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Crystallographic phase retrieval method for liquid crystal bicontinuous phases: indicator-based method.

Toshihiko Oka¹

¹Department of Physics, Faculty of Science, Shizuoka University, Shizuoka, 422-8529, Japan.

Acta Crystallographica. Section A, Foundations and Advances

|September 1, 2022

Summary

This study introduces a new indicator-based method for crystallographic phase retrieval in disordered lyotropic liquid crystals. The method effectively identifies the correct electron density distribution, improving structural analysis.

Keywords:

crystallographic phase retrieval lyotropic liquid crystals triply periodic minimal surfaces

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Area of Science:

Materials Science
Crystallography
Soft Matter Physics

Background:

Lyotropic liquid crystals exhibit significant structural disorder, limiting observable Bragg reflections.
Accurate crystallographic phase retrieval is crucial for understanding their complex structures.

Purpose of the Study:

To develop an indicator-based method for crystallographic phase retrieval in bicontinuous cubic phases of lyotropic liquid crystals.
To identify plausible electron-density distributions despite limited diffraction data.

Main Methods:

Proposed two novel indicators derived from electron density characteristics (max-min difference and Hessian matrix).
Calculated electron densities for all possible phase combinations using test data.
Evaluated indicator effectiveness in identifying the true electron density.

Main Results:

Electron densities corresponding to minimum indicator values closely matched the true electron density.
The developed indicator-based method proved effective for phase retrieval.
Phase retrieval accuracy decreased with increased volume fraction of triply periodic minimal surfaces.

Conclusions:

The indicator-based method offers a robust approach for crystallographic phase retrieval in disordered lyotropic liquid crystals.
This technique enhances the structural characterization of complex liquid crystal phases.
Understanding the influence of specific structural features (minimal surfaces) on accuracy is key for future applications.