Excluded area of superellipse sector particles

Area of Science:

• Physics
• Materials Science
• Complex Systems

Background:

• Superellipse sector particles (SeSPs) are versatile hard-particle shapes for granular and colloidal systems.
• SeSPs allow continuous control over shape parameters like corner sharpness and aspect ratio, modeling diverse forms such as rods, circles, and rectangles.

Purpose of the Study:

• To investigate the space of allowable nonoverlapping configurations for two SeSPs.
• To analyze the geometric constraints and emergent phenomena in SeSP arrangements.

Main Methods:

• Analysis of center-of-mass separation and relative orientation between SeSPs.
• Utilizing radial correlation plots to identify regions of allowed and disallowed configurations.
• Representing translational and rotational degrees of freedom as a hypervolume to detect topological changes.

Main Results:

• Identified circular regions around SeSP endpoints indicating entangled interactions.
• Discovered an 'excluded area' resulting from the overlap of these regions, where particles cannot be placed.
• Observed translational frustration due to distinct boundary regions and a topological change in the configuration space suggesting geometric frustration and a phase transition.

Conclusions:

• The study provides a framework for understanding how SeSP geometry influences particle packing and dynamics.
• The excluded area and translational frustration have implications for controlling bulk material properties.
• This work paves the way for a unified theory linking particle shape to macroscopic behavior.