Orientation distribution functions in uniaxial systems centered perpendicularly to a constraint direction

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 theta)>) order parameter values. Emphasis is put on the domain of n egative values (0.0; -0.5) for the < P-2> order parameter. It is shown that , if the mean values of < P-2> and < P-4> are determined, some qualitative statements about the form of the distribution can be made with good accurac y. We have distinguished four distinct domains in the (< P-4>,< P-2>) half- plane and reported typical shapes for the corresponding distributions. As a n illustrative example, we have made use of the < P-2> and < P-4> parameter values previously determined front polarized Raman confocal microscopic me asurements, 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 o n the thin film, are then discussed. This approach allows us to offer new i nformation about the chromophore orientations, the perturbations in the pri mary photoinduced effects, and the formation mechanisms of such regularly s pared sinusoidal surface relief gratings.