Mechanics of liquid crystals in soft matrices

Thesis

Soft polymer materials that contain liquid-crystal inclusions are used in many responsive devices, including polymer-dispersed liquid crystals, where the final performance depends strongly on the inclusion shape and the director field. This thesis develops models to describe how liquid-crystal inclusions in soft matrices deform and how their directors reorient under mechanical loading and external electric fields. It also studies how polymerisation-induced phase separation (PIPS) can create the inclusion microstructures that later control the reference state.

The work is primarily based on a variational modelling approach in which the governing equations follow from a total free energy description, taking into account the elasticity of the matrix, the spatial variation of liquid crystal order parameter, and the anchoring effect at the inclusion-matrix interface. These models are implemented with finite element method in FEniCSx and used in parametric studies. The results show how the elastocapillary number, anchoring strength, and a dimensionless inclusion volume control whether the composite becomes effectively stiffer or softer, and when stress can strongly reorient the director field.

The model is then extended to include electric fields and effects of spontaneous polarisation. Predictions are compared against experimental measurements of droplet elongation under electric fields. The simulations show how matrix stiffness and interfacial constraints control actuation sensitivity, and how electrically driven inclusion deformation in thin films can generate surface wrinkling with micron-scale amplitudes.

Finally, to link processing to microstructure, a chemo-mechanical phase-field model is developed for PIPS in liquid-crystal containing reactive mixtures. The model couples polymerisation kinetics, diffusion-driven demixing, and the appearance of network elasticity through entanglement. The results identify the Damkohler number and an elasticity ratio as key controls of when phase separation starts and how coarsening proceeds or stops. Overall, the thesis provides a modelling route that links microstructure formation, anisotropic interfacial elasticity and electromechanical response in liquid-crystal polymer composites.

Authors: Bai, Y

• DOI: 10.5287/ora-nrr6dvam8
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: variational theory; multiphysics modelling; liquid crystal; soft matter
• Subjects: Continuum mechanics