Mechanics of assembling two-dimensional materials on a solid substrate by droplet drying

Abstract

Assembly of two-dimensional (2D) nanomaterials by droplet drying offers a straightforward and low-cost route to obtain their bulk forms for widespread applications in manufacturing and printing of functional structures and devices. However, unlike rigid nanoparticles that usually do not experience mechanical deformation, 2D nanomaterials are easily deformed and folded during assembly by evaporative drying, and traditional assembly theory that can address these fundamental deformation mechanisms is currently lacking. In the present study, we have developed an energy-based rotational spring-mechanical slider mechanics model to describe the mechanical deformation and assembly of 2D material graphene on a solid substrate during the evaporation of its droplet solution. In the development of theory, the mechanical folding deformation of 2D material graphene itself is modeled by the rotational spring, and the folding-induced interior interactions of graphene itself and its assembly interactions with neighboring ones and solid substrate all due to van der Waal force are modeled by the mechanical sliders. The surface wettability of substrate and the evaporative modes of droplet on substrate including constant contact angle (CCA), constant contact radius (CCR), and their combination are also incorporated into the mechanics model. In parallel, large-scale molecular dynamics (MD) simulations with the development of coarse-grained model of 2D graphene and its virtual force field interaction with liquid is performed and show remarkable agreement with theoretical predictions on both assembly patterns and dimensional sizes. The effect of graphene size and its interaction strength with substrate on assembly is also elucidated. This work uncovers fundamental assembly mechansim of mechanically deformable nanomaterials by solution drying, and also provides immediate application guidance to ink-based printing techniques for manufacturing deformable nanomaterials-enabled devices with controlled patterns on substrates.