Mathematical Modelling of Dielectric Inclusions and Photoactive Alignment Layers in Liquid Crystal Cells

Abstract

This work concerns two areas. The first is a study of the photoalignment behaviour of thin (approximately 20-50 nm) PAAD films in an effort to determine their molecular alignment upon exposure to polarised light. In conjunction with experimental work carried out by another member of our research group, a complex model is developed to model the transmission of the s- and p-polarised components of light across the experimental system. The model takes into account the mixing of polarisations caused by the photoinduced birefringence of the PAAD film, and couples this with the
interference effects caused by the transmission across the multiple different layers of the system. A new method for modelling multi-layer propagation is developed for this problem, which proves to have both the accuracy and stability of the current leading standard method, but with vast improvements in computation time.

The second area of work concerns the multi-scale modelling of doped dielectric
systems. The method of homogenisation is utilised to derive an effective permittivity to describe composite systems composed of a host medium and small inclusions, which requires the assumption that the system is periodic at the microscopic scale.

This is done for 2D elliptical particles in anisotropic media, and for 3D spheroidal particles in isotropic media. The assumption of periodicity is then relaxed and the applicabality of homogenisation is studied when disorder is entered into the system. The results are then compared to traditional effective medium theories used to solve such host/inclusion problems.

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Identifiers

ORCID for Giampaolo D'alessandro: orcid.org/0000-0001-9166-9356

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