Self-Assembly in Curved Space: Ordering, Defect and Entropy

Abstract

Self-assembly of nanoscale objects is of essential importance in materials science, condensed matter physics, and biophysics. Curvature modifies the principles and sequence of self-assembly in Euclidean space, resulting in unique and more complex structures. Understanding self-assembly behavior in curved space is not only instrumental for designing structural building blocks and assembly processes from a bottom-up perspective but is also critically important for delineating various biological systems. In this review, we summarize efforts made to unveil the physical nature of self-assembly in curved space through experiments and simulations. First, we outline the differences in the physical nature of self-assembly between curved space and Euclidean space by presenting relevant results of experiments and simulations. Second, we explore the principles of self-assembly in curved space at multiple scales and interactions, elucidating important factors that govern the self-assembly process from the perspectives of confinement and structural building blocks. Finally, we enumerate practical applications and control strategies for self-assembly in curved space and outline the challenges and prospects in this field. We hope that this review will encourage further efforts toward fundamental research and broaden the potential applications of designed assemblies in curved space.