Combination of polarized TIRF and ATR spectroscopies for determination of the second and fourth order parameters of molecular orientation in thin films and construction of an orientation distribution based on the maximum entropy method

This article describes two mathematical formalisms for the determination of the second and fourth order parameters of molecular films using optical spectroscopy. Method A uses polarized total internal reflection fluorescence (TIRF) to calculate the second and fourth order parameters, 〈P ₂(cos θ)〉 and 〈P₄(cos θ)〉, using an independently determined value for the angle between the absorption and emission dipoles, γ. Method B uses 〈P₂(cos θ)〉 obtained from attenuated total reflectance (ATR) data, along with polarized TIRF measurements to calculate 〈P₄(cos θ)〉 and (cos² γ). The choice of a specific method should rely on experimental considerations. We also present a method to separate the contributions of substrate surface roughness and dipole orientation with respect to the molecular axis from the spectroscopically determined second and fourth order parameters. Finally, a maximum entropy approach for construction of an orientation distribution from order parameters is compared with the commonly used delta and Gaussian distributions.