Phd Studentship: Mathematical Theories for Liquid Crystals and their Applications

Research theme: Applied Mathematics, Continuum Mechanics, Liquid Crystals

Application deadline: All year round

The successful candidate will join the PhD programme of the Department of Mathematics at the University of Manchester. This 42-month PhD position (funded by the University of Manchester) is a full scholarship which will cover tuition fees for UK-based students and provide an annual stipend in line with EPSRC recommended levels (£20,780 for 2025/26), with an expected start date of 1st October 2025. This scholarship is available only to UK students eligible for home fee status.

Liquid crystals (LCs) are beautiful smart materials that combine fluidity and softness with the structural order of solids. At a basic level, LCs comprise asymmetric molecular building blocks: rod-like, disc-like, box-shaped, bent-core molecules etc. These building blocks assemble/self-organise into different LC phases, all of which have special material directions, known as LC directors, but exhibit different levels of positional organisation/order. Nematic LCs (NLCs) are the simplest LCs with nematic directors but no positional order, cholesteric LCs are twisted or helical NLCs, smectic LCs are layered LCs, along with more ordered and exotic LC phases such as columnar, twist-bend, splay-bend phases. LCs have long fascinated scientists with their exceptional physical properties and responsiveness to external stimuli and have diverse applications across the multi-billion dollar display industry, photonics, metamaterials, robotics, healthcare technologies etc.

The mathematics of LCs is very rich and cuts across analysis, topology, mechanics, partial differential equations and scientific computing, to name a few. There are competing LC theories e.g., molecular-level models with molecular-level information, mean-field models that average molecular details by a mean field, and continuum theories that describe the LC phase by a macroscopic order parameter that describes the macroscopic or measurable LC properties. There are several crucial but open questions wherein mathematics can play a key role, e.g., (i) can we mathematically describe the principles of LC phase formation; (ii) can we design LC systems with prescribed properties and (iii) can we use mathematics to engineer the next generation of LC applications?

We will partially address these open questions in this project. We propose to design and analyse new sophisticated multiscale LC models that will combine the accuracy of molecular models, which contain information about molecular shape and interactions, with the efficiency of continuum theories. We will compare the multiscale predictions to conventional continuum predictions to understand the relationships between the different theoretical frameworks. The analysis will be accompanied by detailed numerical computations in the multiscale modelling frameworks, particularly to explore parameter regimes inaccessible to analytic tools. Finally, we plan to work with experimentalists to examine LCs confined in thin-slab geometries, cylinders, shells and various prototype two-dimensional and three-dimensional geometries. Such systems have potential applications to sensors, photonics, metamaterials, and displays.

Applicants should have, or expect to achieve, at least a 2.1 honours degree or a master’s (or international equivalent) in a relevant science or engineering related discipline. Background knowledge in continuum mechanics, theory of partial differential equations and calculus of variations is desirable.

To apply, please contact the supervisors Professor Apala Majumdar (apala.majumdar@strath.ac.uk) Professor Andrew Hazel (Andrew.Hazel@manchester.ac.uk). Please include details of your current level of study, academic background and any relevant experience and include a paragraph about your motivation to study this PhD project.

Advert information