Decoding spatial orientation in planar materials

Abstract

Structural disorder induces energetic fluctuations, leading to variations in energy levels across different scales, with the spatial orientation of structural units playing a crucial role in shaping the resulting structure-property relationships. In this communication, we derive expressions for higher-order nematic orientation parameters for planar materials analogous to the Hermans orientation parameter used for axially symmetric materials. The measure of anisotropy has been analyzed by integrating the widely used probability density functions representing the orientation distributions in nematic order parameters. These higher-order nematic orientation parameters are essential for accurately determining the ‘true’ orientation distribution function of macromolecules and understanding structure-property relationships in complex planar systems.