Tracking the time evolution of soft matter systems via topological structural heterogeneity

Abstract

AbstractPersistent homology is an effective topological data analysis tool to quantify the structural and morphological features of soft materials, but so far it has not been used to characterise the dynamical behaviour of complex soft matter systems. Here, we introduce structural heterogeneity, a topological characteristic for semi-ordered materials that captures their degree of organisation at a mesoscopic level and tracks their time-evolution, ultimately detecting the order-disorder transition at the microscopic scale. We show that structural heterogeneity tracks structural changes in a liquid crystal nanocomposite, reveals the effect of confined geometry on the nematic-isotropic and isotropic-nematic phase transitions, and uncovers physical differences between these two processes. The system used in this work is representative of a class of composite nanomaterials, partially ordered and with complex structural and physical behaviour, where their precise characterisation poses significant challenges. Our developed analytic framework can provide both a qualitative and quantitative characterisation of the dynamical behaviour of a wide range of semi-ordered soft matter systems.