Capillary attraction at the meniscus between tiny objects plays a crucial role in self-assembly processes. The shape of the meniscus governed by the Laplace equation devotes to a long-range attraction distinct to the DLVO defined forces. Rather than considering trapped particles on ideal smooth surfaces, we use patterned substrates with ordered nano-arrays for theoretical modeling toward the capillary assembly. The vertical elevation of particles is found to change the shape of the meniscus between particles, therefore the interaction energy and capillary force. A minimal model is developed to determine the capillary force between particles and thus the motility of particles, therefore the criterion of the crystallization of colloidal particles. It turns out that the formation of a colloidal crystal or amorphous medium depends on the optimization between the scaled particle separation by its size and the geometrical design of the supporting nano-arrays. Finally, we experimentall...

中文翻译：

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图案表面上的胶体颗粒的毛细管组装

微小物体之间的弯月面处的毛细管吸引在自组装过程中起着至关重要的作用。由拉普拉斯方程控制的弯月面形状具有与DLVO定义的力不同的远距离吸引力。与其考虑在理想的光滑表面上捕获颗粒，不如使用带有有序纳米阵列的带图案的基材对毛细管组件进行理论建模。发现颗粒的垂直高度改变了颗粒之间弯月面的形状，因此改变了相互作用能和毛细作用力。建立了最小模型来确定颗粒之间的毛细作用力，从而确定颗粒的运动性，从而确定胶体颗粒结晶的标准。事实证明，胶体晶体或无定形介质的形成取决于通过其尺寸进行的按比例缩放的颗粒分离与支持纳米阵列的几何设计之间的优化。最后，我们进行实验...