Determination of Molecular Orientational Distribution Using Surface Second-Harmonic Generation Analyzed by the Five-Layer Model and the Modified Maximum-Entropy Method

Abstract

We have determined the molecular orientational distribution functions (ODFs) at air and substrate interfaces for unrubbed and rubbed films of polymer possessing second-harmonic generation (SHG) active side chains. Using a thick polymer film and four different optical geometries, the surface SHG signals from the two interfaces could be successfully separated. To theoretically analyze the surface SHG results, we used the five-layer model, in which a five-layered system consisting of air, an unrubbed or rubbed upper SHG active layer, a SHG inactive polymer bulk layer, a lower SHG active layer and a substrate was considered. The local field factors for both active layers were deduced from the boundary conditions among these five layers. In order to obtain ODFs of the side chains at two SHG active layers, the modified maximum-entropy method was used. After achieving the best fit of the theoretical SHG intensities to the experimental results, we unambiguously determined the unbiased ODFs together with information on the in-plane axial and the polar order parameters for the side chains at the air-polymer and substrate-polymer interfaces of unrubbed and rubbed polymer films.