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 dimers ($\gamma$=1) are similar in local contacting and ordering behaviors despite their shape differences, the amorphous structures of asymmetric dimers ($\gamma$=0.3, 0.5, and 0.7) exhibit distinct features depending on $\gamma$.
We also investigate the origin why asymmetric dimers cannot develop the spatial order macroscopically. Based on the fact that two contacting particles have a strong orientational correlation, we characterized the amorphous structure of asymmetric dimers by analyzing the local configurations of contacting particles. Contacting pairs of asymmetric dimers prefer to form certain geometries \textendash{} parallel, anti-parallel, and chiral. The total fraction of such two-particle configurations increases as either $\gamma$ or $\varphi$ increase, and the increasing number comes from the chiral configuration. The chiral geometry, which is incompatible with ideal 2D-space filling and cannot possess long-range spatial order, results in the disordered packing structure of asymmetric dimers even at high $\varphi$.
약 400여년 전 독일의 Johannes Kepler가 동일한 구체를 가장 빽빽하게 채울 수 있는 구조에 대해 밝혀낸 이후, 주어진 공간에 입자를 채우는 방법은 기초과학분야에서 쉽게 풀리지 않는 방법으로 남아있다. 이러한 packing 문제는 액체, 고체, 비결정질 물질들의 모델 시스템으로서, 응집물질들의 특성에 대한 근본적인 이해를 위해 많은 관심을 받아왔다. 여기서 시스템의 거시적인 특성은 각각을 구성하는 입자의 성질에 많은 영향을 받는데, 특히 입자의 모양은 전체적인 구조를 결정하는데 있어서 큰 역할을 담당하고 있다. 예를 들어, 2차원에서 가장 단순한 형태인 원 모양을 조금씩 변형시키면 다양한 형태의 입자를 만들 수 있는데, 이 때 원 모양 입자의 육각대칭구조는 약간의 입자 모양 변화에도 크게 바뀌게 된다.
본 학위논문에서는 2차원 덤벨의 모양이 시스템의 구조에 미치는 영향에 대해 다루었다. 덤벨 입자는 두 개의 크기가 다른 원 두 개로 이루어져 있으며, 이에 따라 1) 원 사이에 결합이 있다는 점과 2) 크기 차이에 따라 비대칭 형태를 가지고 있다는 점, 두 가지 형태적 특성을 가진다. 이 연구에서는 공기-물 계면에 입자를 띄워서 2차원 시스템을 구성하여, 각각의 형태적 특성이 전체구조에 어떠한 영향을 주는지 알아보았다.
