Characterizing the three-dimensional orientation in polymers using FT-IR spectroscopy with linear polarized light

The quantity of absorbance of linear polarized light depends for a given wavelength on the angle between an absorbing transition moment vector and the electric vector of the polarized light. Fraser used this relationship to interpret the infrared dichroism in axially oriented polymers. This model can be extended to calculate the orientation in three dimensions by transforming the Fraser's equation into a P2-Legendre polynomial. As a result the orientation in three directions-f_x, f_y, and fz-can be calculated directly from the individual absorbances measured with an electric vector along the axes of interest, the structural absorbance A₀ of the sample, and the angle of the transition moment vector in reference to the chain axis. Applying the f values into 'Hermans' Orientation function', it becomes possible to calculate the average angle of the chain axis with reference to the axes of interest.