Theory of light scattering by thin nematic liquid crystal films

Abstract

Light scattering by thin nematic liquid crystal films is considered. The confinement has two important consequences. First, fluctuations with wave vectors not equal to the difference between the wave vectors o f the scattered and the incident light ray can contribute to the scattering. The distribution o f fluctuation wave vectors relevant to the scattering is peaked around this difference and has a width inversely proportional to the film thickness. Second, only a discrete set of fluctuation wave vectors is allowed due to restrictions imposed by the boundary conditions. Consequently, the relaxation times of the different fluctuation modes depend on the film thickness. It appears that the relaxation time decreases due to the confinement. In the limit of vanishing thicknesses the relaxation time goes linearly to zero with the film thickness. The main conclusions are expected to hold qualitatively for other confined nematic systems, e.g., for nematics confined in porous media. [S1063-651X(96)00305-4] PACS number(s): 68.10.Cr, 64.70.Md

Confinement Effects on the Collective Excitations in Thin Nematic Films

“…Because of the small number of experiments done in this field, comparison with anchoring constants found in the literature is difficult. We can, however, qualitatively compare our results to the dynamical measurements done in pores by extrapolation to smaller dimensions [13]. For thicknesses of 60 and 17.5 nm, our extrapolated values are of the order of 60 and 15 ms, respectively.…”

“…Taking into account that the free surface aligns the molecules perpendicularly to the surface and has no in-plane anchoring, we can again apply Eq. (3) in this regime [13], but now in a simplified form with C 2 0. Figure 3 also shows the inverse relaxation time as a function of the inverse thickness for this case.…”

“…Because of the symmetry breaking by the confining surfaces, there are two orthogonal solutions for a given wave vector q, one corresponding to out-of-plane and the other to in-plane fluctuations at the surface. The confinement imposes restrictions on q z , the wave vector component normal to the surface, and therefore only discrete values of q z are allowed in a confined system [13]. For very strong anchoring, or for thicknesses larger than the extrapolation length L i K͞C i , the allowed z component of the wave vector equals q z ͑n 1 1͒p͞d [16], leading to a 1͞d 2 dependence of the relaxation rates.…”

“…Let us briefly recall the predictions of the phenomenological Landau-de Gennes theory [13,14] for a thin nematic film. In the one elastic constant approximation, and taking into account the Rapini-Papoular boundary conditions, the free energy density of a nematic film is [13] …”

“…In the one elastic constant approximation, and taking into account the Rapini-Papoular boundary conditions, the free energy density of a nematic film is [13] …”