Graph theoretical description of phase transitions in supramolecular assemblies of surfactants

Abstract Phase transitions are typically quantified using order parameters, such as crystal lattice distances and radial distribution functions, which can identify subtle changes in crystalline materials or high-contrast phases with large structural differences. However, the structural changes are more difficult to quantify for phases with high asymmetry and multiscale organization as well as for the structural fluctuations preceding phase transitions, which are essential for understanding the system pathways between phases. Here, we show that graph theoretical (GT) descriptors can successfully characterize different phases of a water/surfactant system and pathways between them for hierarchically organized phases. GT centrality parameters and node-based fractal dimension can identify complex phases more accurately than traditional analyses and quantify the system behavior preceding the transitions, capturing fluctuation-induced breakup of aggregates and their long-range cooperative interactions. GT parametrization can be generalized for a wide range of chemical systems, facilitatingidentification of complex supramolecular phases and engineering nanostructures at multiple scales.