There is an increasing body of research studying how to obtain 3D structures at the microscale from the spontaneous folding of planar templates, using thermal fluctuations as the driving force. Here, combining numerical simulations and analytical calculations, we show that the total folding time of a regular pyramid is a non-monotonic function of the number of faces (N), with a minimum for five faces. The motion of each face is consistent with a Brownian process and folding occurs through a sequence of irreversible binding events between faces. The first one is well-described by a first-passage process in 2D, with a characteristic time that decays with N. By contrast, the subsequent binding events are first-passage processes in 1D and the time of the last one grows logarithmically with N. It is the interplay between these two different sets of events that explains the non-monotonic behavior. Implications in the self-folding of more complex structures are discussed.

越来越多的研究正在研究如何利用热涨落作为驱动力，通过自发折叠平面模板来在微观尺度上获得3D结构。在这里，结合数值模拟和解析计算，我们显示出规则金字塔的总折叠时间是面数（N）的非单调函数，最少五个面。每个脸部的运动与布朗过程一致，并且折叠是通过脸部之间一系列不可逆的绑定事件发生的。第一个通过2D的首次通过过程很好地描述，其特征时间随N衰减。相反，随后的绑定事件是一维中的第一个通道过程，最后一个事件的时间与N成对数增长。这两组不同事件之间的相互作用解释了非单调行为。讨论了更复杂结构自折叠的含义。