Saturation Coverage in Binary Mixtures of Oriented Regular Polygons via Random Sequential Adsorption

Abstract

We study saturation in two-dimensional binary mixtures of fixed-orientation regular polygons deposited by random sequential adsorption (RSA). Polygons with (n\in{3,\dots,23}) are considered under an equal-area constraint, isolating shape effects from size effects. Saturated configurations are generated using an adaptive split-voxel RSA algorithm with exact overlap detection based on the Separating Axis Theorem, allowing a systematic exploration of all distinct binary shape combinations. Jamming coverage depends strongly on polygon geometry despite identical particle area. Triangle-containing mixtures yield the lowest coverages, whereas axis-aligned squares achieve the maximum observed value, (\phi_{\rm sat}\approx0.5646). Even-sided polygons consistently outperform neighboring odd-sided polygons, revealing a parity effect associated with centrosymmetry. For odd (n), the pure-species saturation approaches the disk RSA limit (\phi_{\rm disk}\approx0.547) from below according to (\phi_{\rm sat}(n)=\phi_{\rm disk}-c/n^\alpha), with (\alpha\approx2.41\pm0.06), close to the (1/n^2) scaling expected from isoperimetric arguments. Even-sided polygons instead converge from above, indicating a symmetry-driven packing advantage that disappears only in the circular limit. These trends are explained through the excluded area (E_{AB}=\mathrm{Area}(P_A\oplus(-P_B))), computed analytically via Minkowski sums. Centrosymmetry fixes (E_{AA}=4A_0) for even (n), whereas odd polygons have a larger excluded area that decreases monotonically toward the same limit as (n\to\infty). Saturation coverage is negatively correlated with excluded area, consistent with a mean-field RSA description and directly linking geometric symmetry to jamming efficiency.