Random sequential adsorption of unoriented rectangles at saturation

Abstract

This study presents an algorithm to generate a saturated random packing built of identical, unoriented rectangles. The algorithm is based on tracing regions that are unavailable for placing subsequent shapes. If these regions cover the whole packing the algorithm stops because no more objects can be added to the packing; thus it is saturated. The algorithm is used to study packings built of rectangles of side-to-side length ratio $\ensuremath{\epsilon}\ensuremath{\in}[1.0,2.5]$. The densest packings are obtained for $\ensuremath{\epsilon}=1.49\ifmmode\pm\else\textpm\fi{}0.02$, and the packing fraction, in this case, reached $0.549641\ifmmode\pm\else\textpm\fi{}0.000017$. The microstructural properties of the obtained packings are studied in terms of density autocorrelation function and propagation of orientational ordering.