Orientation Distribution Functions in Uniaxial Systems Centered Perpendicularly to a Constraint Direction

Abstract

With the use of information entropy theory, the orientational distribution function of cylindrically symmetric probe molecules in uniaxial systems is reconsidered from the second-rank and fourth-rank Legendre polynomials (<P_2n(cos θ)>) order parameter values. Emphasis is put on the domain of negative values (0.0; −0.5) for the <P₂> order parameter. It is shown that, if the mean values of <P₂> and <P₄> are determined, some qualitative statements about the form of the distribution can be made with good accuracy. We have distinguished four distinct domains in the (<P₄>, <P₂>) half-plane and reported typical shapes for the corresponding distributions. As an illustrative example, we have made use of the <P₂> and <P₄> parameter values previously determined from polarized Raman confocal microscopic measurements, for azobenzene entities oriented in an amorphous copolymer film. The shapes of the orientation functions of such chromophores, located in the top and bottom regions of a holographic diffraction grating inscribed on the thin film, are then discussed. This approach allows us to offer new information about the chromophore orientations, the perturbations in the primary photoinduced effects, and the formation mechanisms of such regularly spaced sinusoidal surface relief gratings.