Metric theory of nematoelastic shells

Area of Science:

• Soft Matter Physics
• Materials Science
• Continuum Mechanics

Background:

• Nematoelasticity describes the coupling between liquid crystal order and mechanical deformation in soft materials.
• Topological defects in liquid crystals can induce significant structural changes and unique morphologies.
• Phase transitions, such as the nematic-isotropic transition, drive material property changes and potential shape evolution.

Purpose of the Study:

• To investigate the three-dimensional reshaping of thin nematoelastic films undergoing a nematic-isotropic transition.
• To analyze the formation of cone and anticone (d-cone) shells around a charge-one topological defect.
• To explore the influence of doping on the resulting shell geometry.

Main Methods:

• Analysis based on the relationship between the shell metric and the tensor order parameter.
• Assumptions of no elastic deformation and no volume change during reshaping.
• Modeling the effect of doping on the curvature of cones.

Main Results:

• The transition leads to the formation of either cone or anticone shells.
• Doping allows for modification of the shell shape, creating cones with curved generatrices.
• Anticones are characterized by an even number of radial creases.
• Curvature singularities at the apex are resolved due to the decay of the nematic order parameter near the defect core.

Conclusions:

• The study elucidates the mechanism of shell formation in nematoelastic films during phase transitions.
• The findings demonstrate control over shell morphology through material doping.
• The resolution of apex singularities highlights the role of defect core properties in determining overall shape.