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Dr Apala Majumdar
University of Bath
International Fellowship

Nematic shells: mathematics and experiments for new advances

Nematic shells are relatively new systems where curvature, surface and material properties can co-operate; Apala Majumdar will use this fellowship to study state-of-the-art experiments and new mathematical techniques to develop missing and much-needed theoretical models

Nematic shell exhibiting a spontaneously twisting director field around a +1 topological defect at the center of the image
Nematic shell exhibiting a spontaneously twisting director field around a +1 topological defect at the center of the image. Courtesy of ESMP, JungHyun Noh, Hsin-Ling Liang, Jan Lagerwall.

In collaboration with Jan Lagerwall (Head of Experimental Soft Matter Physics Group (ESMP), University of Luxembourg).

Nematic liquid crystals (NLCs) are mesogenic materials which combine fluidity with long-range orientational order i.e. the constituent molecules tend to align along certain distinguished directions, making NLCs directional materials. Consequently, NLCs have direction-dependent optical, mechanical and physical properties. Indeed, NLCs are exceptionally responsive materials and their responsiveness to light and external electric fields make them the working material of choice for the multi-billion dollar liquid crystal display industry. NLC research is now undergoing a modern-day renaissance across disciplines. There is an unprecedented interest in how geometry and NLC order co-operate to stabilise exotic morphologies, of which NLCs shells are outstanding examples, and these exotic morphologies are of fundamental scientific interest with immense untapped potential for applications.

This fellowship focuses on new mathematical approaches for studying nematic shells, to characterise the effects of the shell size, symmetry and material properties on the experimentally observed nematic textures and how these textures can be manipulated for altogether new applications in actuators, security applications and even robotics. A particularly intriguing aspect of NLC shells is the spontaneous appearance of nematic defects, which are points or lines where the nematic order disappears, and these defects appear prominently under a microscope. These defects are visually striking and equally importantly, hold the key to new applications. Experimentalists speculate that these defects can bind shells together and in particular, if theoreticians can understand the origins, structure and multiplicity of these defects and how they depend on the experimental conditions, this would constitute a breakthrough in NLC research and ultimately materials science.

The ESMP group in Luxembourg have done some recent trend-setting experimental work on NLC shells, which comprise a thin shell of NLC material between two surfaces, with emphasis on different boundary conditions on the shell surfaces and the accompanying defects. Together we aim to address three cutting-edge questions in NLC shells – (a) modelling of novel twisted defect structures in NLC shells, (b) manipulating defects inside shells and (c) modelling shell instabilities and how these phenomena can be best controlled to design new experiments and guide new applications in optical materials, biomimetic materials and new rheological phenomena altogether.

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