Complex-tensor theory of simple smectics.

Area of Science:

• Soft Matter Physics
• Materials Science
• Continuum Mechanics

Background:

• Lamellar materials, like smectics, exhibit unique properties due to layered self-assembly.
• Smectics, existing between fluid and solid states, are challenging to model, especially in confined spaces.
• Existing models struggle with the orientational and positional ordering characteristic of smectics.

Purpose of the Study:

• To develop a novel theoretical framework for describing simple lamellar smectics.
• To introduce a complex tensor order parameter capturing local ordering, layer displacement, and orientation.
• To enable the simulation of complex mesoscopic structures in smectic systems.

Main Methods:

• Proposed a complex tensor order parameter for describing lamellar smectics.
• Incorporated regularization of singularities within defect cores to handle dislocations and disclinations continuously.
• Developed a theory that simplifies numerical analysis for mesoscopic studies.

Main Results:

• The proposed tensor theory successfully describes local lamellar ordering, layer displacement, and orientation.
• The theory continuously accounts for dislocations and disclinations by regularizing defect core singularities.
• Enabled simulation of arrested configurations and inclusion-induced local ordering.

Conclusions:

• The tensorial theory provides a simplified and continuous mathematical description for simple smectics.
• This advancement facilitates the study of mesoscopic structures in topologically complex lamellar systems.
• The new model aids in understanding the functional properties of self-assembling layered materials.