In a search for a shape maximizing packing fraction for two-dimensional random sequential adsorption.

Area of Science:

• Physical Chemistry
• Materials Science
• Statistical Mechanics

Background:

• Understanding the packing of two-dimensional (2D) objects is crucial for materials science and physical chemistry.
• Previous work focused on smoothed dimers, necessitating further investigation into other shapes for optimal packing.
• Random sequential adsorption (RSA) is a key process influencing the final arrangement and density of adsorbed particles.

Purpose of the Study:

• To identify the two-dimensional shape that maximizes the saturated packing fraction through random sequential adsorption.
• To compare the packing efficiency of ellipses against other shapes like smoothed n-mers and spherocylinders.
• To determine the optimal aspect ratio for ellipses to achieve maximum packing density.

Main Methods:

• Simulations of random sequential adsorption (RSA) for various 2D shapes.
• Comparison of packing fractions for smoothed n-mers, spherocylinders, and ellipses.
• Systematic variation of the long-to-short axis ratio for ellipses.

Main Results:

• The highest saturated packing fraction achieved was 0.58405 ± 0.0001.
• Ellipses with a long-to-short axis ratio of 1.85 ± 0.07 yielded the maximum packing fraction among the studied shapes.
• This packing density is significantly higher than previously studied smoothed dimers.

Conclusions:

• Elliptical shapes, specifically those with an aspect ratio around 1.85, are highly efficient for achieving dense packing in random sequential adsorption.
• The findings provide valuable insights for designing materials with controlled surface arrangements and high densities.
• This study advances the understanding of geometric constraints on packing efficiency in 2D systems.