Fermi–Dirac statistics in correlation between electronic entropy and spatial confinement of liquid crystal-perovskite nanohybrids

Abstract

Entropy, a thermodynamic property generally defined as a measure of chaos or disorder of the system, has been observed to govern order-disorder transitions in several soft matter systems. Amongst the different forms of entropy to engender the orderliness of a system, electronic entropy can be adopted to monitor the spatial arrangement of nanostructures and therefore, can pave the way to the fabrication of designer materials. The periodicity in electronic entropy can be attributed to the probability of occupation of various states of electrons and therefore, can be accounted in the realm of Fermi–Dirac statistics. We have explored the role of electronic entropy as a driving force in the spatial organisation of liquid crystal-perovskite nanohybrids as model systems to engineer the structure-property relationship from both theoretical and experimental perspectives. The salient feature of physical significance is that the mere variation in the composition of the nanohybrids comprised of a nematic liquid crystal, 4-cyano-4′-n-pentylbiphenyl (5CB), and cesium tin chloride (CsSnCl₃) perovskite nanocrystals enables a distinct degree of localization and the emergence of exotic semiconducting and birefringence properties. An algorithm has been developed to calculate the electronic entropy for each of the observed polarised optical microscope images to account for the distinct assembly behaviour associated with compositional changes. Since, the spontaneous self-organisation appears due to interfacial interactions of the building blocks in liquid crystal-perovskite nanohybrids under geometrical confinement, it is indispensable to account for the contribution of all the individual (microscopic) components to the observed (macroscopic) thermodynamically stable architectures. Therefore, the concept of the present work could design a landscape to explore entropic calculations in numerous plausible hierarchical assemblies with advanced functionalities towards the development of optoelectronics and photovoltaic devices.