Size-dependent shape characteristics of 2D crystal blisters

Abstract

Micro- and nano-sized blisters can form spontaneously when two-dimensional (2D) crystals are transferred onto substrates because liquid molecules that are initially adsorbed on 2D material and substrate surfaces can be squeezed and trapped by interfacial forces. In this work, we use a combination of experiments, continuum theories, and coarse-grained molecular dynamics (CGMD) simulations to investigate the shape characteristics of spontaneously formed blisters under 2D crystals with heights ranging from a few ångströms to tens of nanometers. We show three distinct regimes in which the height-to-radius ratios (i.e., aspect ratios) of liquid-filled 2D crystal blisters are size-independent, rough linearly proportional, and inversely proportional to the blister radius. We reveal that the blister shape characteristics are governed by three factors: the 2D crystal elasticity, the interfacial interactions, and the phases of confined substances. The characteristic length scales (to which comparing the blister height or radius can define the boundary between these different regimes) are also discussed. We also provide approximate analytical solutions to the blister aspect ratios, which, together with complementary CGMD simulation results, agree with our experimental measurements.