Fig. 4

Composition \(\to\) shape programming: 2D MoSeS monolayers that self-assemble into 3D shapes. a Topographies generated by the composition patterns displayed within each monolayer (also see Supplementary Movies 1–5). The composition patterns \(J(x,y)\) for P1–P4 were generated using the expressions for bending-dominant composition \(\to\) shape programming given in Table 1. Janus pattern color maps are scaled by their respective maxima \({J}_{0}\). b, c The minimum radius of curvature \({R}_{c}^{\min }\) for the sinusoidal profile P3 in a as a function of b Janus degree \({J}_{0}\) and c Janus wavelength for several values of \(\lambda\) and \({J}_{0}\), respectively. The solid lines, dashed lines, and symbols are the full analytic result (see Methods), the asymptotic expansions in Table 1, and simulation results, respectively. Line colors correspond to Janus degree in both (b) and (c). d, e Atomic representations of the equilibrium shapes and compositions for MoSeS (\(\bar{c}=1/2\)) with 1D sinusoidal Janus patterns (P3) for several choices of d Janus degree (\({J}_{0}\) at \(\lambda =10.4\) nm) and e wavelength (\(\lambda\) at \({J}_{0}=1/2\)), and f with 1D \({J}_{0}=1/2\) Janus strips (P2) of width \(L=1.9\), 5.8, and 11.6 nm