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Unsymmetrical bending occurs when a structural member is subjected to bending moments in a plane that does not align with the member's principal axes. This scenario typically arises in beams and other structural components when loads are applied at non-ideal angles, introducing complexities in stress analysis.
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Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...
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Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...
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Symmetry-specific orientational order parameters for complex structures.

Jack A Logan1, Srinivas Mushnoori2, Meenakshi Dutt2

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Summary
This summary is machine-generated.

This study introduces a new framework using orientational order parameters to characterize complex self-assembled structures. The method effectively identifies crystalline domains and unique amorphous clusters in simulations.

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Area of Science:

  • Materials Science
  • Statistical Mechanics
  • Soft Matter Physics

Background:

  • Complex self-assembled structures are ubiquitous in nature and technology.
  • Characterizing their intricate architectures, especially those formed by anisotropic building blocks, remains a challenge.
  • Existing methods often struggle with diverse symmetries and local structural variations.

Purpose of the Study:

  • To present a comprehensive framework for characterizing complex self-assembled structures.
  • To introduce novel orientational order parameters, including symmetrized bond order parameters (BOPs).
  • To demonstrate the framework's utility in identifying crystalline and amorphous domains.

Main Methods:

  • Development of two classes of tensor order parameters: polyhedral nematic and bond orientational order.
  • Introduction of symmetrized bond order parameters (BOPs) leveraging particle and phase symmetry.
  • Application of the framework to simulated hybrid systems of isotropic and patchy particles with octahedral symmetry.
  • Integration with bond percolation for identifying coherent domains.

Main Results:

  • The framework successfully identifies individual crystalline domains within self-assembled structures.
  • It detects coherent clusters of a unique compact amorphous structure lacking long-range order.
  • The methodology provides both global and local characterization of orientational order.

Conclusions:

  • The proposed framework offers a robust and versatile tool for analyzing complex self-assembled systems.
  • Symmetrized BOPs enhance the characterization of structures with specific symmetries.
  • The method reveals the coexistence of ordered crystalline and disordered amorphous phases.