Soft Matter with Nematic and Magnetic Order: Models, Simulations and Applications

Nematic liquid crystals (NLCs) are classical examples of materials that are intermediate between conventional solids and liquids. NLCs are directional materials with preferred directions of the averaged molecular alignment. NLCs have direction-dependent responses to external electric fields and light, making them the working material of choice for a range of electro-optic applications, notably the thriving liquid crystal display industry. However, NLCs have weak responses to external magnetic fields, so that magnetic fields are not widely used for NLC-based applications. In the 1970’s, de Gennes and Prost, Rault, Cladis and Burger undertook pioneering experimental and theoretical work on ferronematics – suspensions of magnetic (nano) particles in a nematic host. The magnetic (nano)particles induce a spontaneous magnetisation and consequently, ferronematics have much stronger responses to external magnetic fields compared to conventional NLCs. Experimental research in ferronematics is booming, driven by the need to understand the fundamental physics of ferronematics and how we can model ferronematics and their potential applications in photonics and new materials technologies.

In this project, we will develop new mathematical models for ferronematics to account for both the nematic and magnetic order, and how they couple to each other. We will also develop new numerical methods for ferronematic systems and analyse the numerical schemes, including error and convergence analysis. We will apply the mathematical models and numerical schemes to study the experimentally observable states in prototype ferronematics and how we can switch between them, with a long-term goal of designing and controlling ferronematic systems for tailor-made applications.