Determining 3D molecular orientation from polarization-IR spectra: tutorial

Despite the ubiquity of molecular alignment in natural and synthesized materials, accurate mapping of three-dimensional (3D) molecular orientations with sufficient spatial resolving power has remained challenging. Conventional analysis approaches of polarization-based optical imaging cannot measure the out-of-plane angle of molecular orientations without tilting a sample. Recently, we proposed a new theoretical algorithm to determine the 3D orientation angle of aligned molecules using polarization-controlled infrared (IR) spectral data without tilting a sample. The algorithm was based on a concurrent analysis of the absorptances of two non-parallel IR transition dipole moments using a single orientational descriptor. The outcome of the non-iterative calculation is the 3D angle of the mean orientation and the order parameter of the local orientational distribution function. The algorithm was successfully applied to the analysis of polarization-controlled hyperspectral IR imaging of semi-crystalline polymer films. This tutorial derives and summarizes various theoretical descriptions presented in our recent papers and discusses the assumptions and limitations associated with the analysis method.