transition.