在侷限(confinements)下的介微觀流體展現出豐富的結構與動態行為，即使是最簡單的限制—例如平面邊界(flat boundary)—也是如此。平面邊界抑制了相鄰粒子正向邊界的運動、使其排列、並誘導層狀結構(layered structure)的產生。粒子在單層內形成六角晶格(triangular lattice)排列，不同層與層間的相對位置導致不同的立體晶格結構類型(lattice structure type)。這些現象可以在水溶液中的膠體和電漿中的帶電微粒(微粒電漿)這些平台上進行實驗研究。已知當溫度降至臨界點T_L以下時，系統整體便皆為層狀結構。然而，在遠離T_L的更低溫度，侷限下的固體結構仍然未知。 藉由在設計的表面邊界上生長晶格以達控制固態結構的技術稱為磊晶(epitaxy)。表面的幾何結構可以設計為人為圖案或晶格結構。磊晶可以生成超晶格(superlattices)，即具有不匹配晶格常數(lattice constant)和/或晶格方位(lattice orientation)的原子薄層堆疊(atomically thin stacked layers)異質結構(heterostructure)。使用複雜的侷限可以拓展控制結構的能力，然而，一個從根本上來說有趣的問題是:「是否有可能利用平面邊界生成自組裝的超晶格?」 此研究中，使用狹窄侷限在兩平行邊界之間的湯川(Yukawa)耦合固體作為平台，我們研究了耦合常數κ範圍0.3到2之間的外層自組裝超晶格。除了典型的沿邊界正向的密度振盪外，還觀察到鄰近邊界的第一峰值近其餘內部兩倍。這種層內密度的不匹配導致了第一和第二外層的不同堆疊模式，包括鋸齒狀圖案和具有不同晶格常數和/或堆疊層取向的超晶格。此外，我們還觀察到了由於頂層和底層的錨定導致的晶格方位在空間上逐漸變化、在不同內層排列密度下的剪切結構以及在高冷卻速率下的晶界(grain boundary)。 ;Mesoscopic liquids under confinement exhibit rich structural and dynamical behaviors different from those of bulk liquids. The flat confinement boundary suppresses the normal (i.e., transverse) motions of nearby particles, lines up them, and induces the formation of layers. It turns the layered region into a 2+1 dimensional system, in which each particles exhibits triangular lattice packing. Different interlayer positions of neighboring layers lead to different three dimensional (3-D) lattice structure type. The layering region can extend inward up to the scale of correlation length of the bulk liquid, and eventually occupies the entire liquid, after dropping the temperature below the critical temperature T_L. However, the micro-structural in the solid phase at temperature much below T_L remains unknown. Manipulating solid structure via growing lattice above a designed surface is known as epitaxy. The topography of designed surface can be artificial patterned or lattice structure. Superlattices, which are stacked atomically thin layers with mismatch lattice constant and/or mismatch orientation, can be formed by epitaxy. Although complex constraints can be utilized to broaden the capability of manipulation, it is intriguing to ask a fundamental question: ‘Is it possible to generate a self-assembled superlattice nearby a flat boundary?’ In this work, using the Yukawa solid confined tightly between two parallel flat boundaries as a platform, the self-assembled superlattices at the outmost layers are demonstrated numerically under a range of screening parameter κ (defined as the ratio of the 3D Wigner-Seitz radius r_W to the Debye screening length λ_D) between 0.3 to 2.5. It is found that the intralayer lattice constant of the outmost layer is smaller (can be up to two times) than those of rest layers which exhibit nearly uniform intralayer lattice constant. The thereby induced intralayer lattice constant mismatch of the first and second outmost layers leads to the distinct superlattice patterns with different mismatch orientations of the stacking layers, depending on different κ. Also, the gradual variation of spatial orientation is observed and discussed.
