The Effect of Nanoparticle Shape, Orientation, and Heterogeneity on the Optical Birefringence of Polymer Nanocomposites

Embedding plasmonic nanoparticles (NPs) into polymer nanocomposites (PNCs) is a facile method for integrating them into functional devices, whose properties are tunable through varying NP size, shape, and loading. Using anisotropic NPs adds an additional degree of tunability to their orientation order in the PNC, as properties such as conductivity and charge transport can be enhanced in specific directions. In thin films, the film thickness and block copolymer self-assembly can affect the degree of NP orientation, which can be used as a method of control over these properties. However, large-scale control of orientation order in randomly distributed NPs, with both anisotropic NP shapes and heterogeneous shape distributions, remains a challenge. This is partly due to the lack of cost-effective, ensemble-level characterization methods that can independently determine the orientation order and degree of aggregation of anisotropic NPs. Here, we model the complex index of refraction of PNCs with plasmonic NP inclusions in the optical frequency domain by using an effective medium approximation. We quantitatively relate the simulated optical birefringence of the medium to the orientation order parameter of plasmonic nanorods and nanodisks in a robust manner insensitive to heterogeneity in simulated NP size and shape. Experimentally, we measure this orientation order parameter through the birefringent index of refraction using variable-angle spectroscopic ellipsometry (VASE). We demonstrate that we can independently determine the orientation order and degree of aggregation for various PNCs with gold nanorods and nanosphere inclusions. This facile technique provides a powerful method to broadly measure the average orientation order of anisotropic particles in PNCs, which can be correlated to their functional properties.