Evaporation-driven crumpling and assembling of two-dimensional (2D) materials: A rotational spring – mechanical slider model

Crumpling of suspended two-dimensional (2D) materials by droplet evaporation creates a new form of aggregation-resistant ultrafine particles with more scalable properties such as high specific surface areas. However, the underpinned fundamental mechanics theory that addresses large deformation, severe instability and self-assembly of 2D sheets under dynamic solid-liquid interactions during liquid evaporation is lacking. In the present study, we propose a theoretical mechanics framework to quantitatively describe the simultaneous process of crumpling and self-assembling of 2D materials and their competition during droplet evaporation. In this theory, a rotational spring is developed to describe the out-of-plane deformation of crumpling sheets, and a mechanical slider is implemented to describe the interactive binding energy in self-folding of a single sheet or overlapping of neighboring sheets. The spring-slider mechanics model is calibrated with the energy-based continuum mechanics analysis by crumpling a single sheet, and is further extended to a network model to characterize the crumpling and assembling of multiple sheets in the droplet. An equivalent pressure model is developed to unify the resultant forces associated with liquid evaporation including capillary force, vapor pressure, gas pressure, vapor recoil pressure and capillary flow-induced force. A coarse-grained model of 2D materials is developed and its dynamic interaction with liquid molecules during evaporation is mimicked by proposing a controllable virtual van der Waal force field. Molecular dynamics simulation results show remarkable agreement with theoretical predictions, from crumpling and assembling energies of graphene during liquid evaporation to overall size and accessible area of the crumpled particles after the complete evaporation of liquid. Besides, both theoretical predictions and simulation results agree well with independent experiments. The effect of concentration, size, shape, number and size distribution of 2D material graphene sheets in liquid droplets on crumpling and self-assembling energy and shape, size and surface morphology of crumpled particles is also discussed. The mechanics theories and coarse-grained modeling established here are expected to offer immediate and quantitative application guidance to control the crumpling and self-assembling process of 2D materials by liquid solution evaporation processing to fine tune particle size and morphology. More importantly, the fundamental understanding of large deformation, instability, and self-assembly of 2D materials in such dynamic liquid environments could be extended to aerosol-like processing of a broad scope of other low-dimensional nanomaterials such as lipid membranes, nanowires, nanotubes, nanofibers and nanoparticles, for their emerging applications including ultrafine particle manufacturing and various printing processes.