Kinetics of self-folding at the microscale
Nuno A. M. Araújo (Universidade de Lisboa)

Three-dimensional shells can be synthesized from the spontaneous self-folding of two-dimensional templates of interconnected panels, called nets. To design self-folding, one first needs to identify what are the nets that fold into the desired structure. In principle, different nets can fold into the same three-dimensional structure. However, recent experiments and numerical simulations show that the stochastic nature of folding might lead to misfolding and so, the probability for a given net to fold into the desired structure (yield) depends strongly on the topology of the net and experimental conditions. Thus, the focus has been on identifying what are the optimal nets that maximize the yield. But, what about the folding time? For practical applications, it is not only critical to reduce misfolding but also to guarantee that folding occurs in due time. Here, we consider as a prototype the spontaneous folding of a pyramid. We find that the total folding time is a non-monotonic function of the number of faces, 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 that close edges between pairs of faces. The first edge closing is well-described by a first-passage process in 2D, with a characteristic time that decays with the number of faces. By contrast, the subsequent edge closings are all first-passage processes in 1D and so the time of the last one grows logarithmically with the number of faces. 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.