Study on effects of shape of 2D-dumbbells on their structure and frustration of order

Abstract

A particle packing problem has long been a fundamental but unsolved riddle, since Johannes Kepler conjectured the closest packing structure of identical spheres about 400 years ago. Understanding the microscopic process of hard-particle systems is important to describe underlying physics of various substances such as liquids, crystals, glasses, and other jammed media. Particle shape is one of the major parameters governing the structure in these hard-particle systems. In two dimensions (2D), not only the hexagonal crystalline structures but also the phases that the system exhibits are significantly altered, as the shape of particles changes from a disk, which is the simplest form in 2D.

A 2D-dumbbell, which consists of two different disks in size, has two geometrical characteristics: the existence of a bond and asymmetry due to a size difference. We investigate the effects of the geometry of 2D-dumbbells on packing structure at an air-water interface under short-range attractions, varying the area fraction $\varphi$ of the particles. We observe that although the systems at low $\varphi$ exhibit a characteristic structure of attractive particle systems, the short-range attraction between the particles due to capillary interaction does not affect the local structure at the maximally random jammed (MRJ) state. We investigate the influence of a rigid bond on the packing structure by comparing 2D-dumbbell systems with binary-disk systems; we also investigate the effects of asymmetry by controlling the diameter ratio ($\gamma$) of the small and large disks of the dumbbell. First, we find that the existence of a bond restricts local segregations between similar kinds of disks, so that phase-separated glass states are forbidden, contrary to the case of binary-disk systems. Second, we observe that varying $\gamma$ causes a structural order-disorder-order change at high $\varphi$. While the crystalline structures of disks ($\gamma$=0) and symmetric dime...