Quantitative determination of the spatial orientation of graphene by polarized Raman spectroscopy

Polarized Raman spectroscopy has been employed to characterize transverse sections of graphene monolayers upon both a copper substrate and a polyester film. Well-defined Raman spectra can be obtained from the one atom thick transverse sections of graphene because of the strong resonance Raman scattering. The intensity of Raman 2D band (I-2D) is independent of the axis of laser polarization when the laser beam is perpendicular to the surface of the graphene monolayer but I-2D is found to vary as approximately the 4th power of the cosine of the angle between the axis of laser polarization and the plane of graphene when the direction of laser propagation is parallel to the graphene sheet. It is demonstrated that a generalized spherical expanded harmonics orientation distribution function (ODF) can be used to quantify the spatial orientation of the graphene. The roughness of the graphene, evaluated using atomic force microscopy, shows a good correlation with the ODF determined using polarized Raman spectroscopy, showing how the Raman technique may be employed to quantify the spatial orientation of graphene. It is also demonstrated how the technique can be used to quantify the orientation of graphene in high-ordered pyrolytic graphite and graphene paper. (c) 2015 The Authors. Published by Elsevier Ltd.